Citation
Chemical engineering education

Material Information

Title:
Chemical engineering education
Alternate Title:
CEE
Abbreviated Title:
Chem. eng. educ.
Creator:
American Society for Engineering Education -- Chemical Engineering Division
Place of Publication:
Storrs, Conn
Publisher:
Chemical Engineering Division, American Society for Engineering Education
Publication Date:
Frequency:
Quarterly[1962-]
Annual[ FORMER 1960-1961]
quarterly
regular
Language:
English
Physical Description:
v. : ill. ; 22-28 cm.

Subjects

Subjects / Keywords:
Chemical engineering -- Study and teaching -- Periodicals ( lcsh )
Genre:
serial ( sobekcm )
periodical ( marcgt )

Notes

Citation/Reference:
Chemical abstracts
Additional Physical Form:
Also issued online.
Dates or Sequential Designation:
1960-June 1964 ; v. 1, no. 1 (Oct. 1965)-
Numbering Peculiarities:
Publication suspended briefly: issue designated v. 1, no. 4 (June 1966) published Nov. 1967.
General Note:
Title from cover.
General Note:
Place of publication varies: Rochester, N.Y., 1965-1967; Gainesville, Fla., 1968-

Record Information

Source Institution:
University of Florida
Rights Management:
All applicable rights reserved by the source institution and holding location.
Resource Identifier:
01151209 ( OCLC )
70013732 ( LCCN )
0009-2479 ( ISSN )
Classification:
TP165 .C18 ( lcc )
660/.2/071 ( ddc )

UFDC Membership

Aggregations:
Chemical Engineering Documents

Downloads

This item has the following downloads:


Full Text




;J1















EDITORIAL AND BUSINESS ADDRESS:
Chemical Engineering Education
Department of Chemical Engineering
University of Florida Gainesville, FL 32611
PHONE and FAX: 352-392-0861
e-mail: cee@che.ufl.edu

EDITOR
Tim Anderson

ASSOCIATE EDITOR
Phillip C. Wankat

MANAGING EDITOR
Carole Yocum

PROBLEM EDITOR
James O. Wilkes, U. Michigan

LEARNING IN INDUSTRY EDITOR
William J. Koros, University of Texas, Austin


-PUBLICATIONS BOARD

CHAIRMAN *
E. Dendy Sloan, Jr.
Colorado School of Mines

MEMBERS
Pablo Debenedetti
Princeton University
Dianne Dorland
University of Minnesota, Duluth
Thomas F. Edgar
University' of Texas at Austin
Richard M. Felder
North Carolina State Universiot
Bruce A. Finlayson
University of Washington
H. Scott Fogler
University of Michigan
William J. Koros
University of Texas at Austin
David F. Ollis
North Carolina State University
Ronald W. Rousseau
Georgia Institute of Technology
Stanley I Sandler
University of Delaware
Richard C. Seagrave
Iowa State University
Stewart Slater
Rowan University
James E. Slice
University of Texas at Austin
Donald R. Woods
McMaster University


Chemical Engineering Education


Volume 35


Number 2


Spring 2001


> EDUCATOR
86 Don Paul, of the University of Texas at Austin, William J. Koros

> CLASSROOM
92 Efficient, Effective Teaching, Phillip C. Wankat
104 The Business Meeting: An Alternative to the Classic Design Presenta-
tion, James A. Newell
128 Student-Performance Enhancement by Cross-Course Project Assign-
ments: A Case Study in Bioengineering and Process Modeling,
Giilnur Birol, Inane Birol, Ali (inar
148 Undergraduate Process Control: Clarification of Some Concepts,
R. Ravi

> LABORATORY
96 A Supercritical Extraction Experiment for the Unit Operations
Laboratory,
Ronald G. Gabbard, Dana E. Knox
116 Computer Modeling in the Undergraduate Unit Operations Laboratory:
Demonstrating the Quantitative Accuracy of the Bernoulli Equation,
David J. Keffer
122 Using In-Bed Temperture Profiles for Visualizing the Concentration-
Front Movement,
Paulo Cruz, Addlio Mendes, Ferndo D. Magalhdes
134 Developing the Best Correlation for Estimating the Transfer of
Oxygen from Air to Water, Wayne A. Brown

> RANDOM THOUGHTS
102 FAQS. III: Groupwork in Distance Learning,
Richard M. Felder, Rebecca Brent

> CLASS AND HOME PROBLEMS
112 Thermodynamic Properties Involving Derivatives: Using the Peng-
Robinson Equation of State, R.M. Pratt

> CURRICULUM
140 A Project-Based Spiral Curriculum for Introductory Courses in ChE:
Part 3. Evaluation,
David DiBiasio, Lisa Comparini, Anthony G. Dixon, William M. Clark
152 The Interface Between ChE and Mathematics: What do Students
Really Need? Michael D. Graham, Susan L. Ganter

91, 95, 110 Book Reviews
107, 109 Letters to the Editor
111 Call for Papers
120 ASEE, Chemical Engineering Division Program

CHEMICAL ENGINEERING EDUCATION (ISSN 0009-2479) is published quarterly by the Chemical Engineering
Division, American Society for Engineering Education, and is edited at the University of Florida. Correspondence
regarding editorial matter, circulation, and changes of address should be sent to CEE, Chemical Engineering Department,
University of Florida, Gainesville, FL 32611-6005. Copyright 0 2001 by the Chemical Engineering Division, American
Society for Engineering Education. The statements and opinions expressed in this periodical are those of the writers and not
necessarily those of the ChE Division, ASEE, which body assumes no responsibility for them. Defective copies replaced if
notified within 120 days of publication. Write for information on subscription costs andfor back copy costs and availability.
POSTMASTER: Send address changes to Chemical Engineering Education, Chemical Engineering Department., University
of Florida, Gainesville, FL 32611-6005. Periodicals Postage Paid at Gainesville, Florida and additional post offices.


Spring 2001









] educator


DON




PAUL



... of The University of Texas at Austin




WILLIAM J. KOROS
The University of Texas at Austin Austin, TX 78712

I recently conducted an experiment by asking several
colleagues at the University of Texas at Austin what
words came to mind when they thought of Don Paul.
For those who know him well, it is not surprising that the
common descriptors included "smart," "organized," "hon-
est," "practical," and "tough."
While those five words undoubtedly capture his core per-
sonality, the word "productive" also pops to mind when I
think of Don. By any standard, Don's prodigious contribu-
tions to the chemical-engineering and materials-science lit-
erature place him almost in a class by himself. In addition to
coauthoring over 450 archival journal articles and editing
eight books, Don has also mentored 52 PhD students, 47 MS
students, and 46 postdoctoral fellows during his career at
Texas. Serving as the Editor-in-Chief of Industrial and En-
gineering Chemistry Research for fifteen years and being on
the editorial boards of eight other journals has made his
impact on the field of chemical engineering truly enormous.
Don's research interests include the broad areas of poly-
mer science and engineering and chemical engineering. His
eight edited books cover a broad range of topics, but they
have a common thread as a result of his interest in polymers.
Don's current research involves polymer blends, mem-


branes for separations, drug delivery, packaging, and poly-
mer processing. The blend research deals with the thermo-
dynamics of polymer-polymer miscibility, phase diagrams
and interfaces, reactive compatibilization of multiphase mix-
tures, rubber toughening, the control of phase morphology
during processing by both chemical and physical means, and
polymeric nanocomposites. His research on diffusion in poly-
mers involves investigation of structure-property relation-
ships to design better membranes for separation processes,
improved barrier materials, physical aging of thin films, and
"thermal switch" membranes.
Don has also contributed significantly to theories and
models for describing sorption and permeation of small
molecule penetrants in polymers. A broad range of materi-
als, including rubbery, glassy, semicrystalline and liquid
crystalline states of these materials, has been considered.
Synthesis and characterization of novel materials is a key
aspect of his work in all of the above sub-areas.

A BROAD ARRAY OF CONTRIBUTIONS
One of our departmental colleagues once joked that he
held a still-unproven hypothesis that there are really identi-
Copyright ChE Division ofASEE 2001
Chemical Engineering Education










cal twins with the initials DRP wh
office. While highly valuing product
dards for quality are also apparent, a
a creative and insightful investigate
pect of his nature.
Beginning with the 1973 ACS Arti
steady stream of honors bestowed
underlines the respect in which his
chemistry and chemical engineer-
ing communities. In addition to the
Doolittle Award, the ACS has rec-
ognized his contributions through
the Phillips Award in Applied
Polymer Science and the E.V.
Murphree Award for Contributions
to Industrial and Engineering
Chemistry. The AIChE has recog-
nized him with the Stine Materials En
Award and the William H. Walker Av
to the Chemical Engineering Literatu
tion as a Fellow.
He was elected to the National Ac
in 1988 for "outstanding research c
meric materials and for leadership in
education." Don's Council of Chemi
Pruitt Award and the Plastic Institute
Award also emphasize not only hi:
publication and research arenas, but
the interface between industry, goven
Don has presented numerous invite
the Warren McCabe lecture at North
sity, the R.L. Pigford Memorial Lecti
Delaware, the Ashton Hall Cary Lec
tute of Technology, and the Donald
University of Michigan. He has als
engineering community through his
mittees and organizations throughout
the Education Projects Committee of
77 and served as the editor for the
Faculties Directory from 1967-77.
accreditation visitor from 1974-83.
to both the chemistry and the chemi
munities is reflected by his active
ACS and the AIChE.
Don served on the Executive Comn
sion of Polymeric Materials Sciences
1980-85 and in many capacities relate
well beyond his work as Editor in Ch
His work on I&EC Research has seen
of archival journal pages published un
collaborative assistance of many edit
1986. His editorial contributions hav
on editorial boards for The Journal
Spring 2001


o operate from Don's
vity, Don's high stan-
nd his recognition as
or documents this as-

hur Doolittle Award, a
)n Don by colleagues
work is held by the


Polymer Engineering and Science, Journal of Applied Poly-
mer Science, Chemical Engineering Education, Polymer,
Journal of Polymer Science, Polymer Physics, Polymer Con-
tents, and the Imperial College Press Series on Chemical
Engineering.
Beyond the AIChE and ACS, Don has also been involved
in activities of the Council of Chemical Research, serving on
its Governing Board (1981-84) and its Executive Committee


[Don] published a classic paper regarding the
mechanism of hydraulic permeability through membranes
[that] helped call attention to the new program in polymers at UT
and launched the membrane activities that have been a strong
and continuous component of UT's graduate-studies
area for over three decades.

gineering and Science (1983-84). He was a member of the Founding Committee of
ward for Contributions the North American Membrane Society. His work with the
ire as well as by elec- National Academy of Engineering has included service on
the NAE Peer Committee in 1989-92 and 1994 as well as the
ademy of Engineering Membership Committee from 1994-97. The National Re-
ontributions on poly- search Council benefited from his input on its National
chemical engineering Materials Advisory Board from 1988-94, its Committee on
cal Research Malcom Polymer Science and Engineering from 1992-94, its U.S.
's Educational Service National Committee on the International Union of Pure and
s impact in scholarly Applied Chemistry from 1993-96, and its Solid State Sci-
also his leadership at ence Committee from 1994-97. He also served on panels for
nment, and academia. Materials Science and Engineering at NIST and on the panel
ed le i g for International Benchmarking of U.S. Materials Science
ted lectures, including
Carolina State Univ- and Engineering Research.
Carolina State Univer-
ire at the University of Don's story begins in North Carolina where he grew up on
tures at Georgia Insti- a small farm near Washington, NC. He freely acknowledges
L. Katz Lecture at the the strong effect that this background has had on his lifestyle
o served the chemical and motivation. An anecdote regarding this point is useful
contributions to com- here. Don once told me that he recalls going out to hoe
his career. He was on weeds out of a large field one hot North Carolina day.
the AIChE from 1968- Looking at the very large and intimidating field, he decided
Chemical Engineering not to think in terms of its size. Instead, he looked down the
le also was an ABET first row and thought, "I can get to the end of this one."
Don's ability to speak Hoeing his way to the end of the row, he straightened up and
cal engineering com- looked down the next row, deciding "I can get to the end of
work with both the this one, too," You can guess the rest-128 rows later he
looked back on the entire field with a sense of accomplish-
nittee of the ACS Divi- ment and an insight that has remained with him throughout
and Engineering from the years. Whether it is writing papers or books, or educating
ed to ACS publications nearly 150 graduate students and post docs, it is best to take
ief of I&EC Research. it "one row at a time" and to just keep on working.
close to 50,000 pages Don's contributions to teaching have also been widely
ider his watch, with the recognized. He received the General Dynamics Teaching
orial colleagues, since Award in 1977, which is the highest teaching recognition in
e also included service the College of Engineering, and it focuses on contributions
of Membrane Science, to undergraduate education. In 1994, our department nomi-
















PhD Students
D.R. Kemp (1972)
C.E. Locke (1972)
O.M. Ebra-Lima (1973)
W.J. Koros (1977)
A.H. Chan (1978)
C.A. Cruz Ramos (1978)
J.E. Harris (1981)
R.S. Barnum (1981)
E. Woo (1984)
J.-S. Chiou (1985)
Y. Maeda (1985)
A.C. Fernandes (1986)
M.J. El-Hibri (1986)
T.A. Barbari (1986)
M.E. Fowler (1987)
N. Muruganandam (1987)
M.C. Schwarz (1987)
C.-H. Lai (1988)
P.S. Tucker (1988)
A.C. Puleo (1988)
J.H. Kim (1989)
P.C. Raymond (1989)
J.M. Mohr (1990)
J.S. McHattie (1990)
H. Kim (1990)
G.R. Brannock (1990)
T.-W.Cheng (1991)
I. Park (1991)
D.H. Weinkauf (1991)
Y. Takeda (1992)
C.L. Aitken (1992)
C.K. Kim (1992)
T.A. Callaghan (1992)
M. Aguilar-Vega (1993)
J.D. Le Roux (1993)
M. Nishimoto (1994)
P.P. Gan (1994)
B. Majumdar (1994)
A.G. Gonzalez (1995)
M.R. Pixton (1995)
M. Lu (1995)
A.J. Oshinski (1995)
S. Ziaee (1995)
K.A. Schult (1996)
C.T. Wright (1997)
F.A. Ruiz-Trevino (1997)
G.S. Wildes (1998)
W.R. Hale (1998)
M.S. McCaig (1998)
G.D. Merfeld (1998)
R.A. Kudva (1999)
J. H.-C. Chu (1999)
Z. Mogri (2001)


MS Students
D.R. Kemp (1969)
J.H. Troell (1969)
O.M. Ebra-Lima (1970)
J. St. Lawrence (1970)
V. Mavichak (1970)
C.E. Vinson (1971)
D.H. Carranza(1972)
A.E. Mann (1972)
R.E. Robertson (1972)
M. Garcin (1973)
J.O. Altamirano (1974)
J.R. Stell (1974)
J.D. Paciotti (1974)
A.A. Rocha (1974)
W.E. Garmon (1975)
R.L. Imken (1975)
S. McSpadden (1975)
A.J. Meyer (1975)
D. Wahrmund (1975)
T.R. Nassar (1976)
R.N. Mohn (1977)
R.E. Bernstein (1977)
J.C. Tiffany (1978)
G. Wonders (1978)
E. Nolley (1978)
A.J. Erb (1979)
D.W. Bartlett (1979)
C.R. Lindsey (1979)
P.-T. Chang (1980)
M.D. Lorenz (1980)
J.J. Ziska (1980)
P. Masi (1980)
E.A. Joseph (1981)
W.A. Smith (1981)
E.Y. Adham (1982)
T.D. Traugott (1982)
W.E. Preston (1982)
S.R. Murff (1983)
J.D. Keitz (1983)
C. McCutcheon (1983)
J.-L. G. Pfennig (1984)
V.J. Triacca (1989)
G.P. Shaver (1989)
J. Oshinski (1990)
A.B. Lombardo (1994)
S. Gupta (1995)
A. Kelkar (2000)


TABLE 1
Don Paul's Former Graduate Students


nated Don for the University-wide Graduate Teaching Award. We con-
tacted his former graduate students for possible letters of support. The
response was overwhelming. Letters poured in from all over, since by
that time Don's former students had achieved distinguished positions in
many parts of the world. The recurring theme of these letters was an
expression of the writer's feelings of deep appreciation for Don's help in
their educational development by his tough, but ultimately compassion-
ate, mentorship. As one of these former students, I was more than pleased
that Don received this highly competitive award in recognition of his
educational efforts.

Don's BS in chemical engineering was.earned at North Carolina State
University (1961) and his graduate work was carried out at the University
of Wisconsin, Madison (1965). He has been recognized by both of his
alma maters with distinguished graduate awards.
In addition to summer work at DuPont in the nonwoven fabric area in
1960-61, Don was a Research Chemical Engineer at Chemstrand Re-
search Center in North Carolina's Research Triangle Park from 1965 to
1967.


LIFE AND LEADERSHIP IN THE DEPARTMENT

Don joined the University of Texas faculty in 1967 and has been here
now for 34 years. Progressing through the ranks to Associate Professor in
1970 and to Full Professor in 1973, he took an early role as a departmen-
tal leader. He served as the department's Associate Chairman from 1973-
77 and as its Chairman from 1977-85. During his Chairmanship, Don
recognized the need for a forward-looking approach. He assembled a
committee comprised of distinguished leaders in the chemical and petro-
chemical industries as well as from the academic community to evaluate
the curriculum. The committee also analyzed the future needs of the
department and the larger chemical engineering community. Many of the
elements of this visionary plan are still used as the guiding principles for
our department.

One of Don's favorite statements is that "chemical engineering is
defined by what chemical engineers do." That attitude helped position
the department as an early player in the polymer, materials science,
microelectronic, and biotechnology opportunities that have helped main-
tain the vitality of our discipline.
Don was also quick to see the need for better bricks, mortar, and
laboratory facilities to allow the department's movement toward the new
technological areas, while still maintaining connections to its petro-
chemical roots. He was a key person in acquiring the needed resources to
construct our current modem facility, which was occupied in 1986 at the
end of his term as Chairman. Strong connections with our alumni and
industrial friends also led to the establishment of a large number of
endowed positions in the department and college during this period. Don
himself was selected as the T. Brockett Hudson Professor in 1978 and as
the Melvin H. Gertz Regents Chair in Chemical Engineering in 1985.
Following his term as Chairman, Don returned to his active research
and teaching duties in the department and served as a mentor for several
faculty who were at the time making the transition to academia from
industry. During the time he served as Chairman, he managed to maintain
an energetic research program, but when he stepped down from that
Chemical Engineering Education










position, a literal explosion of activity became apparent
through his PhD supervision and his publications.

MAJOR TECHNICAL CONTRIBUTIONS

Don's interests and contributions in polymer engineering
and science have included work in both polymer blends and
membranes. Not surprisingly, he has managed to also com-
bine his insights in these two separate areas to provide im-
portant contributions in advanced blend membrane systems
for gas separation membranes.
Don's work in polymer blends has led to an important
route to new commercial polymer products. His work has
integrated thermodynamics, interfacial phenomena, rheol-
ogy, process, morphology, and properties of these novel
materials to provide a solid scientific foundation for this
field. Since the late 1940s, numerous papers have suggested
that polymer-polymer mixtures were unlikely to be miscible.
This belief discouraged and delayed the development of any
widespread interest in blends. Indeed, the favorable entropy of
mixing for two polymers was known to be very small, if not


entirely negligible. Moreover, the premise at the time was that
enthalpic effects were positive and unfavorable for mixing.
Don was a pioneer in focusing attention on polymer-poly-
mer interactions as the key to developing miscible blends.
He and his colleague, Joel Barlow, published an important
paper showing that intramolecular repulsive interactions in
random copolymers can provide the basis for exothermic
mixing, thereby promoting miscibility with other polymers.
This effect meant that such random copolymers could form
miscible blends, even when the corresponding homopoly-
mers could not. This non-intuitive concept was simulta-
neously recognized by two other groups and is now a corner-
stone of polymer-blend technology.
In 1992, Don and his students initiated a series of papers
that combined this copolymer model with a modern equa-
tion-of-state theory of mixing. Their work allowed a matrix
of interaction energies to be constructed to predict the misci-
bility of multiple polymers and to design copolymers for
controlled phase behavior in blends.
This work is also useful for understanding and designing


UT's chemical engineering faculty at the time of Don's Chairmanship in 1984. Top row: Keith P. Johnston, E.T.
Beynon, James R. Brock, Hugo Steinfink, Douglas R. Lloyd, Joel W. Barlow. Middle row: James R. Fair, Thomas
F. Edgar, Gary T. Rochelle, John G. Ekerdt, James E. Stice, Herbert Grove. Seated; John J. McKetta, Eugene H.
Wissler, William A. Cunningham, Donald R. Paul, Howard F. Rase, Joel Hougen. (Missing: David M. Himmelblau,
W.J. Koros, R.P. Popovich, and R.S. Schechter)
Spring 2001










phase-separated immisciblee) blends
in which polymer-polymer interac-
tions are manifested in the nature of
the interface between the phases.
Don's work in this area has been com-
mercialized through long-standing col-
laborations with various companies.
In addition to the enormous amount
of work in polymer blends, Don has
pioneered the development of mem-
branes. Within his first year as an As-
sistant Professor at Texas, he pub-
lished a classic paper regarding the
mechanism of hydraulic permeability '"
through membranes. This paper helped
call attention to the new program in
polymers at UT and launched the
membrane activities that have been a
strong and continuous component of
UT's graduate-studies area for over
three decades. Soon after completing
this paper on liquid permeation, he pub-
lished a second classic analysis of mem-
branes-this one related to gas trans-
port in glassy polymers. Don cooper-
ated with the group at Monsanto that Don and Sallj
developed the first truly commercially
successful gas separation membrane system, called "Prism."
Over the intervening years, Don and his co-workers have
systematically studied the relationship between polymer struc-
ture and the gas permeation properties of novel materials
synthesized in their labs. Important principles of molecular
design have emerged from his work. These insights have
been codified into a group contribution scheme for predict-
ing membrane performance. Several new materials of sig-
nificant commercial interest have been identified. Moreover,
novel processing schemes involving flourination, crosslinking
(and of course, blending) of polymers and low-molecular-
weight compounds have been studied.

FAMILY
The only commitment that exceeds in length Don's asso-
ciation with the UT department is the one with his extraordi-
nary wife, Sally. Don and Sally met while in graduate school
at Wisconsin in 1963. Her disposition and nature caused her
to take an interest in children with special needs. Completing
her Masters in Speech Therapy meshed well with the timing
of Don's completion of his PhD, and they celebrated by
getting married in 1964. After locating in Austin, they raised
a family that includes Mark, a master pastry chef trained at
the James Beard School in New York City, and Ann, who is
currently an auditor with the State of Texas.
Over the years, Don and Sally shared another favorite


yon


activity-hiking. In addition to hik-
ing, boating, and other outdoor pur-
suits, Don has a great love of cooking
and a passion for music, especially jazz
and blues. His music collection is of
H such a size that only someone with his
organization skill could maintain it in
functional form.
In 1995, the saddest event in Don's
life removed Sally from him and his
children. Her death led to a period of
. deep mourning that eventually yielded
to the tough nature that, as noted in
the introduction, is one of Don's sig-
nature qualities.

THE RECENT PAST AND THE
FUTURE
I recall having lunch with Don eigh-
-, teen months after Sally's death. He
S had his old spark back and told me
J that he wanted to do something sig-
,.- nificant for the institution that had
helped him so much. He said he had
been thinking about the lack of a for-
a hiking trip. mal Materials Science Department at
UT and how this was often cited as a
problem that needed to be dealt with. He said, "I now see
this as a possible advantage, rather than a disadvantage, if it
is handled properly." He unveiled an idea for a materials
institute that would cut across college as well as departmental
boundaries.
Don visualized a network of individuals linked together by
their common interest in materials and with a core of instru-
ments and facilities in a central institute. His vision quickly
spread beyond lunchtime conversation to the offices of deans
and the vice president of research. With the valuable support
of the administration, Don's concept moved toward reality.
At this point, Don's "take-one-row-at-a-time" approach
resurfaced. He made the rounds from the physics department
to the chemistry department to the aerospace, chemical, elec-
trical, and mechanical engineering departments, recruiting
support at the grass-roots level to match the upper-adminis-
tration support. In 1998, the Texas Materials Institute be-
came a reality, and Don was inducted as its first director.
Under his leadership, materials work is now prospering at
UT. New facilities, new positions in various departments, and
colleagueships that would probably not have occurred have
begun-one row at a time. Our colleagues in the department,
in the college, and across the university appreciate and value
Don's catalytic contribution in fostering this unusual and valu-
able addition to our university. We are all indebted to Don for
his uniquely broad and deep contributions. 7
Chemical Engineering Education











MM book review


Elementary Principles of Chemical Processes
3rd Edition
By Richard M. Felder and Ronald W. Rousseau
John Wiley & Sons, 605 Third Avenue, New York, NY 10158-
0012; 675' pages; $111.95 (cloth); (2000)
Reviewed by
D. Hunkeler
Swiss Federal Institute of Technology

The third edition of this classic introductory chemical
engineering text is intended to compliment a first course in
stoichiometry, material and energy balances, and introduc-
tory thermodynamics. As such, it is aimed at engineering
and chemistry students who have completed their first year
of general university education. Freshman physics and chem-
istry are valid prerequisites, although if the course is taught
with the complimentary teaching modules, one could con-
sider offering it earlier. The third edition follows the same
format as the previous two editions, with a preliminary set of
three chapters discussing the units and dimensioning of pro-
cess variables and their associated calculations. This section
is (in some curricula) omitted, due to its coverage in other
courses, but it is a valuable asset since many student difficul-
ties in balances occur due to sloppy "accounting."
The body of the text discusses material balances, first for
non-reactive single-phase processes and then adding
multiphase systems, recycling, and bypass. One of the
strengths of the book is the ease with which the authors'
introduce thermodynamics into the subject matter. Equa-
tions of state for non-ideal gases, compressibility, multicom-
ponent equilibrium, and two-phase partitioning and solid-
liquid-vapor phase diagrams are presented in a comprehen-
sible manner that permits students to begin solving problems
on the day of the lecture. This is something Felder has long
advocated in his interactive teaching approaches, and the
third edition certainly shows the value of the NSF's sponsor-
ing of the concepts which brought it to fruition.
The text also integrates graphical presentations of correla-
tions with computer-based programming challenges. The
students will not realize until subsequent courses, to what
extent they have been introduced to (and to a large extent
mastered) elementary chemical and engineering thermody-
namics. The problems at the end of the chapter do an excel-
lent job of integrating the concepts presented, along with
statistics, into the estimation of thermodynamic data.
Practical problems, related to a series of important unit
operations including various separation methods such as
absorption, adsorption, condensation, crystallization, distil-
lation, and extraction are presented throughout the first eleven
chapters. The authors' also discuss batch, semi-batch, and
Spring 2001


continuous reactors operating under adiabatic and isother-
mal conditions, both at steady state and dynamically. Com-
bustion is treated separately. Liquid-gas processes including
evaporation-compression, humidification, dehumidification, and
scrubbing are also integrated into material and energy bal-
ances. Overall, the new problems are challenging, yet doable.
The third section of the book discusses energy and energy
balances. There is minimal overlap with the discussion of
forms of energy typically presented in freshman physics.
Energy balances on non-reactive processes challenge stu-
dents to organize their solutions. The text pulls itself to-
gether in Chapter 9 when the enthalpy of reaction is used,
and estimated, principally to permit the calculation of a
reactor's energy loss, temperature, or pressure. The balances
are also extended to complete processes. Discussions of
alternative fuels, which may appear old-fashioned, is a take-
home deliverable from this text, as are its extensive data
base (tables, graphs, and CDs) that may convince sopho-
mores they never have to set foot in an engineering library.
The text concludes with a chapter on computer-aided
calculations, which many schools cover in a separate course
(as they do the material on transient processes). But if Chap-
ters 10 and 11 are omitted, Chapters 12 through 14 cannot
be. The authors' offer three case studies (one in the area of
materials and two in commodity chemistry) that need to be
presented at the end of the two-semester sequence to con-
vince students they can, indeed, design plants. It is a motiva-
tion which will drive many of them to integrate kinetics,
reactor design, transport phenomena, and separations into
their working knowledge and become chemical engineers.
As the only chemical engineering course taught to chemists,
in my experience, it provides an excellent sensitization to the
challenges facing industrial organic and polymer chemists
when they develop new (macro) molecules.
The text comes with a CD that includes an animated
encyclopedia of chemical process equipment, the E-Z solve
software for balances along with tutorials, and an index of
learning styles. As fantastic as these are, the real value is that
the physical property database demystifies the coupling be-
tween thermodynamics and engineering, which confuses so
many students. With the database provided, carrying out
material balances is no longer a cumbersome task akin to
financial accounting, but is fun. Felder and Rousseau have
made chemical engineering enjoyable. My students make
significantly less calculation errors on their balances thanks
to the third edition of this book, and they are motivated and
listen better to the concepts their predecessors had ignored.
Overall, the authors' present a way for introductory stu-
dents to respect complexity and understand the need for
engineering approximations. Take the authors' advice to let
the students enjoy problem-based learning-they will better
understand themselves, their career, and their choices. The
book is a service to our profession. 0










rMe classroom


EFFICIENT, EFFECTIVE

TEACHING



PHILLIP C. WANKAT
Purdue University West Lafayette, IN 47907-1283


Good teaching requires that students must learn the
right content, have a good attitude, and learn how-
to-learn. Teaching is efficient for students when
there is a high ratio of (student learing)/(student time on the
course). Because they are so busy, professors also benefit
from courses that are reasonably efficient. A course is effi-
cient for professors when there is a high ratio of (student
learing)/(professor's time on the course). Although there
are times when effective teaching and efficient teaching
conflict, most of the time effective teaching can also be
efficient.
As a professor, you can apply the techniques of time
management and efficiency by becoming familiar with con-
cepts such as missions, goals, priorities, to-do lists, calen-
dars, and prime time.''21 These methods should be applied,r3]
paying special attention to efficient teaching.1361

EFFICIENT TEACHING
OF LECTURE COURSES[3]
Course Development
Designing a course is basically an engineering design
problem. What is the purpose of the course? The purpose of
a required undergraduate course is obviously very different
than the purpose of an elective. You should obtain several
old outlines and syllabi. Talk both to professors who have


Phil Wankat received his BSChE from
Purdue and his PhD from Princeton. He is
currently a Professor of Chemical Engineer-
ing at Purdue University. He is interested in
teaching and counseling, has won several
teaching awards at Purdue, and is Head of
Interdisciplinary Engineering. His research in-
terests are in the area of separation pro-
cesses, with particular emphasis on cyclic
separations, adsorption, and preparative
chromatography.


taught the course and to those who teach prerequisite courses
to see what you can expect the students to know. Talk to
professors who teach follow-up courses to determine what
students must learn in your course.
The syllabus is a contract with the students. Find a good
one and adapt it with appropriate modifications for your
course. Be explicit about rules and regulations. The students
will not know what you expect of them until you tell them
(even then some students will claim ignorance). Start with
firm, and perhaps even tough, rules-then relax later on. As
part of the syllabus, you should develop a tentative course
outline. Plan to spend one or two periods at the beginning of
the semester reviewing material the students are supposed to
know, and plan one period before every major test for catch-
up and review. Cover less, but cover it in more depth than
was previously done. Many students only work when there
are assignments or tests, so there should be something for
the students to do outside of class at least every other week,
preferably more often.
Shortly after the first test, ask for feedback from the stu-
dents, using a "one-minute quiz." Pass out index cards and
ask students what you (and the TAs) can do to help them
learn more. Using the responses you receive, make appropri-
ate changes to improve the course. Midcourse corrections
based on this feedback can rescue a course headed for disas-
ter. Allowing students to have input into test dates and due
dates of projects also indicates your willingness to listen-
and will be greatly appreciated by your students.
Finally, arrange to teach the same course three or four
times in succession. This allows you to reuse much of your
preparation and results in a better course in less time. At the
end of the semester reflectively analyze what worked and
what didn't, then plan changes for the next offering while
the details of the course are still fresh in your mind.


Copyright ChE Division of ASEE 2001


Chemical Engineering Education










Lectures
Lecturing is the most efficient teaching method the first
time a course is taught. Since lectures can be prepared im-
mediately before class, it is easy to adjust the course as you
proceed through the semester. Lectures must actively en-
gage the students in order to be effective. In subsequent
offerings of the course, try modifying the lecture approach
or try other teaching approaches such as cooperative group
techniques.
When you know the material, you can prepare a new fifty-
minute lecture in two hours or less. Repeat lectures can be
prepared in one-half hour. Trying to prepare a lecture in less
time is obviously dangerous. Unfortunately, many new fac-
ulty spend significantly more time than this without becom-
ing good teachers.15'61 Spend the two hours of preparation
time in several short bursts, starting at least a day before the
lecture will be delivered. The first fifteen minutes of prepa-
ration should be used to develop a title and a brief concep-
tual outline. Fill in some of the details later, but do not write
out your notes word-for-word.
Since a student's maximum attention span is 15 to 20
minutes, the standard fifty-minute lecture hour should have
one or two lecture breaks to make it effective. For example,
a good scheduling might be
U Introduction and short review
U Mini-lecture
C Lecture break
C Mini-lecture
C Summary and transition to homework for next class

Good lecture breaks include active learning exercises such
as small-group discussion, small-group problem solving,
brainstorming, and student reflection. Since the audience's
limited attention span forces you to use breaks, you will
naturally cover less material; but the breaks serve to refresh
the students so they pay more attention to the mini-lectures,
and the in-depth processing that occurs during breaks in-
creases student learning.
With a little practice it is possible to be comfortable lec-
turing and to actually enjoy it. If you are uncomfortable the
students will be uncomfortable, regardless of how well-
prepared you are. Quickly prepared, brief lecture notes are
effective since they control content tyranny. By focusing on
the most important points and leaving details to examples,
you don't have to race through every second of the lecture.
Remember that from the students' viewpoint, it is more
important to end on time than to cover everything.
The second time you teach the course, try making partial
lecture transparencies. Include most of the material needed
for the transparency, but skip some of the key points. Give
copies of these notes to the students. This procedure will
eliminate many of the errors inherent in note taking and will


give the students time to think-but it will still require them
to pay attention so they can fill in the key missing items.
You can thus cover more material without sacrificing stu-
dent understanding.


Tests
Write new tests every term. As you teach, create a file of
possible test problems. They can be variants of homework
problems, or problems sparked by student misunderstand-
ings, and so forth. The purpose of the file is to provide
potential problems that can be considered when you write
the test. Avoid disasters by solving the test completely be-
fore using it, and record how long it takes you to solve the
test. Freshmen and sophomores will need about five times as
long, juniors about four times as long, and seniors about
three times as long.
Discussing procedures in class thoroughly before the first
test will help reduce the students' anxiety. A good practice is
to use old tests as ungraded practice tests that the students
can do on their own, posting the solution on a bulletin board
or on the web. This access to old tests helps greatly in
reducing student test anxiety. Be present for the test since
you are the best one to fix any last-minute errors or prob-
lems. There is also less cheating when the professor is present.
If at least half the class is unable to finish the test on time,
the test is too long.
Try to make grading as fair as possible, keeping in mind
that students consider unfair grading to be unethical. For
reasons of consistency, prepare a solution key to allocate
partial credit when appropriate. Fair grading requires a re-
grade procedure. Reduce the hassle of regrades by requiring
written regrade requests.


Attention to Students
Students want and deserve individual attention. They are
very tolerant of fumbling in the lecture if they believe you
care about them. Although the average engineering under-
graduate may not be as smart as your peers in graduate
school were, remember that he or she counts among the best
undergraduates at your school. And sheer technical compe-
tence is less important for success in industry than motiva-
tion, hard work, timing (or luck), communication skills, and
the ability to work well with a diverse assortment of people.
Look for the best in your students, and you will probably
find it-professors with a good attitude usually end up with
students with good attitudes.
If you don't learn the students' names, they will feel like
just numbers on a list and will be much more likely to skip
class, be disruptive, not do the work, and/or cheat. Admit
tedly, learning a lot of new names each semester is difficult,
but the effort is repaid by smoother course operation. Any-


Spring 2001










thing you know beyond their names, such as hometowns or
career goals, will greatly help you gain rapport with them.
Since personal attention to the students' needs requires a
significant expenditure of time, efficiency and effectiveness
can get lost in the competition for their share of time. A
reasonable compromise is to hold scheduled group help ses-
sions (particularly before tests) and a modest number of
scheduled office hours during the week. Be available to the
students during your office hours. Also, asking your teach-
ing assistants to hold office hours provides another opportu-
nity for the students to learn.
Come to class five minutes early and stay five minutes
after class. In addition to giving you a chance to prepare the
classroom, coming early sends the message to the students
that you are looking forward to this class. Staying late offers
a good time to answer questions. The combination of com-
ing early and staying late provides an opportunity for indi-
vidual attention, particularly for those students who will not
use office hours.
When students ask for special arrangements to take tests
or to turn in homework, be flexible, but require them to be
responsible and to inform you in advance if possible. Occa-
sionally students will abuse your generosity. It will usually
be clear when this has happened, however, and you should
make sure it does not happen a second time. If you treat
students as adults, most of them will act accordingly.

A NEW TEACHING-LEARNING PARADIGM
Standard courses use a teacher-centered paradigm. Even
when such courses are well taught, using advanced strate-
gies such as cooperative groups, they suffer from some
deficiencies that appear to be inherent to the basic paradigm.
Students seldom learn how-to-learn on their own and there is
a clear limit to the professor's efficiency in teaching the
course. Relatively mature students can take more responsi-
bility for their learning and be taught with a problem- or
project-centered paradigm.
Engineering students will focus on learning when there is
a task that must be completed. Problem-based learning171
(PBL) is a method for using problems or short projects to
focus student attention on learning. While PBL does help
students learn how-to-learn, it does not increase the
professor's efficiency since preparation and grading of the
projects is very time-consuming. PBL is usually reported as
increasing, not decreasing, the time the professor spends on
the course. For students to learn how-to-learn and to drasti-
cally increase the professor's efficiency while retaining course
effectiveness, a different paradigm is needed.
Fortunately, the efficiency literature gives us a clue as to
what this paradigm should include-delegation.[ ,2] Instead
of the professor planning the material, picking topics, pre-
paring material, lecturing, etc., ask the students do this work.
94


With appropriate feedback from the professor, delegation of
these responsibilities to the students can result in significant
growth in their ability to learn. Delegation can be used for
the entire course81] or for a portion of the course.
Course projects are an effective way to focus students'
attention, and they lend themselves to delegation of respon-
sibilities. Projects lead to more learning if significant class
time is devoted to them. For example, finish the lecture
portion of the class before the end of the term and spend the
remaining class time on project work. If class time is not
devoted to the project, students consider it add-on work.
Although projects can be done by individuals or groups,
group projects result in much more significant efforts. I
assign the groups to ensure that they are diverse in ability,
learning styles, and work styles. Use the principles of good
cooperative group instruction.[4]
The professor sets the tone for the project work. Expect
graduate students and seniors to deliver professional quality
work. Provide examples of papers or reports that surpass the
minimal quality standards. Give guidelines for topics and
some examples, but expect the students to devise their own
topics and titles. Work with the students to narrow the scope
of their projects so that they can be finished in the time
available. For example, one group that started with the topic
of supercritical extraction had 19,000 hits in a computerized
search. Two iterations later, the topic supercritical extraction
of coffee resulted in 65 hits, which is a much more manage-
able number. The topic must be something new for the
students. Do not allow recycling of projects from other courses
and note in writing that recycling projects will be considered
a form of cheating. Although allowing students to do a
project on their master's or PhD research might seem effi-
cient, it is unfair to students who are not doing research in an
area related to the course.
Regular meetings with groups during scheduled class time
and periodic student presentations to the entire class help
combat procrastination. Final reports will be significantly
better if students first turn in a rough draft. Have another
group critique each rough report. These critiques help to
improve the final reports and give the students practice in the
highest level of Bloom's taxonomy-evaluation. If the cri-
tiques are graded, the students will take this exercise seri-
ously. I also critique the drafts with the idea of showing the
groups areas for improvement. Allow about one week for
groups to finish their reports after the critiques are returned.
I also ask the students to fill out forms to critique oral
presentations, but these critiques are not graded. A side
benefit of requiring critiques is that everyone pays attention
and learns from the projects of all groups.
Weekly group meetings instead of lectures help prevent
procrastination, keep the professor informed of group
progress, and provide an inkling of personal interactions
within each group. In addition to commenting on the techni-


Chemical Engineering Education










cal work, take time to discuss work habits when necessary.
For example, most graduate students have not learned how
to rapidly sort articles so that only the most important are
read thoroughly. The professor can also be a cheerleader
when groups feel that they will never be able to finish their
projects. When the members of a group are not getting
along, part of the meeting time can be used to help the
students start processing group interactions. Do not try to
solve their interpersonal problems, however. Make the stu-
dents do this work or at least muddle through it.
The bane of grading group work is freeloaders. Delegate
the responsibility of lowering the grades of freeloaders to the
students. My grade assigned to each project is the highest
grade students in the group can receive for the project. I
require the students in each group to assign what percentage
of this grade (ranging from 0 to 100%) each group member
should receive. I then average these percentages for each
group member and calculate their project grades. This pro-
cedure reduces freeloading and drastically reduces complaints
from other group members when freeloading occurs.
This project-based paradigm is very efficient for profes-
sors. During the project work I typically spend a total of four
hours per week on the course, with most of that time focused
on the students. During project work the students spend much
more time working on the course than the professor does!
Grading reports takes time, but since the reports are better
than in other classes it is easier. The students learn their topic
in depth, they learn how-to-learn, and they actually pay
attention to the feedback on their writing.
A note of caution is in order, however. Most professors
and students are inexperienced with project-based teaching.
Professors need a certain amount of chutzpah to relinquish
the normal control of a lecture course. They also need to
know the material better than they would for a lecture class
since it is impossible to prepare for student questions. Note
that this method is not "turning the students loose." Students
actually receive increased guidance and support. Despite the
support, the freedom and responsibility may overwhelm im-
mature students. Students, particularly those with high grades,
may rebel. Other faculty may be skeptical and probably will
not be supportive if the course flounders. Because of these
risks, a graduate- or senior-level elective course is a good
place to experiment.

IMPROVEMENT AND GROWTH
Master teachers may be born, not made; but good, effi-
cient teaching is a learned skill. Sign up for a teaching
workshop. Study and try out new teaching methods. After
each class, reflect on what worked and what didn't, and
tailor your future actions accordingly. Take notes, with the
aim of improving the course next time. Find someone in
your department with whom you can discuss teaching on a


regular basis. Continual experimentation with teaching meth-
ods helps to prevent boredom and burnout, which can be
major problems. Such experimentation can lead to teaching
improvement and eventual recognition as a master teacher.

REFERENCES
1. Covey, S.R., The Seven Habits of Highly Effective People,
Simon and Schuster, New York, NY (1989)
2. Lakein, A., How to Get Control of Your Time and Your Life,
Signet Books, New York, NY (1973)
3. Wankat, P. C., "Effective, Efficient Teaching," Proceedings
ASEE 1999 Annual Conference, CD ROM pdf file 000167,
(1999)
4. Wankat, P.C. and F.S. Oreovicz, Teaching Engineering,
McGraw-Hill, New York, NY (1993). [Out of print. Avail-
able free as pdf files at ChE/News/Book/>
5. Boice, R., The New Faculty Member, Jossey-Bass, San Fran-
cisco, CA (1992)
6. Boice, R., Advice for New Faculty Members: Nihil Nimus,
Allyn and Bacon, Boston, MA (2000)
7. Woods, D.R., How to Gain the Most from Problem Based
Learning, D.R. Woods, Waterdown, Ontario, Canada, (1994).
[Available from McMaster University Bookstore, 905-572-
7160]
8. Wankat, P.C., "Learning Through Doing: A Course on Writ-
ing a Textbook Chapter," Chem. Eng. Ed., 27(4), 208 (1993)
a


for book review


Multimedia Fluid Mechanics
by G.M. Homsy, et al.
Cambridge University Press (2000) $19.95
Reviewed by
Hossein Haj-Hariri
University of Virginia
The CD by Homsy, et al., is a most welcome and timely
educational tool for students (and instructors!) of introduc-
tory fluid mechanics. Fluid mechanics is a very visual disci-
pline. To date, such visual accompaniment to the mathemati-
cal equations describing flow physics has either come from
labs or from samplings of the fantastic movies put together
in the 1960s. Whereas the material of those movies will
never become outdated, the innovative multi-media approach
adopted by Homsy, et al., adds dimensions to the presenta-
tion that were simply not available forty years ago. This CD
ROM is a true multi-media tool that has no paper counter-
part. In other words, this is not a book typed on a CD-it is
truly all that the box cover promises, and then some.
The approach is based on modules. Currently, there are
three technical modules, with more promised. The current
modules are dynamics, kinematics, and boundary layers.
There is also a module on history, which should be studied
by all students.
Continued on page 101.


Spring 2001











laboratory


A SUPERCRITICAL EXTRACTION

EXPERIMENT

For the Unit Operations Laboratory



RONALD G. GABBARD,* DANA E. KNox
New Jersey Institute of Technology Newark, NJ 07103


upercritical fluid extraction (SCFE) is becoming a
viable unit operation in the chemical process indus-
try. It uses the distinguishing properties of a fluid that
is above its critical point (critical temperature and pressure)
to enhance performance in an extraction process. While the
concept of SCFE has been known for over a century,[1] it has
not been widely used in industry for a variety of reasons.
Foremost among these reasons is the high financial risk
involved with SCFE-specifically, high installation and op-
erating costs for a process with a relatively short track record
of commercial-scale success. Another reason is that a con-
ventional separation technique is usually already available.
Add to this the difficulties caused by the lack of sound
theoretical models available for scale-up and it becomes
obvious why there has been no incentive for SCFE develop-
ment on a wide-scale industrial level. Even the early com-
mercial applications, such as propane deasphalting in the
1930s, the SOLEXOL process of the 1940s, and the ROSE
process in the 1950s, were not enough to generate large-
scale interest. 21
While these reasons remain true today, new motivating
factors have recently paved the way for SCFE to become a
viable extraction alternative. The modern chemical engineer
is faced with environmental regulations that require strict
control of emissions and reductions in hazardous waste. A
change in energy costs has lessened the favorable gap in
operating costs conventional high-heat separation techniques
such as distillation have historically had over high-pressure
SCFE systems. Increased performance demands, such as
lower acceptable limits of either residual solvent or other
contaminants in the food and pharmaceutical industries, have
increased the popularity of SCFE. Also, SCFE solvents (such
Address: BASF Corporation, Polymers Division, South
Brunswick, NJ 08831


as carbon dioxide) are often more environmentally friendly.
As SCFE becomes more and more popular in industry, it is
finding widespread applications from the decaffeination of
coffee to the removal of trace organic contaminants in waste
water.131 Additional work is going on in many other areas
from coal liquefactiont4] to fractionation and purification of
polymers.[51 Some of these processes (such as coffee
decaffeination) are vastly different from the original
deasphalting and ROSE processes, while others (such as
coal liquefaction) are very similar. While these widely vary-
ing applications are using many different solvents, the one
used most predominantly is carbon dioxide.
Supercritical fluid extraction also presents a unique com-
bination of high-pressure phase equilibrium and mass trans-
fer. As such, an experiment dealing with SCFE represents a

Ronald G. Gabbard is Process and Product
Development Manager for the Styropor Busi-
ness Group in the Polymers Division of BASF
Corporation, where he has been doing poly-
mer related research for the last eleven years.
He previously worked as a Process Develop-
ment Engineer at Maxwell House Coffee, and
it was in this capacity that he developed an
interest in SCFE technology. He received his
BS and MS in Chemical Engineering from New
Jersey Institute of Technology.
Dana E. Knox is Associate Chair for the Chemi-
cal Engineering, Chemistry, and Environmen-
tal Science Department at New Jersey Institute
of Technology, where he has been since 1983.
His teaching interests are in graduate and un-
dergraduate thermodynamics and equilibrium
stage processes, and his research interests
are in fluid phase equilibria and thermodynam-
ics. He received his BS, ME, and PhD degrees
in Chemical Engineering from Rensselaer Poly-
technic Institute.


Copyright ChE Division of ASEE 2001


Chemical Engineering Education












... this article discusses a laboratory experiment that both reinforces
fundamental engineering principles and introduces the students to one segment
of this growing technology-specifically solid/SCFE.


valuable addition to the traditional unit operations labora-
tory. With that in mind, this article discusses a laboratory
experiment that both reinforces fundamental engineering prin-
ciples and introduces the students to one segment of this
growing technology-specifically solid/SCFE.
The experiment provides an opportunity for the students to
explore SCFE and to use their engineering skills to deal with
issues of scale-up and high-pressure equipment design and
operation.1[6 From a thermodynamic point of view, it allows
students to explore physical-property prediction at high pres-
sures far away from ideal behavior when experimental data
are not available. They are then asked to use these predic-
tions to correlate an equipment design parameter such as the
mass transfer coefficient. Additionally, students have the
opportunity to evaluate the usefulness of the data they have
collected. They will need to understand that if the data
indicates saturation of the exit stream, their analysis of the
mass transfer coefficient will be invalid because the equa-
tion they are using (see Eq. 1 in the "Analysis" section)
becomes indeterminate. Finally, they will need to have de-
veloped a plan to avoid saturation prior to starting the ex-
periment in order to be successful.


As far as we know, the inclusion of a supercritical extrac-
tion experiment in the senior unit operations laboratory
is unique.

STUDENT EXPERIMENT
The experiment consists of a semi-continuous packed-bed
extraction of naphthalene by supercritical carbon dioxide.
The primary objective is to measure the mass transfer coeffi-
cient for the extraction at a variety of conditions and to
develop a correlation for it as a function of these process
conditions. Carbon dioxide was the chosen solvent because
of its moderate critical conditions (304.2 K, 73.8 bar), its
widespread industrial use, and its environmentally friendly
nature. It is also nontoxic, making it a very safe lab solvent.
Naphthalene was chosen because of its relatively high solu-
bility in supercritical carbon dioxide and the availability of
sufficient data on the system.[51

Equipment
The experiment consists primarily of a supercritical screen-
ing system (see Figure 1) designed and manufactured by
Autoclave Engineers of Erie, Pennsylvania. The pre-as-


Figure 1.

Flow
diagram:
supercritical
fluid
extraction
system.


- Micro-metering
Valve


Spring 2001


Rupture
Disc


Vent










sembled system includes all the necessary basic compo-
nents: feed pump, extraction column, extract receiver, in-
strumentation, and a heated pressure boundary used to de-
pressurize the exit stream. The cost of an Autoclave (814-
838-5700) system typical of the one used in this laboratory
was slightly lower than a similar system made by ISCO
(800-228-4250). The heated pressure boundary was optional
and added to the cost of the ISCO SCF 1200 system. One
additional benefit of the Autoclave system is that it is a little
larger in size than the ISCO system. Since this is intended to
be a unit operations laboratory, we felt that having an ana-
lytical-scale unit would not do justice to the concept of
SCFE as a unit operation. We wanted the students to have
some degree of a "hands-on" experience with the lab that
we felt would not be achieved with smaller analytical-
scale equipment.
A standard CO2 cylinder with a liquid dip tube is used as
the feed tank. The CO2 is cooled by passing the feed tube
through an ice bath prior to entering a Milton Roy 1/4-Hp,
variable-speed positive-displacement (PD) pump. The PD
pump is capable of operating between 40-400 cc/hr. The
pump discharge pressure is controlled by an adjustable back-
pressure control valve that can operate in the range of 8-480
bar. Excess flow, which causes a pressure higher than the
desired set point, is recirculated back to the suction side of
the pump. The pump discharge pressure is measured just
upstream of this control valve. A vapor vent valve is sup-
plied downstream of the back-pressure control valve. This
allows any vaporized CO2 caught in the pump feed line to be
vented off during start-up. Without the vent, the feed pump
would become vapor bound and cavitate. Additional cooling
is obtained by packing the pump head in ice.
Four valves around the extraction column isolate the col-
umn and provide the flexibility needed to operate it in either
an upflow or downflow configuration. The column is 12
inches long, has an inside diameter of 0.688 inches (nominal
1 inch OD), and is rated for approximately 700 bar at 1000C.
It can be electrically heated with two external band heaters.
A surface-mounted thermocouple measures the outer col-
umn wall temperature, and a Watlow proportional/integral
controller is used to control the temperature. The column is
protected from overpressurization by a 1/4-inch diameter
rupture disc that is piped directly to the bottom of the col-
umn. The disc is nominally rated for 480 bar at 22'C.
The pressure boundary on the downstream side of the
column is maintained by a micro-metering needle valve,
also supplied by Autoclave Engineers. The column can be
isolated upstream of this valve with a blocking valve. The
discharge lines from the column, as well as the body of the
micro-metering valve, are electrically heat traced with a
110-volt heating tape. The heat tracing is in place to counter-
act the large Joule-Thomson cooling effect that results when
the CO, flashes across the micro-metering valve and to


prevent the line from freezing.
The extracted material is collected in the extract receiver.
This vessel has a nominal volume of 99 cubic centimeters
and has a drain valve at the bottom. The vessel is protected
by a pressure relief valve set to open at 1.4 bar (at 220C). The
extract and solvent enter the receiver from the top. The
extract, which is no longer soluble in the non-supercritical
solvent, separates from the solvent and is collected in the
vessel while the solute-free CO, is discharged from the top
of the vessel. It then passes through a small filter to a
rotameter and then through the dry test meter. In addition,
the temperature in the extract receiver is measured by a
thermocouple. The rotameter (calibrated for CO2 at standard
temperature and pressure in units of standard cubic feet per
minute) measures the instantaneous CO, flow rate. The CO2
flow is then totalized by a dry test meter. This provides total
standard cubic feet of CO, used during an experiment.


Procedure
The students are provided with the equipment, and are
given detailed safety instructions and a list of "Discussion
Topics" (see Table 1). Additionally, the experiment is con-
ducted under closer-than-normal supervision for the senior
unit operations lab. The students must develop their own
experimental plan that will allow them to answer the ques-
tions outlined in the discussion topics. In developing their
plan, they must decide on the pressures at which to operate
the column, whether to use upflow or downflow through the
column, what flow rates to use, and how long each extrac-
tion should last to provide meaningful data.
An individual experiment consists of charging the extrac-

TABLE 1
Discussion Topics

1. Should the column exit stream be saturated with naphthalene?
2. Discuss how you evaluated the mass transfer coefficient, k.
3. For packed beds, the mass transfer coefficient is often represented
as a function of the N, Nsc, and NG, numbers, if that function
takes the following form, determine the values of the constants a,
b, c, and d.

k a(NRe)b NSc) (NGr)d
4. What is the fugacity coefficient of the solute in the condensed
phase at its sublimation pressure?
5. Use the Peng-Robinson or other suitable equation of state to
predict the solubility of the solute in the supercritical solvent.
How well does the equation of state prediction compare to the
solubility reported in the literature?
6. How much energy input is required to maintain isothermal
conditions across the micro-metering valve?
7. Support your decision to operate the column in either the upflow
or downflow configuration.

Chemical Engineering Education










tion column with a known amount of naphthalene (filling the
rest of the column void with sand), re-assembling the sys-
tem, pressurizing the system to the desired operating pres-
sure at a chosen temperature, and initiating flow of
supercritical carbon dioxide. Periodic measurements of feed-
pump and column pressure, column and extract-receiver
temperature, and instantaneous and cumulative carbon-diox-
ide flow rates are taken.
Once each individual extraction is completed, the column
is re-weighed to obtain the quantity of naphthalene extracted.
The column, rather than the naphthalene recovered in the
extract receiver, is weighed because it is difficult to account
for all the naphthalene in the receiver without the addition of
another solvent. Some naphthalene usually precipitates on
the piping walls after the micro-metering valve assembly.
(This needs to be cleaned out between each experimental run.)
Given this, less error is introduced into the experiment by
doing the simple loss-in-weight measurement on the column.
Safety is a key aspect of the laboratory for two reasons.
First and foremost is to ensure the safety of the students
performing the high-pressure experiment; second is the
heightened appreciation for safety the students gain from
completing a high-pressure experiment such as this. To per-
form this experiment safely, students are required to develop
a level of proactive thinking that they are not typically re-
quired to have in other unit operations laboratory experi-
ments (i.e., fluid flow, efflux time of a tank, or pressure drop
in a packed column). The students must evaluate all the
possible outcomes of their actions prior to doing anything
with the equipment to make sure that the desired result is
obtained safely. Students are not allowed to operate the
equipment until they have demonstrated reasonable safety
awareness to the instructor. This is not to say that the previ-
ously mentioned experiments should be performed casually
or unsafely, but rather that the chance for serious injury is
greater when performing a high-pressure experiment such as
SCFE. This creates an atmosphere in which the students take
lab safety very seriously. Providing this heightened level of
safety awareness was a significant underlying objective of
the laboratory and was one of the key reasons this experi-
ment (High-Pressure Supercriticial Extraction) was consid-
ered rather than something such as a simple wetted-wall
mass-transfer experiment.
Some of the key safety instructions given to the students
are
No work can be done on the extraction column or
associated piping until the system has been depres-
surized and then verified. Verification ofdepressur-
ization is accomplished by opening all valves
around the column and making sure that both inlet
and outlet pressure gauges read zero and that there
is no discharge from either of the two vents. Even if
the column discharge is plugged, the inlet pressure
Spring 2001


gauge should still read zero when the column is
depressurized. If this state is not obtained, the
students are required to obtain help from either the
instructor or the teaching instructor in the lab.
No work should be done on the extraction column
while it is plumbed up and in place on the extrac-
tion unit. All work should be completed while the
column is out of service and on the workbench.
Additionally, step-by-step instructionsfor loading
and unloading the extraction column are located in
the appendix of the student laboratory.
The maximum operating temperature set in the
student laboratory is 55 C. While this was done to
make sure that the column operating pressure
would not exceed design limits, it also prevents
liquid naphthalene from being pushed out of the
column because the 55 C limit is significantly lower
than the 80-82 C naphthalene melting point.
Finally, with regard to safety, the students should be made
aware of the issue of retrograde condensation within SCF
systems. This is the phenomenon that can occur when vapor-
liquid equilibrium exists at a temperature or pressure above
the mixture critical point. In such a situation, increasing the
operating temperature at constant pressure may lead to con-
densation. This can be a problem in the student experiment
where the micro-metering valve and discharge piping are
electrically heat traced to prevent freezing. The students
should be cautioned to use the heat tracing only to maintain
isothermal conditions in this part of the system and not to
add unnecessary heat. Should retrograde condensation occur
at the inlet of the micro-metering valve, the possibility of the
system being plugged increases and the system will need
to be depressurized as outlined above in the first bullet.
The naphthalene-CO2 system is susceptible to retrograde
condensation when the operating pressures are around
125 bar and below.

Analysis
The first step in the analysis is for the students to ensure
that the carbon dioxide exiting the column is not saturated
with naphthalene (first discussion topic in Table 1). This
could happen if either the naphthalene/sand ratio charged to
the column is too large or if the carbon dioxide flow rate is
too small. In these cases, the effective contact time may be
long enough for saturation to occur. This, of course,
would render any mass transfer coefficient calculations
meaningless.
Students can then determine the mass transfer coefficient,
k, from the well-known relationship

Az kACLM (1)

where C, is the average naphthalene concentration in the exit










stream (as determined by material balance), Vo is the empty-
column superficial velocity, A is the surface area per unit
volume, z is the naphthalene packed-bed length, and ACLM
is the log-mean concentration difference across the column
defined as

(Cat 0)- (Csat C)
ACLM =- at c( (2)
fn -
Cat C1

where Csat is the naphthalene concentration at saturation
(i.e., the solubility). Thus ACLM represents the effective
driving force for the extration. All of these quantities can be
determined from measured experimental quantities except
for the surface-to-volume ratio A (which is given to the
students) and Csat, which the students are asked to estimate
from an equation of state such as Peng-Robinson (discussion
topic #5). The subject of high-pressure phase behavior, in-
cluding topics such as equilibrium between a solid and a
supercritical fluid phase, is covered in the undergraduate
thermodynamics sequence at New Jersey Institute of Tech-
nology. The pertinent equation is

at MI M1 Psat VI0 (p- p a 1
C = yI exp (3)
1 V V P RT


where Psat is the vapor pressure of the solid phase at the
system temperature, V1so1 is its molar volume, M, is its
molecular weight, y, is its mole fraction in the supercritical
fluid mixture at saturation, V is the molar volume of the
supercritical fluid mixture, and 41 is the solute fugacity
coefficient in the supercritical fluid mixture. Each of the
latter two quantities are determined by the chosen equation
of state. The equation must be solved iteratively for y, since
the fugacity coefficient is a function of composition. Alter-
natively, the students could obtain a value for Csat from the
literature for this quantity.
The value of A, the surface-to-volume ratio for the packed
bed, has been experimentally estimated using the student
equipment and is given to them. This value is only an order-
of-magnitude estimate as it will change each time the col-
umn is repacked with fresh naphthalene. This is because the
naphthalene crystals are not very uniform in size or shape.
This estimate could be improved by adding a size reduction/
classification step to the naphthalene to make it more uni-
form in terms of size and shape. This operation would not
necessarily be part of the student experiment, but rather an
operation a teaching assistant would perform to ensure that
the naphthalene was uniform.
During the experiment the students should have evaluated
the mass transfer coefficient k at several different sets of
operating conditions. This should allow them to correlate k
with key operating conditions. A typical correlation for SCF


applications might have a form such as17l81

NSh = f(NRe,NSc,NGr) (4)
where NsH is the Sherwood number (kz/DA,), NRe is the
Reynolds number (DVp/ ), Nsc is the Schmidt number
(g/DABP), and NGr is the Grashof number (d3gpAp/p2).
Here, DAB is the diffusivity, D is the column diameter, p is
the fluid density, Ap is the density difference between the
saturated interface and the bulk, unsaturated fluid, g is the
fluid viscosity, and d is the average particle diameter. The
Grashof number, not generally needed in sub-critical fluid
applications, is included to account for buoyancy effects.
These arise due to the relatively high density and low viscos-
ity and thus exceptionally low kinematic viscosities of
supercritical fluids.
The students are thus expected to evaluate the constants in
an expression such as

S= a(NRe)b (Nc)(NGr)d (5)

Obtaining sufficient data to evaluate all four constants should
be one of the objectives when the students develop their
experimental plan. In preparing for the experiment, they are
expected to have consulted the provided references19'01 for
determining quantities such as viscosity and diffusivity.
In their write-up, the students are expected to address each
of the discussion topics listed in Table 1. The first three
topics relate to the experimental determination of k, as al-
ready described. The remaining topics require that the stu-
dents comprehend various thermodynamic aspects of SCFE.
These include fugacities of solids at high pressures, use of
equations of state for high-pressure phase equilibrium, and
the Joule-Thomson effect.

CLOSING REMARKS
Student response to this experiment has been generally
positive. They enjoy the "hands-on" experience associated
with assembling and disassembling the apparatus, the expo-
sure to a non-traditional unit operation, and the combination
of mass transfer and high-pressure thermodynamics in a
practical application.
The principal experimental difficulty has been deposition
of naphthalene in the discharge line and in the micro-meter-
ing valve. This can be alleviated by ensuring that the exiting
stream is well removed from saturation. With proper choice
of operating conditions, however, the experiment works
well as designed. Students can complete several indi-
vidual experiments in the allotted time of two five-hour
laboratory periods.
An alternative experimental set-up would be to replace the
discharge line and condensate receiver with a "U-tube" in a
cold trap. While this idea is yet to be attempted experimen-
tally, one can envision weighing the tubing (including the


Chemical Engineering Education










"U-tube") downstream of the micro-metering valve before
and after each trial as an alternative to obtaining the amount
of naphthalene extracted in the experiment. The mass of the
extracted naphthalene would be a more significant portion of
the total mass of the sample and apparatus being weighed. In
this manner, more accurate results may be possible.
If multiple groups complete the lab during the semester,
another enhancement to the laboratory experience could be
to have the different groups use different solute materials. At
the end of the semester, a comparison of the correlation
constants from each group could be completed and this
could be used to create a generalized correlation. Possible
alternative solutes include biphenyl and benzoic acid. Should
this approach be taken, it is important to remember that the
value of A, the surface-to-volume ratio in Eq. (1), must be
provided for each system investigated.
In summary, this laboratory experiment provides a valu-
able introduction to a modern unit operation in the chemical
process industry while at the same time it encourages cre-
ative thinking in the synthesis of concepts from disparate
areas of chemical engineering.


NOMENCLATURE


A
a,b,c,d
C,


Surface area per unit volume of a packed bed (m2/m3)
Correlating equation parameters
Average concentration of naphthalene in exiting carbon
dioxide (kg/m3)


Cat Concentration of naphthalene in carbon dioxide at
saturation (kg/m3)
ACLM Log mean concentration driving force (kg/m3)
D Column diameter (m)
DAB Diffusivity (m2/sec)
d Particle diameter (m)
g Acceleration due to gravity (m/sec2)
k Mass transfer coefficient (m/sec)
P Pressure (bar)
Psat Vapor pressure of solute (bar)
R Ideal gas constant (m3bar/molK)
T Temperature (K)
V Molar volume of fluid phase (m'/mol)
Vs-' Molar volume of solute (m3/mol)
V Empty column superficial velocity (m/sec)
z Packed bed length (m)
p Density (kg/m3)
[t Viscosity (kg/m sec)
Dimensionless Numbers
N", Grashof number (d3gpAp /2)

NRe Reynolds number (DVOp / )

Nsc Schmidt number (I / DABp)
Nsh Sherwood number (kz / DAB)

REFERENCES
1. Hannay, J.B., and J. Hogarth, "On the Solubility of Solids in
Spring 2001


Gases," Proc. Roy. Soc., 29, 324, London (1879)
2. McHugh, M.A., and V.J. Krukonis, Supercritical Fluid Ex-
traction, Principles, and Practice, 2nd ed., Butterworth,
Stoneham, MA (1994)
3. Eckert, C.A., J.A. Van Alsten, and T. Stoicos, "Supercritical
Fluid Processing," Environ. Sci. Tech., 20, 319 (1986)
4. Maddocks, R.R., J. Gibson, and D.F. Williams, "Supercritical
Extraction of Coal," Chem. Eng. Prog., 49 (1979)
5. McHugh, M.A., and M.E. Paulaitis, "Solid Solubilities of
Naphthalene and Biphenyl in Supercritical Carbon Diox-
ide," J. Chem. Eng. Data, 25, 326 (1980)
6. Gabbard, R.G., "The Development of a Senior Unit Opera-
tions Laboratory on the Supercritical Extraction of Solid
Naphthalene with Supercritical Carbon Dioxide," M.S. The-
sis, New Jersey Institute of Technology (1993)
7. Debenedetti, P.G., and R.C. Reid, "Diffusion and Mass Trans-
fer in Supercritical Fluids," AIChE J., 32, 2034 (1986)
8. Lee, C.H., and G.D. Holder, "The Use of Supercritical Fluid
Chromatography for Obtaining Mass Transfer Coefficients
in Fluid-Solid Systems at Supercritical Conditions," Ind.
Eng. Chem. Res., 34, 906 (1995)
9. Jossi, J.A., L.I. Stiel, and G. Thodos, "The Viscosity of Pure
Substances in the Dense Gaseous and Liquid Phases,"AIChE
J., 8, 59 (1962)
10. Funazukuri, Y., Y. Ishiwata, and N. Wakao, "Predictive
Correlation for Binary Diffusion Coefficients in Dense Car-
bon Dioxide,"AIChE J., 38, 1761 (1992) O


Multimedia Fluid Mechanics
Continued from page 95.
The CD is neither a book nor a collection of movie clips. It
is truly a seamlessly integrated multi-media tool. The user
can read some brief text describing the phenomenon, can
look at the equations and see the meaning of each term, and
also look at some movie clips that will drive the point home.
Most importantly, there are a number of very simple, but
cleverly designed, interactive experiments where the user
can take data off of a running movie clip and process the
automatically tabulated data in order to investigate the di-
mensional relationships and gain valuable insights. These
interactive experiments constitute very nice classroom dem-
onstrations to supplement lectures. An equation feature
that is used cleverly is a roll-over feature where as the
mouse pointer is dragged over each term of the equation,
the term is magnified and highlighted, and its meaning
pops up in a small text box.
I cannot overemphasize how well this CD is done. The
selection of the topics, the level of coverage, and the actual
presentation are all superb. There are many hyperlinks
throughout the CD; however, unlike some other CDs where
the user can hyperlink his/her way into a digital purgatory,
on this CD one can always return to the page of interest
using the small navigation map at the top of the page.
Congratulations to Professor Homsy and his colleagues for
undertaking the much-needed task of creating a new tool for
aiding students of fluid mechanics. Also, congratulations for
holding the line on the price, which is extremely reasonable in
an environment of skyrocketing textbook prices. O











Random Thoughts...






FAQS. III

GROUPWORK IN DISTANCE LEARNING1'



RICHARD M. FIELDER, REBECCA BRENT
North Carolina State University Raleigh, NC 27695


Of all the instructional methods we advocate in our
teaching workshops, the ones we emphasize most
involve students working together in small groups.
Workshop participants invariably ask whether such collabo-
ration is possible in distance learning. The answer is that it
may take some additional effort by the instructor, but it can
be done and done effectively.
In this column we offer ideas for getting students at re-
mote sites to collaborate when attending lectures in a syn-
chronous course, working through lessons in an asynchro-
nous course, and doing homework in either distance mode.
Other references outline the hows and whys of using
groupwork in traditional class settings[2'31 and discuss the
educational value of distance learning compared to tradi-
tional classroom instruction.[41
In synchronous lectures, brief group exercises can be as-
signed just as they are in traditional classrooms. (Ask a
question or assign a short problem to pairs or small groups
of students, stop them after 30 seconds-3 minutes, collect
answers, provide the correct answer if necessary, and move
on.) The instructor may announce in the first class that such
exercises will be interspersed throughout the lectures to
provide practice for the homework and tests, adding that the
students at the remote sites can either do the exercises as
instructed, in which case they will learn how to do them, or
just sit there and watch, in which case they'll quickly get
bored and learn little or nothing. If some students choose not
to participate, the loss is theirs.
A similar procedure may be followed for asynchronous
course offerings that go out on videotape or web-based
media. When the students come to an exercise in a taped or
streamed presentation they can either (a) pause the presenta-
tion, try the exercise (ideally with others who may be physi-
cally or virtually present with them), and then fast-forward
to the point in the presentation where the answer is pre-


sented, or (b) just do the fast-forwarding. The instructor
should present both options in the first class and strongly
suggest that if the students really want to learn the material
they will choose the first one. Students may be helped to
connect with one another in small groups to view the classes
and work through the exercises via instant messaging, e-
mail, threaded discussion, and ftp transfers. In addition,
growing numbers of on-line students-especially those
in industry-have access to videoconferencing facilities
with electronic whiteboards. With those tools, virtual
teams can almost (but not quite) duplicate the in-person
team experience.
The first step in getting students at remote sites to collabo-
rate on problem sets or projects is to organize virtual teams
and set them up to interact electronically using any of the
tools mentioned above. Simply asking students to do some-
thing in groups is not enough to guarantee effective learning,
however, as anyone who has ever tried it knows. Even in
traditional classes students may do little or no work but get
the same grade as their more industrious colleagues, and
serious conflicts may arise between teammates with varying
levels of ability and senses of responsibility. The problems
may be even worse when groups are virtual and don't have
the self-regulating capability provided by face-to-face meet-
ings. It is therefore particularly important in distance classes
to adhere to the defining principles of cooperative learning,
Richard M. Felder is Hoechst Celanese Professor Emeritus of Chemical
Engineering at North Carolina State University. He received his BChE
from City College of CUNY and his PhD from Princeton. He is coauthor of
the text Elementary Principles of Chemical Processes (Wiley, 2000) and
codirector of the ASEE National Effective Teaching Institute
Rebecca Brent is an education consultant specializing in faculty devel-
opment for effective university teaching, classroom and computer-based
simulations in teacher education, and K-12 staff development in lan-
guage arts and classroom management. She co-directs the SUCCEED
Coalition faculty development program and has published articles on a
variety of topics including writing in undergraduate courses, cooperative
learning, public school reform, and effective university teaching.


Copyright ChE Division of ASEE 2001


Chemical Engineering Education










especially positive interdependence (if anyone fails to do his
or her part, everyone loses in some way), individual ac-


countability (all team members are held account-
able for all the material in the assignment), and
regular self-assessment of team functioning.
Standard references offer guidance on how to
meet the criteria for cooperative learning in tra-
ditional classes,'31 and tips for making groupwork
effective in a distance setting are given by
Millis15' and Bailey and Luetkehans.16' The fol-
lowing suggestions are drawn from these sources.
1. Make it clear to the students why
groupwork is being required.15' This admoni-
tion is particularly important for students in dis-
tance courses, whose learning preferences tend
to favor working independently.
2. Form small teams that are balanced in
knowledge and skills.[561 Teams of three or four
are large enough to provide adequate diversity
of opinions, experiences, and learning styles,
but not so large that individual members can
successfully hide. Groups of all strong stu-
dents or all weak students should be avoided.
If possible, at least one member of each team
should have experience with the computer
tools to be used to complete the assignments.


had their say, a resolution is sought.) Consider conducting
such sessions by videoconference or telephone rather than
asynchronously.


... w-Orkin
togeffier in







Uma









and-dane
effi""Ibr


3. Give clear directions regarding both the assignments
and the communication tools.15' Virtual groups may find it
particularly frustrating to have to decipher muddy directions
about what to do and how to do it, and their frustration could
hurt both their motivation and their performance. Give short
preliminary assignments that require the team members to
demonstrate their mastery of the communication software.
4. Monitor team progress and be available to consult
when teams are having problems.'5'6 The tendency of some
students in traditional classes to let groupwork slide in the
face of other time demands is likely to be worse when the
team members never see each other face-to-face. Appoint
team coordinators whose responsibilities are to keep their
teams on task and to report on progress and problems at
regular intervals. Periodically rotate this role among team
members. Prompt groups that are not meeting frequently
enough and offer guidance if they appear to be stuck.
5. Intervene when necessary to help teams overcome
interpersonalproblems.'6 Suggest strategies like active lis-
tening to resolve conflicts. (Each side makes its case, and the
other side has to repeat that case to the first side's satisfac-
tion without attempting to counter it. When both sides have


6. Collect peer ratings of individual citizen-
ship and use the ratings to adjust the team
assignment grades."I Rewarding exceptional
team members and penalizing non-contribu-
tors helps avoid many of the conflicts and re-
sentments that often occur when students work
on group projects. A procedure for collecting
ratings and using them to adjust team grades is
described in the literature.'7]
7. Anticipate problems and get help when
necessary.'5' You can be reasonably certain that
any problem you encounter in groupwork has
already been encountered by others and is ad-
dressed somewhere in the literature. When a
problem arises, check the references12'31 to make
sure you have not forgotten any of the ele-
ments of good practice in cooperative learning
and ask knowledgeable colleagues or faculty
development center personnel to help you
strategize remedies.


I References
1. See public IColumns.html> for previous FAQ columns.
2. Cooper, J., and P. Robinson, "Annotated Bibliography on
Cooperative Learning," CL1 CL resource Rl.asp >
3. For descriptions of different types of active and cooperative
learning exercises and guidance on how to implement them,
see
(a) Millis, B.J., and P.G. Cottell, Cooperative Learning for
Higher Education Faculty, Phoenix, American Council of
Education/Oryx Press (1998)
(b) Johnson, D.W., R.T. Johnson, and K.A. Smith, Active
Learning: Cooperation in the College Classroom, 2nd ed.,
Edina, MN, Interaction Book Co., (1998)
(c) Felder, R.M., and R. Brent, "Cooperative Learning in
Technical Courses: Procedures, Pitfalls, and Payoffs," Eric
Document ED-377038 (1994) unity / lockers / users / f Ifelder Ipublic / Papers /
Coopreport.html >
4. Felder, R.M., and R. Brent, "Is Technology a Friend or Foe
of Learning," Chem. Eng. Ed, 34(4), 326 (2000)
5. Millis, B.J., "Managing-and Motivating!-Distance Learn-
ing Group Activities"
6. Bailey, M.L., and L. Luetkehans, "Ten Great Tips for Facili-
tating Virtual Learning Teams," Distance Learning '98: Pro-
ceedings of the Annual Conference on Distance Teaching and
Learning, Madison, WI, August 5-7, (1998) ERIC Docu-
ment ED-422838
7. Kaufman, D.B., R.M. Felder, and H. Fuller, "Accounting for
Individual Effort in Cooperative Learning Teams," J. Engr.
Ed., 89(2), 133 (2000) 0


Spring 2001


All of the Random Thoughts columns are now available on the World Wide Web at
http://www2.ncsu.edu/effective_teaching/ and at http://che.ufl.edu/-cee/










% -1classroom


THE BUSINESS MEETING

An Alternative to the Classic Design Presentation



JAMES A. NEWELL
Rowan University Glassboro, NJ 08028


here is an increasing consensus among academics
and practicing engineers that effective communica-
tion skills should be an integral part of an engineer-
ing education."'3] When engineers who have been out of
school for ten years are asked "What courses do you wish
you had taken?", Kranzber'41 reports that the most common
answer is "English courses." Both ABET15 and the rest of
the technical community[61 recognize that communications
are part of a broader package of interpersonal, communica-
tion, and teamwork skills that Seat and Lord171 refer to as
"performance skills."
Many educationally focused programs, including the pro-
grams at Rowan"81 and the University of North Dakota,191
have integrated technical communication into their core en-
gineering curriculum. In many cases, however, oral commu-
nication exercises in engineering consist of little more than
giving repeated technical Powerpoint' presentations to an
audience and answering a few brief questions at the end.
Such an exercise emulates a presentation at a technical con-
ference, but resembles very little else in the business world.
There is no doubt that this presentation format is valuable,
but it should not be the only experience that an undergradu-
ate engineering student receives.


Jim Newell is Associate Professor of Chemi-
cal Engineering at Rowan University. His
technical research interests are in high-
performance polymers and carbon materi-
als. His pedagogical interests focus on com-
munications and assessment of leading out-
comes. He currently serves as Secretary/
Treasurer of the Chemical Engineering Divi-
sion of ASEE.


Conducting a business meeting instead of a final presenta-
tion in a senior plant-design course provides an alternative to
ANOTHER formal oral presentation. In this model, student
teams plan and conduct a formal business meeting with
faculty and industrial representatives serving in formalized
roles. Details of the process are provided below.

THE PROCESS
Each design team is asked to conduct a business meeting
with the Executive Committee of their company/customer.
The Executive Committee consists of the
Chief Executive Officer
Engineering Director
Finance Director
Marketing/Sales Director
Safety/Environmental Director
Proposed Plant Manager

Obviously, the number of members on the Executive Com-
mittee and their specific roles can be altered to accommo-
date the number of faculty and/or industrial representatives
attending the presentations. Each group makes a formal pre-
sentation to this committee, including a description of the
proposed process, relevant design issues, an economic analy-
sis, and recommendations. This presentation should not ex-
ceed thirty minutes. During the presentation, the committee
limits itself to questions of clarification.
Following the formal presentation, the members of the
committee will ask questions of the design group. Commit-
tee members may address their questions to the team as a
whole, or to specific members. Although there is no time
limit to the questioning period, 20 to 25 minutes represents a
typical length of time. During the presentation, the speaker


Copyright ChE Division of ASEE 2001


Chemical Engineering Education










stands at the overhead projector or computer while the other
group members are seated facing the committee. All group
members are seated during the questioning.

TEAM ROLES
Each member of the design group should perform a spe-
cific function on the team. At least three distinct roles that
must be filled are

The Team Leader This member is responsiblefor
providing the introductory materials and anything dealing
with the "big picture." Team-leader responsibilities
include making sure that all members of the group are
given sufficient opportunities to participate in the
questioning and that every question receives an adequate
answer.
The Economics Expert This member is responsible for
presenting the economic analysis and fielding detailed
questions about economic calculations and other issues.
The Engineering Expert This member is responsible for
presenting the technical aspects of the process including
equipment selection, sizing, and processing issues. This
person should be prepared to justify technical assump-
tions and other process decisions.

Teams with four members can divide either the economics
or engineering issues between two members, but there must
be only one team leader. Obviously, these positions may be
further divided, or additional roles may be added to
accommodate larger teams.
Student learning is disserved if individual members of a
design team spend the semester focusing on only a single
aspect of the design process. To avoid this dilemma, the
faculty member's selection of the engineering expert and the
economics expert should be made and announced to the
team only 48 hours before the presentation. Using this ap-
proach, team members cannot know which section of mate-
rial they will be responsible for discussing and are more
likely to work on all aspects. The team may pick its own
leader.

GRADING
An ongoing concern with group projects is how to effec-
tively account for individual performance in team projects.1101
In this business meeting, grading can account for both team
and individual performances. It is reasonable for students to
feel that their grades should not be destroyed by a weak
performance from an unmotivated student. At the same time,
a weak member can negatively impact the effectiveness of
the team presentation. Thus, a division between team and
individual points seems appropriate. On the presentation
itself, the team as a whole is graded on a five-point scale
based on the following items:


[ Visual Aids (Clarity; Font Size; Usefulness)
[1 Organization (Appropriate Structure and Flow?)
E Introduction (Grabs Attention? Appropriate Content?)
E[ Body (Completeness; Accuracy; Clarity; etc.) [x3]
E Summary (Concise? Covered Key Points?)
El Overall Effectiveness (Speaker's Goals Accomplished?)
Total Possible Points: 40

Thus, each team member receives the same score from these
40 points. Individual team members are also evaluated on

E Delivery (Volume; Clarity; Rate; etc.)
E Poise and Appearance (Appropriate Dress? Nervousness?
etc.)
Total Possible Points: 10

Thus, every team member can receive up to fifty points
from the presentation. Forty of these points are the same for
every member, while ten points vary from member to mem-
ber. This division of team and individual grading makes all
members accountable for the success of the team while at the
same time it maintains individual distinctions.
The questioning period also results in a portion of the
grade, but the mechanism is different for the experts and the
team leader. Each expert is evaluated on the following

aI Poise (Calmness, Ability to "Think on One's Feet") [x2]
I Ability to Answer [x2]
[ Interaction with Audience (Eye Contact? Demeanor)
Total Possible Points: 25

Thus, each expert has 25 possible points for his or her role
during questioning. The experts' total for the presentation
and questioning is divided by 7.5 to provide a 1-10 grade.
The team leader has additional responsibilities during the
questioning, so his or her scoring is more involved. It is
evaluated on

E Poise (Calmness, Ability to "Think on One's Feet") [x2]
a Ability to Answer [x2]
E Interaction with Audience
E Distribution (All Group Members Used?) [x2]
1 Responsibility (Questions Suitably Answered?) [x2]
Total Possible Points: 45

Each team leader has his or her total score divided by 9.5,
resulting in the same 1-10 grading as the experts. It is impor-
tant to note that the team leader does not receive more credit
than the other team members, but that more of the team


Spring 2001











leader's grade is determined by the questioning. A sample
grading sheet is shown in Table 1. Obviously, the categories
can be expanded, altered, or weighted differently to accom-
modate different priorities of design faculty.

SELECTION OF EXPERTS AND TEAM LEADERS
Design teams select their own team leaders, while experts
are assigned by the faculty member in charge, with only 48
hours advance notice. The team leader is responsible for
sending all members of the Executive Committee a brief e-



TABLE 1
Final Meeting Grade Report
(NOTE: x2 = double-weighting; x3 = triple weighting)

Evaluator

Project


Common Presentation Grades:
Visual Aids (Clarity; Font Size; Usefulness)
Organization (Appropriate Structure and Flow?)
Introduction (Grabs Attention?: Appropriate Content?)
Body (Completeness; Accuracy; Clarity; etc.) [x3]
Summary (Concise? Covered Key Points?)
Overall Effectiveness (Goals Accomplished?)


Total Points


Team Leader Economics


Technical


Delivery
Poise and Appearance

(Questioning)
Poise [x2]
Ability to Answer [x2]
Audience Interaction

Distribution [x2]
Responsibility [x2}

Individual Totals


Group Leader Economics


Technical


Team Total
Individual Total
Grand Total



Score


mail that includes
A formal invitation to the meeting, including mention
of the time and place
A statement identifying the team leader and other
experts
A brief summary of the topic to be discussed during
the meeting
The e-mail must be sent at least 24 hours before the meeting.

RESULTS
The business-meeting format has proven successful at two
different universities. Students reported that they "felt more
like a team" and were "less stressed" by the presentation
format. Students with internship or other industrial experi-
ence reported that the format was more realistic and closer to
what they experienced in their jobs. Overall, the students
rated the new format a 4.73 out of a possible 5.00 when
asked to rate the effectiveness of the business meeting.
The faculty have also enjoyed this method. Because of the
group format, there was more time for detailed questioning.
It was also easier to evaluate both group and individual
performances. Other universities, including the Universidad
Nacional de Salta in Argentina, have expressed interest in
this idea and it is presently being implemented at the Israel
Institute of Technology. Overall, the business meeting pro-
vided a useful alternative to a classical oral presentation.

REFERENCES
1. Bakos, J.D., "A Department Policy for Developing Commu-
nication Skills of Undergraduate Engineers," J. ofEng. Ed.,
75, 101 (1986)
2. Elbow, P., "Teaching Thinking by Teaching Writing," Phi
Delta Kappan, p. 37 (1983)
3. Newell, J.A., D.K. Ludlow, and S.P.K. Sternberg, "Progres-
sive Development of Oral and Written Communication Skills
Across an Integrated Laboratory Sequence," Chem. Eng.
Ed., 31(2), 116 (1997)
4. Kranzber, M., "Educating the Whole Engineer," ASEE
PRISM, p. 28, November (1993)
5. Engineering Criteria 2000, Engineering Accreditation Com-
mission, Accreditation Board for Engineering and Technol-
ogy, Inc., Baltimore, MD (1998)
6. "Manufacturing Education Plan: Phase I Report, Industry
Identifies Competency Gaps Among Newly Hired Gradu-
ates," Society of Manufacturing Engineers (SME), Dearborn,
MI (1997)
7. Seat, E., and S. Lord, "Enabling Effective Engineering
Teams: A Program for Teaching Interaction Skills," J. of
Eng. Ed., 88(4), 385 (1999)
8. Newell, J.A., A.J. Marchese, R.P. Ramachandran, B.
Sukumaran, and R. Harvey, "Multidisciplinary Design and
Communication: A Pedagogical Vision," Internat. J. Eng.
Ed., 15(5), 376 (1999)
9. Ludlow, D.K., and K.H. Schulz, "Writing Across the Cur-
riculum at the University of North Dakota," J. of Eng. Ed.,
83(2), 161 (1994)
10. Kaufman, D.B., R.M. Felder, and H. Fuller, "Accounting for
Individual Effort in Cooperative Learning Teams," J. of
Eng. Ed., 89(2), 133 (2000) O
Chemical Engineering Education


I











Setters to the editor


Editorial Note: The "Class and Home Problems" section on pages 366-368 of the Fall 2000 issue of CEE
presented Erich A. Muller's article, "A Thermodynamics Problem with Two Conflicting Solutions." In it, tanks
A isothermall) and B (adiabatic) arefilled with an ideal gas and connected by pipes and a valve. Initially, PA >
p,. If the valve is opened and equilibrium attained, will it have been necessary to add (or remove) heat from
tank A? Professor Muller's article has elicited the following two letters. His reply is also appended.


We appreciate the interest that Professor Muller's problem has generated, and request that any further
correspondence on this problem be e-mailed to him at
emuller@usb.ve


To the Editor:
The recent article by Milller1il presents an interesting dis-
cussion of pedagogically important issues. We wish to com-
ment on two aspects of the article. First, we believe that it is
pedagogically more sound to treat Miller's "two conflicting
solutions" as (non-conflicting) solutions to different prob-
lems that arise from two different equilibrium models of the
situation, as implied in his comments. Second, we believe
that his "Comments on the Equation for the Uniform State,
Uniform Flow Model" can be improved regarding the basic
assumptions underlying use of the unsteady-state energy-
balance equation for a control volume and its general appli-
cation in first-law analysis. We elaborate on both these points
in the following.
Concerning the analysis of the situation described in the
article, we note that his "Solution #1" relates to a model in
which it is stated that "tank B is adiabatic"; that is, there is
no heat transfer to or from tank B (Q = o) at any time to any
other body, although this does not preclude exchange of
energy via flow of matter through the connecting line and
valve. Practically speaking, the equilibrium state for the
contents of tank B is a partial equilibrium state with respect
to the contents of tank A: mechanical, but not thermal,
equilibrium. Regardless of where the control surface is placed
(around tank A alone or around tanks A and B together), the
conclusion reached is as Muller states: QA> 0. Solution #1 is
the solution to the problem arising from one particular model
of the situation.
His "Solution #2" relates to a different model of the situa-
tion, in which it is stated that there is "a heat transfer be-
tween the tanks" (presumably through the connecting line
and valve). In this case, tank B evidently has an adiabatic
enclosure with a (small?) diathermal hole in it. This changes
the equilibrium aspect of the model to be addressed, to one
allowing for both mechanical and thermal equilibrium with


respect to the contents of both tanks. This also changes the
conclusion reached for the resulting problem to, as MUller
also states, QA = 0.
We thus believe that it is pedagogically better to treat the
two cases as two different models of the situation and to
compare the results of a first-law analysis of the resulting
problems, rather than to present the results as two conflicting
solutions of the same problem. Miller cannot on the one
hand state that "tank B is adiabatic" and on the other state
that there is "a heat transfer between the tanks." Thermody-
namics requires precise, rather than "shrewd," statements of
models and systematic analysis of resulting problems.
Concerning his "Comments on the Equation for the Uni-
form State, Uniform Flow Model," we feel that Miiller's
justification of his starting point for solution #1, as a conse-
quence of a general first-law analysis for a control volume,
can be strengthened. This strengthening is pedagogically
important, to enable students to appreciate points at which
approximations are made to exact equations.
His "generalized energy balance," Eq. (7), should be re-
placed by (we also change the sign of W, in accordance with
recommended practice)

d Fmniis +e e)=
dt msys sys k,sys p, sys)]

+ W + Y ri(t)[h(t)+ k(t)+ ep(t)
inlets

e m(t)[h(t) + ek(t)+ ep(t)] (A)
exits

In Eq. (A), u, ek, ep, and h deote specific internal energy,
kinetic energy, potential energy, and enthalpy, respectively,
and a tilde (~) denotes an appropriately defined intensive


Spring 2001










quantity. Thus, for a property within the control volume
(sys)

Ju(z,t)p(z,t)dV
sys _(t)- (B)______
msys(t) Jp(z,t)dV (B)
v
and similarly for ek,sys and ep,ys- In Eq. (B), dV is a vol-
ume element, p is density, and z denotes a point within the
control volume. Correspondingly, for a property at an inlet
or exit

Sh(x,t)p(x,t)un(x,t)dA
h(t)= t p(x, u(x,t)dA (C)
A

and similarly for ek(t)and ep(t). In Eq. (C), dA is an area
element of an inlet or exit area, x denotes a point on the area,
and un is the flow velocity normal to dA. Eqs. (A) to (C)
must be supplemented with the mass-conservation equation

dmsys
dry m(t)- mh(t) (D)
inlets exits
The validity of Eq. (A) rests on two generally accepted
concepts not introduced by Muiller: the continuum hypoth-
esis and a local equilibrium hypothesis. The former allows
integration of point properties over volumes and areas, as in
Eqs. (B) and (C), and the latter allows calculations using
macroscopically based property relationships.
Equations (A) and (D) are differential equations. As in
some introductory texts,[2'31 it is tempting to deal instead with
their integrated forms, between times t, and t2, say,


m2( U2 ek,2 ep,2)-ml +1 ek,1+ep,l
t2
=Q12 +W12 + h(t)[h(t)+ek(t+ep(t)]dt-
inlets t

r m(t)(t)+ek(t)+e (t)]dt (E)
exits t,

m2- m1= mi I me (F)
inlets exits

Equations {(A),(D)} and {(E),(F)} are exact. Equation (E) is
only formal result and may not always be useful, however.
This form is deceiving since it implies neglect of any inter-
dependence of the left and right sides of Eq. (A).
Simplification of Eqs. {(A),(D)} or {(E),(F)} involves
invoking appropriate approximations for special cases of the
spatial and temporal dependence of the properties at the
inlets and exits and of the system. Important special cases
are


uniformflow, for which the properties at an inlet or exit
are independent of position x (giving h(t)=h(t)) (or for
each phase of the flow)
uniform state, for which the properties of the system are
independent of position z (giving uisy (t) Usys (t)) (or
for each phase within the system)
steady-property flow, for which the properties at an
inlet or exit are independent of time t
steady flow, for which mr at an inlet or exit is indepen-
dent of time t (steady flow usually implies steady-
property flow, but the converse is not necessarily true)
steady state, for which the properties of the system are
independent of time t; this entails the vanishing of the
left side of Eq. (A) (steady state usually implies steady
flow and steady-property flow)

The uniform flow (UF) assumption at inlets and exits
(incorporated without comment by Miiller in his Eq. 7) and
the uniform state (US) assumption for the system are often
used in the absence of any information concerning spatial
dependence of the properties. (The former is consistent with
a plug-flow assumption and the latter with a well-stirred
vessel assumption.) Together, they form part of the basis for
an unsteady-state flow model referred to by Miiller as the
"Uniform-State Uniform-Flow (USUF) model." This desig-
nation by itself is misleading, however, since this model
includes a third assumption that corresponds to the steady-
property flow assumption defined above. As essentially
pointed out by Miiller, these three assumptions (together
with neglect of kinetic and potential energy terms) allow Eq.
(E) to be simplified to Miller's Eq. (1), his "working equa-
tion" of the USUF model.
More generally, for unsteady-state flow processes, the
steady-property flow assumption does not hold, and the USUF
model is invalid. We do not believe that it should be empha-
sized pedagogically since it severely restricts the first-law
analysis to rather special cases, such as the discharge situa-
tion described by Miiller in his solution #1 and filling a
vessel from a constant-property source/reservoir. We recom-
mend instead that a first-law analysis deal directly with the
differential equations (A) and (D) as such. This approach
handles all situations (including the USUF model as a spe-
cial case), and is consistent with the approach of some intro-
ductory texts14'51 and recent pedagogical articles.16'71

R.W. Missen
University of Toronto
W.R. Smith
University of Guelph
References
1. Miiller, E.A., "A Thermodynamics Problem with Two Con-
flicting Solutions," Chem. Eng. Ed., 34(4), 366 (2000)


Chemical Engineering Education










2. Sonntag, R.E., C. Borgnakke, and G.J. van Wylen, Funda-
mentals of Thermodynamics, 5th ed., Wiley, New York, NY,
pp. 163-173 (1998)
3. Cengel, Y.A., and M.A. Boles, Thermodynamics, 3rd ed.,
McGraw-Hill, New York, NY, pp. 222-229 (1998)
4. Elliott, J.R., and C.T. Lira, Introductory Chemical Engi-
neering Thermodynamics, Prentice-Hall PTR, Upper Saddle
River, NJ, pp. 72-77 (1999)
5. Sandler, S.I., Chemical and Engineering Thermodynamics,
3rd ed., Wiley, New York, NY, pp. 30-36 (1999)
6. Wisniak, J., "Discharge of Vessels: Thermodynamic Analy-
sis," J. Chem. Ed., 74, 301 (1997)
7. de Nevers, N., "Non-Adiabatic Container Filling and Emp-
tying," Chem. Eng. Ed., 33, 26 (1999) 0



To The Editor:

In the Fall 2000 Class and Home Problems Column, E.A.
Miillermll proposes a thermodynamics problem designed to
demonstrate that two seemingly correct but incompatible
solutions can be found from the thermodynamic analysis of
a particular process, and furthermore that such incompatible
solutions provide an opportunity to improve one's under-
standing of thermodynamic analysis.
Miller proposes the following: Consider two tanks, A and
B, connected with a valve and initially filled with (ideal) gas
at the same temperature, but the pressure in A is greater than
the pressure in B. Tank B is well insulated (adiabatic), but
tank A is maintained at constant temperature by thermal
contact with a heat source or sink.
Miller asks: "If the valve that connects both tanks is
opened and equilibrium is attained, will it have been neces-
sary to add (or to remove) heat from tank A?" (Denoted as
QA)
For this problem, it is clear that tanks A and B will be at
the same pressure at the end of the process. But Mtiller
clearly intends that tanks A and B are also at the same
temperature when equilibrium is attained. For tanks A and B
to reach the same temperature at equilibrium would require
that tanks A and B be in thermal contact. Clearly, the contra-
diction is that tank B cannot be well insultated (adiabatic)
and in thermal contact with tank A. This contradiction ap-
pears in both solutions presented in the paper.
Solution #1 is obtained by considering an energy balance
on a control volume around tank A and shows that QA > 0.
Miller subsequently argues that this solution is incorrect by
considering an energy balance on a control volume around
tank B; for this system, the paper (correctly) shows that
energy must be removed from tank B if the temperature of
tank B is unchanged. Since Mtiller is treating the tempera-
ture of tank B to be the same as tank A (and the temperature
of tank A is unchanged), energy must be removed from tank
B, which violates the requirement that tank B be adiabatic.
Spring 2001


In fact, since tank B is well insulated, the energy balance on
tank B in the paper correctly shows that the temperature in
tank B will increase at equilibrium.
Solution #2 is obtained by considering an energy balance
on a control volume around both tanks and the connecting
piping, so that the change in internal energy must equal the
heat transfer to tank A (QA). Since Miiller intends the tem-
peratures in the two tanks to be equal at equilibrium, the
internal energy is unchanged, and QA = 0. As discussed
earlier, the temperature in tank B actually increases during
the process, so the internal energy of the system increases,
and AA > 0.
Another way to show QA # 0 is to consider a system such
as the contents of tank A after equilibrium is attained. Now,
suppose QA = 0. The contents of such a system could then be
considered to undergo an adiabatic reversible expansion (since
QA = 0). Note however that (TT/MP)s > 0 for all gases (real
and ideal). Therefore, when the pressure in tank A decreases,
the temperature in tank A also decreases-but this is a con-
tradiction since tank A must be maintained at a constant
temperature. Therefore, QA cannot equal 0.
Irrespective of the difficulties expressed above, Miiller's
point is well made that one's understanding is improved by
resolving the dispute between seemingly incompatible ther-
modynamic analyses.

Thomas O. Spicer
University ofArkansas

Reference
1. Miiller, E.A., "A Thermodynamics Problem with
Two Conflicting Solutions," Chem. Eng. Ed., 34(4), 366
(2000)





Author's Response to Letters to the Editor

I have received many comments, personally and publicly,
on the problem I presented in the Fall 2000 issue of CEE. As
with Levenspiel's original thermo problem, each and every
comment is different, ranging from "You chose the wrong
answer" to "Send me another one of these problems."
The main message of the paper is that if you use equations
straight out of a book and apply them to a problem without
fully understanding the assumptions behind the equations,
you have a chance of coming to a false conclusion. Never-
theless, I think some readers "missed the point," and I be-
lieve further discussion is in order.
The initial problem is clearly stated, especially with regard
to the final state: "equilibrium is attained." In a simple
system such as this, thermodynamic equilibrium requires the










simultaneous achievement of three conditions: homogeneity
of pressures (mechanical equilibrium), homogeneity of tem-
perature (thermal equilibrium), and homogeneity in chemi-
cal potential diffusivee equilibrium); i.e., only if all three
conditions (PA = pB, TA = T", and tA = LB) are simulta-
neously met can we affirm that the system will not change in
time if left alone.
Solution #1, as Missen and Smith note, pertains to the
achievement of mechanical equilibria, but as is also noted in
the original article, leaves a temperature gradient among
tanks A and B. Given enough time, mass diffusion must take
place, transferring energy from tank B to tank A. So, even
though tank B has adiabatic walls and thus no heat transfer
to the surroundings, it does transfer energy due to a tempera-
ture difference.
In hindsight, the phrase "Given enough time, this tempera-
ture gradient will produce a transfer between the tanks"
should read, "Given enough time, this temperature gradient
will produce a mass transfer and consequent energy transfer
between the tanks" in order to be unambiguous.
It is clear, however, that there are not two solutions to the
problem, even if the catchy title implies so. Only one solu-


tion is possible. Any argument attempting to set solution #1
as the correct one must first disprove solution #2-an im-
possible task.
Many students and teachers (and Spicer's note is a clear
example) apply the textbook equations directly to a problem
without further thought on the problem. It is in this sense that
I totally agree with the second point noted by Missen and
Smith. I believe that one should teach the general energy
balance, and for each particular case simplify it accordingly.
The point of the original class problem is that if one starts
directly with Eq. (2), one may elude some of the assump-
tions behind its derivation. One should always start with a
generalized equation such as Eq. (7)* and integrate it accord-
ing to the given problem. Categorizing systems as steady
state, uniform flow, etc., and stating formal equations in
each case only entices the student to learn a myriad of
equations, making things more difficult and prone to errors.
Erich A. Miiller
Universidad Simon Bolivar
*Equation (7) is identical (with the exception of the arbitrary sign
given to the work) to Eq. (A) of Missen and Smith, not to Eq. (E) as
stated in their comment.


W book review


Advanced Transport Phenomena
by John C. Slattery
Published by Cambridge University Press, The Edinburgh Building, Cam-
bridge, UK; 734 pages; available in paperback and hardcover

Reviewed by
David C. Venerus
Illinois Institute of Technology

Advanced Transport Phenomena is a new textbook writ-
ten by Professor J.C. Slattery that represents a revision of an
earlier text by the same author: Momentum, Energy and
Mass Transfer in Continua (1981). Transport phenomena is
a fascinating and interdisciplinary subject that is covered by
at least one required course in all graduate chemical engi-
neering programs and remains an active area of research.
Like its predecessor, the new book is intended for graduate
students in engineering.
The text is organized into three topics according to the
main subjects of transport phenomena: momentum, energy,
and mass transfer. In addition, there are two shorter topics
that are covered; kinematics (coming before the three main
topics) and tensor analysis (an appendix). Each of the three
main topics is divided into three sub-topics that can roughly


be described as the formulation, application, and reduction
of transport balance equations. This matrix style of organi-
zation, where the columns are the main topics (momentum,
heat, and mass) of transport phenomena and the rows pro-
vide the components and applications for each topic, is simi-
lar to that used in the classic text Transport Phenomena by
Bird, Stewart, and Lightfoot (BSL), and allows the instructor/
reader the flexibility to cover the topics by column or by row.
The style and teaching philosophy of the author are re-
vealed in Chapter 1 (kinematics) where concepts such as
motion, velocity, and phase interfaces are introduced. Vari-
ous transport theorems are developed and used to derive the
differential mass balance, or continuity equation, and the
jump mass balance from the mass conservation postulate.
Hence, the approach taken here and throughout the book is
to start from general postulates about the physical world
and to convert these postulates into useful conservation
equations using formal mathematical tools.
The sub-topic structure is itself instructional in that the
reader is forced to recognize the similarities (and differ-
ences) between momentum, heat, and mass transfer. In Chap-
ters 2, 5, and 8 (Foundations for...), differential forms of the
conservation equations and their corresponding two-dimen-
sional forms (jump balances) are derived simultaneously.


Chemical Engineering Education





















This is followed by rather lengthy developments on the
behavior of materials where the most widely used (classi-
cal) constitutive equations are eventually presented. In Chap-
ters 3, 6, and 9 (Differential Balances in...), various trans-
port problems are formulated using the conservation and
constitutive equations derived in preceding chapters. These
problems, which range in complexity from one-dimensional,
steady-state problems to two-dimensional problems that in-
clude boundary-layer theory, are solved using both analyti-
cal and numerical techniques. Chapters 4, 7, and 10 (Inte-
gral Averaging in...) are devoted to deriving reduced forms
of the differential balance equations: time-averaged (turbu-
lent flows), area-averaged, local volume-averaged (pseudo
continuous media), and global volume-averaged (macro-
scopic balances).
Appendix A provides a comprehensive review of tensor
analysis and includes operations in both rectangular Carte-
sian and curvilinear coordinate systems.
Scattered throughout each chapter are several worked
examples, and each chapter ends with a series of exercises
(for which a solution manual is available). At the end of
each "Foundations of..." chapter, there is a summary sub-
section where the reader will find tables with the conserva-
tion equations expressed in rectangular Cartesian, cylindri-
cal, and spherical coordinate systems.
There is no question that Advanced Transport Phenom-
ena is a comprehensive and carefully prepared textbook.
The use of material volumes and transport theorems (rather
than stationary differential volumes, as is BSL) to derive
differential conservation equations is appropriate for gradu-
ate-level courses. Significant attention is given to the be-
havior of materials and to the entropy inequality and its use
in the formulation of constitutive equations.
Another positive aspect of this book is the utilization of
jump balances to derive boundary conditions. Jump bal-
ances are rarely covered in modern texts on transport phe-
nomena, but are invaluable in situations involving free and/
or moving boundary problems. I particularly like the tables
in Chapter 2 where the jump mass and jump linear momen-
tum balances are given for several special surfaces in the
three main coordinate systems.
Where the optimal balance is between being mathemati-
cally rigorous and comprehensive while also developing
Spring 2001


physical insight on transport problems is, of course, a mat-
ter of preference. Many readers of this book might find that
there is too much emphasis on the first two at the expense of
the third. As I read through certain portions of the book, I
sometimes found myself leafing through page after page of
derivation to find the punch line. (From my own rough
estimate, there are on average a little more than seven
equations per page, or, in the 700-page book, a total of
about 5000 equations!) For example, in section 5.3, roughly
ten pages are used to transform some general postulates
about the thermal behavior of materials into useful results
(i.e., viscosity and thermal conductivity are positive, Fourier's
law, internal energy can be expressed in terms of density,
pressure, temperature, and a heat capacity). Unfortunately,
discussion about the physical implications for the different
constitutive assumptions used in the development is scant.
Another comment is that the book is almost comprehen-
sive to a fault. For example, readers may find the results
from the integral averaging chapters of marginal value,
either because the subject is too complex to be developed at
an advanced level (e.g., turbulence and pseudo continuous
media), or because it was too simple and therefore inappro-
priate for a graduate-level text (e.g., macroscopic balances).
Also, it is unlikely that one will find a situation that calls for
the macroscopic moment-of-momentum balance or the jump
entropy inequality. These portions of the book could have
been better used to provide more physical insight or to
analyze moving boundary problems, which are so prevalent
in materials science and engineering. Having said that, edu-
cators and researchers in this field will be glad to have a
single book where the equations needed to handle such a
wide variety of transport problems can be found.
Advanced Transport Phenomena is a comprehensive text-
book that provides systematic coverage of a challenging
subject. It can be used as a primary text for a first-year
graduate course on transport phenomena; students with prior
exposure to the subject at the level provided by BSL will
have a sufficient background. It could also serve as a solid
reference book for more advanced graduate courses on fluid
mechanics or on heat and mass transfer. My overall impres-
sion of the book is positive; I recommend it to those with an
interest in teaching graduate-level transport phenomena or
to those interested in learning advanced topics in this im-
portant and fascinating field. 0


CALL FOR PAPERS
Fall 2001 Graduate Eduction Issue of
Chemical Engineering Education
We invite articles on graduate education and research for our fall 2001 issue. If you are interested in contributing,
please send us your name, the subject of the contribution, and the tentative date of submission.
Deadline is June 1. 2001
Respond to: cee@che.ufl.edu










e, class and home problems



The object of this column is to enhance our readers' collections of interesting and novel
problems in chemical engineering. Problems of the type that can be used to motivate the student
by presenting a particular principle in class, or in a new light, or that can be assigned as a novel
home problem, are requested, as well as those that are more traditional in nature and that
elucidate difficult concepts. Manuscripts should not exceed ten double-spaced pages if possible
and should be accompanied by the originals of any figures or photographs. Please submit them to
Professor James O. Wilkes (e-mail: wilkes@umich.edu), Chemical Engineering Department,
University of Michigan, Ann Arbor, MI 48109-2136.




THERMODYNAMIC PROPERTIES

INVOLVING DERIVATIVES

Using the Peng-Robinson Equation of State

R.M. PRATT
The National University of Malaysia Bangi, Selangor, 43600, Malaysia


Equations of state are among the marvels of chemical
engineering. Though simple and convenient, they
may be used to model both liquid and vapor behavior
for non-polar and low-polar mixtures.1'12] Consequently, such
methods are the preferred tools of the hydrocarbon process-
ing industry. It is not often, especially in thermodynamics,
that you can do so much with so little. In this article, we
calculate thermodynamic properties that contain derivatives,
a topic not normally found in textbooks.
There are two motivations for presenting this material.
First, the calculations are simple, requiring no iteration or
trial-and-error solutions. They are, however, useful items to
add to the engineer's toolkit, and they require only critical
property and ideal-gas heat-capacity data. Second, it enables
the student to use some seemingly abstract equations of
thermodynamics to directly make numerical calculations.
It is rewarding to see these relationships used to make
actual calculations and to observe relative magnitudes of
various quantities.
To illustrate the methods, we use the Peng-Robinson equa-
tion of state applied to a binary vapor hydrocarbon mixture.
There is an almost endless number of derivatives that can be
calculated-we will consider only a few of the more com-
monly encountered ones. It is trivial to simplify the ensuing
equations for the special case of a pure component or to
apply the equations to any number of components. The
equations are valid for both liquid and vapor phases.


PROBLEM STATEMENT
Using the Peng-Robinson equation of state, calculate the

1) Joule-Thompson coefficient, J = a-)H

ap)H
2) Fluid sonic velocity, c = s

for a binary vapor mixture of n-butane and n-pentane at
390K and 11 bar that consists of 35.630 mole % n-butane.
Take kij for this binary pair to be zero.

SOLUTION
We will solve this problem in three steps. First, we will
use the Peng-Robinson equation of state to evaluate the three
derivatives involving P, v, and T, i.e., (P / 3v)T, (aT / 3P)v,


Copyright ChE Division ofASEE 2001
Chemical Engineering Education


Ronald M. Pratt is a lecturer in the engineer-
ing department at the National University of
Malaysia. He obtained his BS in mathematics
and in chemical engineering at the Colorado
School of Mines, his MS in mathematics at the
Fuxin Mining Institute in Liaoning Province,
China, and his PhD in chemical engineering at
the Colorado School of Mines. Research inter-
ests involve molecular dynamics and fractal
modeling.










and (av / 3T),. Then we will find the real fluid heat capaci-
ties, C, and Cp, and finally we will apply these results to
calculate the two thermodynamic derivatives indicated above.

Solution of the Peng-Robinson Equation of State for
(aP/ aV)u, (OT/ P),, and (bv/ )T)p


The Peng-Robinson equation is written as
RT a
P=
v-b v(v+b)+b(v-b)
where
R universal gas constant
T absolute temperature
V molar volume

a ac +m[l- TI T]-
a 0.45723553 R2T 2/P
m 0.37464 + 1.54226 w 0.26992 co2


b 0.077796074 RT/Pc
Tc critical temperature
Pc critical pressure
c pitzer acentric factor
The critical properties for the
two components of our sys-
tem are taken from Smith and
Van Ness (Table 1):[31
For convenience, the Peng-
Robinson equation is often


TABLE 1
Critical Property Data f
n-butane and n-pentan
n-butane n-pentan
T,(K) 425.1 469.7
P,(bar) 37.96 33.7
c 0.200 0.25


quantities applied to the mixture as a whole, and subscripted
values for pure component quantities. From Eq. (1), we
calculate the pure component parameters using R=83.14
cm3-bar/mol-K:
a, = 15911115 cm'-bar/mol2 a, = 23522595 cm6-bar/mol2
b, = 72.43235 cm3/mol b, = 90.14847 cm3/mol
and then, from Eq. (3), we find that


a = 20631852 cm6-bar/mol2 b = 83.836216 cm3/mol
(1) We now solve Eq. (2) for the compressibility factor, Z.
This equation is easily solved using Newton-Raphson itera-
tion15) or by using the cubic formula.'" In either case we
calculate the vapor phase compressibility factor (largest
of the three real roots) to be 0.7794 for the vapor. Conse-
quently, the molar volume, v, of the vapor mixture is
ZRT/P = 2297.54 cm3/mol.
With knowledge of the molar volume and compressibility,
we now calculate the three PVT derivatives, which follow
directly from the equation of state. Knowledge of these
quantities is prerequisite to finding most any derivative ther-
modynamic property. We know that these three derivatives
for must satisfy the "cyclical rule," which may be written as


e




2


written in a cubic polynomial form for the compressibility
factor Z=Pv / RT
f(Z)=Z3 +aZ2 +pZ+y =0 (2)
where
a-=B-l
p A 2B 3B2
y B3 +B2 -AB
and

A aP /(RT)2
B-bP/RT
For an N-component fluid with composition, {w }, we
calculate the mixture parameters, a and b, from the empirical
relations:
N N N
a= I wiwj a ( (1-kij) and b= wibi (3)
i=lj=l i=1
The binary interaction coefficient, k,, is exactly zero for i=j;
for itj, kij is close to zero for hydrocarbons. Values of ki, for
many component pairs are available in the literature,"41 al-
though for most hydrocarbon pairs it is safe to take kj=0. We
will henceforth use values without subscripts to refer to


(a p)(aT)-1 a(4)

Therefore, once we have values for any two of the three PVT
derivatives, the third may be calculated from Eq. (4). We
will evaluate each derivative independently, however, and
use Eq. (4) to check our work.
The first derivative in Eq. (4) is found by direct differen-
tiation of Eq. (1),

(aPI -RT 2a(v+b)
I-)T (v-b)2 [v(v+b)+b(v b)]2

Substituting in the values determined above, we find that

0P) =-0.0035459 bar/(cm3/mol)

The second derivative in Eq. (4) is also found by direct
differentiation of Eq. (1),

(aP) R a' (6)
9T), v=-b v(v+b)+b(v-b) (
and is found to be 0.0434866 bar/K. Therefore,
T = 22.99558 K / bar
tp)v
The third derivative in Eq. (4) is a bit trickier since Eq. (1)
is not readily explicit in volume or temperature. It is there-
fore found implicitly, using Eq. (2),

la pR Ti(az +zj (7)


Spring 2001









where


(M) (B-Z)+() (6BZ+2Z-3B2 -2B+A-Z2
OTlp OTlP


(az )
Oyjp-


3Z2+2(B-1)Z+(A-2B-3B2)


tion for the mixture is a mole fraction weighted average of
the pure component values, i.e.,
N
C=I- WCID (12)

Inserting the known temperature of 390K into the above
equations, we calculate for each component


MA = P ( a 2a)
T) P RT2-- T)


(aB) -bP
OT)p RT2


CID =113.050 J/mol-K
vi


CID =141.376J/mol-K
V2


The derivative term, a'=da/dT, may be evaluated directly
from Eq. (3) as

a' ij 1-kij) ai' aji (8)
SdT 2i=ij=1 ai ya

where
dai -miai
ai' =T- m-1= (9)
dT [+mi(l- JT/Tc) JTT

The pure component parameters are found from Eq. (9) as
a,'=-25547.0 cm6-bar/mol2-K
a,' =-38460.2 cm6-bar/mol2-K
and da/dT for the mixture is found from Eq. (8) to be
a'=-33543.8 cm6-bar/mol -K.
Substituting known values in to Eq. (7), we find that
(v = 12.26396 cm3 / mol- K
vT)
If we multiply the three numbers together we will see that
we have satisfied Eq. (4).

Calculation of the Heat Capacities
C, and C,

We first find C,. We will consider this real fluid property
to be a sum of an ideal gas contribution and a residual
correction for non-ideal behavior:
Cv =CID +C (10)
The ideal-gas contribution is found using heat-capacity data
applicable to gases at very low pressures, which are avail-
able in many thermodynamics textbooks. We will use the
simple correlation in Smith and Van Ness[31
CD =R(A+BT+CT2+DT-2-1) (11)
which is not recom-
mended for temperatures TABLE 2
below 298K nor valid for
n-butane n-pentane
temperatures over 1500K.
A 1.935 2.464
For n-butane and n-pen-
B 36.915 x 10' 45.351 x 10i
tane, the coefficients are
given in Table 2. C -11.402 x 106-14.111 x 10-
The ideal gas contribu- D 0 0


and for the mixture
CID131.283J/mol-K
To calculate the residual contribution to Eq. (10), we use
the standard equation found in many textbooks14,61 for the
residual internal energy derived from the Peng-Robinson
equation of state

R T_ [ Z+B(1+V)1
UR= Ta'-a ze +(1 ) (13)
b,8 Z+B( l-f2)

The value of CR is calculated from its definition

S- aR )v

Evaluation of the partial derivative of Eq. (13) with respect
to temperature yields


C- Ta n z+B(i 2(14)
bF8 -- I (14)

with the temperature derivative of Eq. (8) yielding

a" d2a
a-
dT2

I a,aj a 2 .2 a
i=1j=l I j a~ + + aj~ a+
i=1 j=, lTaaj 7a, C]a, C-. Ca3


where


a" d2ai da acimi T (1+ m')
a- dT2 dT 2TTc, (16)

These equations appear complicated, but the calculation is
straightforward, albeit tedious. Pure component parameters
for a" are found from Eq. (16) to be

a'= 53.2619cm6 bar / ol2 K2
a' = 80.7496 cm6 -bar/mol2 K2

and a" for the mixture is found from Eq. (15) to be
a"= 70.2732cm6 -bar/mol2 -K2
Chemical Engineering Education









If doing hand calculations, very little error (usually less than
2%) is introduced by using the mole fraction weighted aver-
age in calculating a". In this case, we would calculate a" to
be 70.9557 cm6-bar/mol2-K2. Substituting the above mixture
quantities into Eq. (14) (using ZL=0.779438) gives CR=1.152
J/mol-K.
Using Eq. (10), we now obtain Cv=132.436 J/mol-K.
We will use an equation analogous to Eq. (10) to calculate
C,
Cp =CID +C (17)

and since CpDDCID+R, we readily calculate C'D to be
139.597 J/mol-K. The residual contribution may be calcu-
lated from the general relationship between C, and Cp,

C =CR+T ) ( R (18)

The two partial derivatives are already calculated above and
can be substituted into Eq. (18); we find that C = C+124.85
cm'-bar/mol-K and therefore Cp=136.37 cm3-bar/mol-K, or
13.637 J/mol-K. Adding the ideal gas and residual contribu-
tions according to Eq. (17) yields
Cp =153.235J/mol-K


Calculation of Thermodynamic Properties
J and c


Now that we have values for the three PvT derivatives as
well as the two heat capacities, Cv and Cp, we can calculate
a large number of thermodynamic derivatives. We will only
evaluate two of the more commonly encountered ones, the
Joule-Thompson coefficient, J, and the speed of sound in a
fluid, c.
It is simple to calculate the Joule-Thompson coefficient,(dT/
aP)H, using the working equation161

J 1 [T(av -v] (19)

since all the required values have been calculated. Substitut-
ing into Eq. (19), we obtain
J=1.62195 K/bar

The fluid sonic velocity (VP/ap) is calculated from the
working equation161

Cp (P
c = v C a-Y (20)

All the required values have been calculated. Substituting
into Eq. (20) yields c=147.164 (cm3-bar/mol)05. Since these
Spring 2001


are unusual velocity units, some units conversion is in order.
The average molecular weight of the vapor mixture is 67.152
g/mol and we find that the sonic velocity is

rkg )
c221657cm -bar 0 S2 ) m 1000g Imol
mol bar 100cm kg 67.152g

3.2251x108 cm2
s-
or c=179.586m/s=646.5km/hr

We can compare this result with the low pressure (ideal gas)
limiting value
cID
c = IRT=185.683(cm -bar/mol)5 =226.590m/s
ID glD
C v

DISCUSSION
Calculation of derivative properties is easy if there is an
equation of state available to model the PVT behavior of the
fluid. Two such properties have been evaluated here using
the Peng-Robinson equation of state. It is trivial to evaluate a
large number of other derivative properties once we know
the three PVT derivatives and the two heat capacities. In this
age of computers, it is worthwhile for the student to develop
a spreadsheet or set of computer subroutines to calculate
thermodynamic properties of hydrocarbons and hydrocar-
bon mixtures.171 Including these and other thermodynamic
derivatives would be very easy, indeed.
It is interesting to estimate some of these derivatives by
using their finite-difference approximations and to compare
these estimates with results using the equations discussed
above. For example, Cp is approximated by evaluating the
enthalpy H=HI+UR+RT(Z-1) at two nearby temperatures at
11 bar (and same composition)

C-( AH) 30012.449-29705.977 153.236J/mol-K
P AT 391-389
which is essentially the same as the result obtained above,
with any error due to the finite-difference approximation.

REFERENCES
1. Winnick, J., Chemical Engineering Thermodynamics, Wiley,
New York, NY (1997)
2. Sandler, I.S., Chemical and Engineering Thermodynamics,
3rd ed., Wiley, New York, NY (1999)
3. Smith, J.M., H.C. Van Ness, and M.M. Abbott, Introduction
to Chemical Engineering Thermodynamics, 5th ed., McGraw-
Hill, New York, NY (1996)
4. Walas, S.M., Phase Equilibria in Chemical Engineering,
Butterworth-Heinimann, Boston, MA (1985)
5. Carnahan, B., H.A. Luther, and J.O. Wilkes, Applied Nu-
merical Methods, Wiley, New York, NY (1969)
6. Kyle, B.G., Chemical and Process Thermodynamics, Prentice
Hall, NJ (1994)
7. Savage, P.E., "Spreadsheets for Thermodynamics Instruc-
tion," Chem. Eng. Ed., 29(4) (1995) 0










r M.f laboratory


COMPUTER MODELING IN THE

UNDERGRADUATE

UNIT OPERATIONS LABORATORY

Demonstrating the Quantitative Accuracy

of the Bernoulli Equation


DAVID J. KEFFER
University of Tennessee Knoxville, TN 37996-2200

he purpose of this experiment is to demonstrate the
predictive capabilities of the Bernoulli equation in
determining the time it takes a liquid to drain, under
the influence of gravity, from a tank and through an exit
pipe, as a function of initial tank charge, exit-pipe diameter,
and exit-pipe length. The project is comprised of an experi-
mental component and a modeling component.
In the modeling component, predictions of the efflux time
are obtained from several different approximate solutions of
the Bernoulli equation; in the experimental component, the
flux time for water draining from a tank through various exit
pipes is measured. Comparisons between the experimental
and theoretical values are then made. The purposes of the
comparison are

To evaluate which terms of the Bernoulli equation
are important
To test the limits of applicability of the Bernoulli
equation
To demonstrate the value of a rigorous computer
modeling

Descriptions of fluid-flow experiments appear in the lit-
erature. For example, Hesketh and Slater described an efflux
from a tank experiment where students fit height-versus-
time data, assuming there are no pressure losses within the
system.t11 In this work, we include head losses due to various
friction terms. Hanesian and Pera described an experiment


in optimizing pipe diameter with respect to capital and oper-
ating costs.[21 A key difference in the latter experiment is that
the system was operating at steady state. In the experiment
described here, efflux from a tank, there is no steady state,
and thus the resulting equations are differential in nature.

EXPERIMENTAL SYSTEM
Our system is situated inside a cylindrical tank (tank ra-
dius = R,) filled with water to height, H. The tank has a
cylindrical pipe (pipe radius = Rp) of length L extending
from the base of the tank (see Figure 1). The length and the
diameter of the stainless steel exit pipe are variables depend-
ing on which of the eight available pipes is used. The pipe
dimensions are given in Table 1.
The experimental apparatus is intentionally kept as simple
as possible. When the students first see the tank and pipes,
they frequently smirk and comment that the experiment is
too "low-tech" to teach them anything of value, but through
this experiment they learn that "The best experiment is the

David Keffer has been an Assistant Profesor
at the University of Tennessee since January,
2000. His research involves the computational
description of the behavior of nanoscopically
confined fluids. He has transferred the tools of
his research-solving algebraic, ordinary, and
partial differential equations-to the under-
graduate engineering curriculum by integrat-
ing modern computer modeling and simula-
tion tools, not only in numerical methods
courses but in any engineering course.


Copyright ChE Division ofASEE 2001


Chemical Engineering Education










simplest experiment that still has enough guts to demon-
strate the underlying physics of the system."131

MATHEMATICAL MODEL
The mathematical model used to describe efflux from the
tank is based on the mass and mechanical energy balances.
If we define our system as the dotted line in Figure 1, and if
we stop timing the efflux when the water level reaches H',
then the control volume is always full and we have a mass
balance of the form

in = v AT = VTR. = out= VpApvpntR (1)

assuming an incompressible fluid, where vT is the flow
average velocity in the tank, AT is the cross-sectional area of
the tank, and RT is the radius of the tank. The subscript P
designates analogous variables and parameters of the exit
pipe. The average velocity of the fluid in the tank is defined
as
dH
VT(t)= dt (2)
where t is time. Equation (2) can be substituted into Eq. (1)
to yield an expression for the velocity in the pipe

SdH R (
vp = T (3)
Vp- dt R2 {
P
The mechanical energy balance (Bernoulli equation in-


Figure 1. Schematic of the experimental apparatus.


TABLE 1
Pipe Dimensions
Length Inside Diameter
(inches) (inches)
30 3/16
24 3/16
12 3/16
6 3/16
1 3/16
24 1/8
24 1/4
24 5/16


cluding friction terms) has the general form

gAz Av2 AP (4)
+ +--+2h, =0 (4)
gc 2gc P
where g is gravity, Az = L+H', Av2=vT2-Vp2, AP is the pres-
sure drop, p is the density of the fluid, and h, are the terms
contributing to the head loss due to friction.
Again, if we define our system as the dotted line in Figure
1, we have the advantage that the accumulation term within
the system over which the material and mechanical energy
balance is drawn is zero, since the system is constantly full
of liquid. This results in a non-zero pressure drop corre-
sponding to the height of the water in the tank, less H', the
final height at which we stop the experiment.
In this system, we can consider frictional head loss due to
the pipe wall, the contraction, and the tank wall

Shf = hf,pipewall +hf,contraction + hf,tankwall (5)
We define each term in the Bernoulli equation

AP= pg(H- H') (6)
gc
The Darcy equation gives the friction head loss for flow in a
straight pipe,


hf,pipewall = 4P ) V (7)

where fp is a dimensionless friction factor and Dp is the
diameter of the pipe.141 If we assume turbulent flow in the
pipe, we can obtain an estimate of the friction factor, fp,
using an empirical relation, known as the Blasius equation,
applicable to turbulent flow with Reynolds numbers in the
range of 4000 S0.0791 (8)
P N0.25
Re,P
The Blasius equation for a smooth pipe is used because it
will allow for an analytical solution to the resulting differen-
tial equation. The friction loss due to contraction is given
by"51
2 D2,v 2
h K -05 1 P P (9)
f,contraction c 2g 0.5 1- 2g
gc DT ) gc

If we assume laminar flow in the tank, the friction loss due
to the tank wall is

hftaal =4f f H v2 = 64 (10)
takwa 2gc NRe,T D T2g

The assumption of turbulent flow in the pipe and laminar
flow in the tank can be verified experimentally. For the
diameters and lengths used in this experiment, these as-
sumptions are confirmed.


System


2Rp-


Spring 2001










If we combined Eqs. (1) through (10), we obtain a me-
chanical energy balance of the form 61

(dH 1.75 2(0.0791)p0.25LD35
-g(L+H)+ d p025D75 T +

(D4 )
DdH 2 D 2p dH ]2 32HP(dH
dt) 2 4 T L dt D- p -dt


(11)

Equation (11) is a first-order nonlinear ordinary differential
equation. It has no known analytical solution.
If we rely on our engineering intuition to neglect terms of
less significance, however, we might omit the kinetic energy
term, the friction loss due to contraction, and the friction loss
due to laminar flow in the tank. If we make these three
assumptions, we will find that we can obtain an analytical
solution to the resulting differential equation

[2(0.0791)0o.25D3.5 4/7 7 H 3 H(t)3/7()
S p.25D3.75 T L 1+ 1+ L L L

where Ho is the initial height of the water in the tank at time
zero. Thus, we can find the time it takes for the water level in
the tank to fall to a height, H, from the initial height, Ho. This
approximation is what is often used to describe the system in
unit operations laboratories solely because it has an analyti-
cal solution. We will see in the next section, however, that
this approximation gives not only quantitatively but also
qualitatively incorrect results.


The more rigorous approach is to numerically solve the
ordinary differential equation (ODE) in Eq. (11). We can use
a standard numerical ODE-solution technique (e.g., Euler's
method or a Runge-Kutta method) if we can arrange the
ODE into the form
dH
= f(H,t) (13)

Equation (11) cannot be put in this form. Therefore, we
cannot easily solve for the velocity in the tank, DH/dt, at
every Euler or Runge-Kutta time step as is required by those
algorithms. But for any given time, t, for which we know the
height, H, we can obtain the numerical value of the tank
velocity by using a technique to solve a single nonlinear
algebraic equation, such as the Newton-Raphson method.
Combining the Newton-Raphson and Runge-Kutta methods
is a relatively simple algorithm to implement and involves
nesting the iterative algebraic equation solver inside the
routine that obtains the tank velocity for the ODE solver. For
the undergraduates in the unit operations laboratory, we
provide just such a routine, written for MATLAB."61 The
students are familiar individually with the Runge-Kutta and
Newton-Raphson techniques and the majority of them di-
rectly comprehend the combination of the two methods.
We have integrated the modeling component of this ex-
periment with the curriculum-wide "Web Resource for the
Development of Modern Engineering Problem-Solving
Skills" instituted in the Department of Chemical Engineer-
ing at the University of Tennessee.17 This web resource acts
as a stand-alone self-teaching module that students at any
level in the program-from sophomores to graduate stu-
dents-can access to obtain the basic algorithms to solve
systems of linear algebraic equations, systems of nonlin-
ear algebraic equations, systems of ordinary differential


Figure 2. Efflux time as a function
of exit pipe length for the experi-
mental case, the approximation to
the mechanical energy balance with
an analytical solution (Eq. 12), and
for more complete mechanical en-
ergy balance, solved numerically
(Eq. 11). The data are for water at
85 F draining from a six-inch di-
ameter baffled tank from an initial
height of 11 in. to a final height of 2
in. through a pipe with a nominal
diameter of 3/16 in.


180

160

140



1oo

80

60

40
60-


o







0 experiment
analytical solution,eqn (2)
-numerical solution, eqn (11)


0 10 20 30 40 50 60 70 80
exit pipe length (cm)


Chemical Engineering Education










equations, numerical integration, and linear regression
and analysis of variance.

EXPERIMENTAL RESULTS
In the lab the students examine the effects on efflux time
of the initial water charge, the exit-pipe diameter, and the
exit-pipe length. Here, we limit ourselves to the effect of the
exit-pipe length. In Figure 2 we plot the flux time versus
exit-pipe length for the experimental case, for the approxi-
mation to the mechanical energy balance with an analytical
solution (Eq. 12), and for the complete mechanical energy
balance, solved numerically (Eq. 11). The data are for water
at 85'F draining from a six-inch diameter baffled tank from
an initial height of 11 in. to a final height of 2 in. through a
pipe with nominal diameter of 3/16 in. The water density
and viscosity were obtained from the literature.[8]
At short pipe lengths, we see that the experimental efflux
time decreases with increasing pipe length, because gravity
and the hydrostatic pressure term in Eq. (11) create a driving
force for flow proportional to (L+H). As we increase L, the
driving force increases and the tank drains faster. In contrast,
at longer pipe lengths, the experimental efflux time in-
creases with increasing pipe length, because we have
reached a point where skin friction due to the pipe wall is
the dominating factor.
The approximation to the Bernoulli equation that has an
analytical solution (Eq. 12) fails to model this behavior both
qualitatively and quantitatively. The trend for Eq. (12) is a
monotonic increase in efflux time with increasing pipe length.
The average relative error of Eq. (12) with respect to the
experimental data is 32.6%.
The more complete Bernoulli equation in Eq. (11) models
the experiment both qualitativelty and quantitatively. The
average relative error of Eq. (11) with respect to the experi-
mental data is 3.1%.
Plots have also been generated regarding the dependence
of efflux time on pipe diameter and initial water height. Both
the analytical solution (Eq. 12) and the numerical solution to
Eq. (12) model the behavior qualitatively, namely that efflux
time decreases as pipe diameter increases or initial water
height decreases. But as was the case with the pipe length, the
quantitative agreement is substantially better using Eq. (11).

CONCEPTUAL LESSONS
OF THE EXPERIMENT

After the students have collected the experimental data in
the laboratory, they take the data to the computer lab and
model it using both Eqs. (11) and (12). Additionally, they
look at variant models, adding one term at a time-kinetic
energy, friction due to contraction, and friction due to the
laminar flow in the tank wall. Adding the terms individually
allows the student to determine the effect of each term in the


mechanical energy balance on the efflux time.
The students can also explore the comparison of experi-
ment and theory in terms of error analysis. For example, they
can calculate the Reynolds number at each experimental
data point and show that for any given theoretical model the
accuracy decreases as the Reynolds number drops and reaches
the lower limit of applicability of the expression used for the
turbulent friction factor.
Finally, the students (primarily juniors) obtain a first-hand
demonstration of the quantitative accuracy of the Bernoulli
equation. The experience helps them understand the signifi-
cance, validity, and limitations of the otherwise abstract
mathematical expressions with which they are presented in
classroom lectures on fluid flow.

CONCLUSIONS
In this work we have described a very simple efflux from a
tank experiment, of the sort commonly employed in under-
graduate unit operations laboratory courses. We have shown
that relying only on a simplified analytical solution to the
Bernoulli equation not only fails to quantitatively model the
experimental results but also qualitatively fails to capture the
correct trends. We have provided a more complete me-
chanical energy balance, outlined its numerical solution,
and shown that it both qualitatively and quantitatively
models the experiment.
The inclusion of a computer simulation in the experiment
allows the students to demonstrate for themselves the conse-
quences of over-simplified engineering approximations and
the value of a rigorous mathematical model.

ACKNOWLEDGMENTS
The author would like to thank Professor John Prados in
the Department of Chemical Engineering at the University
of Tennessee for his aid and encouragement in this work.

REFERENCES
1. Hesketh, R.P., and C.S. Slater, "Cost Effective Experiments
in Chemical Engineering Core Courses," Proc. of ASEE
Ann. Conf., Charlette, NC (1999)
2. Hanesian, D., and A. Perna, "Estimation of Optimum Pipe
Diameter and Economics for a Pump and Pipeline System,"
Proc. ofASEE Ann. Conf, Milwaukee, WI (1997)
3. Davis, H.T., University of Minnesota, Department of Chemi-
cal Engineering and Materials Science, personal communi-
cation (paraphrased)
4. Perry, R.H., and D. Green, Perry's Chemical Engineering
Handbook, 6th ed., McGraw-Hill, New York, NY (1984)
5. "Flow of Fluids Through Valves, Fittings, and Pipes," Crane
Technical Paper No. 410, Crane Co., New York, NY (1979)
6. Keffer, D., "ChE 310 Course Website," at clausius.engr.utk.edu/che310/index.html>
7. Keffer, D., "AWeb Resource for the Development of Modern
Engineering Problem-Solving Skills," at clausius.engr.utk.edu/webresource/index.html>
8. Geankoplis, C.J., Transport Processes and Unit Operations,
3rd ed., Prentice Hall, Englewood Cliffs, NJ (1993) O


Spring 2001
















2001 ASEE Annual Conference






June 24 27, 2001 Albuquerque, New Mexico



Technical Sessions


SMonday, June 251

Session 1313 10:30 a.m. Capstone Design Issues in Chemical Engineering
Moderators: Chris Wiegenstein and David Miller
1. "Capstone Chemical Engineering Laboratory Courses at Michigan Tech"
A.J. Pintar, E.R. Fisher, and K.H. Schulz
2. "Open Beginning Projects: A Flexible Approach to Encouraging Student Curiosity and Creativity"
S.S. Moor
3. "A Hands-On Multidisciplinary Design Course for Chemical Engineering Students"
J.M. Keith, D. Charu, J. Meyer, and N. Norman
4. "The Inclusion of Design Content in the Unit Operations Laboratory"
D. Ridgway, V.L. Young, and M.E. Prudich
5. "An Introduction to Process Simulation for the Capstone Design Course"
D. Miller, T.N. Rogers, and B.A. Barna
6. "Graduate Bridging and Continuing Eduction in Chemical Engineering via the Web"
R.M. Worden, D. Briedis, and C.T. Lira

Session 1413 12:30 p.m. Non-Traditional Topics in Chemical Engineering
Moderators: Nada Assaf-Anid and Ann Marie Flynn
1. "Introducing Emerging Technologies into the Curriculum Through a Multidisciplinary, Industrially-Sponsored Research Experience"
J.A. Newell, S.M. Farrell, R.P. Hesketh, and C.S. Slater
2. "Integration and Use of a Novel Semiconductor Procesing Simulator to Teach Stream Recycle Issues to Chemical Engineering Students"
P. Blowers and E. Weisman
3. "A Course on Health, Safety, and Accident Prevention"
A.M. Flynn, J. Reynolds, and L. Theodore
4. "Training Chemical Engineers in Bioprocessing"
C. Preston, D. Briedis, and R.M. Worden
5. "Biotechnology and Bioprocessing Laboratory for Chemical Engineering and Bioengineering"
S. Sharfstein and P. Relue
6. "Bacterial Disinfection in the Classroom: Engineering-Based Experimental Design"
N.M. Assaf-Anid

Tuesday, June 26

Session 2213 8:30 a.m. Laboratory Automation and Classroom Demonstrations
Moderators: Connie Hollein and Jim Henry
1. Laboratory Remote Operation: Features and Opportunities"
J.M. Henry
2. "Using Web-Based Supplemental Instruction for Chemical Engineering Laboratories"
C.R. Nippert
3. "Virtual Reality Laboratory Accidents"
J.T. Bell and H.S. Fogler
4. "Exercise in Chemical Engineering for Freshmen"
S.M. Farrell and R.P. Hesketh
5. "Teaching Chemical Engineering with Physical Plant Models"
K.H. Pang
6. "Engineering Experiments Utilizing an Automated Breadmaker"
R.P. Hesketh, C.S. Slater, and C.R. Flynn
7. "Utilizing Experimental Measurements to Introduce Underrepresented Pre-College Students to Science and Engineering"
A. Perna and D. Hanesian
120 Chemical Engineering Education












Session 2565 2:30 p.m. Math Requirements in the Chemical Engineering Curriculum
Moderators: Anton Pintar and Jenna Carpenter
1. "Mathematics and Chemical Engineering Education"
A. Pintar, F. Carpenter, M. Cutlip, M. Graham, and J. Puszynski
2. "Mathematics in Chemical Engineering: From the 'Ball-Park' to the 'Lap-Top'"
R. Toghiani and H. Toghiani

Session 2613 4:30 p.m. A Galaxy of Stars
Moderators: David Kauffman and Melanie McNeil
Senior chemical engineering faculty who have been leaders in the analysis, development, and dissemination of educational techniques will be members
of a panel to discuss the current state of chemical engineering education and how it has progressed, or digressed, over the past three decades, and how it
will change in the coming decades. They will introduce "rising stars" in the field, who will also participate in the panel discussion. Senior panel members
include Richard Felder, James Stice, and Billy Crynes.

SWednesday, June 27 1

Session 3213 8:30 a.m. The Latest in Pedagogy in Chemical Engineering
Moderators: Joe Shaeiwitz and Wallace Whiting
1. "The Role of Homework"
P. Wankat
2. "Using Critical Evaluation and Peer-Review Writing Assignments in a Chemical Engineering Process Safety Course"
D.K. Ludlow
3. "Criterion-Based Grading for Learning and Assessment in the Unit Operations Laboratory"
V.L. Young, M.E. Prudich, and D.J. Goetz
4. "Mid-Semester Feedback Enhances Student Learning"
R. Wickramasinghe and W.M. Timpson
5. "Development and Implemmentation of a Computer-Based Learning System in Chemical Engineering"
N.L. Book, D.K. Ludlow, and O.C. Sitton
6. "Evaluation of IT Tools in the Classroom"
S. Soderstrom and C. Lorenz

Session 3413 12:30 p.m. The Master as the First Professional Degree
Moderator: David Kauffman
There is a great deal of discussion concerning the need for a more-than-four-year program for the first professional level in engineering. A panel of experts
will give background information and discuss issues raised by the audience. Panelists include Thomas Hanley, Gerald May, and Paul Penfield.

Session 3513 2:30 p.m. Computers and Computation in the Chemical Engineering Curriculum
Moderators: Anneta Razatos and Donald Visco
1. "Template-Based Programming in Chemical Engineering Courses"
D.L. Silverstein
2. "Sealing Analysis-A Valuable Technique in Engineering Teaching and Practice"
E.M. Kopaygorodsky, W.B. Krantz, and V.V. Guliants
3. "Is Process Simulation Effectively Utilized in Chemical Engineering Courses?"
M.J. Savelski, K.D. Dahm, and R.P. Hesketh
4. "Scientific Visualization for Teaching Thermodynamics"
K.R. Jolls
5. "Integrating Best Practice Pedagogy with Computer-Aided Modeling and Simulation to Improve Undergraduate Chemical Engineering Education"
J.L. Gossage, C.L. Yaws, D.H. Chen, K. Li, T.C. Ho, J. Hopper, and D.L. Cocke




-Socey-Wide Picnai ChE Division Lectureship ChE Division Awards Banquet
Su; j~n we 24, 5:;00p.m. Monday June 25, 4:30 p.m. Monday, June 25,6:30 p-m.
:-.a lt AWl_ e __i-' Moderator: Doug Hirt Albuquerque Petroleum Club
__ :- ,; : Speakerotolbe announced Speaker to be ianounced
'i- a.. ---- _" --W -" -. "- --


F _4: p- A aeCsE Division Bui2ness -ASEE AimuatA eceptkis
Baf*st -:Luancheon and Awards Banquet
:Tusd a, June-26, 7:0 -an. Tuesday, June 26, 12:30p.m. Wednesday, June 27, 6:00p.m.


Spring 2001










,]1 laboratory


USING IN-BED TEMPERATURE PROFILES

FOR VISUALIZING THE

CONCENTRATION-FRONT MOVEMENT



PAULO CRUZ, ADILIO MENDES, FERNAO D. MAGALHAES
University of Porto 4200-465 Porto, Portugal


Purification of gas streams through adsorption in a
packed column is an important process in chemical
engineering. The experimental study of such systems
involves determination of breakthrough curves for the ad-
sorbable components in the column. Both theoretical and
practical implementations of this process are common in
undergraduate courses, but students do not readily assimilate
some of its aspects. The retention of a concentration front in
an adsorbent bed and its implications on the formation of
shock waves, for instance, are not easy to visualize mentally,
especially when experimental information concerns only the
outlet concentration history.
In our senior undergraduate laboratory, we have devel-
oped an experiment that has been successful in helping stu-
dents grasp the concepts of concentration-front movement in
fixed beds. Due to the structure of the curricular program,
most students actually take this lab course before the ad-
vanced separation course in which the theory associated
with these processes is detailed. This does not seem to im-
pair the students' ability to interpret and understand the
experimental results and theoretical concepts, however.
In addition to the measurement of the outlet breakthrough
curve, a set of thermocouples within the bed allows for the
indirect "visualization" of the advancement of the concen-
tration front.
A process simulation program, developed for this purpose,
also lets students gain sensitivity for the relative importance
of the different operation parameters and physical proper-
ties. This easy-to-use software is available for downloading
at
http://raff.fe. up.pt/~lepae/simsorb.html
In this paper we start by briefly describing the Solute
Movement Theory, which is a basic tool for interpreting this
kind of process, and the mathematical model used in the


software simulation, which involves a more detailed de-
scription. Later we will illustrate how students can use both
in the interpretation of experimental results.

THEORETICAL BACKGROUND
A certain gas, A, diluted in an inert carrier gas stream
travels in a column packed with a non adsorbent solid at the
same velocity as the carrier. If, however, the solid adsorbs
gas A, then its velocity will be lower than the carrier's.
Simply put, the gas is "retained" by the solid, i.e., it cannot
proceed along the column while the adsorption sites are not
filled. This idea is more-or-less simple and intuitive.
Things become a bit more complicated, though, when one
tries to interpret phenomena such as the formation of differ-
ent kinds of concentration-front waves. This is when the
Solute Movement Theory (SMT) comes in handy. It predicts
(for simplified but meaningful conditions) the solute veloc-
ity as a function of concentration. Its main result states that an
infinitesimal element of solute, with concentration cA, will
travel the column at a velocity us, which depends (inversely) on
the slope of the adsorption isotherm for cA (dqA/dcA)
v
us v (1)
Us =I 1-E dqA
Se dcA

Paulo Cruz is a PhD student in Chemical Engineering at the University of
Porto, Portugal. He received his degree in chemical engineering from the
same University in 1998. His research interests are in multicomponent
mass transport and sorption in porous solids and membranes.
Ad6lio Mendes received his licentiate and PhD from the University of
Porto, Portugal, where he is currently Associate Professor. He teaches
chemical engineering laboratories and separation processes. His main
research interests include membrane and sorption gas separations.
Ferndo Magalhies is Assistant Professor of Chemical Engineering at
the University of Porto, Portugal. He received his PhD from the University
of Massachusetts in 1997. His research interests involve mass transport
and sorption in porous solids and membranes.
Copyright ChE Division of ASEE 2001
Chemical Engineering Education










where v is the interstitial velocity of the inert carrier gas, e is
the packing porosity, p is the absorbent's apparent density,
and qA is the concentration of A adsorbed in the solid, in
equilibrium with cA. The reader can find the details of our
approach for deriving Eq. (1), based on a differential mass
balance to the column, at
http://raff.fe.up.pt/~lepae/simulator.html
For other approaches see, for example, the book by Wankat.r11
SMT implies, of course, a series of simplifying assump-
tions, the major being
1. local adsorption equilibrium
2. plug flow in gas phase
3. negligible pressure drop along the column
4. isothermal operation
5. low adsorbate concentration
Assumptions 4 and 5 imply that the interstitial gas velocity
can be assumed constant.
It is quite clear, from Eq. (1), that stronger adsorption
(higher dqA/dcA) implies slower solute movement (lower us).
On the other hand, if there is no adsorption, then u, = v, and
the solute moves at the same speed as the inert carrier gas.
Let us now consider that the column, initially without
solute, is subject to an inlet concentration step of magnitude
c9. Suppose that two well-defined linear regions, as shown in
Figure 1, compose the adsorption isotherm for this solute.
Solute elements with concentrations between 0 and c, will,
according to Eq. (1), have a velocity

uv (2)
Us (1- E) q
l+p c
On the other hand, for solute elements with concentrations
On the other hand, for solute elements with concentrations
between c, and c2 the velocity is

Us2 = -- (q2-q1 (3)
l+p
S(C2 -Cl,

Velocity u,, is lower than us,. Due to the particular shape
of the isotherm, high concentrations tend to move faster than
low ones. This would apparently lead to the situation de-












cl c2
q2

---------. .- ---- ~ ~~ ~ ~ ~~







Cl C2

Figure 1. Idealized adsorption isotherm.
Spring 2001


picted in Figure 2: high concentrations moving ahead of low
concentrations!
This is obviously a physical impossibility. High concen-
trations cannot exist without the lower ones. What actually
occurs is the formation of a shock wave. The concentration
front shown on the left in Figure 2 preserves its shape as it
moves along the column, with a velocity intermediate be-
tween ut and us2. This velocity can be derived from a mass
balance to the shock wave, the result being

u = (4)
-s +p-E q2
e c2
E C2

As will be shown later, dispersion effects (not accounted for
in SMT) cause the concentration front to develop some
distortion as it moves along the column.
And what will happen in the case of desorption, i.e., when,
assuming the same isotherm, a negative concentration step is
applied at the column entrance (Figure 3)?
Once again, the higher concentrations (between c, and c,)
tend to move faster. But now these can actually move ahead
of the lower ones, causing a progressive deformation of the
originally sharp concentration front. We have, then, a dis-
persive or diffusive wave."I
This discussion can be easily extended to the analysis of
more realistic systems, where the adsorption equilibrium is
described by, say, a Langmuir-type isotherm. Such isotherms,
where dq/dc decreases with increasing c, are called favor-
able isotherms. It is easy to understand that in the opposite
case, i.e., for an unfavorable isotherm, the conditions dis-
cussed here for the formation of shock and diffuse waves
would be reversed.
The way SMT describes adsorption in a packed column is
quite simplistic. More realistic considerations, such as axial

C2 ---------... --- ..-------

Cl --------------
< -- shock wave
z
Figure 2. Hypothetical progression of a step in concentra-
tion, corresponding to the isotherm shown in Figure 1.
This is the basis for the formation of shock waves.

C 2 ...........-------- ------------------ ----- ___
C2





Figure 3. Hypothetical progression of a negative step in
concentration, corresponding to the isotherm shown in
Figure 1. This would be a dispersive wave.










dispersion, intra-particular mass transport resistance, and
non-isothermal behavior, can be added if one establishes a
more complex mathematical model for this process. The
differential mass and energy balances of our "complex model"
(CM) are presented in the Appendix.
Students are expected to be able to interpret each term in
the balance equations, even though the resolution of a sys-
tem of partial differential equations is beyond their abilities.
For that we supply our homemade software simsorb, which
uses finite difference discretization of the spatial coordinate
(routine PARSET from package FORSIMVI) and performs
the time integration with routine LSODA. It uses a MS-
Excel interface for inputting the data and for plotting the
results. This software is available for downloading at
http://raff.fe. up.pt/~lepae/simsorb. html
The input spreadsheet already contains the set of physical
parameters and operating conditions used in simulating our
experimental results. The adsorption isotherms (of the type
Langmuir-Freundlich) were experimentally measured at our
lab and the Peclet number (axial dispersion) estimated from
an available correlation.2 Values for the global heat-transfer
coefficient and the intra-particle diffusion coefficient were
not measured directly. They were obtained by fitting the
model to experimental results. This is done previously by the
class tutor, so when the students run the simulator for the
first time they observe a good agreement between the model's
output and their experimental results. Students can later run
the simulator with other input data and analyze its effects on
the system's performance. An example of this is given later
in this paper.

INTERPRETING EXPERIMENTAL RESULTS

The previous theoretical introduction is es-
sentially the first contact that students have
with Solute Movement Theory. Even if they
seem to understand it relatively well, the sedi-
mentation of concepts demands a more tan-
gible, i.e., experimental, approach. Ideally, it
would be possible to directly observe the evo-
lution of a concentration front within a packed
column. This is, of course, not the case. Only
inlet and outlet concentrations are, in prin-
ciple, accessible. By measuring the tempera-
ture at different points in the column's axis,
however, one can obtain indirect informa-
tion on the behavior of the concentration
front along it.
One may point out that the existence of
measurable thermal effects is certainly con-
trary to the SMT's original hypothesis of iso-
thermal operation. Nonetheless, as long as Figur
these are not excessive, a good compromise


can be obtained between the applicability of SMT and an
"on-line visualization" of the progress of the concentration
front, as we shall see.
For our lab course we use the adsorbate/adsorbent pair
CO2/activated carbon. Carbon dioxide was chosen since, in
addition to being quite safe to work with and having a low
cost, it has a high heat of adsorption in activated carbon. We
used activated carbon from Chemviron Carbon in the form
of extruded pellets (6.3 mm x 3.6 mm).
Our setup is shown schematically in Figure 4. The column
is 250 mm long and 50 mm in internal diameter. Seven
evenly spaced holes were drilled in its side to allow for
insertion of the thermocouples. The column is placed inside
an oven. This has a twofold purpose: to keep the surrounding
temperature constant (the oven is set to a temperature slightly
above room temperature) and to allow for complete regen-
eration if necessary. Actually, we noticed that for this sys-
tem (CO2/activated carbon), high-temperature regeneration
is not needed; pure helium flow at operation temperature
suffices for removing the adsorbed CO2 (within the sensor's
detection limit). The inlet flow rates of helium (the carrier
gas) and carbon dioxide are controlled with two needle valves
and monitored with electronic flow meters. The outlet con-
centration of carbon dioxide is measured with an infrared
CO2 sensor. The inlet feed concentration can be checked
before starting a run by directing the feed into the sensor
through a column by-pass. A data-acquisition system con-
nected to a computer allows for continuous visualization
and, if desired, storage of all data (flow rates, tempera-
ture, composition).
Students are asked to perform two breakthrough experi-
ments:


*e 4. Experimental setup for breakthrough experiments
with in-bed temperature measurement.
Chemical Engineering Education










1. Response to a positive concentration step at the inlet
(from pure helium to about 5% molfraction CO,)
2. Response to a negative concentration step at the inlet
(from 5% CO2 back to pure helium) after stage 1 has
reached steady state.
Complete execution time is about 1.5 hours, leaving enough
time for the students to plot the data in the computer and
start analyzing the results.
As an example, we next provide some typical plots ob-
tained for the operating conditions listed in Table 1.
The breakthrough curve (i.e., the history of the CO, con-
centration measured at the column's outlet) obtained for a
positive concentration step is shown in Figure 5.
As discussed previously, SMT predicts, for a positive inlet
step and a favorable isotherm, the formation of a shock wave
(a sharp vertical front). On the other hand, the experimental
curve shows a notorious tilt and rounded edges. It is actually
noticeable-a pronounced "tailing" as the front approaches
the steady-state concentration. This departure from "ideal-
ity" is associated with dispersion effects that oppose the
compressive nature of the front, such as axial dispersion,
intra-particular mass transfer resistance, and non-
isothermality. Students are asked to identify and discuss
these phenomena. By using the software simulator, they will
actually be able to identify the predominant dispersive effect
in this case.


TABLE 1
Operating Conditions

Operation Ambient Operation Helium Carbon Dioxide
Temperature Pressure Pressure Flowrate Flowrate
(C) (Pa) (Pa) (mN(PTN)/s) (m'(PTN)/s)
38.1 1.00x 10'5 2.60 x 10' 4.35x 105 2.48 x 106


6

5

4

S3




0-
0 200 400 600 800 1000 1200 1400
Time (s)

Figure 5. Breakthrough curve (exit CO, mol fraction as a
function of time) for a positive concentration step at the
inlet. The solid line refers to the fit of the complex model.
The dashed line is the result from Solute Movement Theory:
an ideal shock wave with breakthrough time computed
from Eq. (4).
Spring 2001


Figure 6 shows the corresponding temperature histories
along the column. Data from the last thermocouples are not
shown since they are placed at the beginning and at the end
of the packed bed where heat is being dissipated through the
column's inlet and outlet flanges. This effect masks the
temperature information provided by the two thermocouples.
Thermocouples 2 and 6, on the other hand, depict quite well
the progress of the concentration front along the column.
The observed increase in temperature is associated with
the exothermal adsorption of CO, at the concentration front.
The significant amplitude of the temperature increase (about
7C), as well as the long length of time that it takes for
cooling down, usually surprises the students. It is a good
way to make them start questioning the validity of the
isothermality hypothesis, often applied without proper re-
flection in chemical engineering problems.
A more subtle observation is associated with the succes-
sive broadening of the temperature peaks along the column
or, more clearly visible, the decrease in the temperature
maximum measured in each thermocouple. Note: the second
peak shown in Figure 6 was recorded with a slightly differ-
ent thermocouple and therefore it has a different response
time. Aside from this deviation from the general trend, one
may then conclude that this broadening is associated with
the increasing dispersion of the concentration front as it
travels along the column. Eventually, the dispersive and
compressive effects compensate each other at some point in
the column and the shape of the front stabilizes. This is the
so-called constant pattern regime.1]
Despite the clear evidences of non-isothermality and dis-
persive effects, students are asked to use SMT (more ex-
actly, Eq. 4) to predict the time it takes for the shock wave to
reach each thermocouple and to compare this with the experi-
mental results, using the maximum temperature in each peak
as a reference for the passage of the concentration front.
Note that (for such a comparison to be meaningful) we have


44

S43

41
540
39

37
0 100 200 300 400 500 600 700 800 900 1000
Time (s)

Figure 6. Temperature histories obtained at evenly spaced
points inside the column, for a positive concentration step
at the inlet. The solid lines refer to the fit of the complex
model.











to assume that the temperature front travels in combination
with the concentration front. Under some conditions (mainly
for adiabatic systems), the temperature front may lead the
concentration front.131 The reasonability of our assumption is
reinforced by comparing simulated concentration and tem-
perature profiles. In addition, as can be seen from Table 2,
there is a good agreement between the SMT estimations and
the experimental results. It is remarkable that the simple
SMT model still seems to have some predictive value under
these operating conditions.
In relation to the desorption step, the resulting break-
through curve is shown in Figure 7. SMT predicts that a
negative concentration step associated with a favorable iso-
therm leads to a diffuse wave. The presence of other disper-
sion phenomenon adds to this effect, causing the experimen-
tal concentration front to have a very pronounced tilt.
Figure 8 shows the temperature history profiles. The peaks
are now inverted, since desorption is an endothermic pro-
cess. Now there is a clear broadening of the peaks as the
front travels along the column, agreeing with its disper-
sive nature (in addition to the aforementioned dispersion
phenomena).
The qualitative differences between the results obtained
from the positive and negative steps are quite evident to the
students and contain a lot of material for discussion. The
quantitative analysis in terms of SMT is also quite interest-
ing. In addition, students are asked to run the simulation
program and to compare its results to the experimental data
(see Figures 5 to 8 and Table 2). The complex model, by
considering several dispersion effects and non-isothermality,
is able to reproduce quite nicely the shapes of the break-
through curves and temperature peaks.
Students are encouraged to run the simulator with other
input parameters and therefore gain sensitivity to how these
affect the results. It is particularly interesting to study those

TABLE 2
Time for the Concentration Front
to Reach Each Thermocouple Position
The experimental time refers to the time when the maximum tempera-
ture is reached, the theoretical time from SMT uses Eq. (4), and
the theoretical time from CM uses the results from
the complex model simulations.

Thermocouple Experimental Theoretical Theoretical
position time time from SMT time from Cm
(m) (min) (min) (min)
0 0.0 0
0.042 3.0 2.1 2.3
0.083 4.8 4.2 4.2
0.125 6.6 6.3 6.2
0.167 8.4 8.4 8.3
0.208 10.3 10.4 10.5
0.250 12.1 12.5 12.5


6

5



03






0 200 400 600 800 1000 1200 1400
Time (s)

Figure 7. Breakthrough curve (exit CO, mol fraction as a
function of time) for a negative concentration step at the
inlet. The solid line refers to the fit of the complex model;
the dashed line is the result from Solute Movement Theory,
with breakthrough times for each concentration computed
from Eq. (1).




30




327




31
0 100 200 300 400 500 600 700 800 900 1000
Time (s)

Figure 8. Temperature histories obtained at evenly spaced
points inside the column for a negative concentration step
at the inlet. The solid lines refer to the fit of the complex
model.



6



4



2
--h=7W/(m2K)
1- h = 700W/(m2K)

0 i
0 200 400 600 800 1000 1200 1400
Time (s)

Figure 9. Breakthrough curves obtained with the complex
model for two different values of the global heat-transfer
coefficient, h. The value h=7W/(m2K) is the one used in
fitting the experimental data (Figures 5 to 8). The value
h=700 W/(m2K), on the other hand, is equivalent to assum-
ing that heat transfer to the exterior is instantaneous.
Chemical Engineering Education










parameters that are probably more difficult (or impossible)
to change experimentally, such as the global external heat
transfer coefficient, the heat of sorption, or the intra-particu-
lar mass-transfer coefficient. For example, increasing the
global heat-transfer coefficient gives rise to a quite different
breakthrough curve (see Figure 9). The outlet concentration
front is now much closer to a perfect sigmoid, approaching
steady state much more rapidly. This seems to indicate that
heat accumulation inside the column is the major cause for
the "tailing" of the breakthrough curve. As the front passes,
the temperature rises significantly, and the amount adsorbed
is lower than for isothermal operation. As the column cools
down again, the adsorption equilibrium is shifted toward the
adsorbed state and more CO2 is retained in the column. The
consequence is that the outlet concentration will take longer
to reach steady state.
In addition to complementing the discussion of the results,
using the simulation program has an extra pedagogic pur-
pose: it shows students how process modeling in general can
be useful in helping to understand and optimize a real system.

CONCLUDING REMARKS
The experimental study of adsorption in packed beds can
be complemented if, in addition to measuring the outlet
breakthrough curves, one obtains the temperature histories
in different points along the bed. Such an experimental setup
is quite simple and economic and provides valuable qualita-
tive and quantitative information that students can process
without major difficulties. Solute Movement Theory is a ba-
sic tool for that analysis. In addition, using a software simula-
tor based on a more detailed mathematical model provides a
better description of the process and allows students to perform
"virtual" experiments and understand how different factors


influence the behavior of the adsorption system.

ACKNOWLEDGMENTS
The authors wish to thank the Chemical Engineering De-
partment for providing financial support for the setup of this
experiment.

NOMENCLATURE
c, concentration of A in the inter-particular gas phase (mol/m3)
Cp5 heat capacity of gas (J/mol/K)
Cp, heat capacity of adsorbent (J/kg/K)
Dax axial dispersion coefficient (m2/s)
D. intra-particle diffusion coefficient (m2/s)
h overall heat-transfer coefficient (J/m2/K/s)
P pressure (Pa)
qA concentration of A adsorbed in the solid (mol/kg)


qA
Rb
rp
t
T
u
v
Z
Greek
AH
E

P


average concentration of A adsorbed in the solid (mol/kg)
bed radius (m)
particle radius (m)
time (s)
temperature (K)
interstitial solute velocity (m/s)
interstitial carrier gas velocity (m/s)
axial coordinate (m)
Letters
heat of adsorption (J/mol)
packing porosity
gas constant
adsorbent's apparent density


REFERENCES
1. Wankat, P., Rate-Controlled Separations, Elsevier Applied
Science, London, pp. 239-251 (1990)
2. Edwards, M.F., and J.F. Richardson, "Gas Dispersion in
Packed Beds," Chem. Eng. Sci., 23, 109 (1968)
3. Yang, R.T., Gas Separation by Adsorption Processes, Impe-
rial College Pres, London, pp. 161-165 (1997) O


- APPENDIX


The main assumptions of the model are:
1. Plug flow with axial dispersion
2. Negligible radial gradients
3. Negligible pressure drop
4. Variable interstitial velocity
5. Instantaneous thermal equilibrium
between stationary and mobile phases
6. Negligible thermal axial dispersion
7. Constant heat capacities
8. Intra-particular mass transport de-
scribed by linear driving force model
9. Negligible film mass transfer resistance
10. Helium does not absorb
11. No heat accumulation at the wall
Global mass balance (where the total concen-
tration has already been rewritten as a func-
tion of total pressure assumed constant and


temperature):

av v aT a( 1 'aT 1 IT 91T 1- qA
az T az -zax)z 2 z- T t P E at-

Inter-particular solute mass balance

a(vcA) Dax A +aA I-E aqA
az a --+ at + P --= 0


(A2)


Intra-particular solute mass balance (using the linear driving force model)


(A3)


A- 15i qA -qA)
t rp


Energy balance


E -vCpg + E- -Cpg +p( s AH p( E) + h (T- Ta)= 0

(A4)


Spring 2001 12










classroom


Student-Performance Enhancement by

CROSS-COURSE

PROJECT ASSIGNMENTS

A Case Study in Bioengineering and Process Modeling



GULNUR BIROL, INANQ BIROL, ALI INAR
Illinois Institute of Technology Chicago, IL 60616


A wide range of practical, industrial, and medical ap-
plications has increased the demand for "bio-
related" courses in the university curriculum. Stu-
dents from biology, chemical engineering, and electrical
engineering departments, all with different interests and ex-
pectations, enroll in these courses. Due to the diverse nature
of the population in such classes, a variety of educational
approaches and tools are necessary, both for accumulating
knowledge and for implementing the theory.
The typical undergraduate student takes four or five courses
per semester, but for many students this load may become
too difficult to handle because of all the assignments, projects,
and midterm examinations. From time to time, this necessi-
tates a trade-off among the tasks in the "to-do list." This
need led us to initiate a cross-course platform that offered a
joint term project to those students taking the "Introduction
to Bioengineering" (IB) and "Process Control" (PC) courses.
With this initiative, we tested the hypothesis that integrating
cross-course concepts in bioengineering and process control
courses through a unified project could provide a stimulat-
ing learning environment. The integrated project would
also challenge the students to think beyond each course
in an isolated manner.

BACKGROUND
Biotechnology/biomedical engineering courses at the un-
dergraduate and graduate levels are offered regularly in the
Chemical and Environmental Engineering Department at the
Illinois Institute of Technology. Among the undergraduate-
level courses, "Introduction to Bioengineering" provides an
introductory knowledge of biotechnology and biomedical
Copyright ChE Division of ASEE 2001


engineering from a chemical-engineering point of view. One-
half of the semester is spent on biomedical engineering,
while the other half is used for biochemical engineering.
Topics covered in the course are listed in Table 1.
Typically, two-thirds of the IB class population has a
strong interest in biomedical engineering, while one-third is
interested in biotechnology. The department offers a bio-
medical specialization program, and students interested in

Gilnur Birol holds BSc, MSc, and PhD degrees
,n ,:r em.cal engineering from Bogazici Univer-
sl Istanbul. She was a senior research associ-
Sale at1 T's Department of Chemical and Environ-
mntr a Engineering. She is currently a research
prol Sicor in Northwestern University's Biomedi-
cal Engineering Department. Her research inter-
e.tl inoiuaO giucose-insulin interaction in human
biJi mriar,.:,l- pathway analysis and modeling
ard monrri'.lng ,f bioprocesses.

Inanc Birol received his BSc and MSc degrees
in Electrical-Electronics Engineering and PhD
degree in Physics all from Bogazici University,
Istanbul, and is currently a senior research as-
sociate at the Illinois Institute of Technology. His
current research interests include study of com-
plexity via autocatalytic reactions, model order y
reduction and web-based programming.


A All ginar received his BS degree in chemical
S engineering from Robert College, Turkey (1970),
Sand his MEngng (1973) and PhD (1976) de-
grees from Texas A&M University. His teaching
and research interests are process modeling
and control, statistical process monitoring and
fault diagnosis, and use of knowledge-based
systems for real-time process supervision and
control.


Chemical Engineering Education












... we tested the hypothesis that integrating cross-course
concepts in bioengineering and process control courses through
a unified project could provide a stimulating learning environment.


careers in medicine and in the medical industries are ex-
pected to take this course. Many undergraduate students
who take the IB course register concurrently for the PC
course since it is a senior-year core course. Some stu-
dents take the PC in their sixth semester to avoid poten-
tial conflicts in their schedules. Table 2 shows the con-
tent of the PC course.
There are roughly 10-15 students who register for the IB
course each semester, while 25-35 students register for the
PC course. In both courses, homework assignments are usu-
ally given on a weekly basis and form 20% of the course
grade. Students are encouraged to discuss the problems and
to exchange ideas with the instructors and teaching assis-
tants. Since the number of students is relatively low, it gives
them an opportunity to interact with the course instructors
on a one-to-one basis.
In the IB course, the homework assignments are theory-
intensive and can be solved using a calculator or an Excel
worksheet, while in the PC course, homework problems are
computation-intensive and knowledge of Matlab is required
to solve them. In order to have a uniform student profile in
Matlab competence, the instructor tutors introductory topics
in a computer-laboratory environment, holds office hours in
a computer lab, and assigns study hours under the supervi-
sion of the teaching assistant. Furthermore, supplementary
web-based tutorial material about Matlab and a trouble-
shooting service on the source codes are provided through
the Internet.

SCOPE
We wanted to form a cross-course platform where stu-
dents could use their knowledge from two different fields-
bioengineering and process control-emphasizing the use of
common tools from process dynamics, differential equa-
tions, and computer simulations. Concentrating on a unified
project, students would then have an opportunity to analyze
the results from a wider perspective.
To that end, glucose-insulin interaction was chosen as the
model system to be investigated. Its dynamic behavior is
interesting for process modeling and control, and the unique
interactions taking place in various organs in the body are of
importance in bioengineering. The choice of this model sys-
tem turned out to be a very attractive project in both courses.
Students were quite interested in the project, both because of
its academic impact and because of the challenges that it
offered in investigating a real-life problem. All of the bioengi-


TABLE 1
Course Contents: "Introduction to Bioengineering"

E Part I: Biomedical Engineering
The History of Biomedicine: A Brief Review
Overall Description of the Human Body
Physical, Chemical, and Rheological Properties of Blood
Modeling the Body as Compartments, Sources, and Streams
Transport through Cell Membranes
Artificial Kidney Devices
Artificial Heart-Lung Devices

E[ Part II: Biochemical Engineering
Review of Microbiology and Chemicals of Life
Kinetics of Enzyme-Catalyzed Reactions
Kinetics of Key Rate Processes in Cell Cultures
Design and Analysis of Biological Reactors
Transport Phenomena in Bioprocess Systems



TABLE 2
Course Content: "Process Control"

E Incentives for chemical process control, design aspects, and
control hardware
E Analysis of the dynamic behavior of chemical processes
Fundamental models, input-output models, state space
models
Linearization of nonlinear systems
Laplace transforms, transfer functions
Dynamic behavior of first- and higher-order systems
Time delay, inverse response
Empirical models from plant data
E[ Analysis and design of feedback control systems
Feedback control (PID control, time-domain criteria,
internal-model control)
Stability analysis, root locus analysis
Frequency response techniques, Bode diagrams
Performance of feedback control
El Enhancements of single-loop control (cascade, feedforward,
inferential control)
E Model predictive control
[I Multivariable processes: interaction, multi-loop control,
muiltivariable control
E Process control design


Spring 2001


129












TABLE 3
Summary of Student Profiles and Project Descriptions
(UG-Undergraduate: G-Graduate)


Students
(Their backgrounds, special
interests, specifications, etc.)

UG Biology
UG ChE
UG ChE
UG ChE, Biomedical Program
UG ChE, Biomedical Program
UG ChE
UG ChE, Biomedical Program
UG ChE
G ChE, Interest in Transport Phe.
G ChE, Interest in Biotechnology
UG ChE, Attended Medical School
UG ChE
UG ChE


Project
ID

1
2
2 and A
3 and A
3
3
4
4 and B
B
5 and B
C
C
D


Courses
ChEIB ChE PC
Taking Taken


Project
ID Project Topic


1 Comprehensive review of glucose-insulin interactions 1
2 Effect of food on glucose insulin interactions 2
3 Glucose insulin interactions in a healthy man 3
4 Effect of exercise on glucose insulin interactions 2
5 Studying metabolic pathways of liver 1


A Modeling pancreas of a healthy man 2
B Modeling metabolic pathways of liver to control glucose
level in blood 3
C Effect of daily activities on dosage of insulin 2
D Optimal timing and dosage of insulin 1


neering students and one-fourth of the process control
students volunteered to work on this project.

PROJECT DESCRIPTION

The purpose of this project was to analyze the dy-
namic behavior of glucose-insulin interaction in a
healthy person and/or in a diabetic patient. A pharma-
cokinetic model of diabetes mellitus originally devel-
oped by Puckett'" had been used previously, and an
MS student who was working on this project at IIT
wrote Matlab codes for it.121 These codes were given to
the students so they could spend their time and energy
in understanding the fundamental phenomena involved
in the glucose-insulin interaction rather than writing
and debugging code. A summary of the student pro-
files in both courses performing a project, along with
the project topic, is given in Table 3. Students were
grouped by taking into account their backgrounds and
the status of their course registrations. In the IB course
we tried to match students so that at least one of them
was concurrently taking, or had already taken, the PC
course. In the process control course, we rearranged
them so that if all the group members were taking both



Figure 1.
(a) Block diagram representing the pancreas as
a PID controller and the human body
as a multi-input-output process;
(b) The effect of food intake on blood glucose
and insulin regulated by pancreas.


Chemical Engineering Education


Students


Food Intake Blood Insulin


+ P Blood Glucose


+ P






(a)



250 80
- 70
S200 0
60
g Upper Limit
L0 5 r 150 50
E 40
..so .so
5 0 30 "-

Lower Limit "
10
0 o
0 1 2 3 4
Time (hr)

(b)











courses they switched members to ensure that no student did exactly the
same project in both courses.

Introduction to Bioengineering

The projects were assigned after the instructor covered the topics in
the course, and the students were allowed five weeks to work on the
projects. At the end of this period, students presented their findings in a
ten-minute presentation session as a final project, worth 20% of their





I- GLUCOSE

> GLUCOSE S 4. GLUCOSE-P GLYCOOEN
CO, NEX-P \
FRUCTOSE 6.5
OLYCERA HYDE O .p- "HY TOROYACETONE
-ACYL A QLYCERDLM-
-PHOSPHENOLPYRUVATE ACYLA LYCEOL

---- PYRVWAT. ACETYL-CA
0 MALATE OALOAC-TATE -*CrRATE



coc Liver Tissue
Plasma 0


Q. o *


00 0 00 0 00 100






0 5 o 00 0 50 0o 0 0 100
1rm phr) tiro pr) (mo 5
'00



,00 00 00
0,0. 0
;1, (h,, Sn. B

(b)



Figure 2. (a) A simplified metabolic pathway network of the liver;
(b) Concentration profiles of intermediate metabolites
for several sample runs.

Spring 2001


course grade.
A variety of students from different backgrounds
participated: there was one graduate student with
biotechnology as his area of interest, seven chemical
engineering undergraduate students, and one biol-
ogy undergraduate student. There were also four
graduate students auditing the course who did not
prepare a project but participated in the work by
giving feedback during the presentations. Four of the
undergraduate students were registered in the Bio-
medical Engineering Program and were going to
continue their education in medicine. The biology
student was registered in the Biotechnology Cer-
tificate Program. A suggested timeline for these
projects was

C Literature review (I week): Students were given
a brief description for each of the projects and
were asked to make a literature survey to
provide background material on the specific
topic of interest.

C Mathematical Model (I week): A mathematical
model in Matlab code was provided and the
students were expected to spend a week on
understanding the code and using it efflii nilv
under the supervision of both the instructor and
the graduate student who wrote the code.

C Modification of the Model (I week): Depending
on the project description, some modifications
in the Matlab code were needed. Students made
such changes to the original code.

C Testing and Validating the Results (1 week):
The numerical results after the necessary
modifications have been produced and vali-
dated against the available literature data.[13'44J

C Preparing the Report (I week): Students were
given a week to write their detailed final reports
and to prepare their oral presentations. This
enhanced their ability to support their work and
ideas and provided immediate feedback on what
the students learned from this experience.

The student from the Biology Department carried
out a comprehensive review on glucose-insulin in-
teractions in the human body, with an emphasis on
the interactions in different organs. The three Bio-
medical Program students concentrated on glucose-
insulin interactions in a healthy person and tried to
understand the underlying mechanisms (see Figure
1). The graduate student put her efforts into studying
the metabolic pathways of the liver using metabolic
engineering concepts, initiating a promising research
topic"51 (see Figure 2). Other students worked on


," q











investigating the effects of exercise or food intake
on glucose-insulin interactions in a diabetic pa-
tient (see Figure 3).

Process Control

In the process control course, students were asked
to work for two weeks on the project and to report
their findings through project reports and presen-
tations. This would account for two homework
assignments and 4% of their overall grade. The
description of a suggested project on the control of
glucose level in blood was

In healthy people, the pancreas controls
the glucose level in blood. When the
pancreas does not function properly, the
person is diagnosed as a diabetic patient,
and his blood glucose level is controlled
by insulin injections. Such a patient has to
be careful about his diet as well as his
exercise.

Investigate different cases on a model
human body: a healthy person, a patient
under nominal conditions, the food intake
of a patient, and the exercise of a patient.



1 Upper Limt





0 *





(a) 0 4 8 12 16 20 24
Tine(hr)
0 50





10 1



ao 10 1

0 --'- 0
) 0 4 8 12 16 20 24
Mme(hr)



Figure 3. A typical blood glucose
and insulin concentration profile for
repetitive intake of food.


Test closed-loop and open-loop controllers on the model
equations. Involve tasks such as finding the parameter
subspace where the system works in a healthy regime,
determine the appropriate dosage of insulin injection for a
patient, and find the food and exercise tolerance limits for a
patient.

The other project titles in the PC course were "Search for a Power
Law," "Internal Model Control," "Complex Systems," and "Popula-
tion Dynamics."

Student groups were told to select one of these topics or to come up
with their own project proposals. More than one group was allowed to
select one title, but all groups were expected to work separately and to
pursue different tasks.
Students in the IB course were invited to select the "Control of
Glucose Level in Blood" project. Apart from the four students in IB,


TABLE 4
Project Questionnaire


Low High


1. What was your level of competence using Matlab before the project?
2. What is your level of competence using Matlab after the project?
3. What is the difficulty level of this project compared to other course projects?
4. What is the relevance of your project title to your area of interest?
5. How would you rate the challenge of the project?
6. Overall, how would you rate this project?
7. How many hours did you spend on this project?


8. Are you taking Introduction to Bioengineering
Are you taking Process Control


No Yes
No Yes


9. Facilities/tools at IIT were okay.
10. If I had more time, I would prepare a better project.


I received help dealing with the project from the instructor and TAs...
11. ...as exchange of ideas
12. ...as exchange of knowledge
13. ...as technical support


I received help dealing with the project from my friends...
14. ...as exchange of ideas
15. ...as exchange of knowledge
16. ...as technical support

17. This project was a useful learning tool for me.
18. It is easily applicable to other areas.
19. The goals were reasonable
20. I used my knowledge from other courses
21. 1 would consider engaging further research in this field


1 2 3 4 5
1 2 3 4 5



1 2 3 4 5
1 2 3 4 5
1 2 3 4 5



1 2 3 4 5
1 2 3 4 5
1 2 3 4 5

1 2 3 4 5
1 2 3 4 5
1 2 3 4 5
1 2 3 4 5
1 2 3 4 5
12345
12345



12345
12345
12345



12345
12345
12345

12345
12345
12345
12345
12345


Chemical Engineering Education










four more students picked this topic, signify-
ing the appeal of biomedical topics among the
students. They formed a valuable "control group"
similar to IB students involved in the project
who were not taking PC, which gave us the
opportunity to monitor cross-course interactions.
Student interest in this topic was also evi-
denced by the contribution of other class mem-
bers during project presentations. Two of the
eight students performing a project on this topic
were graduate students with interests in bio-
technology and transport phenomena. One of
the undergraduate students had previously at-
tended medical school and provided valuable
perspective on the subjects.
Some of the PC students were assigned the
task of devising a control mechanism centered
on different organs, such as the pancreas and


... TheproIect
plkyed-aa
imetri gote in

- -B..-_ --




7 4=


'-


the liver, as well as investigating the timing and dosage
effects of insulin injections. Other students considered projects
on topics other than the glucose-insulin interaction.
After the oral presentations in both classes, students were
given a questionnaire to provide feedback to the instructors.
They were carefully informed that the questionnaire (see
Table 4) would be used only for course enhancement and
educational research purposes and that it would not have any
effect on grading.
Evaluation of the returned questionnaires indicated that all
students showed improvement by at least one level in their
competence in Matlab, accounting for an average increase of
70%. Although they find this project difficult (4.15 out of
5.00) and challenging (4.40) with respect to other class
projects, they found it quite relevant to their own area of
interest (3.50) and were willing to engage in further re-
search in the field (3.47). Most of them reported that they
needed more time to deliver a better project (4.20), which
is an indication of their interest and willingness to be
involved in it.
The students tended to receive help from instructors and
TAs (3.60) rather than their peers (2.50). They found it a
useful learning tool (3.75) with quite reasonable goals (3.45),
although they were near-neutral to the applicability in other
areas (3.35).
Overall, the students rated the project an average of 3.90.
The fact that they have used their knowledge from other
classes (3.70) suggests that the initiation of a cross-course
platform may become a very useful learning tool, supporting
our hypothesis.

CONCLUSIONS AND FUTURE DIRECTIONS
Diversity of interests, technical abilities, and states of
knowledge among students provided unique feedback for


future improvements in this cross-course
project assignment. The choice of the project
topic turned out to be an attractive one due to
the popularity of biomedical engineering in
education and research. The project played an
important role in triggering the scientific curi-
osities of the students and providing an oppor-
tunity to adapt their knowledge to different
fields. As a follow-up, we developed addi-
tional educational software in order to help
students to explore many case studies.


The cross-course project approach to teach-
ing bioengineering and process control de-
scribed in this paper directly benefited four
S students taking both courses concurrently. The
other four who had taken the process control
S class in the previous semester found that the
project helped them integrate their acquired
knowledge in process control to a bioengineering project.
Hence, eight out of nine bioengineering students were served
by this cross-course initiative. As a result of this experience,
we are looking forward to offering such a cross-course plat-
form in future courses.

ACKNOWLEDGMENTS
The Fall 1999 students in the Introduction to Bioengineer-
ing and Process Control courses are gratefully acknowl-
edged. Special thanks also go to F. Ceylan Erzen for provid-
ing the Matlab codes.

REFERENCES
1. Puckett, W.R., "Dynamic Modeling of Diabetes Mellitus,"
PhD Thesis, University of Wisconsin-Madison (1992)
2. Erzen, F.C., G. Birol, and A. Cinar, "Glucose-Insulin Inter-
action: An Educational Tool," Proceedings of the World Con-
gress on Medical Physics and Biomedical Engineering, Chi-
cago, Illinois, July (2000)
3. Pehling, G., P. Tessari, J.E. Gerich, M.W. Haymond, F.J.
Service, and R.A. Rizza, "Abnormal Meal Carbohydrate Dis-
position in Insulin-Dependent Diabetes," J. Clinical Invest.,
74,985(1984)
4. Sorensen, J.T., "A Physiologic Model of Glucose Metabolism
in Man and Its Use to Design and Assess Improved Insulin
Therapies for Diabetes," PhD Thesis, MIT, Cambridge, MA
(1985)
5. Kizilel, S., R. Kizilel, G. Birol, I. Birol, and A. Cinar, "Glu-
cose-Insulin Interaction in a Healthy Human Body: Investi-
gation of Stimulating Different Metabolic Pathways of Liver,"
World Congress on Medical Physics and Biomedical Engi-
neering, Chicago, IL, July (2000)
6. Erzen, Fetanet Ceylan, Giilnur Birol, and Ali Cinar, "Simu-
lation Studies on the Dynamics of Diabetes Mellitus," Pro-
ceedings of the IEEE International Bioinformatics and Bio-
medical Engineering (BIBE) Symposium, Washington, DC,
November (2000)
7. Erzen, F.C., Giilnur Birol, and Ali Cinar, "An Educational
Simulation Package for Glucose-Insulin Interaction in Hu-
man Body," AIChE Annual Meeting, Los Angeles, CA, No-
vember (2000) O


Spring 2001










" laboratory


DEVELOPING THE BEST CORRELATION

FOR ESTIMATING THE TRANSFER

OF OXYGEN FROM AIR TO WATER


WAYNE A. BROWN
McGill University Montreal, Quebec, Canada H3A 2B2


he study of engineering is usually carried out in a
defined sequence. Students are first taught a set of
basic tools that includes, for example, mathematical
concepts and solution procedures along with the various
conservation laws. They then apply these concepts to el-
ementary problems associated with their chosen discipline.
In the final stages of the educational process, the simple
concepts are extended to allow the students to apply them to
multifaceted engineering problems.
Due to the complexity of systems of practical interest,
theory developed around simple systems cannot normally be
applied in the form derived. Often the theory is used to
identify the set of governing variables, and a relationship
between these variables is then established empirically. To
generalize these solutions over a number of experimental
conditions, variables are often gathered into dimensionless
groups. Although the number of independent dimensionless
groups is governed by Buckingham's "Pi" theorem,'I a num-
ber of useful groups have already been defined. These di-
mensionless groups represent ratios of competing effects,
expressed in terms of experimental variables. Thus, devel-
opment of an empirical relationship depends somewhat on
the experience of the engineer or researcher. If particular
effects are not identified as being important in the primary
analysis, then they cannot be reflected in the final solution.
It is imperative that students be taught the following re-
garding problem analysis:
There are many different design equations that can be
developed, depending on what assumptions are made.
These assumptions are choices and are left to the
judgment of the process engineer.
The engineer should always use the applicable set of
data to formulate a process design.


More than one approach to a given problem may lead
to a reasonable answer. The best approach is to
consider many different methods of achieving a
solution, but emphasis should be placed on the
solution achieved by using the set of data most
applicable to the problem at hand.
It is often not possible to verify the results of an
estimated parameter since a practical and accurate
alternative measurement method may not exist. Thus,
one may have to accept the results of an empirical
correlation.
We developed, and describe here, a laboratory exercise in
an attempt to convey some of the above messages. It is based
on the experimental determination of the overall mass-trans-
fer coefficient describing the transfer of oxygen to water in
an agitated tank.

OBJECTIVES OF THE LABORATORY
The objectives of the laboratory exercise were to
Analyze a problem involving the transfer of oxygen to water
and formulate a set of mathematical equations to adequately
describe the process
Fit the developed equations to experimental data to deter-

Wayne A. Brown has held the position of
Assistant Professor in the Department of
Chemical Engineering at McGill University
since 1999. Prior to that he worked for five
years in the oil sand industry, first as a pro-
cess engineer and then as a research scien-
tist. He received his formal training at McGill,
receiving his BEng (1989), MEng (1991), and
PhD (1998) from the Department of Chemical
Engineering.


Copyright ChE Division of ASEE 2001


Chemical Engineering Education











On a practical level, the lab deals with benign materials. As such, there are no fume hood
requirements or disposal problems. The lab can easily be extended to examine
the effect of other variables, such as temperature, oxygen
partial pressure, and liquid volume.


mine the mass-transfer coefficient
Study the influence of the measuring device on estimates of
the mass-transfer coefficient
Develop the semi-empirical equations first put forth by
Richards to estimate the mass-transfer coefficient
Compare experimental results with estimates obtained from
the Richards equation
"Tailor" the Richards relation so that it makes the most use
of the data collected

EQUATION DEVELOPMENT
Mass Transfer Coefficient from Experimental Data
The transfer of oxygen from a gas to a liquid phase can be
divided into a number of transfer resistances.t21 The set of
equations that describes the transfer of oxygen from a gas
phase to water in a batch system is dependent on the assump-
tions applied. Some of the issues to be considered are:
The change in concentration of oxygen in the air over the
residence time in the liquid phase
The transfer of inert components from the air, in addition to
oxygen
The composition of the particular gases used
The change in gas holdup with time
The mixing characteristics of the gas phase
The mixing characteristics of the liquid phase
The presence of additives in the liquid phase
The change in volumetric gas flow rate due to the transfer of
matter from the gas to liquid phases
The resistance to mass transfer across the gas-liquid
interface
The influence of surface aeration
The implications of various assumptions on the resulting
differential equations are discussed elsewhere.t3-91 For the
current experimental setup, the following assumptions are
assumed reasonable:
There is negligible change in oxygen concentration in the
gas phase.
The gas holdup stays constant with time.
The concentrations of oxygen in the gas and liquid phases
are in equilibrium at the gas-liquid interface.
The liquid is well mixed.
These assumptions lead to the following equations for the
gas and liquid phases:


dL KLa(C -CL) (1)

dCG
dC 0 (2)
dt
where KLa is the volumetric mass-transfer coefficient.
These equations can be integrated subject to the initial
conditions CL(O) = 0 and CG(0) = CG to yield

CL(t)= C -e-KLat) (3)

C G (t) = C (4)

The problem is further complicated when the measure-
ment method is considered in the analysis. One of the most
common and convenient methods for measuring dissolved
oxygen is through application of a dissolved oxygen elec-
trode. To make a measurement, oxygen dissolved in the
surrounding fluid must diffuse to the probe membrane, across
the membrane, and finally through the probe solution to the
active electrode tip. A number of approaches have been
applied successfully to model this process, such as Fick's
second law.'91 However, if the bulk solution in the tank is not
viscous, transport through the electrode membrane can be
treated as a first-order process, described by an equation of
the form

dC i (5)
dCt- (CL- C) (5)

Here, the diffusion through the probe solution is neglected.
Substituting Eq. (3) into Eq. (5) and integrating the result
subject to the initial condition

C(0) = 0 (6)
an expression relating the overall mass-transfer coefficient
to the probe output can be derived


C(t)=C + KLa ek
P CL+ k -KLa


k
p e-K at
k p a KL
p L" )


Using this equation, the overall liquid mass-transfer coef-
ficient can be determined directly from the probe output. To
determine the probe time constant, Eq. (5) is solved, subject
to the conditions given by Eq. (6) and Eq. (8):

CL (t)= CL (8)
In Eq. (8), C* is a constant for a given oxygen partial


Spring 2001










pressure and system temperature. Using Eqs. (6) and (8), Eq
(5) can be integrated to yield

C,(t)= C( 1-ekpt) (9)

Generalized Correlation of Oxygen-Transfer Data
The volumetric mass-transfer coefficient, KLa is a complex
function, dependent on the system geometry, the properties of
the liquid, and the process operating conditions. In terms of
basic variables, the function can be expressed as

KLa=
KLa(di,ni,hi,wi,li,dT,hL,nB,WB,pf,~f,of,Do2 ,N,vs,vt,g) (10)

In developing his correlation, Richards considered KL and "a"
separately. For geometrically similar vessels, dimensionless
groups related to geometry do not vary. In this particular
situation, the overall mass-transfer coefficient per unit trans-
fer area, KL, associated with the transfer of oxygen from a gas
phase to a Newtonian fluid is expected to be a function of the
variables

KL =fn(N,di,pf,tfDo2 (11)

From Buckingham's Pi theorem, three dimensionless groups
can be created. Thus, as suggested by Rushton,"'l the relation-
ship can be written

KLd Nd2pf ~ (12
D K 9 lD Pf (12)
D02 -y Do2 f

Here, K, is a constant that accounts for the geometry of the
particular system. For convective mass transfer between spheri-
cal particles and a liquid, a has been shown empirically to
have a value in the range of 0.4< a 0.6.1 In his derivation,
Richards used a value of a =0.5. Thus, for constant diffusivity
and fluid properties, and assuming that the gas consists of
spherical bubbles, Eq. (12) reduces to

KL = K2N05 (13)
Richards' development is completed by noting that the inter-
facial area for mass transfer is correlated adequately by
Calderbank's equation1I"


a= K3 (PG /VL 0PL (14)


As shown through the dimensional analysis performed by
Rushton, et al., PG is itself a function of a subset of the
variables introduced in Eq. (10).112] For the assumption of
constant fluid properties applied above, the Richards correla-
tion for the overall mass transfer coefficient is obtained by
multiplying Eqs. (13) and (14) to yield

KLa = K4(PG / VL)4V.5N0.5 (15)
Data from a number of different systems have been correlated


using the relation developed by Richards.[13,'41
In applying the Richards equation, data on the power
requirements of the gassed system are not always readily
available. Therefore, as part of the current development, it
is useful to express the correlation in terms of the more
commonly measured variables as they appear in Eq. (10).
Useful for this purpose is the empirical correlation put
forth by Michel, et al.,[ 15

(p2Nd3 )0.45
Pi = QO 5 (16)
PG K 5 Q 0 .5 6 ,

Note that this equation is not dimensionless, and thus care
should be taken when extrapolating outside the range in
which the data was collected. An estimate of the ungassed
power requirements can be obtained from the dimension-
less relationship based on the Rushton's power number.[121
For geometrically similar vessels, function is of the form

P (d Np diN2
Po- K6 = fn(Re, Fr) (17)
N3d p f (7)

The Froude number (Fr) is only important if a vortex is
formed. As most systems are baffled, the dependence of
the power number (Po) on Fr is usually not considered, and
Eq. (17) reduces to a function of Re only. This function is
often expressed graphically. Since the dimensionless groups


Nitrogen ---
M1 S1
Air Si
M2 S2

Figure 1. Experimental apparatus. Temperature (TI), pres-
sure (PI), gas flow rate (FI), and dissolved oxygen (DO),
were measured continuously. Only the signal from the
dissolved oxygen probe was sampled by the data acquisi-
tion board, however. Solenoid valves S1, S2, and S3 were
used to choose the source of the gas added to the fermen-
tor, while valve VI was used to adjust the flow rate.
Valve C1 was used to purge the Erlenmeyer flask with
nitrogen for determination of the probe time constant.
Details of the procedure can be found in the text.
Chemical Engineering Education


Speed
controller


To vent



------*
To data acquisition
(D/A) board










related to geometry have not been included, however, a
single curve for each impeller configuration is required.
Thus, using Eqs. (15) through (17), an estimate of the mass-
transfer coefficient can be obtained.

EXPERIMENTAL
Apparatus
A 4-L tank was used for all experiments (see Figure 1).
The vessel was 13 cm in diameter and had a height of 30 cm.
No baffles were installed. All experiments were performed
using 2 L of distilled water, resulting in a liquid depth of
approximately 15 cm. A flat-blade propeller was used that
was 6.5 cm in diameter from tip to tip. The propeller had 4
blades and was located 2 cm from the bottom of the vessel.
Air was introduced into the bottom of the tank through a
sparger that consisted of four equally spaced holes, directed
radially outward. The temperature was controlled by means
of a 300-W heater connected to a controller (Omega Model
BS5001J1). Dissolved oxygen was measured using a dis-
solved oxygen electrode (Ingold DL-531) in conjunction
with a digital meter equipped with an analog output (Cole-
Parmer Model 01971-00). Data from the meter was logged
on a personal computer by means of a data-acquisition board
and bundled data-acquisition software (LABTECH notebook
for Windows).
Experiments were run over a range of gas flowrates (2-4 L
min-1) and stirring speeds (100-1200 rev min'). Prior to each
set of experiments, the probe was calibrated using nitrogen
and oxygen saturated solutions of water. All experiments
were performed at 300C and at atmospheric pressure.
Determination of Probe Time Constant
The dissolved oxygen probe was placed into a flask of


Figure 2. Fit of Eq. (3) (dotted line) and Eq. (7) (thick solid
line) to experimental data (thin solid line). Experimental
data were generated at an air flowrate of 3 L min' and a
stirring speed of 1100 rev min1. In calculating Kza by Eq.
(3), only data between 30 and 98% saturation were consid-
ered, as described in the text.
Spring 2001


water that had been purged to saturation with nitrogen (see
Figure 1). After a reading of 0% had been established, the
probe was quickly immersed into the vessel containing 2 L
of water saturated with oxygen to 100%. Under these condi-
tions, the dynamics of the probe are described by Eqs. (5),
(6), and (8). To facilitate the determination of the probe
constant, a linearized form of Eq. (9)

( Cr
(n = kpt (18)

was used. From Eq. (18), a plot of en(C /i(c Cp) ver-
sus t should yield a straight line with a slope of kp. The slope
of the best-fit line was determined by linear regresion.
Determination of Ka
The vessel was first purged with nitrogen until the dis-
solved oxygen probe stabilized at a value of 0%. The purge
gas was then switched instantaneously to air through means
of a series of solenoid valves (see Figure 1). An estimate of
the mass-transfer coefficient was then obtained by fitting
Eq. (7) to the data collected. As the model function cannot
be linearized, a nonlinear regression algorithm was used to
extract the best estimate of KLa from each data set.

RESULTS AND DISCUSSION
As a preliminary exercise to the laboratory, students were
asked to develop the appropriate equations with which to
estimate KLa. It became apparent to the students during this
exercise that the set of equations generated depends on the
assumptions that were made with respect to specific aspects
of the problem. For instance, if it was assumed that the rate
of mass transfer from the gas to liquid is small compared to
the dynamic associated with the probe, then (1 / KLa) >> Ip,
and the effect of the probe is negligible. Under these circum-
stances, the rate of mass transfer can be calculated adequately
from Eq. (3); but if this is not the case, then the probe
dynamics must be taken into account.J61 Thus, a function
such as Eq. (7) is required.
The probe constant was calculated by each group of stu-
dents using a graphical approach. Typical values obtained
for Tp were between 14 and 17 s. From Eq. (5) the probe
output should attain a value of 63% saturation when t = Tp.
From the experimental data used to determine Tp, this con-
dition was verified (data not shown). Therefore, Eq. (5)
proved to be an adequate representation of the dynamics of
the probe.
Typical data obtained by the students for calculation of
KLa is shown in Figure 2. It has been shown that truncating
data collected early in the experiment can minimize the
effect of the probe on the estimate of KLa."71 Therefore,
under appropriate conditions, reasonable estimates of KLa
can be obtained from Eq. (3) and knowledge of the probe
dynamics is not required. Even when these conditions are










met, however, due to the exponential nature of Eq. (3) the
best estimates of KLa are obtained from Eq. (3) using data
collected at times on the order of the time constant, = 1/ KLa.
As such, it is recommended that data above 30% saturation
never be discarded. ~71
For the current exercise, when neglecting the effect of the
probe, only data between 30 and 98% saturation were con-
sidered when determining KLa using Eq. (3). When the probe
dynamics were considered, however, Eq. (7) was applied
and all of the data collected were used. Using the data shown
in Figure 2, Eq. (3) and Eq. (7) yield KLa estimates of 134 h-'
and 285 h', respectively. Therefore, serious errors result if
the probe dynamics are not considered. This is to be ex-
pected since the dynamics of the mass-transfer process and
the probe are on the same order for these data. Thus, the
concept that the measuring device is an integral part of a
process is reinforced.
From Figure 2 it is apparent that Eq. (7) adequately repre-
sents the data, where Eq. (3) does not. In addition, for two
first-order processes in series, the sum of the time constants
of each process should equal the time at which the overall
process achieves a value of 63%. For the data presented, a
value of 63% is achieved at approximately 30 s. The sum of
the time constants, +1 / KLa, is equal to 29 s. Therefore,
the assumptions that led to the development of Eq. (7) ap-
pear to be appropriate-other formulations could also fit the
data as well or possibly even better, however. For instance,
unsteady-state diffusion to the active element in the probe
could have been solved using the appropriate form of the
diffusion equation.71 The solution to this problem can then
be fit to the data to determine the probe time constant.
The range over which the dynamics of the probe can be
neglected was studied by comparing estimates of KLa ob-
tained using Eqs. (3) and (7) (see Figure 3). From this figure,
it can be seen that the two estimates deviate at relatively low
values of KLa. Quantitatively, it is apparent that the impact
of the probe becomes important when the probe time con-
stant is 20% of the time constant associated with the transfer
process, 1/KLa. This "rule of thumb" has also been suggested
by others.[171
The data generated by the students was then compared
with the Richards equation. This was accomplished by plot-
ting the KLa estimates obtained by the students on the same
axes as the data used to generate the relationship in the
original work by Richards (see Figure 4). When originally
presented, KLa was quoted in units of mML-'h'atm-.113] This
selection of units was most probably related to the sodium
sulphite oxidation method that was used to generate the data.
Data generated using this technique are often displayed as
H'KLa, where H' is Henry's constant."J8 To facilitate com-
parison with the data generated by the students, data used to
generate the original correlation were divided by Henry's
constant at 300C (see Figure 4). In the laboratory exercise,


axes complete with the data used by Richards were handed
out in printed form to each lab group. Thus, the comparison
exercise necessitated that the points be plotted by hand.
Therefore, the students were forced to critically examine the
deviation of the experimental values from the Richards equa-
tion. The data generated scatters within the bounds of the
original data sets. This scatter is rather large, however. For
instance, KLa values of between 75 and 250 h-' correspond to
a value of 300 on the abscissa. Thus, estimates by the corre-


500 2.0
0

E 400
S1.5
s o
300
S1-

200

S0.5
S100

0 0.0
0 100 200 300 400 500
KLa considering probe dynamics (hr')
Figure 3. Comparison of estimates of KLa obtained by
considering (Eq. 7) and neglecting (Eq. 3) the probe dy-
namics. Closed circles represent the KLa estimates, while
open circles represent the ratio of the probe time constant
to the time constant of the transfer process, where T= 1K La.
The solid line indicates a perfect correspondence between
the two estimates of KLa.

500
450
400
350
-300
-250 *
.
200 0
150 ** *
100
50 o "

0 100 200 300 400 500 600 700 800
(PGJVL)'04(Vs).'SNo
Figure 4. Assessment of the applicability of the Richards
equation to experimental apparatus. The ordinate has the
units indicated, while the abscissa has units of (HP/1000
L)o04(cm/min)O.5(RPM) 5. Black (Richards't13) and gray (Coo-
per "8]) circles represent the data originally used by Richards
to assess his correlation. Results were divided by Henry's
constant at 300C, as described in the text. The solid line
represents the best fit to these data, as suggested by
Richards. Open circles represent data generated as part of
the current laboratory exercise. The dotted line represents
the results of Eq. (19).

Chemical Engineering Education










lation are on the order of 50%. This finding is often diffi-
cult for many students to accept, as critical analysis of em-
pirical correlations on this level is new for them.
The correlation developed by Richards underestimates the
data generated by the students in almost all of the cases
(Figure 4). There are two plausible explanations for this
result. First, the original development of the correlation was
meant to apply to geometrically similar vessels."31 There-
fore, it is possible that the consistent offset from the Richards
correlation is related to geometric differences between the
systems used to generate the various data sets.
The Richards equation can be tuned for a specific geom-
etry as follows: For the experimental system at hand, only N
and Q are varied; furthermore, for Reynolds numbers associ-
ated with all stirring speeds, it can be shown that Po is
constant in Eq. (17).1141 Thus, Eqs. (15) through (17) can be
reduced to

KLa = K7N176Q0.4 (19)

This equation has one adjustable parameter (K7) that ac-
counts for geometry and the fluid properties of the system.
As a first step to improving the correlation, K, was deter-
mined using only the student data. The resulting equation
was plotted on Figure 4. Because only data specific to the
system under study was used, Eq. (19) is a better representa-
tion of the system used in the study, as is evident in the
superior fit.
A second plausible explanation to account for the differ-
ences noted between the Richards correlation and the experi-
mental data is related to surface effects. In its development,
the Richards correlation assumes that the tanks are well

450
-400
.350
E300
0
E250
i200
-150
5.100 o
v9, ^ oa
o50 e
0
0 50 100 150 200 250 300 350 400 450
Measured KLa (h1)

Figure 5. Ability of various correlation equations to fit the
experimental data. Black circles represent results of the
Richards correlation as originally presented (Eq. 15). Open
circles represent the Richards correlation tailored for the
geometry of the experimental system (Eq. 19). Grey circles
represent the equation resulting when surface effects are
considered through inclusion of the Froude number (Eq.
22).
Spring 2001


baffled.1"3 As a result, surface effects are negligible and no
dependence on the Froude number is expected. The Froude
number was also not considered in application of Eq. (17)
for the same reason. The experimental apparatus used by the
students had no baffles. Thus, a dependence of the KLa on the
Froude number is expected, especially for larger values of N.
To address this shortcoming in the original derivation, the
Richards correlation is further modified to account for pos-
sible surface effects. The Froude number is defined as

Fr-= diN2 (20)

The desired equation can be obtained from Eqs. (19) and
(20), and has the general form of

KLa K7 (di N2+1.76Q0.4 (21)

Although the value of X is not known, it is recognized that
Eq. (21) is also a function of N and Q only. The specific
value of X could be determined through regression using the
experimental data collected. In the resulting equation, the
exponent of N would be tailored to the data collected by the
students, while the functionality of Q would be dictated by
the data sets originally used by Richards. Therefore, a more
reasonable approach is to tailor all exponents to the experi-
mental data generated by the students. The result of this
exercise is the equation

KLa = K8N135Q0.60 (22)
The ability of this equation to capture the relevant features
of the experiment is readily seen in Figure 5. While the
Richards equation represents the data well, the best fit re-
sults when the equation is tailored to the experimental data
collected. Thus, while an adjusted correlation coefficient, r2,
of 0.81 is associated with the fit of Eq. (19), this value
increases to 0.98 when Eq. (22) is applied. This result may
seem obvious, as Eq. (22) has three adjustable parameters,
while it appears as if Eq. (19) has only one. In actuality,
however, both equations have three adjustable parameters.
The difference is that the exponents in Eq. (19) were ob-
tained from correlations fit using other sets of data, while
those in Eq. (22) were fit to the data obtained with the
current system only.
The difference among the three approaches becomes readily
apparent at this point. As the equations are further tailored to
the experimental data, the mathematical form better fits the
data. Thus, the spectrum of possibilities associated with
process design can be elucidated. When no data are avail-
able, the engineer must rely heavily on data generated from
dimensionally similar systems. This approach is only justi-
fied, however, in the absence of reliable data associated with
the system of interest. As data become available, the pre-
Continued on page 147.










curriculum


A PROJECT-BASED


SPIRAL CURRICULUM FOR


INTRODUCTORY COURSES IN ChE

Part 3. Evaluation


DAVID DIBIASIO, LISA COMPARINI,* ANTHONY G. DIXON, AND WILLIAM M. CLARK
Worcester Polytechnic Institute Worcester, MA 01609


his series reports on the development, delivery, and
assessment of a project-based spiral curriculum for
the first sequence of courses in chemical engineer-
ing. The program represents significant restructuring of the
introductory chemical engineering curriculum. Traditionally,
a compartmentalized course sequence designed to build a
conceptual foundation is taught during the sophomore and
junior years, followed later by more integrated projects. Our
new curriculum requires students to learn and apply chemi-
cal engineering principles by completing a series of open-
ended design projects starting during their sophomore year.
The new curriculum is spiral in that students' understanding
of basic concepts is reinforced by revisiting them in different
contexts with ever-increasing sophistication.
A more detailed explanation of the concepts, curriculum
design, and implementation behind this effort was described
in the first two part of this series.1'21 Part 1 described the
curriculum design, and Part 2 detailed the implementation.
In this paper we present the details of the assessment design,
describe the results of our assessment, and draw conclusions
about the success of the new curriculum.

BACKGROUND
The background describing the need for the new curricu-
lum, the published research upon which it was based, and the
philosophy behind our approach was presented in the first
paper of this series.111 In this section we summarize the
literature upon which our assessment plan was based.
An extensive array of literature exists regarding assess-
ment of student learning. An excellent bibliography is avail-
able from the Department of Education[31 and two good
resources are available from the National Science Founda-

* Current Address: School of Family Studies, University of
Connecticut, Storrs, CT 06269-2058


tion.14'51 There are also a number of references that outline
the details of assessment plans aimed at continuous im-
provement.'6-91 Most of the philosophy and techniques de-
scribed in those articles are adaptable to individual educa-
tional research and curriculum reform efforts.
Assessment tools are generally categorized according to
the types of methods and when they are applied during an
educational project. There are two broad classes describing
the timing of assessment. Formative assessment refers to
periodic data collection and evaluation prior to project
completion. It is used to improve the intervention during the
project and helps answer the question, "Is it working?"
Summative assessment concerns data collection and evalua-
tion at project completion. It is used to make conclusions
about project retention, alteration, or elimination and nor-
mally answers the question, "Did it work?"
There are two general classes of assessment types. Quanti-
David DiBiasio is Associate Professor of Chemical Engineering at WPI.
He received his BS, MS, and PhD degrees in chemical engineering from
Purdue University. His educational work focuses on active and cooperative
learning and educational assessment. His other research interests are in
biochemical engineering, specifically biological reactor analysis.
Lisa Comparini is a post-doctoral fellow in the Department of Family
Studies at the University of Connecticut. She received her PhD in Develop-
mental Psychology from Clark University where she focused on issues of
language, communication, culture, and development. While her primary
area of interest is in communicative practices within the family context, her
interest in issues of development and communication extend to other
interactive contexts, including the classroom.
Anthony G. Dixon is Professor of Chemical Engineering at WPI. He holds
a BSc degree in mathematics and a PhD degree in chemical engineering
from the University of Edinburgh. His research has included development
of interactive graphics software to aid in teaching process design and
mathematics to engineers.
William M. Clark is Associate Professor of Chemical Engineering at WPI.
He holds BS and PhD degrees in chemical engineering from Clemson
University and Rice University, respectively, and has thirteen years of
experience teaching thermodynamics, unit operations, and separation pro-
cesses. His educational research focuses on developing and evaluating
computer-aided learning tools.
Copyright ChE Division of ASEE 2001
Chemical Engineering Education










tative methods are those familiar to most engineers. They
include exams (standardized, course exams, comprehensive,
oral); surveys with statistical analysis (particularly pre/post);
database analysis; written reports (laboratory, design, or re-
search project); graded oral presentations; and graded port-
folios. These methods are generally perfor-
mance-based and measure what students can
actually do. Within a discipline-specific con- ThL
text, it is relatively easy to evaluate student
CUIT/
performance, but the design of the tool itself
may be problematic. These methods can be is
used to evaluate both team and individual per- in
formance. Performance-based tools (authentic stua
evaluation) were pioneered at Alverno Col- unler
lege.'110 O'Connert111 described a design-
competition approach to performance assess- f
ment, and Miller, et al.,[12' present a com- COi
prehensive assessment plan involving mul- is rei
tiple types of evaluations. by re
Qualitative methods typically involve analy- the
sis of text and visual information. They in- di~
clude videotaping, audiotaping, direct obser-
vation, portfolios, self-reports, open-ended sur-
veys, interviews, focus groups, performances,
and journals. Engineers have been somewhat iCnr
slow, however, in finding productive ways to SopAhi
adopt these methodologies that are used in de-
velopmental psychology and cognitive science.
Most of the methods involve qualitative analy-
sis that is unfamiliar to technologists. The main advan-
tage of methods such as videotaping is that they record
actual work-not student interpretations of what was
asked of them in a survey. By observing students doing
chemical engineering, we can probe how and why they
learn. This can yield rich information about the learning
process. Sometimes this information is quantified, but
usually the results are qualitative.
Marcus1131 summarized the main features of good and poor
assessment plans. The keys to a good assessment plan are:
use of both control groups and target groups to minimize
variation, including control for contaminating elements; mul-
tiple measurements using multiple tools; a mix of formative,
summative, quantitative, and qualitative tools; and use of an
external evaluator. Good plans define measurable objectives
and design the assessment methods directly from those ob-
jectives. They implement continuous feedback for improve-
ment, use pre- and post-measurements, and include longitu-
dinal studies when possible. The evaluation plan should
uncover program flaws as well as attributes.
Poor assessment plans overemphasize one set of outcomes
(for example, affective rather than cognitive) or one type of
measurement (all quantitative); vaguely define the perfor-
mance criteria; do not link data collection to the program;
Spring 2001


rely on traditional tests for nontraditional interventions;
and develop in-house instruments when validated ones
are available.[131
Because any single assessment method has advantages
and disadvantages, triangulation (the use of multiple mea-


e new
iculum
piral
that
dents'
standing.


Das.
DOS
Icep
nfoi
visi
am i
Fere
rtex
iev

teas
Sfica


surements) is a key to valid assessment. Evalua-
tion events that occur during and after the inter-
vention are also important. When multiple mea-
surements taken at different time points con-
verge on common results, one can confidently
draw conclusions about the observed process or
outcomes.

METHODS


iC Our assessment plan was designed to probe
ts student learning in basic chemical engineering
reed and students' ability to demonstrate learning in
i both team and individual contexts. We also ex-
ing amined attitudes, satisfaction, and confidence
In about chemical engineering. For longitudinal
nt data, we looked at individual student perfor-
mS mance in follow-on courses in the junior and
er-. senior years. Our overall plan combined forma-
tive and summative measures and employed both
Ing qualitative (interviews, open-ended question-
tion. naires, videotaping of student group work) and
quantitative (pre/post surveys, standard course
evaluation surveys, individual exams, and team
problem-solving competitions) tools. External consultants
were used extensively throughout the project.

Intervention and Comparison Cohorts
At the beginning of each implemention year we randomly
selected a cohort of incoming sophomores to participate in
the spiral curriculum. During the first implementation year,
this was about one-third of the class. In the second imple-
mentation year, half of the incoming class was randomly
selected. Selecting half in the second year meant we elimi-
nated class size as a variable in our analysis. Students not
selected were taught in the traditional fashion in a separate
section and represented our comparison cohort. Each year
we made minor adjustments (prior to the start of the aca-
demic year) to insure demographic similarity between the
intervention and comparison groups. We also examined
grades of each cohort in their first year at WPI. There were
no significant differences in first-year performance between
the two cohorts.
Since participation in the spiral curriculum was voluntary,
students could withdraw at any time during the academic
year and move into the comparison section. Only one stu-
dent did that during the two years of implementation. No
students were allowed to self-select into the experimental
section. In the following discussion we will refer to the










intervention group as the spiral-taught cohort and the tradi-
tionally taught students (the control group) as the compari-
son cohort. Spiral-taught thus refers to all the components of
the new curriculum, not simply just the spiral topic structure.
We did our best to control contaminating variables. Both
cohorts were taught essentially the same material, using the
same textbooks. Both cohorts met for the same number of
class periods each week and, as schedules allowed, during
the same class hour each day. When scheduling did not
allow the latter, we avoided vastly different meeting times.
For example, if the comparison group was scheduled at
11:00 a.m., we scheduled the spiral-taught section for close
to that hour and avoided times such as 8:00 a.m. or 4:30 p.m.

Problem-Solving Competitions: Team and Individual
Team At the end of each implementation year, we held a
team-based problem-solving competition. All sophomores
were invited to participate. Spiral-taught students were placed
in teams and comparison students were placed in separate
teams. Most students were teamed with others with whom
they had not previously worked. We constructed teams with
a mix of abilities (judged by grade records) and gender. All
participants were paid, and the winning teams from each
cohort were awarded additional prize money. This structure
meant that from the student standpoint, they were competing
only with peers (not comparison groups versus spiral groups).
The participation rate was 75% for the first year and 90% in
the second year.
Teams were given an open-ended chemical-process prob-
lem to solve and had two hours to develop their solution. The
problem involved a simple reaction/separation process for
the production of formaldehyde from the decomposition of
methanol. Students were given the reaction and the desired
production rate. They had to develop the process flowsheet,
make reactor and material-balance calculations, and choose
and design a separation scheme.
Each team selected one group member to present its solu-
tion. These ten-minute presentations were videotaped. The
presentation videotapes and written student work were sent
to three external experts in chemical engineering. Judges
were given the problem solution, some guidelines for rating
student work, and a form for reporting their analysis of each
team's solution. The judges ranked all teams from best-to-
worst on the basis of the technical work, not on the presenta-
tion quality. The highest ranked spiral team and the highest
ranked comparison team were each awarded prize money.
We were interested in the comparative rankings of spiral
versus comparison teams. Judges were volunteers from
academia and industry and had no knowledge of whether the
teams were spiral-taught or comparison teams. We also vid-
eotaped each team during its two-hour working sessions to
help us understand something about the process of solving
chemical engineering problems.


Individual At the end of the second implementation year
we held an individual exam competition. Students were given
an exam that tested four basic areas of chemical engineering.
The exam was open-book and was designed at about Bloom
levels 3-4: application and analysis. Again, all sophomores
were invited and paid to participate. The participation rate
was 61% of the total sophomore class. We offered the exam
to juniors to probe long-term retention of basic knowledge.
Only four participated, however, yielding too small a sample
to draw conclusions. We blind-graded each individual exam
using a numbering system that preserved student anonymity.
To promote conscientious participation, we offered more
cash to students scoring above 70% on the exam.
Questionnaires. Surveys, Interviews
We contracted developmental psychologists from the
Frances L. Hiatt School of Psychology at Clark University
for our external consultants. Kevin O'Connor and Lisa
Comparini were the consultants, with Comparini being with
us for most of the project. All questionnaires and surveys
were designed by the consultants, and all interviews (in
person or electronic) were conducted by Comparini. Both
O'Connor and Comparini were intimately involved in the
design of the competitions described above. Comparini con-
ducted the analysis of the questionnaires and surveys.

RESULTS
The results from the major assessment measures are sum-
marized below. In all cases, the results were positive regard-
ing the success of the spiral curriculum project. Assess-
ment design allowed us to probe program effects from a
variety of different views. The converging results clearly
demonstrate the superior educational benefits the new
curriculum provided.
Team Problem-Solving Competition
Spiral-taught student teams were judged signifi-
cantly higher than comparison teams in both
years of the team competition.
In the first year, all three judges ranked the spiral teams as
the top three of the six participating teams by a wide margin.
In the second year, spiral-taught teams were unanimously
ranked as the top two of eight total, and four of the top five
teams were spiral-taught groups. This clearly demonstrates
the ability of spiral-taught students to perform at higher
levels than comparison students on open-ended problems.
In general, the judges' comments indicated that spiral-
taught teams demonstrated better overall problem analysis
than comparison teams. A more global, systems-oriented
approach was taken by higher-ranked teams. Spiral-taught
teams also showed more progress in generating a flowsheet,
completing material balances, and handling equilibrium con-
version calculations. Poorer team solutions (primarily com-
parison groups) were characterized by incomplete flowsheets,
Chemical Engineering Education










trouble handling reaction products, and an inability to com-
pletely couple the reaction and separation portions of the
process. Very often, comparison teams focused too much on
one particular aspect and failed to demonstrate knowledge of
the "big picture."
This performance assessment was a major milestone in
our evaluation. Since one of our objectives was to improve
students' abilities to solve open-ended problems in team
situations, the results were very encouraging. Our evaluation
plan was not designed to probe individual effects. For ex-
ample, we did not run a section that had topic spiraling and
no cooperative learning. We strongly believe, however, that
repeated exposure to spiraled topics (a critical mechanism in
improving knowledge retention) coupled with substantive
team work is a major reason for the results.
Individual Exam Competition
Spiral-taught students performed better, as indi-
viduals, on basic chemical engineering prob-
lems.
We were not able to conduct this competition in the first
implementation year, but we did conduct it at the end of the
second implementation year. Twenty students participated,
ten from each cohort. The results are summarized in Table 1
and Figure 1. As a group, the spiral-taught students showed
better understanding of chemical engineering. The average
score was higher for spiral-taught students and more of them
scored above the 50% and 70% levels.
Figure 1 shows that spiral-taught students performed the
same or better than comparison students in three of the four
areas tested. Those four areas were material balances, classi-
cal thermodynamics, staged equilibrium separations, and so-


lution thermodynamics. A clear difference in learning mate-
rial balances was shown. Spiral-taught students were con-
tinuously using this material in different contexts throughout
the sophomore year. A similar difference, though not as
dramatic, was seen for classical thermodynamics. It is sig-
nificant that for the case of staged separations, the spiral-
taught students had been exposed to the specific material
tested (basic McCabe-Thiele calculations) several months
prior to the exam. The comparison students were enrolled in
the traditional course concerning this material at the time of
the exam. Spiral-taught students did not do as well on the
solution thermodynamics problem. This area was the most
difficult to build into the spiral curriculum and we recognize
that it is one area of the curriculum needing improvement.
A typical criticism of cooperative learning is that some
students will be carried by their group. The individual exam
results and the longitudinal data shown below serve to dis-
prove that notion in our case. Again, the combination of
topic spiraling, repeated exposure to open-ended problems,
and extensive group work was successful in improving indi-
vidual student learning.

Longitudinal Effects
Spiral-taught students received higher grades
than comparison students in follow-on junior-
and senior-level chemical engineering courses.
We tracked students throughout their academic programs
to understand how participation in the new curriculum corre-
lated with later performance. Examination of grades in our
unit operations laboratory showed that teams comprised of
two or more spiral-taught students generally received higher
report and oral presentation grades than teams comprised


Figure 1.
Average score of each
cohort on individual problems.
Maximum score per problem was
10 points.
Spring 2001


Material Bal. Classical Staged Sep. Solution
Thermo. Thermo.


solid = spiral-taught open = comparison


TABLE 1
Average Total Scores for Individual
Exam Competition
(Total possible points = 40)

Average # Scores # Scores
Cohort Score >50% >70%
Spiral-Taught 21.7 5 3
Comparison 18.8 3 2











Examination of grades in our unit operations
laboratory showed that teams comprised
of two or more spiral-taught students
generally received higher report
and oral presentation grades
than teams comprised mostly
of comparison students.

mostly of comparison students.
WPI's upper-level program is heavily project-based. It
makes sense that students experienced in project-based learn-
ing would show higher levels of performance in similar
academic activities as they became juniors and seniors. These
projects are similar to senior-level research (BS thesis)
projects done at other schools. The first cohort of spiral-
taught students graduated this year. Contaminating factors
such as mixing of students among spiral-taught and com-
parison cohorts and upper-level project grade inflation (80%
of these projects receive A's) made this analysis uninforma-
tive. Of the nine graduating seniors who received awards for
outstanding project work, however, five were from the spi-
ral-taught curriculum. For that class, only a third of the
graduates were in the spiral-taught cohort.
An alternative to probing project performance is to com-
pare grades of comparison and spiral-taught students in up-
per-level courses. These courses represent the core knowl-
edge of the discipline and include: fluid, heat, and mass
transport; kinetics and reactor design; two process design
courses; and two unit operations lab courses. A variety of
faculty members, course formats, and teaching methods are
used in this mix: large lecture, group work, laboratories, and
team-based capstone design. WPI awards only four letter
grades (A, B, C, and NR)-there is no D grade. The NR (No
Record) grade, typically covers the traditional D-F range
and is a failure grade that results in no course credit.
In all cases, spiral-taught students received a higher per-
centage of A's and a lower percentage of C's than compari-
son students. For the class of 2000, spiral-taught students
represented 33% of the class, yet they accounted for 40% of
the A's and only 22% of the C's, from a total of eight core
junior- and senior-level courses. For the class of 2001, spi-
ral-taught students represented 50% of the class and ac-
counted for 64% of the A's and only 29% of the C's, from a
total of five core junior- and senior-level courses. For both
cohorts over two years of data, a total of 35 failing grades
were earned in all courses examined. Only three of those
were from spiral-taught students, and the same student
earned all of them.
This data demonstrates the ability of spiral-taught students
to perform at higher levels despite different course formats
and variable teaching styles and standards in their upper-
level courses.


Attitudes About the Curriculum, the Discipline.
and the Faculty
Spiral-taught students showed more positive at-
titudes about chemical engineering and higher
confidence in the major than comparison stu-
dents.
Student course evaluations are required for all WPI courses.
A standard form is used that primarily examines student
satisfaction with the instructor. We examined the aggregate
responses from all sophomore-level chemical engineering
courses for sections taught by all instructors. There were no
significant differences between spiral instructors and other
faculty. In fact, the percent of positive student responses for
the spiral curriculum instructors, as a group, was equal to or
higher than that for instructors in the traditional sections
(i.e., those teaching the comparison cohort).
When the project started, we planned to implement pre/
post surveys during each year. During the first implementa-
tion year we observed that results from these surveys gave
little information, particularly for the time invested adminis-
tering them to each cohort. We also made a philosophical
decision that surveys with closed wording, forced-choice
responses, and fixed topics were not appropriate for our
project. We felt this type of evaluation tool, which restricts
students responses to predetermined questions, did not allow
us to probe a range of possible topics and responses from the
students' perspectives. Hence, we used open-ended ques-
tionnaires for the remainder of the project.
All sophomores were given a questionnaire at the end of
each implementation year. Students were asked about their


TABLE 2
Results from End-of-Year Questionnaire
[Number of students responding each year is in ()]


Spiral-Taught Comparison


97-98 98-99
(n=14) (n=15)


Positive comments
Number of topics

Negative comments
Number of topics


45 61
19 19


Confidence in choice of major


Positive change
Negative change
No change


12 12
0 1
0 2


97-98 98-99
(n=18) (n=ll)


Chemical Engineering Education










expectations for the year and whether or not they were met.
They were asked about their choice of major and their confi-
dence in pursuing chemical engineering. We asked what
were the 2 to 3 most-valuable and the 2 to 3 least-valuable
aspects of their sophomore-year classes. Additional ques-
tions included estimates of work effort, quality of teaching
assistants, and any general comments. A summary of the
content analysis of the results is shown in Table 2. We
should keep in mind that these responses were taken from a
fairly open-ended questionnaire. The numbers in a particu-
lar category do not necessarily represent responses to the
same questions. They represent relatively spontaneous num-
bers of mentioned topics, rather than responses to forced-
choice questions.
The overall results show that spiral-taught students were
more satisfied with their academic experience and more
confident with their choice of major than their peers in the
comparison section were. There were about twice as many
positive comments made by spiral-taught students on a
broader number of topics than by comparison students. The
positive comments included topics such as group work, lab
work, interaction with the professors, and the projects. Many
of the negative comments made by spiral-taught students
were about problems that they reported improved during the
year (such as "kinks" in early course organization and chang-
ing professors) and were generally not about the quality of
their overall learning experience.
Negative student comments were particularly revealing.
Spiral-taught students complained most about their high
workload and about the teaching assistants. The comparison
students' complaints were often stated in terms of a deficit
(not enough application, not enough material covered, not
enough group work, not enough projects, not enough indi-
vidual attention, not being in the spiral class) and were more
suggestive of a dissatisfaction with their overall experience.

Retention in CM
Spiral-taught students showed higher
retention rates in the major than did TA
comparison students. Retent
Sophomot
Retention is a key issue when new cur-
ricula are implemented. We are probably
similar to most departments in that the big-
gest loss of students from the major occurs Academic Year
and Section
during the sophomore year. Historically, our
retention rate is about 80%, meaning that 96-97
20% of the students enrolling in the first No separate secti
chemical engineering course leave the major 97-98
by the end of their sophomore year. Comparison
Spiral-taught
We found retention was higher during the
98-99
sophomore year for spiral-taught students 98-99C
Comparison
compared to the comparison cohort. Table 3 Spiral-taught
shows the retention data. Note that in 98-99,
Spring 2001


retention in the traditional courses was significantly lower
than normal while spiral student retention was maintained at
80%. We interviewed many of the students who left the
spiral curriculum and found that reasons were typically re-
lated to leaving engineering for one of the sciences (chemis-
try, biochemistry). An interesting anecdote is that one student
who left late in the year said she remained in the spiral curricu-
lum so long only because she liked it so much-eventually it
became clear that chemical engineering was not her preferred
discipline and she switched to civil engineering.

The Process of Learning Chemical Engineering
We are currently involved in a detailed analysis of the
problem-solving session videotapes taken during the team
competition. These are the two-hour tapes of each team that
were not used for judging team solutions. The tapes have all
been transcribed and are being analyzed using techniques
similar to Linde, et al., 41 to study the problem-solving pro-
cess in spiral-taught and comparison teams. Our methodol-
ogy for this analysis combines the expertise of a develop-
mental psychologist with that of a chemical engineer.[15
Preliminary results indicate that the spiral-taught teams
exhibited significantly different teamwork skills than did the
comparison teams. Since spiral-taught teams presented bet-
ter solutions, we are interested in characterizing their pro-
cess and connecting it to our curriculum design.
We observed that spiral-taught teams behaved more like
practicing chemical engineers attacking a problem, while
comparison teams behaved like students of chemical engi-
neering. We've observed significant differences in the use of
tools of the profession (authority figures, textbooks, pub-
lished data, etc.) that points to a model of teamwork some-
what different than the traditional engineering model. None
of the teams (comparison or spiral) exhibited any evidence
of team dysfunction due to typical problems such as domi-
nant individuals (either intellectually or personality-based),
gender bias, lack of participation, or lack of
motivation. Successful teams, as rated by
_E 3 external judges, had a greater ability to con-
)ata for struct a framework for solving the problem.
iE Students Unsuccessful teams struggled to do so, and
such teams were unable to move toward a
Total
Students framework even when individual members
cent at seemed capable of starting the process. We
ined Year End are currently articulating the theoretical ba-
sis for these observations and formulating
;0 62 an in-depth description of the model and its
relation to the new curriculum.
0 32 Areas Needing Imorovement


Despite the success of the curriculum as
described above, we are aware of three aeas
where improvement is needed. We attempted
to incorporate writing into the curriculum to


,BL
ion I
e Ch



Per
Reta


ons 8

8


88 14

68 17
80 16










exploit the writing-to-learn philosophy. But our efforts lacked
consistency, and due to time taken to deliver the new cur-
riculum, we could not implement all we had envisioned.
Although spiral-taught students had multiple writing oppor-
tunities, a concerted program to improve writing was not
possible. Some anecdotal evidence from upper-level writing
samples supports the notion that we did have some positive
impact on spiral-taught students' writing abilities.

We struggled with spiraling the concepts associated with
solution thermodynamics. This is some of the most difficult
material that sophomores encounter. In fact, many schools
do not teach it until the junior year. The optimal time and
location in the curriculum for introducing some of these
theoretical concepts is not known. We made improvements
from the first to the second implementation year, but our
sense is that more work is needed to sort out how students
may best understand these concepts.

The final project, for both implementation years, was a
significantly different and more complex project than any of
those earlier in the year. We asked students to design a
project that could be used in future course offerings. The
technical material involved some topics of chemical engi-
neering (transient material and energy balances) that are not
normally a part of the sophomore year. We believe that
students showed mastery of the technical material, but they
could not translate that knowledge sufficiently into the con-
text of the project. Hence they developed mediocre-to-poor
projects regardless of the team. There appears to be a general
intellectual limit to their ability to integrate concepts from
earlier in the year and extrapolate them to new situations.
We are currently examining that limit by analyzing our
evaluation data from those projects.

SUMMARY

We believe our assessment results clearly show the ben-
efits of all the educational activities implemented in the
spiral curriculum. In fact, we were quite surprised that dif-
ferences between spiral-taught and comparison cohorts were
so dramatic in so many different areas. Results from a vari-
ety of measurements and analysis converged upon a consis-
tent answer.

Compared to traditionally taught students, spiral-taught
students displayed equal or better understanding of basic
chemical engineering principles, were better in teams at
solving open-ended problems, had higher satisfaction levels
with their academic experience, had higher retention rates,
performed better in upper-level courses, and were more con-
fident about their choice of chemical engineering as a major.
Although our evaluation plan could not delineate effects of
individual curricular improvements, we believe that frequent
open-ended project experiences built around a spiral topic
structure were the major reasons for project success.


After extensive discussions, the WPI chemical engineer-
ing department voted to permanently adopt the curriculum
described in this series of three papers for all our sophomore
students beginning in the fall of 2001.

ACKNOWLEDGMENTS
The authors would like to thank the Department of Educa-
tion for support of this work under the Fund for the Improve-
ment of Post-Secondary Education (FIPSE), Award No.
P116B60511.

REFERENCES
1. Clark, W.M., D. DiBiasio, and A.G. Dixon, "A Project-Based,
Spiral Curriculum for Introductory Courses in Chemical
Engineering: 1. Curriculum Design," Chem. Eng. Ed., 34(3),
222 (2000)
2. Dixon, A.G., W.M. Clark, and D. DiBiasio, "A Project-Based,
Spiral Curriculum for Introductory Courses in Chemical
Engineering: 2. Implementation," Chem. Eng. Ed., 34(4),
296 (2000)
3. Marcus, D., "Notes on Evaluation Design," Fund for the
Improvement of Postsecondary Education, Department of
Education, web site, accessed August, 1996, at
http://www.ed.gov/offices/OPE/FIPSE/biblio.html
updated January 9, (1998)
4. Frechtling, J., editor, User-Friendly Handbook for Project
Evaluation, National Science Foundation, NSF 93-152 (1996)
5. Frechtling, J., L.S. Westat, eds., User-Friendly Handbook
for Mixed Method Evaluations, National Science Founda-
tion, NSF 97-153 (1997)
6. Olds, B.M., and R.L. Miller, "A Measure of Success," ASEE
Prism, p. 24., December (1997)
7. Rogers, G., "EC2000 and Measurement: How Much Preci-
sion is Enough?" J. Eng. Ed., 89(2), 161 (2000)
8. DiBiasio, D., "Outcomes Assessment: An Unstable Process?"
Chem. Eng. Ed., 33(2), 116 (1999)
9. Rogers, G., "Outcomes Assessment: Opportunity on the
Wings of Danger," Chem. Eng. Ed., 33(2), 106 (1999)
10. Mentkowski, M., and G. Loacker, "Assessing and Validating
the Outcomes of College," in Assessing Educational Out-
comes: New Directions for Institutional Research, Jossey-
Bass (1985)
11. O'Connor, K., "Overcoming Obstacles to Boundary Crossing
in Multi-Institution Product Realization Projects," proceed-
ings of the Technology Reinvestment Project Grantees Con-
ference, NSF (1997)
12. Miller, J., D. DiBiasio, J. Minasian, and J. Catterall, "More
Students Learning, Less Faculty Work?-The WPI Davis
Experiment in Educational Quality and Productivity," in
Student Assisted Teaching and Learning: Strategies, Mod-
els, and Outcomes," M. Miller, J. Groccia, and J. Miller,
Anker Publishing (2001)
13. Marcus, D., "Evaluation for Second and Third Year and
Beyond," Annual FIPSE Project Director's Meeting, Wash-
ington, D.C., October (1997)
14. Linde, C., J. Roschelle, and R. Stevens, "Innovative Assess-
ment for Innovative Engineering Education: Video-Based
Interaction Analysis," Report to the NSF Synthesis Coali-
tion, Institute for Research on Learning, Palo Alto, CA
(1994)
15. Clark, W., L. Comparini, D. DiBiasio, and A. Dixon, "The
Process of Learning Chemical Engineering: What Works
and What Doesn't," ASEE meeting, St. Louis, MO, June
(2000) 0
Chemical Engineering Education











Estimating the Transfer of Oxygen
Continued from page 139.

ferred approach is to tailor the functional form derived from
existing correlations in an attempt to maximize the use of the
specific information available.
The laboratory exercise also has secondary benefits. First,
the exercise bridges the gap between biotechnology and
classical chemical engineering. Students are often under the
impression that the area of biotechnology represents a radi-
cal departure from the chemical engineering principles ap-
plied to other industries. This laboratory serves to demon-
strate that the "high tech" fields have been developed on the
same set of principles as the mature industries. On a practi-
cal level, the lab deals with benign materials. As such, there
are no fume hood requirements or disposal problems. The
lab can easily be extended to examine the effect of other
variables, such as temperature, oxygen partial pressure, and
liquid volume.

CONCLUSIONS
When faced with a design problem, the chemical engineer
often must turn to empirical expressions, generalized through
the application of dimensionless groups. But as data become
available that are specific to the system of interest, the basic
proven empirical expression should be tailored to reflect
these data. Extracting the relevant parameters of interest
(i.e., KLa) from experimental data generated for this purpose
is subjective, based heavily on the assumptions made by the
engineer. Although many approaches may be adequate, oth-
ers may lead to erroneous results. A key variable to consider
when analyzing the problem is the influence of the measur-
ing element on the resulting data set.

NOMENCLATURE
a area available for mass transfer per unit volume of
ungassed liquid (m2m3)
CG concentration of oxygen in the gas phase (mol L-')
C concentration of oxygen in the gas phase at t=0 (mol L ')
CL concentration of oxygen in the liquid (mol L-')
CL concentration of oxygen in the liquid in equilibrium with
the gas phase (mol L-')
C concentration of oxygen in the liquid, as measured by the
dissolved oxygen probe (mol L-')
d. impeller diameter (m)
dT tank diameter (m)
Do2 diffusivity of oxygen in water (m2s-')
g acceleration of gravity (m s 2)
h height of impeller from bottom of tank (m)
hL height of liquid (m)
1i length of impeller blades (m)
H' Henry's constant for oxygen and water (mmol L atm-')
K empirical constant
K overall mass-transfer coefficient per unit transfer area,
Spring 2001


based on the liquid phase (m s')
KLa volumetric mass-transfer coefficient, based on the liquid
volume (hr-')
k (I / p)(-1)
n number of baffles
n number of blades on impeller
N stirring speed (rev s-')
P power input into ungassed liquid (W)
PG power input into gassed liquid (W)
vs superficial gas velocity, based on cross section of vessel
(m s-')
v, terminal rise velocity of a gas bubble (m s-')
w width of baffles (m)
w, width of impeller blades (m)
Q gas flow rate (L s')
t time (s)
Greek symbols
a, P, y, X exponents in Eqs. (12), (17), and (21)
Tp time constant of the dissolved oxygen probe (s)
T time constant of the transfer process (l/KLa)(s)
lf liquid viscosity (cp)
pf liquid density (kg m 3)
of surface tension at gas-liquid interface (mN m ')

REFERENCES
1. Geankoplis, C.J., Transport Processes and Unit Operations,
Prentice-Hall, Inc., NJ (1993)
2. Bailey, J.E., and D.F. Ollis, Biochemical Engineering Fun-
damentals, 2nd ed., McGraw-Hill, Inc., New York, NY (1986)
3. Linek, V., J. Sinkule, and P. Benes, Biotechnol. Bioeng., 38,
323(1990)
4. Linek, V., V. Vacek, and P. Benes, Chem. Eng. J., 34, 11
(1987)
5. Benedek, A., and W.J. Heideger, Biotechnol. Bioeng., 13,
663 (1971)
6. Sheppard, J.D., and D.G. Cooper, J. Chem. Tech. Biotechnol.,
48,325 (1990)
7. Ruchti, G., I.J. Dunn, and J.R. Bourne, Biotechnol. Bioeng.,
23,277 (1981)
8. Chang, H.N., B. Halard, and M. Moo-Young, Biotechnol.
Bioeng., 34, 1147 (1991)
9. Wernau, W.C., and C.R. Wilke, Biotechnol. Bioeng., 25, 571
(1973)
10. Rushton, J.H., Chem. Eng. Prog., 47, 485 (1951)
11. Calderbank, P.H., Trans. Instn. Chem. Engrs., London, 36,
443(1958)
12. Rushton, J.H., E.W. Costich, and H.J. Everett, Chem. Eng.
Prog., 26, 395 (1950)
13. Richards, J.W., Prog. Ind. Microbiol. 3, 143 (1961)
14. Kargi, F., and M. Moo-Young, in Vol 2 of The Principles of
Biotechnology, Engineering Considerations, C.O. Cooney and
A.E. Humphrey, eds; in Comprehensive Biotechnology: The
Principles Applications and Regulations ofBiotechnology in
Industry, Agriculture and Medicine, M. Moo-Young, ed.,
Pergamon Press, New York, NY
15. Michel, B.J., and S.A. Miller, AIChE J., 262 (1962)
16. Tribe, L.A., C.L. Briens, and A. Margaritis, Biotechnol.
Bioeng., 46, 388 (1994)
17. Merchuk, J.C., S. Yona, M.H. Siegel, and A.B. Zvi, Biotechnol.
Bioeng., 35, 1161 (1990)
18. Cooper, C.M., G.A. Fernstrom, and S.A. Miller, Ind. Eng.
Chem., 36, 504 (1944) a










" classroom


UNDERGRADUATE

PROCESS CONTROL

Clarification of Some Concepts


R. RAVI*
Indian Institute of Technology Kanpur Kanpur 208 016, India


Teaching undergraduate process control can be an en-
joyable experience for an instructor given the wide
range of quality chemical engineering textbooks that
are now available.[1-6 After teaching the course a couple of
times, however, I felt there was still a need for clarification
of some fundamental concepts, especially in the areas of
frequency response and stability. In this article I hope to
achieve such a clarification through some simple, yet illus-
trative, examples.

FREQUENCY RESPONSE:
ONLY FOR STABLE SYSTEMS?
In the context of process control, the frequency response is
usually associated with the response of a linear, time invari-
ant (constant coefficient) system to a sinusoidal input. In the
most common way of "deriving" the frequency response
result, the output response is shown to be a sinusoidal func-
tion of the same frequency (c) as the input, once the tran-
sients have died out. Further, the ratio of the amplitude of the
output to that of the input, called the amplitude ratio (AR), is
shown to be equal to IG(j(o)], while the phase difference (p)
between the output and the input is shown to be arg[G(jo)],
where G(s) is the transfer function representation of the
system of interest and j=Y-1.
Thus, the frequency response calculation is reduced to the
calculation of the magnitude and phase of the complex num-
ber, G(jo), as a function of the frequency. This information
is usually represented in the form of a Bode diagram or a
Nyquist plot.
The key point of our discussion is the condition
"once the transients have died out."
Clearly, this happens if the system is stable, i.e., if all the
poles of the transfer function G(s) lie in the left half (of the
* Present address: Indian Institute of Technology Madras,
Madras 600028, India
148


complex) plane (LHP). Thus it might appear that frequency
response makes sense only for stable systems. But we do
find Bode diagrams and Nyquist plots for the pure capacity
(G(s)=A/s) and the PI controller, G(s)= [Kc(rls+ l)]/Tls, both
of which are (open-loop) unstable.
Do these diagrams mean anything then? In the case of the
pure capacity system, one can show that the response to a
sinusoidal input is bounded and is a superposition of a con-
stant and a sinusoidal function whose amplitude and phase
are in fact provided by G(jco), as for a stable system. (It
should be noted that a system with a zero pole is to be
regarded as unstable in spite of a bounded response to a
sinusoidal input. Recall that the step response of such a
system grows with time.)
But what about a system with a pole in the right half plane
(RHP) for which the response to a (bounded) sinusoidal
input will have a time-growing component arising out of the
unstable pole? Does the Bode diagram (or the Nyquist plot)
for such a system obtained from the corresponding G(jw)
have any meaning?
The answer to the last question is "yes."
The common way of deriving the frequency response re-
sult is only a method of measuring the frequency response
for stable systems and does not constitute a fundamental

R. Ravi obtained his BTech from the Indian
Institute of Technology, Madras, in 1984,
and his PhD from Purdue University in 1991.
His research interests are in applied statis-
tical mechanics and process control. For
the past few years, his abiding passion has
been the understanding of the origins of
thermodynamics and fluid mechanics.




Copyright ChE Division of ASEE 2001
Chemical Engineering Education










definition of it. The fundamental definition is provided by a
basic result of linear systems theory.[7] There exists a peri-
odic solution for a linear time invariant system subjected to a
periodic forcing; this periodic solution has the same fre-
quency as that of the input forcing, and its amplitude and
phase at the particular frequency are determined (as ex-
plained above) from the complex number G(jw). This result
holds whether the system is stable or not.
In general, the response of a linear system to a periodic
forcing will be the superposition of the periodic solution and
a non-periodic component, and the frequency response is
defined with respect to the periodic component. Thus, the
Bode diagram for an unstable system makes sense in that it
represents the same relationship between the periodic com-
ponent of the (output) response and the input periodic forc-
ing as it does for a stable system.
This point is not of minor significance as it gives universal
status to Bode diagrams or Nyquist plots as signatures of
systems they represent, be they stable or unstable. The open-
loop method of measuring the frequency response (after
waiting for the transient to die out) will not work for un-
stable systems (pure capacity being an exception).
In the next section, we point out two possible methods of
measuring the frequency response of unstable systems-one
an open-loop method and the other a closed-loop method.
Although both methods are valid in principle, the latter is
more practicable. The reasons are outlined below.



Frequency Response of Unstable Systems


We illustrate the procedures through a simple system with
one unstable pole

Go(s)= (1)
(s a)

Open-Loop Method
For the Open-Loop Method we consider a sinusoidal input
u(t)= Au sin(o)t+ (u) (2)
The response of the system to this input can be shown (for
instance, by a straightforward Laplace inversion) to be


After teaching [undergraduate
process control] a couple of times, I
felt there was a need for clarification of
some fundamental concepts, especially
in the areas of frequency response and
stability. In this article I hope to
achieve such a clarification
through some simple, yet
illustrative, examples.



KAu(cocos ~u +asin u)eat
y(t) =
a2 +02

+A IGo(jco)lsin{cot+pu +arg[Go(j(o)]} (3)

This suggests a way of "stabilizing" the response by choos-
ing 0u such that
) cos u +asin Ou =0 (4)
so that only the stable periodic component of the solution
remains, enabling the determination of its amplitude and
phase. In practice, thus, one is left to choose a unique value
of ou (between 0 and 27) for each o; this can be problem-
atic given that the value of the unstable pole, a, is not known
a priori. Hence, we discuss a more practicable method in-
volving closed-loop stabilization.

Closed-Loop Method
We consider the same first-order unstable system. It is
easy to show that the system can be stabilized in a feedback
loop using a proportional controller of gain Kc greater than
a/K (Figure 1 illustrates the scheme). In fact

y(s)_ KcK CL() (5)
r(s) s+ CL) (
where b=KK-a > 0.
If a sinusoidal variation is given in the reference signal, r,


r(t)= Ar sin Ct (6'
e can show that (by Laplace inversion, for instance)


Figure 1.
An open-loop unstable system
in a feedback loop with a
proportional controller.


Spring 2001










y(t)= Cie-bt + Ay sin (wt + Oy)


where


K KA ro
C = r; ; Ay=Ar'GCL(jo);' y=arg[GCL(jc)] (8)

The signal u(t) = K,[r(t)-y(t)] can be expressed as
u(t)= -KcCle-bt + Au sin (ot +( u) (9)
It is possible to show that
A
A -= Go(jo)l and y -4u =arg([Go(jc)]) (10)

i.e., the amplitudes and the phases of the "input" and the
"output" signals of the unstable system, Go(s), are related as
before by the complex number Go(jw). The stabilization
effect is noted in the e-b term (note: b > 0) in both y and u in
contrast to the open-loop case where we get the time-grow-
ing term, e", in the output (for the same input Ar sin ot). For
concreteness and simplicity, we illustrate the above result
with a numerical example.181 We choose

Go(2s) (11)

It is easy to see that a unity gain (Kc = 1) proportional
controller stabilizes the above system in a feedback loop. In
fact

y(s) 2 (12
r(s) s+l ()
If we choose the input to be
r(t)= 0.5 sin 2t (13)
then we can show that

y(t)= e- +(0.2)12 sin [2t -1.1 (rad)] (14)

Further

u(t)= r(t)-y(t) = e-t +0.5 sin [2t+0.93(rad)] (15)

and

IGo(2j)=- and arg[Go(2j)]= -2.04 rad (16)

Thus, we see that
A
IGo(2j) = and arg[Go(2j)] = y -(u (17)

Of course, the above analysis is based on a given system
transfer function. This is not known a priori and, in fact, the
purpose of the frequency response experiment is to deter-
mine the transfer function. But what one has to do is to tune
the proportional controller to obtain a stable system. Then,
for a known sinusoidal input, r(t), at various frequencies,
one would have to measure the amplitude and phase of both


(7) u(t) and y(t) (after the transients die out) to construct the
transfer function, Go(s).


FREQUENCY RESPONSE
AND STABILITY CRITERIA


We now turn to another aspect of frequency response and
stability, the famous Nyquist stability criterion. The Nyquist
criterion helps one to infer the stability of a feedback control
system from the Nyquist (polar) plot of the loop transfer
function, GL(s), which is the product of the transfer functions
of all the elements in the control loop. The advantage of
stability criteria based on frequency response is their ability
to deal with non-polynomial G,(s) that the Routh-Hurwitz
criteria cannot treat rigorously. This advantage is particu-
larly relevant to chemical engineering systems that often
contain a time-delay element.
Most chemical engineering textbooks on process control
do not give as much prominence to the Nyquist criterion as
they do to the Bode stability criterion, which is easier to use.
An exception is the Luyben1[2 book where a detailed discus-
sion with illustrative examples can be found. It is to be noted
that the Bode criterion is not general and specifically cannot
be applied in cases where the Bode diagram for G,(s) is not
monotonically decreasing. It is our objective here to high-
light the potential sources of error in the application of the
Nyquist criterion. It is not uncommon to find special state-
ments of the criterion that might work in many cases but
fail to yield the correct result for at least some systems.
Often, these special statements are not accompanied by
the conditions under which they hold. Thus it is desirable
to always use the general form of the criterion that is
given below.
Let N be the number of net rotations of the Nyquist plot of
G,(s) (-mo< << o) about the point (-1,0). This is the net angle
traced out by the line segment from (-1,0) to the Nyquist plot
as the frequency changes from -- to -. The sign convention
is a positive value for N if the net rotation is in the counter-
clockwise direction and negative if it is in the clockwise
direction. Let PR be the number of poles of l+GL(S) (note that
this is the same as the number of poles of GL(S)) in the RHP.
Then
ZR =PR-N (18)
where ZR is the number of zeros of 1+G,(s) in the RHP.
Hence, ZR is the number of roots of the characteristic equa-
tion l+GL(s)=0 that lie in the RHP. Clearly, ZR must be zero
for a stable system.
It is not our objective here to give a proof of the above
statement (see, for instance, Ref. 9), but we illustrate its
proper use through a simple example. In our opinion, the
following points are crucial:
- While the portion of the Nyquist plot from -- to 0 is


Chemical Engineering Education













(a)
0.4 Im Figure 2.
0.2 Nyquist plots for
r a)
0.0
(-1,0) Re GLI(S)= 2( 1)
-0.2 2(s-1)
and
-0.41
-1.5 -1.0 -0.5 0.0 0.5 b)
GL2(S) =
(s- 1)
The dotted (---)
portion is for
(b)
2.0 < (0 < 0
Im while the solid (--)
1.0 ,-4 ., portion is for
S 0< 0)< o <.
0 \ (-1,0) Re The direction of
-o1.0 the arrow is in the
direction of
-2.0 increasing o.
-30 -20 -1.0 0.0 1.0 increasing 0.




simply the mirror image (about the real axis) of the
portion from 0 to -, not using the full plot can lead to
erroneous conclusions.
The precise meaning of the commonly used notion of
"encirclement" about the (-1,0) point must be under-
stood. It is not uncommon1691 to have cases where the
(-1,0) point is entirely within Nyquist plot and hence
appears "encircled," but the net encirclement is, in
fact, zero. Further, the direction of encirclement is
crucial. Encirclement in itself does not necessarily
mean that the closed-loop system is unstable.
1 The number of RHP poles of GL(S) must be known.
We demonstrate the above points by choosing a simple
system-the same one we chose in the previous section

Go(s)= 2 (19)

in a feedback loop with a proportional controller of gain
Kc=1/4 and K2=l It is easy to see that the first control system
is unstable, while the second is stable, by considering the
characteristic equations I+GL](s)=O and I+GL2(s)=0, respec-
tively. But our objective here is in the application of the
Nyquist criterion.
Figure 2a shows the Nyquist plot of

2Kci 1
GL1(S)= s-1 2(s-1) (20)

The figure clearly shows that N=0 as the net angle traced out

Spring 2001


by the full Nyquist plot (with reference to the (-1,0) point) is
zero. Since PR=I, we get

ZR =PR-N=I-0=I (21)
Thus the closed-loop system is unstable with one root of the
characteristic equation in the RHP. Note here that even
though the Nyquist plot does not encircle the (-1,0) point, the
closed-loop system is unstable.
Figure 2b shows the Nyquist plot for

GL2(S) 2 -Kc s2- (22)

Here the Nyquist plot encircles (-1,0) once. Note that the net
angle traced is 27r, but this is in the counterclockwise direc-
tion, implying that N=l. Again, since PR=1, we obtain

ZR = PR -N =0 (23)
Thus the closed-loop system is stable, even though the Nyquist
plot encircles the (-1,0) point. Note further that if we restrict
ourselves to the 0 to segment, we will not see any encircle-
ment.
Thus, we have highlighted the aspects we set out to illus-
trate-the importance of considering the entire frequency
range (-- to -), the importance of the direction of encircle-
ment, and the necessity of knowing the number of unstable
poles of GL(S).

CONCLUSIONS
We have clarified the concept of frequency response for
linear time-invariant systems, demonstrating its validity for
unstable systems as well. We have also highlighted some
pitfalls in the use of the Nyquist criterion and pointed out
how to avoid them.

REFERENCES
1. Coughanowr, D.R., Process Systems Analysis and Control,
McGraw-Hill Book Company, New York, NY (1991)
2. Luyben, W.L., Process Modeling, Simulation, and Control
for Chemical Engineers, McGraw-Hill Book Company, New
York, NY (1990)
3. Marlin, T.E., Process Control: Designing Processes and Con-
trol Systems for Dynamic Performance, McGraw-Hill Book
Company, New York, NY (1995)
4. Ogunnaike, B.A., and W.H. Ray, Process Dynamics, Model-
ling, and Control, Oxford University Press, New York, NY
(1994)
5. Seborg, D.E., T.F. Edgar, and D.A. Mellichamp, Process
Dynamics and Control, John Wiley & Sons Inc., New York,
NY (1989)
6. Stephanopoulos, G., Chemical Process Control, Prentice-
Hall, Englewood Cliffs, NJ (1984)
7. Brockett, R.W., Finite Dimensional Linear Systems, John
Wiley & Sons, Inc., New York, NY (1970)
8. Wolovich, W.A., Automatic Control Systems: Basic Analysis
and Design, Harcourt Brace (1994)
9. D'Azzo, J.J., and C.H. Houpis, Feedback Control System
Analysis and Synthesis, McGraw Hill Book Company, New
York, NY (1966) 3










Bj, curriculum


THE INTERFACE BETWEEN

ChE AND MATHEMATICS

What Do Students Really Need?


MICHAEL D. GRAHAM
University of Wisconsin-Madison Madison, WI 53706-1691
SUSAN L. GANTER
Clemson University Clemson, South Carolina


he Mathematical Association of America (MAA),
through its Committee on the Undergraduate Pro-
gram in Mathematics (CUPM), is conducting a Cur-
riculum Foundations Project, a major analysis of the under-
graduate mathematics curriculum. The goal of the project is
to develop a curriculum document that will assist college
mathematics departments as they plan their programs for the
next decade. Historically, CUPM curriculum recommenda-
tions have had a significant influence on the design of
undergraduate mathematics programs. These important
and influential guidelines were last revised in 1981. There-
fore, the CUPM curriculum guidelines need to be recon-
sidered; such a review and the resulting recommenda-
tions are likely to have widespread impact on the teach-
ing of undergraduate mathematics.
Given the impact of mathematics instruction on engineer-
ing, the sciences, and the quantitative social sciences (espe-
cially instruction during the first two years), significant in-
put from these partner disciplines is needed to inform the
MAA curriculum document. The CUPM subcommittee
on Calculus Reform and the First Two Years (CRAFTY)
gathered much of this necessary information between
Fall 1999 and Spring 2001 through a series of invita-
tional disciplinary workshops funded and hosted by a
wide variety of institutions (see Table 1).
Each workshop is focused on a particular partner disci-
pline or on a group of related disciplines, the objective being
a clear, concise statement of what students in that area need
to learn in their first two years of college mathematics. The
workshops are not intended to be dialogues between math-
ematics and the partner disciplines, but rather a dialogue
among representatives of the discipline under consideration,


with mathematicians there only to listen to the discussions
and to provide clarification on questions about the math-
ematics curriculum. For this reason, almost all of the indi-
viduals invited to participate in each workshop are from the
partner disciplines.
The major product of each workshop is a report or group
of reports summarizing the recommendations and conclu-
sions of the workshop. These are written by the representa-
tives from the partner disciplines, with the mathematics
community as the primary audience, and they address a
series of questions formulated by CRAFTY (see Table 2).
Uniformity of style is achieved across the reports by using
the same basic questions for each workshop. Having a com-
mon list of questions also aids in comparing the reports of
different workshops. The questions are simply designed to
guide the workshop discussions, however, and therefore are

Mike Graham received his BS from the Univer-
sity of Dayton in 1986 and his PhD from Cornell
University in 1992, both in chemical engineer-
ing, and did postdoctoral work at the University
of Houston and Princeton University. His re-
search interests encompass instabilities and
nonlinear dynamics in flows of complex fluids,
molecular and multiscale simulation of polymeric
liquids, and interfacial and multiphase flows.


Susan L. Ganter is Associate Professor of Math-
S ematical Sciences at Clemson University. She
Shas directed several local and national evalua-
tion studies, including a recent residency at the
National Science Foundation in which she inves-
tigated the national impact of the calculus reform
S initiative and helped to develop the evaluation
plan for the Institution-wide Reform Program in
the Division of Undergraduate Education.


Copyright ChE Division of ASEE 2001


Chemical Engineering Education











intentionally vague. In addition, workshop participants are
asked to focus primarily on the first question category, "Un-
derstanding and Contents," with the other questions being of
secondary importance.
The reports from each workshop are then widely circu-
lated within the specific disciplines, as well as in the math-
ematics community, in order to solicit a broad range of
comments. At the completion of this process in the spring of
2001, the reports will be published and used in the formula-
tion of the MAA curriculum document. A curriculum con-
ference that includes invitees from all disciplines will be
convened in Fall 2001 to synthesize the workshop findings
and begin writing the MAA curriculum document, sched-
uled to be published in 2002.
In addition to providing input into the larger CUPM re-
view, the reports serve as valuable resources for initiating
discussions at individual institutions between mathematics
departments and partner disciplines. Some mathematics de-
partments have already begun using the reports to stimulate


TABLE 1
MAA Curriculum Foundations Workshops

Physics and Computer Science
Bowdoin College Maine Oct. 28-31, 1999
William Barker: barker@bowdoin.edu
Interdisciplinary (Math, Physics, Engineering)
USMA West Point Nov. 4-7, 1999
Don Small: ad5712@usma.edu
Engineering
Clemson University South Carolina May 4-7, 2000
Susan Ganter: sganter@clemson.edu
Health-Related Life Sciences
Virginia Commonwealth University May 18-20. 2000
William Haver: whaver@atlas.vcu.edu
Technical Mathematics (at two sites)
Los Angeles Pierce College California Oct. 5-8, 2000
Bruce Yoshiwara: byoshiwara@hotmail.com
J. Sargeant Reynolds Community Col. Virginia Oct. 12-15, 2000
Susan Wood: swood@jsr.cc.va.us
Mary Ann Hovis: hovisma@ltc.tec.oh.us
Statistics
Grinnell College Oct. 12-15, 2000
Thomas Moore: mooret@math.grin.edu
Business. Finance and Economics
University of Arizona Arizona Oct. 28-29, 2000
Deborah Hughes Hallett: dhh@math.arizona.edu
William McCallum: wmc@math.arizona.edu
Mathematics Education
Michigan State University Michigan Nov. 1-3, 2000
Sharon Senk: senk@pilot.msu.edu
Biology and Chemistry
Macalester College Nov. 2-5, 2000
David Bressoud: bressoud@macalester.edu
Mathematics Preparation for the Major
Mathematical Sciences Research Institute Feb. 9-11, 2001
William McCallum: wmc@math.arizona.edu

Spring 2001


interdepartmental discussions. Such discussions, as well as
those at the CRAFTY workshops, generate good will be-
tween mathematicians and colleagues in partner disciplines.
In general, colleagues from partner disciplines value math-
ematics and welcome the opportunity to state their views
about mathematics education, provided their opinions are
taken seriously. Promoting and supporting informed discus-
sions with the partner disciplines may ultimately be the most
important outcome of the MAA Curriculum Foundations
Project.

THE CRAFTY ENGINEERING WORKSHOP
AT CLEMSON UNIVERSITY

One of the CRAFTY workshops was sponsored and hosted
by Clemson University on May 4-7, 2000. It focused on the
needs of engineering from the first two years of college

TABLE 2
MAA Curriculum Foundations Workshop Questions

Understanding and Content
What conceptual mathematical principles must students master in
the first two years?
What mathematical problem-solving skills must students master
in the first two years?
What broad mathematical topics must students master in the first
two years?
What priorities exist between these topics?
What is the desired balance between theoretical understanding
and computational skill?
How is this balance achieved?
What are the mathematical needs of different student populations
and how can they be fulfilled?

Technology
How does technology affect what mathematics should be learned
in the first two years?
What mathematical technology skills should students master in
the first two years?
What different mathematical technology skills are required of
different student populations?

Instructional Interconnections
What impact does mathematics education reform have on
instruction in your discipline?
How should education reform in your discipline affect mathemat-
ics instruction?
How can dialogue on educational issues between your discipline
and mathematics best be maintained?

Instructional Techniques
What are the effects of different instructional methods in
mathematics on students in your discipline?
What instructional methods best develop the mathematical
comprehension needed for your discipline?
What guidance does educational research provide concerning
mathematical training in your discipline?










mathematics instruction. The workshop had thirty-eight in-
vited participants, with roughly equal representation from
each of four areas in engineering (chemical, civil, electrical,
mechanical) and mathematics. The workshop resulted in
four documents, one for each of the four engineering areas,
addressing the MAA questions specified at the outset of the
workshop.
This paper focuses on the recommendations of the chemi-
cal engineering group. It is not intended to be a definitive
document, but rather a working paper that generates discus-
sion among chemical engineers in order to provide addi-
tional feedback for the mathematics community. Therefore,
the authors welcome comments and additional ideas.

REPORT OF THE
CHEMICAL ENGINEERING GROUP
The Chemical Engineering group members are listed in
Table 3.
What Chemical Engineers Do
Since this report was originally written for mathemati-
cians, an appropriate introduction is to discuss what chemi-
cal engineers do, why mathematics is needed, and how it is
used. A reasonably broad definition is that chemical engi-
neers design materials and the processes by which mate-
rials are made.
Traditionally, chemical engineers have been associated
with the petroleum and large-scale chemical industries, but
(especially in recent years) chemical engineers have also
been involved in pharmaceuticals, foods, polymers and ma-
terials, microelectronics, and biotechnology. The core sub-
jects that underlie and unify this broad field are thermody-
namics, chemical reaction processes, transport processes (i.e.,
the spatial and temporal distribution of mass, momentum,
and energy) and process dynamics, design, and control.
On top of this fundamental framework, a central emphasis
of chemical engineering education is model building and
analysis. A good chemical en-
gineer brings together the fun-
damentals to build and refine a T
TA
mathematical model of a pro- Chemical Engine
cess that will help him or her
understand and optimize its per- I Jenna P. Carpenter Inte
formance. To be good at model Engineering, Civil Engin
building and analysis, students Technological University
must have at hand the math- I Michael B. Cutlip Profes
ematical background to under- Director of the Honors Pr
stand and work with the core E Michael D. Graham Ass
scientific areas, as well as to Engineering University
find solutions to the final model leader/recorder)
that they build. In this context, E Anton J. Pintar Associal
Michigan Technological
the "solution" to a mathemati-
E Jan A. Puszynski Profes,
cal problem is often in the un- Engineering South Dak
derstanding of the behavior of


the process described by the mathematics, rather than the
specific closed form (or numerical) result.
Here is an example: A starting point for understanding any
process is writing down the conservation laws that the sys-
tem or process satisfies...for conserved quantities, accumu-
lation = input output. Depending on the level of detail of
the model, this equation might be, for example, a large set of
linear algebraic equations that determine the relationships
between fluxes of chemical species throughout the process
(a species balance), or it might be a set of parabolic partial
differential equations governing the temperature and compo-
sition of the fluid in a chemical reactor. In the thermodynamics
of multiphase systems, energy is conserved but takes on a
variety of forms; a good knowledge of multivariable differen-
tial calculus is essential here to keep track of everything.

Mathematics for Chemical Engineering
The purpose of the original report was not to prescribe the
mathematics curriculum-chemical engineers do not want
mathematics instruction to provide only what students can
"get by" with knowing. Nor is it appropriate to come down
on either side of the "traditional" vs. "reform" debate-it is
likely that both sides are right, to an extent. Instead, some
general thoughts on subject matter and emphasis are pre-
sented here.

Precalculus Foundations
By foundations, we mean
Basic knowledge offamilies offunctions
(polynomical, exponential,...) in terms of data, graphs,
words and equations, basic trigonometric identities
and geometry, properties of logarithms, etc.
Equations, inequalities
Basic logic and algorithms
Small linear systems of equations
Coordinate systems
Basic arithmetic and manipulation skills

Mastery of the above ar-
eas is crucial. Probably the
,E 3 most important thing the
g Group Members mathematics community can
do here is to actively investi-
.cademic Director, Chemical gate the pedagogy of K-12
g and Geosciences Louisiana
education-to help sort out
f Chemical Engineering and which "reforms" are produc-
n University of Connecticut tive from those that are
e Professor of Chemical merely "fads" and to encour-
isconsin-Madison (discussion age schools not to neglect the
education of the more math-
fessor of Chemical Engineering ematically inclined students
sity by focusing the curriculum
Chemistry and Chemical
Chemistry and Chemical too narrowly on the average
hool of Mines and Technology too narrow on the average
performer. Another impor-
Chemical Engineering Education


BBL
erin

rim A
eering

ssor o
-ograr
ociate
ofW

e Pro
Unive
sor of
ota Sc










tant role here is to provide programs that help K-12 math-
ematics teachers understand some applications of the math-
ematics that they teach (engineering faculty should do much
more here).

Linear Mathematics
Chemical engineering students would benefit
from earlier exposure to the basics of linear
systems in RN, particularly
The geometry of linear spaces partner
Vector algebra (especially in 3D)
Ax = b (existence and uniqueness,
Gausian elimination, geometric interpre-
tation, over- and underdetermined
systems, and least squares problems)
Ax = Xx (characteristic polynomial and
diagonalization, Jordan form, range and nullspace of
A, geometry)
At the University of Wisconsin-Madison, for example, there
is a course on "linear mathematics" that introduces these
notions and applies them to systems of ordinary differential
equations (see next section). Many chemical engineering
students take this in lieu of the traditional differential equa-
tions class.

Calculus and Differential Equations

The importance of visualization in calculus cannot be
overemphasized, especially as a guide to differential and
vector calculus in multiple dimensions, plotting (e.g., what
function is linear on a log-log plot?), working in cylindrical
and spherical coordinate systems, and converting between
coordinate systems. Somewhat less time could be spent on
techniques for evaluating complicated integrals, with the
time spent instead on, for example, visualizing the applica-
tion of the chain rule in multiple dimensions. Understanding
of truncated Taylor series for local approximation of func-
tions is very important and should be seen early and often. In
differential equations, a thorough knowledge of linear con-
stant coefficient systems (initial value problems and bound-
ary value problems; see previous section) is preferable to
emphasis on existence theory and series solutions for non-
constant coefficient problems. Some qualitative theory for
nonlinear systems is also desirable.

Probability and Statistics
Alumni surveys typically show that this is the most com-
mon application of mathematics for the practicing chemical
engineer with a bachelor's degree, in addition to the exten-
sive use of spreadsheets. Key issues here include parameter
estimation, experimental design, sampling, and the origins
and properties of various distribution functions.
Spring 2001


Students interested in graduate school should be encour-
aged by their mathematics professors, as well as their engi-
neering advisors, to take additional mathematics courses. A
final general comment: students should have some idea of
the power of a theorem, but for engineers, concepts are more


... [the] discussions ... generate good will
between mathematicians and colleagues in
irtner disciplines. In general, colleagues from
r disciplines value mathematics and welcome
the opportunity to state their views about
mathematics education, provided their
opinions are taken seriously.


important than proofs. In other words, it is appropriate for
chemical engineering students to learn mathematical facts
without always seeing the associated proofs.

Technique and Technology
A fair amount of the discussion at the MAA engineering
workshop, within the chemical engineering group and oth-
ers, centered around the use of technology in the mathemat-
ics courses for engineers. In the discussions, "technology"
meant a number of different things, from numerical methods
to graphing calculators to symbolic manipulation packages.
We'd like to emphasize here some points to be kept in mind
when thinking of the introduction of these tools into math-
ematics courses. We do this in the form of responses to two
questions, representing both sides of the issue (admittedly,
these questions are straw men):
"My laptop can do that. Why should I learn to do it by
hand?"
Sense ofform of mathematical expressions, under-
standing of what manipulations are available, facility
with these manipulations
Fluency in the language of mathematical concepts
Appreciation and recognition of mathematical rigor
Discipline, maturity, confidence of mastery
Closed form results are best, if available
Recognition of limitations of closed form results,
where things get difficult
Knowledge of what computers do
"Use of computers dumbs down the mathematics course-
why use them?"
Solution of realistic (complex) problems, many of
which involve numerical solutions. In upper-level
courses, extensive use is made of programs such as
MATLAB, Octave (available at octave>), MathCad, Mathematica, and Polymath










Efficient exploration of solution and design space
Visualization, especially in multidimensional and
vector calculus
Relieffrom tedium
Confidence in results derived by hand
Ultimately, the technology should take a back seat in
mathematics courses until it becomes necessary for solving
interesting problems. For example, in a linear algebra course,
students should be able to do LU decomposition of a 3x3
system by hand before they are shown that a computer
algebra system can complete the process with one com-
mand. At the same time, it is useful to point out the relation-
ship between numerical techniques and exact ones (e.g., a
Riemann sum can be evaluated numerically to approximate
an integral). Students should have a solid understanding
regarding limitations of numerical methods and their accu-
racy. They should clearly see the power of analytical solu-
tions when such solutions can be found.


A Suggestion for Coupling Mathematics
and Engineering Education
One set of issues that arose repeatedly in the MAA engi-
neering workshop discussions was the concern that students
do not see connections between mathematical tools and con-
cepts and the wide utility of these in engineering. A related
concern was the time lag between exposure to mathematics
and its application to the solution of real engineering prob-
lems. The notion of "just-in-time" learning was discussed,
and the suggestion was made that mathematics courses be
more application- or example-driven and be more evenly
spread through the curriculum, rather than "front loaded"
into the first two years. The chemical engineering group
shared these concerns, but also thought that
1) Part of the beauty and power of mathematics is that it
is example-independent-calculus applies to econom-
ics just as it does to mechanics
2) The time spent developing the background for engi-
neering applications is time not spent on mathematical
principles and tools
3) A straightforward "just-in-time" approach will not
satisfy all engineering majors (e.g., electrical engi-
neers do not need Laplace transforms at the same time
as chemical engineers).
An alternative structure can be considered for addressing
these concerns, which are essentially about how to connect
mathematics and engineering in the students' minds. Spe-
cifically, the college mathematics curriculum could include
discipline specific supplements, especially in the calculus
sequence. These could be workbooks or web pages contain-
ing, for example,
Engineering background material, e.g., some basic


thermodynamics, and how specific mathematical
principles and/or tools (such as total differentials and
partial derivatives in several dimensions) are used
Exercises or projects integrating mathematics and
engineering
Additional discipline-specific emphases, e.g., trigono-
metric identities and manipulations for electrical
engineering students.

These could be used independently by the students, or
used in a one-credit course running in parallel with the
calculus courses, or simply be resources for mathematics
instructors wishing to gain perspective on engineering appli-
cations or bring engineering applications into the mathemat-
ics classroom. This is perhaps overambitious, but certainly
worth considering. It was suggested that, within chemical
engineering, CACHE (Computer Aids for Chemical Engi-
neering ) could play a role in studying
this possibility in conjunction with MAA.

CONCLUDING REMARKS
It is clear that the application of mathematical concepts
and the generation of mathematical solutions to engineering
problems are essential to the educational programs of all
undergraduate engineering students. Enhanced cooperation
between mathematics faculty and engineering faculty can
lead to a better experience for our students. Without excep-
tion, the participants felt that the workshop was a very pro-
ductive way to promote dialogue between the mathematics
and engineering education communities and encouraged the
organization of more workshops of this type. Another venue
that mathematicians can explore is the American Society for
Engineering Education , which has a math-
ematics division. On the other hand, it may be productive for
engineering educators to attend MAA meetings.
Perhaps most importantly, mechanisms need to be imple-
mented to promote interaction between engineering and math-
ematics faculty within individual universities-good rela-
tionships at this level will enable mathematics faculty to
understand what material the engineering faculty would like
to see reinforced and emphasized, as well as enabling engi-
neering faculty to gain a better understanding of the issues
surrounding mathematical preparation of entering freshman
engineering majors.

ACKNOWLEDGMENTS
We are grateful to Professors J.B. Rawlings and W.H. Ray
(University of Wisconsin-Madison) and J.F. Brady (Califor-
nia Institute of Technology), and to Sangtae Kim (Vice-
President and Information Officer, Eli Lilly) for their critical
reading and insightful comments on an earlier version of this
paper. This document reflects the joint efforts of the entire
chemical engineering working group. 1


Chemical Engineering Education

















AUTHOR GUIDELINES


This guide is offered to aid authors in preparing manuscripts for Chemical Engineering Education (CEE), a quarterly journal
published by the Chemical Engineering Division of the American Society for Engineering Education (ASEE).
CEE publishes papers in the broad field of chemical engineering education. Papers generally describe a course, a laboratory, a
ChE department, a ChE educator, a ChE curriculum, research program, machine computation, special instructional programs, or
give views and opinions on various topics of interest to the profession.


Specific suggestions on preparing papers *
TITLE Use specific and informative titles. They should be as brief as possible, consistent with the need for defining the
subject area covered by the paper.

AUTHORSHIP Be consistent in authorship designation. Use first name, second initial, and surname. Give complete mailing
address of place where work was conducted. If current address is different, include it in a footnote on title page.

ABSTRACT: KEY WORDS Include an abstract of less than seventy-five words and a list (5 or less) of keywords

TEXT We request that manuscripts not exceed twelve double-spaced typewritten pages in length. Longer manuscripts may
be returned to the authors) for revision/shortening before being reviewed. Assume your reader is not a novice in the field.
Include only as much history as is needed to provide background for the particular material covered in your paper. Sectionalize
the article and insert brief appropriate headings.

TABLES Avoid tables and graphs which involve duplication or superfluous data. If you can use a graph, do not include a
table. If the reader needs the table, omit the graph. Substitute a few typical results for lengthy tables when practical. Avoid
computer printouts.

NOMENCLATURE Follow nomenclature style of Chemical Abstracts; avoid trivial names. If trade names are used, define
at point of first use. Trade names should carry an initial capital only, with no accompanying footnote. Use consistent units of
measurement and give dimensions for all terms. Write all equations and formulas clearly, and number important equations
consecutively.

ACKNOWLEDGMENT Include in acknowledgment only such credits as are essential.

LITERATURE CITED References should be numbered and listed on a separate sheet in the order occurring in the text.

COPY REQUIREMENTS Send two legible copies of the typed (double-spaced) manuscript on standard letter-size paper.
Submit original drawings (or clear prints) of graphs and diagrams on separate sheets of paper, and include clear glossy prints of
any photographs that will be used. Choose graph papers with blue cross-sectional lines; other colors interfere with good
reproduction. Label ordinates and abscissas of graphs along the axes and outside the graph proper. Figure captions and legends
will be set in type and need not be lettered on the drawings. Number all illustrations consecutively. Supply all captions and
legends typed on a separate page. State in cover letter if drawings or photographs are to be returned. Authors should also include
brief biographical sketches and recent photographs with the manuscript.


Send your manuscript to
Chemical Engineering Education, c/o Chemical Engineering Department
University of Florida, Gainesville, FL 32611-6005













CALL FOR PAPERS

FALL 2001
GRADUATE EDUCATION ISSUE OF

CHEMICAL ENGINEERING EDUCATION


Deadline is June 1, 2001




Full Text
xml version 1.0 encoding UTF-8
REPORT xmlns http:www.fcla.edudlsmddaitss xmlns:xsi http:www.w3.org2001XMLSchema-instance xsi:schemaLocation http:www.fcla.edudlsmddaitssdaitssReport.xsd
INGEST IEID ETEPCTN2S_ZCF537 INGEST_TIME 2012-02-17T16:31:25Z PACKAGE AA00000383_00150
AGREEMENT_INFO ACCOUNT UF PROJECT UFDC
FILES



PAGE 1

i:: Q ... ... i::: l.l :::i "c::s i:: ... i.. i:: ... i:: i.. ,:, ... l.l Q vi i:: i::: l.l ... i.. "' i.. 15 i:: ... i:: Q i:: ... "' ... ... .. i::: ... l.l ... 15 i:: ... -== i.. v i:: ... ... i:: :::i ... ... ... ... "' i::: i:: l.l .... ... 15 i:: i::: -== l.l v ... i.. 15 chemical engineering education of the University of Texas. Austin Efficient. Effective Teaching (p. 92) Wankat I Undergraduate Process Control: Clarification of Some Concepts (p. 148) Rmi I Random Thoughts FAQS. III: Groupwork in Distance Learning (p. 102) Felder, Brellf I Computer Modeling in the Undergraduate Unit Operations Laboratory (p. 116) Keffer I A Supercritical Extraction Experiment for the Unit Operations Laboratory (p. 96) Gabbard, Knox I T h e Business Meeting An Alternative to the Classic Design Presentation (p. 104) Nell'e/1 I Student-Performance Enhancement by Cross-Course Project Assignments (p. 128) Biro/, Biro/, <;inar I The Interface Between ChE and Mathematics What do Students Really Need'? (p. 152) Graham, Gallter I Using In-Bed Temperture Profiles for Visualizing Concentration-Front Movement (p. 122) Cru::., Mendes, Magalhiies I A Project-Based Spiral Curriculum for I ntroductory Courses in ChE: Part 3. Eva l uation (p. 140) DiBiasio. Comparini. Dixon. Clark I Developing the Best Correlation for Est i mating the Transfer of Oxygen from Air to Water (p. 134) Brown I Thermodynamic Properties I nvolving Derivatives: Using the Peng-Robinson Equation of State (p. 112) Pratt ::===================::: C alendar of Ev ent s ---------.... Chemical Engineering Division. June meeting
PAGE 3

EDITORIAL AND BUSINESS ADDRESS: Chemical E11gi11ee ri11g Education Department of Chemical Engineering University of Florida Gainesville, FL 32611 PHONE a11d FAX: 352 -392-0 861 e -mail: cee@c h e.ufl.edu EDITOR Tim Anderson ASSOCIATE EDITOR Phillip C. Wankat MANAGING EDITOR Carole Yocum PROBLEM EDITOR James 0. Wilkes, U. Mi c higan LEARNING IN INDUSTRY EDITOR William]. Koros, Univ e rsity of Texas, Austin PUBLICATIONS BOARD CHAIRMAN E. Dendy Sloan, Jr. Colorado School of Mines MEMBERS Pablo Debenedetti Prin ceto n University Dianne Dorland University of Minnesota Duluth Thomas F. Edgar University of Texas at Austin Richard M. Felder North Carolina State University Bruce A. Finlayson University of Washington H. Scott Fogler University of Mi c hi gan William J. Koros University of T exas at Austin David F. Ollis North Carolina State U ni ve r sity Ronald W. Rousseau G eo r g ia In stit ut e ofTeclmolog y Stanley I Sandler University of D e lawar e RichardC Seagrave Io wa State Universit y Stewart Slater Rowan University Jame s E. Stice University of T ex as at Austin Donald R. Woods McMaster U ni ve r s i ty Spring 2001 Chemical Engineering Education Volume 35 Number 2 Spring 2001 EDUCATOR 86 Don P a ul of the University of Texas at Austin William J Koros CLASSROOM 92 Efficient Effective Teaching Phillip C. Wankat 104 The Business Meeting: An Alternative to the Classic De s ign Presenta tion, Jam es A. Newell 128 Student-Performance Enhancement b y Cross-Course Project Assign ment s: A Case Study in Bioengineering and Process Modeling Gulnur Biro[ !nan <; Bir o [ Ali <;inar 148 Undergraduate Proce ss Control: Clarification of Some Concepts, R. Ravi LABORATORY 96 A Supercritical Extraction Experiment for the Unit Operations Laboratory Ronald G. Gabbard, D ana E. Kn ox 116 Computer Modeling in the Undergraduate Unit Operations Laboratory : Demonstrating the Quantitative Accuracy of th e Bernoulli Equation, David J K effer 122 Using In-Bed Temperture Profile s for Visualizing the Concentration Front Movement Paulo Cru z, Ad e lia Mendes Fernii.o D. Magalhii.es 134 Developing the Be s t Correlation for Estimating the Tran sfe r of Oxygen from Air to Water Wa y ne A. Br own RANDOM THOUGHTS 102 FAQS. III : Groupwork in Di s tance Learning, Ri c hard M. Felder Reb ecca Br e nt CLASS AND HOME PROBLEMS 112 Thermodynamic Properties Involving Derivatives: Using the Peng Robinson Equation of St a te R .M. Pratt CURRICULUM 140 A Project-Based Spiral Curriculum for Introductory Courses in ChE: Part 3. Evaluation, Da v id DiBia sio, Li sa Comparini Anthon y G Dixon William M. Clark 152 The Interface B e twe e n ChE and Mathematics : What do Students Really Need? Michael D. Graham, Susan L. Ganter 91, 95, 110 Book Reviews 107, 109 Letters to the Editor 111 Call for Papers 120 ASEE, Chemical Engineering Division Program CHEM I CAL ENG I NEE RJ NG EDUCATION ( ISS N 0009-2479 ) is published quart e rl y by th e Chemical E11gineeri11g Divisio11 American Society for E11gi11eeri11g Education and is e dited al the University of Florida. Correspo 11d e 11 ce r egarding editorial matter circulation and changes of addres s shou l d be sent to CEE Chemica l Engineer in g Department University of Florida Gainesville FL 32611. Copyright 2001 by th e Chemical E11gi11eerbrg Division A m erica n Socie t y for Enginee ring Education. The s tat ements and opinions exp r essed in this periodical are those of the writers and n ot n ecessarily t ho se of the C h E Dillision ASEE, which body assumes 110 responsibility for th e m. Defective cop i es replaced if notified within 120 days of publi ca lior, Write/or information 011 subscription costs and for back copy costs a11d availability. POSTMASTER: Se nd address c/ra11ges to Chemical Engineering Education Chemical Engineering Department., University of Florida, Gainesville, FL 32611-6005. Periodicals Po s tage Paid at Gainesville, Florida and additional post offices. 85

PAGE 4

t A-h-3.._e_d_u_c a_to_r _________ ) DON PAUL ... of The University of Texas at Austin WILLIAM J KoRos Th e University of Texas at Austin Austin, TX 78712 I recently conducted an experiment by asking severa l colleagues at the University of Texas at Austin what words came to mind when they thought of Don Paul. For tho se who know him well, it is not s urpri s ing that the common descriptors included smart," "o rganized ," hon e s t ," practical ," and tough ." While tho se five words undoubtedly capture his core per so nality the word productive also pop s to mind when I think of Don By any standard, Don's prodigious contribu tion s to the chemical-engineering and material s -science lit erature place him almost in a clas s by himself. In addition to coauthoring over 450 archival journal articles and editing eight book s, Don ha s also mentored 52 PhD s tudents 47 MS st udent s, and 46 postdoctoral fellows during his career at Texa s. Serving as the Editor-in-Chief of Industrial and En gineering Chemistry Res earch for fifteen years and bein g on th e editorial board s of eight other journals has made hi s impact on the field of chemical engineering truly enormous. Don s research interests include the broad areas of poly mer sc ience and engineering and chemical engineering. Hi s eight e dited book s cover a broad range of topics, but they ha ve a common thre a d as a result of hi s interest in polymers. Don 's current re searc h involve s polymer blend s, mem86 branes for separations, drug delivery packaging and poly mer processing The blend research deals with the thermo dynamic s of polymer-polymer mi sc ibility pha se diagrams and interface s, reactive compatibilization of multiphase mix ture s, rubber toughening the control of phase morphology during proce ssi ng by both chemical and ph ysica l mean s, and polymeric nanocom]Jo sites. Hi s research on diffusion in poly mer s involves investig atio n of structure-property relation s hip s to de s ign better membranes for separation proce sses, improved barrier material s, physical aging of thin films and thermal switch membranes Don has also contributed sig nificantly to theorie s and models for describing sorption and permeation of s mall molecule penetrants in polymer s. A broad range of materi als, including rubbery g la ssy, semicrystalline and liquid crystalline states of these materials ha s b ee n considered Synthesis and characterization of novel mat er ial s i s a key aspect of his work in all of the above s ub-are as A BROAD ARRAY OF CONTRIBUTIONS One of our departmental colleagues once joked that h e held a s till-unproven hypothe sis that ther e are reall y identiCopyrig ht C h E Di vis i on of ASEE 2001 Chemical Enginee rin g Education

PAGE 5

cal twins with the injtials DRP who operate from Don s office Wrule hlghly valuing productivity Don's high stan dards for quality are also apparent and his recognition as a creative and insightful investigator documents this as pect of his nature. Beginning with the 1973 ACS Arthur Doolittle Award a steady stream of honors bestowed on Don by colleagues underlines the respect in which hjs work is held by the chemjstry and chemical engineerPol y mer Engine e rin g and S c ienc e Journal of Appli e d Pol y m e r S c i e n ce, Chemical Engin ee ring Edu c ation, Pol y m e r Journal of Pol y mer Science Polymer Physi c s Polym e r Con t e nts and the Imperial College Press Series on Chemical Engineering. Beyond the AIChE and ACS, Don has also been involved in activities of the Council of Chemjca l Research serving on it s Governing Board ( 1981-84) and it s Executive Committee ing commuruties In additio n to the D oolitt l e Award the ACS has rec ognize d his contributions through the Phillips Award in Ap pli ed Polymer Science and the E.V. Murphree A war d for Contributions to Industrial and Engineering [Don] published a classic paper regarding the mechanism of hydraulic permeability through membranes [that] helped call attention to the new program in polymers at UT and launched the membrane activities that have been a strong and continuous component of UT's graduate-studies area for over three decades. Chemistry. The AIChE has recogruzed him with the Stine Materials Engineering and Science Award and th e William H Walker Award for Contributions to the Chemical Engineeri n g Literature as well as by elec tion as a FelJow He was e l ecte d to th e National Academy of Engineering in 1988 for "o ut standing research co ntr ibutio n s on poly meric materials and for leadershlp in chemical engineering ed u cation Don 's Council of Chemica l Research Malcom Pruitt Awar d and the Plastic Instit ut e s Educationa l Service Award also emphasize not only hl s impact in scholarly publication and research arenas but also his leadershlp at the interface between industry government, an d academia Don h as presented num erous invited lectures including the Warren McCabe lecture at North Carolina State Univer sity, the R .L. Pi gford Memorial Lecture at the Univers it y of Delaware the As ht on Hall Cary Lectures at Georgia Insti tute of Technology and the Donald L. Katz Lecture at the U ni vers it y of Micrugan. He h a s al s o served the chemical engineering comm urut y through his contributions to com mittees a nd organjzations throughout his career. He was on the Education Projects Committee of the AIChE from 196877 and served as th e edi t or for the Chemical Engineering Faculties Directory from 1967-77. He a l so was an ABET accredita t io n visitor from 1974-83 Don s ab ilit y to speak to both the chemistry a nd the c h emical engineering com mun ities i s reflected by his active work with both the ACS and the AIC hE Don serve d on the Executive Committee of the ACS Divi sio n of Polymeri c Materials Sciences and Engineering from 1980-85 a nd in many capacities related to ACS publications we ll beyond his work as Editor in Chlef of &EC R esearch. His work on &EC R esear c h h as see n close to 50,000 pages of archival journal pages publi shed under hls watch with the colla b orative assistance of many editoria l colleag u es since 1986. His e dit o ri a l co ntribution s ha ve also included service o n editorial bo ards for The Journal of Membrane Science, Sprin g 2001 ( 1983-84). He wa s a member of the Founding Committee of the North American Membrane Society. His work with the National Academy of Engineering has included service on the NAE Peer Committee in 1989-92 and 1994 as well as the Membership Comrruttee from 1994-97 The National R search Counci l benefited from hls input on its National Materials Advisory Board from 1988-94 its Committee on Polymer Science and Engineering from 1992-94 its U.S. National Committee on the International Union of Pure and Applied Chemjstry from 1993-96 and its Solid State Sci ence Committee from 1994-97 He also served on panels for Materials Scie n ce and Engineering at NIST a nd on the panel for International Benchmarking of U.S Materials Science and Engineering Research. Don's story begins in North Carolina where he grew up on a small farm near Washington NC. He freely acknowledges the strong effect that thi s background has had on his lifestyle and motivation. An anecdote regarding thi s point is useful h ere Don once told me that he recalls going o ut to hoe weeds out of a large field one hot North Carolina day Looking at the very large and intimidating field, he decided n o t to think in term s of its size Instead, he looked down the first row and thought I can get to the end of this one." Hoeing hi s way to the end of the row, he straightened up and l ooked down the next row deciding "I can get to the end of this one too ," You can gue s s the rest-128 rows later he l ooked back o n the entire field wit h a sense of accomplish ment and an insight th at h as remained with him throughout the years. Whether it is wri tin g papers or books, or e du cating nearly 150 gradua te students and post docs it is best to take it one row at a time" and t o just keep on working D on s contrib ution s to teachjng h ave also b een widely recognized He received the General Dynamics Teac hin g A ward in 1977 which i s the highest teac hin g recognition in the College of Eng in eeri n g and it foc u ses on co ntr i buti ons to underg ra duate education. In 1994 our department norru87

PAGE 6

TABLE 1 Don Paul's Former Graduate Students PhD Students MS Students D R Kemp (1972) D.R. Kemp (1969) C.E. Locke (1972) J H. Troell ( 1969 ) O.M Ebra-Lima (1973) O.M. Ebra-Lima ( 1970 ) W.J. Koro s (1977) J St. Lawrence (1970) A.H. Chan (1978) V. Mavichak (1970) C.A. Cruz Ramo s ( 1978 ) C.E. Vinson ( 1971) J.E Harri s ( 1981 ) D.H Carranza (1972) R.S Barnum (1981) A.E. Mann ( 1972 ) E. Woo (1984) R.E. Robert son ( I 972) J.-S Chiou (1985) M. Garcin (1973) Y. Maeda ( 19 85) J.O Altamirano ( 1974 ) A.C. Fernandes ( 19 86) J.R Stell (1974) M.J El-Hibri ( 1986 ) J.D Paciotti ( 1974 ) T.A Barbari (1986) A.A. Rocha (1974) M.E. Fowler (1987) W.E. Garmon ( 1 975) N. Muruganandam (1987) R.L. Imken ( 1 975) M C. Schwarz ( 1987 ) S. McSpadden ( 1975 ) C.-H. Lai ( 198 8) A .J Meyer ( 19 75) P.S Tucker ( 1988 ) D. Wahrmund (1975) A.C. Puleo ( 1988 ) T.R. Nassar ( 1 976) J H Kirn ( 19 89) R.N Mohn ( 1 977) P .C. Raymond ( 1989 ) R .E. Bernstein (1977) J .M. Mohr ( 1990 ) J.C. Tiffany ( 1 978) J .S. McHattie (1990) G. Wonders (1978) H Kim (1990) E. Nolley ( I 978) G.R. Branno ck (1990) A.J. Erb (I 979) T .W.Cheng (1991) D W. Bartlett ( 1979 ) 1. Park (199 1 ) C.R Lind sey ( 1 979) D H Weinkauf(l9 9 1 ) P.-T Chang (1980) Y. Takeda ( 1992 ) M.D. Lorenz (1980) C.L. Aitken (I 992) J .J Ziska (1980) C.K. Kim ( 1992 ) P Masi (1980) T.A. Callaghan ( 1992 ) E.A. Joseph ( 1981) M. Aguilar-Vega (1993) W.A. Smith (1981) J.D. Le Roux (1993) E.Y. Adham (1982) M. Nishimoto (1994) T.D. Traugott (I 982) P .P. Gan ( 1994 ) W.E. Preston ( 1982 ) B. Majumdar ( 1994 ) S.R. Murff ( 19 83) A.G. Gonzalez ( 1995 ) J.D Keitz (1983) M.R. Pi xto n ( 1995 ) C. McCutcheon ( 198 3) M. Lu ( 1995 ) J .-L. G. Pfennig (198 4 ) A.J. O s hinski (1995) VJ. Triacca ( 1 989) S. Ziaee ( 1995 ) G.P Shaver ( 1989 ) K.A. Schult ( 1 996) J. Oshinski (1990) C.T. Wright (1997) A.B Lombardo ( 1994 ) F.A. Ruiz-Trevino ( 1997 ) S. Gupta ( 1995 ) G S Wildes ( 1998 ) A. Kelk a r (2000) W.R Hale (1998 ) M.S. McCaig (1998) G D Merfeld (1998) R.A. Kudva ( 1999 ) J H .-C. Chu (1999) Z. Mogri (200 I ) 88 nated Don for the University-wide Graduate Teaching Award. We con tacted his former graduate students for possible l etters of s upport. The response was overwhelming Letters poured in from all over, since by that time Don 's former students had achieved di s tinguished positions in many parts of the world. The recurring theme of these letters was an expression of the writer 's feelings of deep appreciation for Don 's help in their educational development by his tough but ultimately compassion ate, mentorship. As one of these former students, I was more than pleased that Don received this highly competitive award in recognition of his educational efforts Don s BS in chemical engineering was earned at North Carolina State University (1961) a nd his grad u ate work was carried out at the University of Wisconsin, Madison (1965). He has been recognized by both of hi s alma maters with distinguished graduate awards. In addition to summer work at DuPont in the nonwoven fabric area in 1960-61, Don was a Research Chemical Engineer at Chemstrand Re search Center in North Carolina's Research Triangle Park from 1965 to 1967 LIFE AN D L EADERSHI P IN T H E DE PAR TM EN T Don joined the University of Texas faculty in 1967 and has been here now for 34 years. Progressing through the ranks to Associate Professor in 1970 and to Full Professor in 1973 he took an early role as a departmen tal leader. He served as the department's Associate Chairman from 197377 and as its Chairman from 1977-85. During his Chairmanship Don recognized the need for a forward-looking approach. He assembled a committee comprised of distinguished leaders in the chemical and petro chemical industries as well as from the academic community to evaluate the curricu lum. The committee also analyzed the future needs of the department and the larger chemical engineering community. Many of the elements of this visionary plan are still used as the guiding principles for our department. One of Don's favorite stateme nt s is that "chemical engineering is defined by what chemical eng ineer s do ." That attitude helped position the department as an early player in the polymer, materials science, microelectronic, and biotechnology opportunities that have helped main tain the vitality of our discipline. Don was also quick to s ee the need for better brick s, mortar, and laboratory facilities to allow the department's movement toward the new technological areas, while still maintaining connection s to its petro chemical roots. He was a key person in acquiring the needed resources to construct our current modern facility which was occupied in 1986 at the end of his term as Chairman Strong connections with our alumni and industrial friends also led to the establishment of a large number of endowed positions in the department and colJege during this period. Don himself was selected as the T. Brockett Hudson Professor in 1978 and as the Melvin H. Gertz Re ge nt s Chair in Chemical Engineering in 1985 Following hi s term as Chairman Don returned to his active research and teaching duties in the department and served as a mentor for several faculty who were at the time making the transition to academia from industry During the time he served as Chairman he managed to maintain an energetic research program but when he stepped down from that Chemical Engineering Education

PAGE 7

position, a literal explosion of activity became apparent through his PhD supervision and his publications MAJOR TECHNICAL CONTRIBUTIONS Don 's interests and contributions in polymer engineering and science have included work in both polymer blends and membranes. Not surprisingly, he has managed to also com bine his insights in these two separate areas to provide im portant contributions in advanced blend membrane systems for gas separation membranes Don 's work in polymer blends has led to an important route to new commercial polymer products His work has integrated thermodynamics interfacial phenomena, rheol ogy process, morphology, and properties of these novel materials to provide a solid scientific foundation for this field. Since the late 1940s, numerous papers have suggested that polymer-po l ymer mixtures were unlikely to be miscible. This belief discouraged and delayed the development of any widespread interest in blends Indeed the favorable entropy of mixing for two polymers was known to be very small, if not entirely negligible. Moreover the premise at the time was that enthalpic effects were positive and unfavorable for mixing. Don was a pioneer in focusing attention on polymer-poly mer interactions as the key to developing miscible blends He and his colleague, Joel Barlow published an important paper showing that intramolecular repulsive interactions in random copolymers can provide the basis for exothermic mixing thereby promoting miscibility with other polymers. Thi s effect meant that s uch random copolymers could form miscible blend s, even when the corresponding homopoly mer s could not. This non-intuitive concept was simulta neously recognized by two other groups and is now a corner stone of polymer-blend technology. In 1992 Don and his students initiated a series of papers that combined this copolymer model with a modern equa tion-of-state theory of mixing. Their work allowed a matrix of interaction energies to be constructed to predict the misci bility of multiple polymers and to design copolymers for controlled phase behavior in blend s. This work i s also useful for under s tanding and designing . ,: ... I .:t. !P. > "1" . . -ij,, ,. ,, . [j} f I 1, .+~_:; .. '.. ~ .. .'.: .. -. 'f H r .. '~1.~.:.~ t .: 11ll t -., _,, f ~; J ~,x rr . rr . -.;. _, =I I ' ' . J JL ..... ~!-:X ... ,;,;. ,,:1,;"I, _....., .. UT's chemical engineering faculty at the time of Don 's Chairmanship in 1984. Top row: Keith P. Johnston E.T Beynon, James R Brock Hugo Steinfmk, Douglas R. Lloyd Joel W Barlow. Mi d dle row: James R Fair, Thomas F. Edgar Gary T Rochelle John G Ekerdt, James E. Stice, Herbert Grove Seated; John J McKetta, Eugene H. Wissler, William A. Cunningham Donald R. Paul, Howard F. Rase Joel Hougen. (Missing : David M Himrnelblau W.J. Korns R.P. Popovich and R.S. Schechter) Spring 2001 89

PAGE 8

phase-separated (immiscible) blends in which polymer-polymer interac tions are manifested in the nature of the interface between the phase s. Don s work in this area has been com mercialized through long-standing col laborations with various companies activity-hiking. In addition to hik ing boating, and other outdoor pur suits Don ha s a great love of cooking and a passion for music especially jazz and blues. Hi s music collection is of s uch a size that only someone with his organization skill could maintain it in functional form. In 1995 the sa ddest event in Don 's life removed Sally from him and hi s children. Her death led to a period of deep mourning that eventually yielded to the tough nature that as noted in the introduction, is one of Don 's sig nature qualitie s. THE RECENT PAST AND THE FUTURE In addition to the enormous amount of work in polymer blends Don has pioneered the development of mem branes. Within his first year as an As sistant Professor at Texas he pub lished a classic paper regarding the mechanism of hydraulic permeability through membranes. This paper helped call attention to the new program in polymers at UT and launched the membrane activities that have been a strong and continuous component of UT' s graduate-studies area for over three decades. Soon after completing this paper on liquid permeation, he pub lished a second classic analysis of mem branes-this one related to gas trans port in glassy polymers. Don cooper ated with the group at Monsanto that developed the first truly commercially Don and Sally on a hiking trip. I recall having lunch with Don eigh teen months after Sally's death He had his old s park back and told me that he wanted to do something sig nificant for the institution that had helped him so much He said he had been thinking about the lack of a for mal Materials Science Department at successful gas separation membrane system, called Prism. Over the intervening years, Don and his co-workers have systematically studied the relationship between polymer struc ture and the gas permeation properties of novel materials synthesized in their labs. Important principle s of molecular design have emerged from his work These insights have been codified into a group contribution sc heme for predict ing membrane performance Several new materials of sig nificant commercial interest have been identified. Moreover novel processing schemes involving flourination, crosslinking (and of course, blending) of polymers and low-molecular weight compounds have been studied. FAMILY The only commitment that exceeds in length Don 's asso ciation with the UT department is the one with his extraordi nary wife, Sally Don and Sally met while in graduate school at Wisconsin in 1963. Her disposition and nature caused her to take an interest in children with special needs Completing her Masters in Speech Therapy meshed well with the timing of Don s completion of his PhD, and they celebrated by getting married in 1964. After locating in Austin, they raised a family that include s Mark a master pastry chef trained at the James Beard School in New York City and Ann, who is currently an auditor with the State of Texas. Over the years, Don and Sally shared another favorite 90 UT and how this was often cited as a problem that needed to be dealt with. He said I now see this as a possible advantage rather than a disadvantage if it is handled properly." He unveiled an idea for a materials insitute that would cut across college as well as departmental boundaries. Don visualized a network of individual s linked together by their common interest in materials and with a core of instru ment s and facilities in a central in s titute His vision quickly spread beyond lunchtime conversation to the offices of deans and the vice president of research. With the valuable support of the administration, Don 's concept moved toward reality. At this point Don's take-one-row-at-a-time approach resurfaced. He made the rounds from the physics department to the chemistry department to the aerospace, chemical, elec trical and mechanical engineering departments recruiting support at the grass-roots level to match the upper-admini tration s upport. In 1998, the Texa s Material s In stit ute be came a reality and Don was inducted as it s first director. Under his leadership materials work i s now prospering at UT. New facilities, new positions in various departments and colleagueships that would probably not have occurred have begun-one row at a time Our colleagues in the department, in the college and across the university appreciate and value Don 's catalytic contribution in fostering this unusual and valu able addition to our univer sity We are all indebted to Don for his uniquely broad and deep contributions. 0 Chemical Engineering Edu ca tion

PAGE 9

.,~ ... 6_._b o o_k_T<_e_v_, e w _____ ___ ) Elementary Principles o f Chemical Processes 3rd Edition By Richard M Felder and Ronald W. Rousseau John Wiley & Sons, 605 Third Avenue New York, NY 101580012; 675' pages; $111.95 (cloth) ; (2000) Revi e wed by D. Hunkeler Swiss Federal Institute of Technolog y The third edition of this classic introductory chemical engineering text is intended to compliment a first course in stoichiometry, material and energy balances, and introduc tory thermodynamics. As such, it is aimed at engineering and chemistry students who have completed their first year of general university education. Freshman physics and chem istry are valid prerequisites, although if the course is taught with the complimentary teaching modules one could con sider offering it earlier. The third edition follows the same format as the previous two editions with a preliminary set of three chapters discussing the units and dimensioning of pro cess variables and their associated calculations. This section is (in some curricula) omitted, due to its coverage in other courses but it is a valuable asset since many student difficul ties in balances occur due to sloppy "accounting The body of the text discusses material balances, first for non-reactive single-phase processes and then adding multiphase systems, recycling, and bypass. One of the strengths of the book is the ease with which the authors' introduce thermodynamics into the subject matter. Equa tions of state for non-ideal gases compressibility multicom ponent equilibrium, and two-phase partitioning and solid liquid-vapor phase diagrams are presented in a comprehen sible manner that permits students to begin solving problems on the day of the lecture. This is something Felder has long advocated in his interactive teaching approaches and the third edition certainly shows the value of the NSF's sponsor ing of the concepts which brought it to fruition. The text also integrates graphical presentations of correla tions with computer-based programming challenges. The students will not realize until subsequent courses, to what extent they have been introduced to (and to a large extent mastered) elementary chemical and engineering thermody namics. The problems at the end of the chapter do an excel lent job of integrating the concepts presented along with statistics, into the estimation of thermodynamic data. Practical problems, related to a series of important unit operations including various separation methods such as absorption, adsorption, condensation, crystallization, distil lation, and extraction are presented throughout the first eleven chapters. The authors' also discuss batch, semi-batch, and Sprin g 200/ continuous reactors operating under adiabatic and isother mal conditions both at steady state and dynamically. Com bustion is treated separately. Liquid-gas processes including evaporation-compression, humidification, dehumidification and scrubbing are also integrated into material and energy bal ances. Overall, the new problems are challenging, yet doable. The third section of the book discusses energy and energy balances. There is minimal overlap with the discussion of forms of energy typicalJy presented in freshman physics. Energy balances on non-reactive processes challenge stu dents to organize their solutions The text pulls itself to gether in Chapter 9 when the enthalpy of reaction is used, and estimated, principally to permit the calculation of a reactor's energy loss, temperature, or pressure. The balances are also extended to complete processes. Discussions of alternative fuels which may appear old-fashioned is a take home deliverable from this text as are its extensive data base (tables, graphs, and CDs) that may convince sopho mores they never have to set foot in an engineering library. The text concludes with a chapter on computer-aided calculations which many schools cover in a separate course (as they do the material on transient processes). But if Chap ters 10 and 11 are omitted Chapters 12 through 14 cannot be The authors' offer three case studies (one in the area of materials and two in commodity chemistry) that need to be presented at the end of the two-semester sequence to con vince students they can, indeed design plants. It is a motiva tion which will drive many of them to integrate kinetics, reactor design, transport phenomena and separations into their working knowledge and become chemical engineers. As the only chemical engineering course taught to chemists, in my experience, it provides an excellent sensitization to the challenges facing industrial organic and polymer chemists when they develop new (macro) molecules. The text comes with a CD that includes an animated encyclopedia of chemical process equipment, the E-Z solve software for balances along with tutorials and an index of learning styles. As fantastic as these are, the real value is that the physical property database demystifies the coupling be tween thermodynamics and engineering which confuses so many students With the database provided, carrying out material balances is no longer a cumbersome task akin to financial accounting, but is fun. Felder and Rousseau have made chemical engineering enjoyable. My students make significantly less calculation errors on their balances thanks to the third edition of this book, and they are motivated and listen better to the concepts their predecessors had ignored. Overall, the authors' present a way for introductory stu dents to respect complexity and understand the need for engineering approximations. Take the authors' advice to let the students enjoy problem-based learning-they will better understand themselves, their career, and their choices. The book is a service to our profession. 0 91

PAGE 10

.ta.-..5 ... 311-c_l_a_s_s_r_o_o_m _ ___ ___ ) EFFICIENT, EFFECTIVE TEACHING P HILLIP C. w ANKAT Purdue University West Lafayette, IN 47907-1283 G ood teaching requires that students must learn the right content, have a good attitude, and learn how to leam. Teaching is efficient for students when there is a high ratio of (student learning)/(student time on the course) Because they are so busy, professors also benefit from courses t h at are reasonably efficient. A course is effi cient for professors when there is a high ratio of (student leaming)/(professor's time on the course) Although there are times when effective teaching and efficie n t teaching conflict, most of the time effective teaching can also be efficient. As a professor, you can apply the techniques of time management and efficie n cy by becoming familiar with con cepts such as missions goals priorities, to-do lists, calen dars, and prime time. 11 2 1 These methods should be applied ,EJl paying special attention to efficient teaching 5 J EFFICIENT TEACHING OFLECTURECOURSES 00 Co ur se D eve l opment Designing a course is basically an engineering design problem. What is the p u rpose of the course? The purpose of a required undergrad u ate course is obvio u sly very different t h an the purpose of an elective You should obtain several old outli n es and syllabi. Talk both to professors w h o have Phil Wanka t received his BSCh E from P u r due a n d his PhD from Princeton. He is currently a Professor of Chemical E ngineer ing at Purdue University. He is interested in teaching and counseling, has won several teaching awards at P urdue, and is Head of Interdisciplinary Engineering. His research in terests are in the area of separatio n pro cesses, wi t h particular emp h asis on cyclic separations adsorption, and preparative chromatography. taught the course and to those who teach prerequisite courses to see what you can expect the students to know. Talk to professors who teach follow-up courses to determine what students must learn in your course. The syllabus is a contract with the students. Find a good one and adapt it with appropriate modifications for your co u rse Be explicit about rules and regulations The students will not know what you expect of them until you tell them (even then some students will claim ignorance). Start with firm, and perhaps even tough, ru l es-then relax later on. As part of the syllabus, you should develop a tentative course outline. Plan to spend one or two periods at the beginning of the semester reviewing material the students are supposed to know, and plan one period before every major test for catch up and review. Cover less, but cover it in more depth than was previously done Many students on l y work when there are assignments or tests, so there should be something for the students to do outside of class at least every other week, preferably more often. Shortly after the first test, ask for feedback from the stu dents using a one-minute quiz Pass out index cards and ask students what you (and the TAs) can do to help them learn more. Using the responses you receive, make appropri ate changes to improve the co u rse. Midco u rse corrections based on this feedback can resc u e a course headed for disas ter. Allowing students to have input into test dates and d u e dates of projects a l so i n dicates your willingness to listen a n d will be greatly appreciated by your students. Finally, arrange to teach the same course three or four times in succession. This allows you to reuse much of your preparation and results in a better course in less time. At the end of the semester reflectively analyze what worked and w h at didn't, then plan changes for the next offering while t h e detai l s of the course are still fresh in your mind. Copyright ChE Division of ASEE 2001 92 Chemical Engineering Education

PAGE 11

Lectures Lecturing is the most efficient teaching method the first time a course is taught. Since lecture s can be prepared im mediately before class, it is easy to adjust the course as you proceed through the semester. Lectures must actively en gage the students in order to be effective. In s ub se quent offerings of the course, try modifying the lecture approach or try other teaching approaches suc h as coopera ti ve gro up techniques. When you know the material, you can prepare a new fifty minute lecture in two hour s or le ss. Repe at l ec ture s can b e prepared in one-half hour. Tryin g to prepare a lecture in le ss time is obviously dangerous. Unfortunately, many new fac ulty s pend sig nific a ntly more time than this without becom ing good teacher s.r 5 61 Spend the two hours of preparation time in severa l short bursts starting at lea st a day before the lecture will be deli vere d The first fifteen minutes of prepa ration should be u se d to develop a title and a brief concep tual outline. Fill in so me of the detail s later but do not write out your note s word-for -word. Since a stu dent' s maximum attention spa n is 15 to 20 minutes the sta ndard fifty-minute lecture hour s hould have one or two lecture break s to make it effective. For example, a good scheduling might be I] Introdu ction and short review IJ Mini-lecture I] L ecture break IJ Mini-lecture I] Summary and transition to homework for next class Good lecture breaks include active learning exercises s uch as s mall-group di sc u ssio n s mall-group problem so l v ing brain s torming and s tudent reflection Since the audience' s limited attention span forces you to us e breaks, you will naturally cover les s material; but the break s serve to refre s h the students so they pay more attention to the mini-lectures, and the in-depth processing that occurs during break s in creases s tudent learning. With a little practice it is pos si ble to be comfortable lec turing and to actually enjoy it. If you are uncomfortable the students will be uncomfortable regardless of how well prepared you are. Quickly prepared brie f lecture note s are effective since they control content tyranny By focusing on the most important points and le aving detail s to examples, you don t have to race through every second of the lecture Remember that from the students' viewpoint, it is more important to end on time than to cover everything. The seco nd time you teach the course, try making partial lecture transparencies Include most of the material needed for the transparency but ski p some of the key point s. Give copies of these note s to the students. Thi s procedure will eliminate many of the errors inherent in note taking and will Spring 200 1 give th e st udent s time to think-but it will s till require them to pay attentio n so they can fill in the key missing items. You can thus cover more material without sac rificing stu d e nt und e r stan ding. Tests Write new tests every term. As you teach create a file of po ssi ble test problems. They ca n be variants of homework problems, or problem s sparked b y s tudent misunder sta nd ing s and so forth. The purpose of the file is to provide potential problem s that can be considered when you write the test. Avoid di sasters by so l ving the test completely be fore using it and record how long it takes you to solve the te st. Freshmen and so phomore s will need about five times as lon g, junior s about four times as lon g, and seniors about three times as long Di sc u ssi n g procedures in class thoroughly before the first test will h e lp reduce the stude nt s' anxiety. A goo d practice i s to use old te s t s as un gra ded practice tests that the students can do on their own, po s tin g the so lution on a bulletin board or on the web. This access to old tests help s greatly in reducing s tudent test anxiety. Be present for the test s ince you are the best one to fix any last-minute errors or prob lem s. There i s also le ss cheating when the professor is pre se nt. If at lea st half the class is unable to finish the te st on time the test is too lon g. Try to mak e grading as fair as possible, keeping in mind that s tudent s consider unfair grading to be unethical. For reasons of consistency prepar e a so lution key to allocate partial credit when appropriate. Fair grading requires a re grade procedure Reduce the ha ss le of regrades by requiring written regrade request s. Attention to Students Students want and deserve individual a ttention They are very tolerant of fumblin g in the lecture if they believe you care about them. Although the average engineering under graduate ma y not be as s mart as your peer s in graduate school were, remember that he or she counts among the best undergraduate s at your sc hool. And s heer technical compe tence is less important for s ucce ss in industry than motiva tion hard work, timing (o r luck ), communication skills, and the a bility to work well with a diver se assortment of people. Look for the best in your students, and you will probably find it-professors with a good attitude usually end up with s tudent s with good attitudes. If you don t learn the s tudent s' names they will feel like just numbers on a list and will be much more likely to s kip class, be di s ruptive not do the work, and/or cheat. Admit tedly learning a lot of new name s each se mester is difficult but the effort is repaid by s moother course operation. Any93

PAGE 12

thing you know beyond their names, such as hometowns or career goals, will greatly help you gain rapport with them. Since personal attention to the students needs requires a significant expenditure of time, efficiency and effectiveness can get lost in the competition for their share of time. A reasonable compromise is to hold scheduled group help ses sions (particularly before tests) and a modest number of scheduled office hours during the week. Be available to the students during your office hours Also asking your teach ing assistants to hold office hours provides another opportu nity for the students to learn. Come to class five minutes early and stay five minutes after class. In addition to giving you a chance to prepare the classroom, corning early sends the message to the students that you are looking forward to this class. Staying late offers a good time to answer questions The combination of com ing early and staying late provides an opportunity for indi vidual attention, particularly for those students who will not use office hours. When students ask for special arrangements to take tests or to turn in homework, be flexible, but require them to be responsible and to inform you in advance if possible Occa sionally students will abuse your generosity. It will usually be clear when this has happened however and you should make sure it does not happen a second time If you treat students as adults most of them will act accordingly A NEW TEACHING-LEARNING PARADIGM Standard courses use a teacher-centered paradigm. Even when such courses are well taught, using advanced strate gies such as cooperative groups they suffer from some deficiencies that appear to be inherent to the basic paradigm. Students seldom learn how-to-learn on their own and there is a clear limit to the professor s efficiency in teaching the course. Relatively mature students can take more responsi bility for their learning and be taught with a problemor project-centered paradigm. Engineering students will focus on learning when there is a task that must be completed Problem-based learningl 7 J (PBL) is a method for using problems or short projects to focus student attention on learning. While PBL does help students learn how-to-learn, it does not increase the professor s efficiency since preparation and grading of the projects is very time-consuming. PBL is usually reported as increasing, not decreasing, the time the professor spends on the course. For students to learn how-to-learn and to drasti cally increase the professor's efficiency while retaining course effectiveness a different paradigm is needed. Fortunately, the efficiency literature gives us a clue as to what this paradigm should include-delegation.P 21 Instead of the professor planning the material, picking topics pre paring material, lecturing, etc. ask the students do this work. 94 With appropriate feedback from the professor, delegation of these responsibilities to the students can result in significant growth in their ability to learn Delegation can be used for the entire coursel 8 1 or for a portion of the course. Course projects are an effective way to focus students attention, and they lend themselves to delegation of respon sibilities Projects lead to more learning if significant class time is devoted to them For example, finish the lecture portion of the class before the end of the term and spend the remaining class time on project work. If class time is not devoted to the project, students consider it add-on work. Although projects can be done by individuals or groups, group projects result in much more significant efforts. I assign the groups to ensure that they are diverse in ability, learning styles, and work styles Use the principles of good cooperative group instruction_f 4 1 The professor sets the tone for the project work. Expect graduate students and seniors to deliver professional quality work. Provide examples of papers or reports that surpass the minimal quality standards. Give guidelines for topics and some examples but expect the students to devise their own topics and titles Work with the students to narrow the scope of their projects so that they can be finished in the time available. For example, one group that started with the topic of supercritical extraction had 19,000 hits in a computerized search Two iterations later, the topic supercritical extraction of coffee resulted in 65 hits which is a much more manage able number. The topic must be something new for the students. Do not allow recycling of projects from other courses and note in writing that recycling projects will be considered a form of cheating. Although allowing students to do a project on their master's or PhD research might seem effi cient it is unfair to students who are not doing research in an area related to the course. Regular meetings with groups during scheduled class time and periodic student presentations to the entire class help combat procrastination. Final reports will be significantly better if students first turn in a rough draft. Have another group critique each rough report. These critiques help to improve the final reports and give the students practice in the highest level of Bloom s taxonomy-evaluation. If the cri tiques are graded the students will take this exercise seri ously I also critique the drafts with the idea of showing the groups areas for improvement. Allow about one week for groups to finish their reports after the critiques are returned. I also ask the students to fill out forms to critique oral presentations, but these critiques are not graded. A side benefit of requiring critiques is that everyone pays attention and learns from the projects of all groups. Weekly group meetings instead of lectures help prevent procrastination, keep the professor informed of group progress, and provide an inkling of personal interactions within each group. In addition to commenting on the techniChemi c al Engin ee rin g Edu c ation

PAGE 13

cal work, take time to discuss work habits when necessary For example, most graduate students have not learned how to rapidly sort articles so that only the most important are read thoroughly The professor can also be a cheerleader when groups feel that they will never be able to finish their projects. When the members of a group are not getting along, part of the meeting time can be used to help the students start processing group interactions. Do not try to solve their interpersonal problem s, however. Make the stu dents do this work or at least muddle through it. The bane of grading group work is freeloaders. Delegate the responsibility of lowering the grades of freeloaders to the students My grade assigned to each project is the highe st grade students in the group can receive for the project. I require the students in each group to assign what percentage of this grade (ranging from Oto 100 % ) each group member should receive. I then average these percentage s for each group member and calculate their project grades. This pro cedure reduces freeloading and drastically reduces complaints from other group member s when freeloading occurs. This project-based paradigm is very efficient for profes sors. During the project work I typically spend a total of four hours per week on the course, with most of that time focused on the st udents During project work the students spend much more time working on the course than the professor does! Grading reports takes time but s ince the reports are better than in other classes it is easier. The students learn their topic in depth they learn how-to-learn and they actually pay attention to the feedback on their writing. A note of caution is in order, however. Most professors and students are inexperienced with project-ba se d teaching. Professors need a certain amount of chutzpah to relinquish the normal control of a lecture course. They also need to know the material better than they would for a lecture cla ss since it is impossible to prepare for student questions Note that this method is not turning the students loose ." Students actually receive increased guidance and support. Despite the support, the freedom and responsibility may overwhelm im mature students Students particularly those with high grades, may rebel. Other faculty may be skeptical and probably will not be supportive if the course flounders. Because of these risks, a graduateor senior-level elective course i s a good place to experiment. IMPROVEMENT AND GROWTH Master teachers may be born not made; but good, effi cient teaching is a learned skill. Sign up for a teaching workshop. Study and try out new teaching methods After each class reflect on what worked and what didn t, and tailor your future actions accordingly. Take notes, with the aim of improving the course next time. Find someone in your department with whom you can discuss teaching on a Sprin g 2001 regular basis Continual experimentation with teaching meth ods help s to prevent boredom and burnout which can be major problems. Such experimentation can lead to teaching improvement and eventual recognition as a master teacher. REFERENCES 1. Covey, S.R., The Seven Habit s of Highl y Effective P eo pl e, Simon and Schuster, New York, NY ( 1989 ) 2. Lakein, A. H ow to Get Control of Your Time and Your Lif e, Signet Books New York NY ( 1973 ) 3. Wankat, P. C., "Effective, Efficient T eaching," Proceedings ASEE 1999 Annual Conference CD ROM pdf file 000167 ( 1999 ) 4. Wankat, P.C. and F S. Oreovicz, Teaching Engin eeri ng, McGraw-Hill New York, NY ( 1993). [Out of print Avail able free as pdf files at 5. Boice R. The New Fa c ult y Member Jossey-Bass, San Fran cisco CA ( 1992 ) 6. Boice, R., Advic e for N ew Faculty Members: Nihil Nimus, Allyn and Bacon Boston MA ( 2000 ) 7. Woods D .R., How to Gain the Most from Problem Based Learning D.R. Woods, Waterdown, Ontario Canada, ( 1994 ) [Available from McMaster University Bookstore 905-5727160] 8. Wankat, P.C., Learning Through Doing : A Course on Writ ing a Textbook Chapter ," Chem. Eng. Ed ., 27 (4), 208 (1993) 0 [ A.-5-3.._b o o_k_ri_e_v_ i e_w ______ __,) Multimedia F l uid Mechanics by G.M. Hom sy, e t al. Cambrid ge Uni ve rsity Pr e ss (2000) $ 1 9.95 Re viewe d by Hossein Haj-Hariri University of Virginia The CD by Homsy et al. i s a most welcome and timely educational tool for students (a nd instructors!) of introduc tory fluid mechanics. Fluid mechanics i s a very visual disci pline. To date, such visual accompaniment to the mathemati cal equations describing flow physics has either come from labs or from samplings of the fantastic movies put together in the 1960s Whereas the material of those movies will never become outdated, the innovative multi-media approach adopted by Homsy et al., adds dimensions to the presenta tion that were s imply not available forty years ago. This CD ROM is a true multi-media tool that has no paper counter part In other words, this is not a book typed on a CD-it is truly all that the box cover promises, and then some. The approach is based on modules Currently there are three technical module s, with more promised. The current modules are dynamics kinematics, and boundary layers There is also a module on history, which sho u ld be studied by all students. -------------Continued on page 101. 95

PAGE 14

18j9::j laboratory ) -----------=--A SUPERCRITICAL EXTRACTION EXPERIMENT For the Unit Operations Laboratory RONALD G. GABBARD,* DANAE. KNox New Jersey Institute of Technology Newark, NJ 07103 S upercritical fluid extraction (SCFE) is becoming a viable unit operation in the chemical process indus try. It uses the distinguishing properties of a fluid that is above its critical point (critical temperature and pressure) to enhance performance in an extraction process. While the concept of SCFE has been known for over a century,l 11 it has not been widely used in industry for a variety of reasons. Foremost among these reasons is the high financial risk involved with SCFE-specifically, high installation and op erating costs for a process with a relatively short track record of commercial-scale success. Another reason is that a con ventional separation technique is usually already available. Add to this the difficulties caused by the lack of sound theoretical models available for scale-up and it becomes obvious why there has been no incentive for SCFE develop ment on a wide-scale industrial level. Even the early com mercial applications, such as propane deasphalting in the 1930s the SOLEXOL process of the 1940s and the ROSE process in the 1950s, were not enough to generate large scale interest.r2 1 While these reasons remain true today, new motivating factors have recently paved the way for SCFE to become a viable extraction alternative. The modern chemical engineer is faced with environmental regulations that require strict control of emissions and reductions in hazardous waste A change in energy costs has lessened the favorable gap in operating costs conventional high-heat separation techniques such as distillation have historically had over high-pressure SCFE systems. Increased performance demands, such as lower acceptable limits of either residual solvent or other contaminants in the food and pharmaceutical industries, have increased the popularity of SCFE. Also SCFE solvents (such Address: BASF Corporation Polymers Division South Brunswick NJ 08831 as carbon dioxide) are often more environmentally friendly As SCFE becomes more and more popular in industry it is finding widespread applications from the decaffeination of coffee to the removal of trace organic contaminants in waste water. f3 1 Additional work is going on in many other areas from coal liquefactionl 4 l to fractionation and purification of polymers. l 5 l Some of these processes (such as coffee decaffeination) are vastly different from the original deasphalting and ROSE processes, while others (such as coal liquefaction) are very similar. While these widely vary ing applications are using many different solvents the one used most predominantly i s carbon dioxide. Supercritical fluid extraction also presents a unique com bination of high-pressure phase equilibrium and mass trans fer. As such, an experiment dealing with SCFE represents a Ronald G Gabbar d is Process and Product Development Manager for the Styropor Busi ness Group in the Polymers Division of BASF Corporation where he has been doing poly mer related research for the last eleven years. He previously worked as a Process Develop ment Engineer at Maxwell House Coffee and it was in this capacity that he developed an interest in SCFE technology He received his BS and MS in Chemical Engineering from New Jersey Institute of Technology. Dana E. Kno x is Associate Chair for the Chemi cal Engineering Chemistry and Environmen tal Science Department at New Jersey Institute of Technology where he has been since 1983. His teaching interests are in graduate and un dergraduate thermodynamics and equilibrium stage processes and his research interests are in fluid phase equilibria and thermodynam ics He received his BS ME, and PhD degrees in Chemical Engineering from Rensselaer Poly technic Institute Copyri g ht ChE Divisi o n of ASEE 2001 96 Ch e mi c al Engineerin g Education

PAGE 15

... this article discusses a laboratory experiment that both reinforces fundamental engineering principles and introduces the students to one segment of this growing technology-specifically solid/SCFE valuable addition to the traditional unit operations labora tory. With that in mind, this article discusses a laboratory experiment that both reinforces fundamental engineering prin ciples and introduces the s tudent s to one segmen t of this growing techno l ogy-specifically so lid/SCFE. The experiment provide s an opportunity for the s tudents to explore SCFE and to use their engineering ski ll s to deal with issue s of sca l e-up and high-pre ssure equipment design and operation.l 61 From a thermodynamic point of view, it allows s tudent s to explore physical-property prediction at high pre s ure s far away from ideal beha vior w h en experime ntal data are not available They are then asked to u se these predic tions to correlate an equipment design parameter s uch as th e ma ss transfer coefficient. Additionally st udent s have the opportunity to evaluate the u sefu lne ss of the data they have co ll ected. They will need to und erstan d that if the data i ndi cates saturation of the exit strea m their analysi s of the ma ss transfer coefficient will be invalid becau se the eq u tion they are u s in g (see Eq. 1 in the "Ana ly sis" sec tion ) become s indeterminate. Finally they will need to ha ve de veloped a plan to avoid sa turation prior to starti ng the ex periment in order to be s ucce ssfu l. CO 2 Supply Feed Micro-metering Valve Spr in g 2001 Supercritical E xt ract i on Column Rupture Disc p As far as we know the inclusion of a s upercritical extrac tion experiment in the se nior unit operations laboratory is uniqu e. STUDENT EXPERIMENT The experiment consists of a se mi-continuous packed-bed extraction of naphthal ene by s upercritical carbo n dioxide The primary ob j ective is to mea s ure the mas s tra n sfer coeffi cient for the extraction at a variety of conditions and to de ve lop a correlation for it as a function of these process conditions Carbon dio x ide was the chosen so lvent because of its moderate critical conditions (304.2 K 73.8 b a r ), it s widesp read industrial u se, and its environmentally friend l y nature. It is also nontoxic maki n g it a very safe lab so lvent. Naphthalene was chosen becau se of its relatively hi g h so lu bility in s upercritical car bon dioxide and the availability of s u fficient data on the sys tem .l5 1 Equipment The experiment consists primarily of a s upercritical scree in g sys tem (see Figure 1) designed and manufactured by Autoclave Engineers of Erie, Penn sy lvania. The pre-a s E l ectric Heat Tracing .------, : Ll l ---, i ' ...._ _ ----J Extract PRV Receiver ---+-----l T Vent Figure 1. Flow diagram: supercritica l fluid ext raction system 97

PAGE 16

sembled system includes all the necessary basic compo nents : feed pump extraction column, extract receiver, in strumentation, and a heated pressure boundary used to de pressurize the exit stream. The cost of an Autoclave (814838-5700) system typical of the one used in this laboratory was slightly lower than a similar system made by ISCO (800-228-4250). The heated pressure boundary was optional and added to the cost of the ISCO SCF 1200 system. One additional benefit of the Autoclave system is that it is a little larger in size than the ISCO system. Since this is intended to be a unit operations laboratory we felt that having an ana lytical-scale unit would not do justice to the concept of SCFE as a unit operation. We wanted the students to have some degree of a "hands-on" experience with the lab that we felt would not be achieved with smaller analytical scale equipment. A standard CO 2 cylinder with a liquid dip tube is used as the feed tank The CO 2 is cooled by passing the feed tube through an ice bath prior to entering a Milton Roy 1/4-Hp, variable-speed positive-displacement (PD) pump. The PD pump is capable of operating between 40-400 cc/hr. The pump discharge pressure is controlled by an adjustable back pressure control valve that can operate in the range of 8-480 bar. Excess flow which causes a pres s ure higher than the desired set point is recirculated back to the suction side of the pump. The pump di sc harge pressure is measured just upstream of this control valve. A vapor vent valve is s up plied downstream of the back-pressure control valve. This allows any vaporized CO 2 caught in the pump feed line to be vented off during start-up. Without the vent, the feed pump would become vapor bound and cavitate. Additional cooling is obtained by packing the pump head in ice. Four valves around the extraction column isolate the col umn and provide the flexibility needed to operate it in either an upflow or downflow configuration. The column is 12 inches long has an inside diameter of 0.688 inches (nominal 1 inch OD) and is rated for approximately 700 bar at 100 C. It can be electrically heated with two external band heaters. A surface-mounted thermocouple measures the outer col umn wall temperature and a Watlow proportional/integral controller is used to control the temperature. The column is protected from overpressurization by a 1/4-inch diameter rupture disc that is piped directly to the bottom of the col umn The disc is nominally rated for 480 bar at 22 C. The pressure boundary on the downstream side of the column is maintained by a micro-metering needle valve, also supplied by Autoclave Engineers. The column can be isolated upstream of this valve with a blocking valve. The discharge lines from the column, as well as the body of the micro-metering valve, are electrically heat traced with a 110-volt heating tape. The heat tracing is in place to counter act the large Joule-Thomson cooling effect that results when the CO 2 flashes across the micro-metering valve and to 98 prevent the line from freezing. The extracted material i s collected in the extract receiver. This vessel has a nominal volume of 99 cubic centimeters and has a drain valve at the bottom The vessel is protected by a pressure relief valve set to open at 1.4 bar (at 22C). The extract and solvent enter the receiver from the top. The extract, which i s no longer soluble in the nons upercritical solvent, separates from the so lvent and is collected in the vessel while the solute-free CO 2 is discharged from the top of the vessel. It then pa sses through a s mall filter to a rotameter and then through the dry test meter. In addition, the temperature in the extract receiver is measured by a thermocouple. The rotameter (calibrated for CO 2 at standard temperature and pressure in units of standard cubic feet per minute) measures the instantaneous CO 2 flow rate. The CO 2 flow is then totalized by a dry test meter. This provides total standard cubic feet of CO 2 u sed during an experiment. Procedure The students are provided with the equipment, and are given detailed safety instructions and a list of Discussion Topics" (see Table 1 ). Additionally, the experiment is con ducted under closer-than-normal supervision for the senior unit operations lab. The st udents must develop their own experimental plan that will allow them to answer the ques tions outlined in the discussion topics. In developing their plan they must decide on the pressures at which to operate the column, whether to u se upflow or downflow through the column, what flow rates to use, and how long each extrac tion should last to provide meaningful data. An individual experiment consists of charging the extracTABLE 1 Discussion Topics 1 Should th e column exit stream be sa turat ed with naphthalene? 2. Discuss how you eva luat ed the mass tran sfe r coeffic ient k. 3. For packed beds, th e mass transfer coeffic i ent is often repr ese nt ed as a function of the NR e' N 5 , and N 0 rl numbers if that function takes th e following form, determine the values of the constants a b c a nd d 4. What is the fugacity coefficient of the so lut e in the co nd ensed phase at it s sublimation pressure? 5. Use the Peng-Robinson or other s uitabl e eq uati on of sta t e to predict the solubility of the solute in the s upercritical so lv e nt. How well does th e equa ti on of s t a t e prediction compare to the solubility reported in the literatur e? 6. How much energy input is required to maintain isothermal condition s across the micro-metering valve ? 7. Support your decision to operate the column in eithe r the upflow or downflow config urati on Chemical Engin e erin g Edu c ation

PAGE 17

tion column with a known amount of naphthalene (filling the rest of the column void with sand), re-assembling the sys tem, pressurizing the system to the desired operating pres sure at a chosen temperature, and initiating flow of supercritical carbon dioxide. Periodic measurements of feed pump and column pressure, column and extract-receiver temperature and instantaneous and cumulative carbon-diox ide flow rates are taken. Once each individual extraction is completed, the column is re-weighed to obtain the quantity of naphthalene extracted. The column, rather than the naphthalene recovered in the extract receiver is weighed because it is difficult to account for all the naphthalene in the receiver without the addition of another solvent. Some naphthalene usually precipitates on the piping walls after the micro-metering valve assembly. (This needs to be cleaned out between each experimental run.) Given this, less error is introduced into the experiment by doing the simple loss-in-weight measurement on the column. Safety is a key aspect of the laboratory for two reasons. First and foremost is to ensure the safety of the students performing the high-pressure experiment; second is the heightened appreciation for safety the students gain from completing a high-pressure experiment such as this. To per form this experiment safely students are required to develop a level of proactive thinking that they are not typically re quired to have in other unit operations laboratory experi ments (i e. fluid flow, efflux time of a tank, or pressure drop in a packed column). The students must evaluate all the possible outcomes of their actions prior to doing anything with the equipment to make sure that the desired result is obtained safely. Students are not allowed to operate the equipment until they have demonstrated reasonable safety awareness to the instructor. This is not to say that the previ ously mentioned experiments should be performed casually or unsafely, but rather that the chance for serious injury is greater when performing a high-pressure experiment such as SCFE. This creates an atmosphere in which the students take lab safety very seriously Providing this heightened level of safety awareness was a significant underlying objective of the laboratory and was one of the key reasons this experi ment (High-Pressure Supercriticial Extraction) was consid ered rather than something such as a simple wetted-wall mass-transfer experiment. Some of the key safety instructions given to the students are No work can be done on the extraction column or associated piping until the s y stem has been depres suri z ed and then verified. Verification of depressur ization is accomplished by opening all valves around the column and making sure that both inlet and outlet pressure gauges read z ero and that there is no discharge from either of the two vents. Even if the column discharge is plugg e d, th e inlet pressure Sprin g 2001 gauge s hould still read z ero when the column is depressuri z ed. If this state is not obtained, the students are required to obtain help from either the instreuctor or the teaching instructor in the lab. No work should be done on the extraction column whil e it is plumbed up and in place on the extrac tion unit. All w ork should be completed while the c olumn is out of servi ce and on the workbench. Additionall y step-b y -step instructions for loading and unloading the extraction column are located in the appendix of the student laboratory. The maximum operating temperature set in the student laboratory is 55 C. While this was done to make sure that the column operating pressure would not exceed design limits it also prevents liquid naphthalene from being pushed out of the c olumn because the 55 C limit is significantly lower than the 80-82 C naphthalene melting point. Finally, with regard to safety, the students should be made aware of the issue of retrograde condensation within SCF systems This is the phenomenon that can occur when vapor liquid equilibrium exists at a temperature or pressure above the mixture critical point. In such a situation, increasing the operating temperature at con s tant pressure may lead to con densation This can be a problem in the student experiment where the micro-metering valve and discharge piping are electrically heat traced to prevent freezing The students should be cautioned to use the heat tracing only to maintain isothermal conditions in thi s part of the system and not to add unnecessary heat. Should retrograde condensation occur at the inlet of the micro-metering valve, the possibility of the sy s tem being plugged increa s e s and the system will need to be depressurized as outlined above in the first bullet. The naphthalene-CO 2 system is susceptible to retrograde condensation when the operating pressures are around 125 bar and below. Analysis The first step in the analysis i for the students to ensure that the carbon dioxide exiting the column is not saturated with naphthalene (fust discussion topic in Table 1). This could happen if either the naphthalene/sand ratio charged to the column is too large or if the carbon dioxide flow rate is too small. In these cases the effective contact time may be long enough for saturation to occur. This, of course, would render any mass transfer coefficient calculations meaningless. Students can then determine the mass transfer coefficient, k from the well-known relationship c,vo kt,C Az LM (I) where C, is the average naphthalene concentration in the exit 99

PAGE 18

stream (as determined by material balance) V 0 is the empty column superficial velocity, A is the surface area per unit volume, z is the naphthalene packed-bed length, and ~CLM is the log-mean concentration difference across the column defined as ( c sa t o)(c s at c ) ~C I I I LM c s at -0 fn I qat _C1 (2) where qat is the naphthalene concentration at saturation (i e., the solubility). Thus ~CLM represents the effective driving force for the extration. All of these quantities can be determined from measured experimental quantities except for the surface-to-volume ratio A (which is given to the students) and qt, which the students are asked to estimate from an equation of state such as Peng-Robinson (discussion topic #5). The subject of high-pressure phase behavior, in cluding topics such as equilibrium between a solid and a supercritical fluid phase, is covered in the undergraduate thermodynamics sequence at New Jersey Institute of Tech nology. The pertinent equation is M M p s at [ y s ol (P p s at )] C sa t I I I I I 1 I -yYI -ypexp RT <1>1 (3) where Pi5" 1 is the vapor pressure of the solid phase at the system temperature, V 1 5 01 is its molar volume M 1 is its molecular weight, y 1 is its mole fraction in the s upercritical fluid mixture at saturation, V is the molar volume of the supercritical fluid mixture, and $ 1 is the solute fugacity coefficient in the supercritical fluid mixture Each of the latter two quantities are determined by the chosen equation of state. The equation must be solved iteratively for y 1 since the fugacity coefficient is a function of composition. Alter natively, the students could obtain a value for 1 from the literature for this quantity. The value of A the surface-to-volume ratio for the packed bed has been experimentally estimated using the student equipment and is given to them. This value is only an order of-magnitude estimate as it will change each time the col umn is repacked with fresh naphthalene. This is because the naphthalene crystals are not very uniform in size or shape. This estimate could be improved by adding a size reduction/ classification step to the naphthalene to make it more uni form in terms of size and shape. This operation would not necessarily be part of the student experiment, but rather an operation a teaching assistant would perform to ensure that the naphthalene was uniform During the experiment the students should have evaluated the mass transfer coefficient k at several different sets of operating conditions This should allow them to correlate k with key operating conditions. A typical correlation for SCF 100 applications might have a form s uch as 1 7 81 N s h = f(NR e N sc, N ar ) (4) where N s H is the Sherwood number (kz/D A 8 ) NR e i s the Reynolds number (ov 0 p!) N s c is the Schmidt number (/DABP), and N G r is the Grashof number (ct 3 gp~p/ 2 ). Here, D A B is the diffusivity D i s the column diameter, p is the fluid density, ~p is the density difference between the saturated interface and the bulk unsaturated fluid, is the fluid viscosity and d is the average particle diameter. The Grashof number not generally needed in s ub-critical fluid applications, i s included to account for buoyancy effects These arise due to the relatively high den s ity and low viscos ity and thus exceptionally low kinematic viscosities of supercritical fluids The student s are thus expected to evaluate the constants in an expression s uch a s (5) Obtaining sufficient data to evaluate all four constants s hould be one of the objective s when the student s develop their experimental plan In preparing for the experiment, they are expected to have consulted the provided referencesf 9 ,10J for determining quantities such as viscosity and diffusivity. In their write-up the s tudents are expected to address each of the discussion topics listed in Table l The fir s t three topics relate to the experimental determination of k as al ready de s cribed. The remaining topics require that the s tu dents comprehend various thermodynamic aspects of SCFE. These include fugacities of solids at high pres s ures use of equations of s tate for high-pressure phase equilibrium and the Joule-Thomson effect. CLOSING REMARKS Student response to this experiment has been generally positive. They enjoy the hands-on experience associated with as s embling and disa s sembling the apparatus the expo sure to a non-traditional unit operation and the combination of mass transfer and high-pressure thermodynamics in a practical application The principal experimental difficulty has been deposition of naphthalene in the discharge line and in the micro-meter ing valve. This c a n be alleviated by ensuring that the exiting stream is well removed from saturation With proper choice of operating conditions however the experiment works well as designed Students can complete s everal indi vidual experiments in the allotted time of two five-hour laboratory periods. An alternative experimental set-up would be to replace the discharge line and condensate receiver with a "U-tube in a cold trap. While this idea is yet to be attempted experimen tally, one can envision weighing the tubing (including the C h e mi ca l En gi n ee rin g Ed u c ati o n

PAGE 19

"U-tube ) downstream of the micro-metering valve before and after each trial as an alternative to obtaining the amount of naphthalene extracted in the experiment. The mass of the extracted naphthalene would be a more significant portion of the total mass of the sample and apparatus being weighed. In this manner more accurate results may be possible. If multiple groups complete the lab during the semester, another enhancement to the laboratory experience could be to have the different groups use different solute materials. At the end of the semester a comparison of the correlation constants from each group could be completed and this could be used to create a generalized correlation. Possible alternative solutes include biphenyl and benzoic acid. Should this approach be taken, it is important to remember that the value of A, the surface-to-volume ratio in Eq. (1 ), must be provided for each sy s tem investigated In summary this laboratory experiment provides a valu able introduction to a modern unit operation in the chemical process industry while at the same time it encourages cre ative thinking in the synthesi s of concepts from disparate areas of chemical engineering NOMENCLATURE A Surface area per unit volume of a packed bed ( m 2 /m 3 ) a b c d Co1Te l ating equation parameter s C 1 Average concentration of naphthalene in exiting carbon dioxide ( kg/m 3 ) qat Concentration of naphthalene in carbon dioxide at saturation (kg/m 3 ) ~CLM Log mean concentration driving force ( kg/m 3 ) D Column diameter ( m ) D AB Diffusivity ( m 2 /sec ) d Particle diameter ( m ) g Acceleration due to gravity ( m/ s ec 2 ) k Ma s s transfer coefficient ( m/sec ) P Pressure (bar ) P '" Vapor pres s ure of s olute ( bar ) R Ideal ga s constant (m 3 bar/molK ) T Temperature ( K ) V Molar volume of fluid phas e ( m 3 /mol ) V 01 Molar volume of solute ( m 3 /mol) v 0 Empty column superficial velocity ( m/ s ec ) z Packed bed length (m) p Density ( kg/m 3 ) Viscosity (kg/m sec) Dim e nsionless Numbers N G Grashofnumber (d 3 gp~p/ 2 ) NR e Reynolds number (Dv 0 p / N 5 Schmidt number / D ABP) N 5 h Sherwood number (kz ID AB) REFERENCES 1. Hannay J.B., and J. Hogarth On the Solubility of Solids in Sprin g 2001 Gase s," Pro c Ro y So c 29 324 London (1879 ) 2 McHugh M.A. and V.J. Krukonis Sup e r c riti c al Fluid Ex tra c tion, Prin c ipl es, and Practi ce 2nd ed. Butterworth Stoneham MA ( 1994 ) 3. Eckert, C A. J.A. Van Alsten and T. Stoicos Supercritical Fluid Processing ," En v iron Sci. T e ch ., 20 319 ( 1986 ) 4 Maddocks, R.R. J Gibson and D.F Williams Supercritical Extraction of Coal, Ch e m. Eng. Prag ., 49 ( 1979 ) 5 McHugh M.A. and M E. Paulaitis "Solid Solubilities of Naphthalene and Biph e nyl in Supercritical Carbon Diox ide ," J Ch e m Eng. D at a 25 326 ( 1980 ) 6 Gabbard R.G. The Development of a Senior Unit Opera tions Laboratory on the Supercritical Extraction of Solid Naphthalene with Supercritical Carbon Dioxide M S The sis, New Jerse y Institute of Technology ( 1993 ) 7 Debenedetti P.G ., and RC. Reid Diffusion and Mass Trans fer in Supercritical Fluids ," AIChE J. 32 2034 ( 1986 ) 8 Lee, C H ., and G.D Holder The Use of Supercritical Fluid Chromatography for Obtaining Mass Transfer Coefficients in Fluid-Solid Systems at Supercritical Conditions, Ind Eng. Ch e m. R es., 34 906 ( 1995 ) 9 Jossi J A ., L I. Stiel, and G Thodos The Viscosity of Pure Substances in th e Dense Gaseous and Liquid Phases, AIChE J. 8 59 ( 1962 ) 10. Funazukuri Y. Y. Ishiwata and N. Wakao Predictive Correlation for Binary Diffusion Coefficients in Dense Car bon Dioxide ," AIChE J. 38 1761 ( 1992 ) 0 Multimedia Fluid Mechanics Continu e d from pa ge 95 The CD is neither a book nor a collection of movie clips. It i s truly a seamles s ly integrated multi-media tool. The user can read s ome brief text describing the phenomenon, can look at the equations and see the meaning of each term and also look at some movie clips that will drive the point home. Most importantly there are a number of very simple, but cleverly designed interactive experiments where the user can take data off of a running movie clip and process the automatically tabulated data in order to investigate the di mensional relation s hips and gain valuable insights. These interactive experiments constitute very nice classroom dem onstrations to supplement lectures. An equation feature that is used cleverly i s a roll-over feature where as the mouse pointer is dragged over each term of the equation, the term is magnified and highlighted, and its meaning pops up in a small text box I cannot overemphasize how well this CD is done. The selection of the topics, the level of coverage, and the actual presentation are all superb There are many hyperlinks throughout the CD ; however, unlike some other CDs where the user can hyperlink his/her way into a digital purgatory, on this CD one can always return to the page of interest using the small navigation map at the top of the page. Congratulations to Professor Homsy and his colleagues for undertaking the much-needed task of creating a new tool for aiding students of fluid mechanics. Also congratulations for holding the line on the price which is extremely reasonable in an environment of skyrocketing textbook prices. 0 JOI

PAGE 20

Random Thoughts ... FAQS. Ill GROUPWORK IN DISTANCE LEARNING 1 1 R ICHARD M. F ELDER, REBECCA BRENT North Carolina State University Raleigh, NC 27695 0 f all the instructional methods we a dvocate in our teaching workshops the ones we emphasize mo s t involve students working together in small groups Workshop participant s invariably ask whether such collabo ration is possible in di stance learning. The answer i s that it may take so me additional effort b y the instructor, but it can be done and done effectively. In this column we offer ideas for getting students at re mote sites to collaborate when attending lectures in a syn chronous course, working through les so ns in an asynchro nous course and doing homework in either distance mode. Other references outline the how s and whys of u si ng groupwork in traditional class sett ing s 12 3 l and discus s the educational value of distance learning compared to tradi tional classroom instruction_ l 4 l In sy nchronous lecture s, brief group exercises can be as signed just as they are in traditional classrooms. (Ask a question or assign a short problem to pairs or small groups of students, stop them after 30 seconds-3 minutes collect answers, provide the correct answer if necessary and move on.) The instructor may announce in the first class that s uch exercises will be interspersed throughout the lecture s to provide practice for the homework and tests adding that the students at the remote s ite s can either do the exercises as instructed in which case they will learn how to do them, or ju s t sit there and watch, in which case they'll quickly get bored and learn little or nothing If so me s tudents choose not to participate the loss is theirs. A s imilar procedure may be followed for asynchronous course offerings that go out on videotape or web-based media. When the students come to an exercise in a taped or streamed presentation they can either (a) pause the presenta tion, try the exercise (ideally with others who may be physi cally or virtually present with them), and then fast-forward to the point in the presentation where the answer is prese nted or (b) just do the fast-forwarding The instructor should present both options in the first class and strongly s uggest that if the st udents really want to learn the material they will choose the first one. Students may be helped to connect with one another in small groups to view the classes and work through the exercises via instant messaging, mail threaded discussion and ftp transfer s. In addition growing number s of on-line st udents-especially those in industry-have access to videoconferencing facilities with electronic whiteboards. With those tools, virtual teams can almost (but not quite) duplicate the in-person team experience. The first s tep in getting students at remote sites to collabo rate on problem se t s or projects i s to organize virtual teams and set them up to interact electronically u sing any of the tools mentioned above Simply asking students to do some thing in groups is not enough to guarantee effective learnin g, however as anyone who ha s ever tried it know s. Even in traditional classes students may do little or no work but get the same grade as their more industrious colleagues and serious conflicts may arise between teammates with varying levels of ability and senses of responsibility The problem s may be even worse when groups are virtual and don t have the se lf-regulating capability provided by face-to-face meet ings It is therefore particularly important in di s tance classes to adhere to the defining principles of cooperative learning R i chard M. Felde r is Hoechst Celanese Professor Emeritus of Chemical Engineering at North Carolina State University. He received his BChE from City College of CUNY and his PhD from Princeton. He is coauthor of the text E l ementary Principles of Chemical Processes (Wiley 2000) and codirector of the ASEE National Effective T eaching Institute Rebecca B r ent is an education consultant specializing in faculty devel opment for effective university teaching classroom and computer-based simulations in teacher education and K-12 staff development in lan guage arts and classroom management. She co-directs the SUCCEED Coalition faculty development program and has published articles on a variety of topics including writing in undergraduate courses cooperative learning public school reform and effective university teaching Copyright ChE Divi s ion of ASEE 2001 10 2 Chemical Engin ee ring Edu ca ti on

PAGE 21

especially positive interdependence (if anyone fails to do his or her part everyone loses in so me way) individual ac countability (all team members are held accounthad their say, a resolution i s so ught.) Consider conducting s uch sessio n s by videoconference or telephone rather than asynchronously. able for all the material in the assignment), and regular self-assessment of team functioning Standard references offer guidance on how to meet the criteria for cooperative learning in tra ditional cla sses, 131 and tips for making groupwork effective in a distance setting are given by Millis 1 51 and Bailey and Luetkehans 161 The fol lowing suggestions are drawn from these so urces ... working together in small 6. Collect peer ratings of indivi d u a l c i tizen ship and use the r atings to adjust t h e te am assignment grades. l 5 J Rewarding exceptional team member s and penalizing non contribu tors helps avoid many of the conflicts and re sentments that often occur when students work on group project s. A procedure for collecting ratings and u s ing them to adjust team grades is described in the literature. 171 1. Make it clear to the students why groupwork is being r equi r ed .l5 1 This admoni tion is particularly important for students in dis tance courses whose learning preferences tend to favor working independently groups ... in distance learning ... may take 7. Anticipate problems and get he l p when necessary .l5 1 You can be reasonably certain that any problem you encounter in groupwork has already been encountered by others and is ad dres se d somewhere in the literature. When a problem arises, check the references l 2 3 1 to make sure you have not forgotten any of the ele ments of good practice in cooperative learning and ask knowledgeable colleagues or faculty development center per so nnel to help you strategize remedies 2. For m small teams t h at are b a l a nced in knowledge and skills. l 5 61 Teams of three or four are large enough to provide adequate diver sity of opinions, experiences and learning s tyle s, but not so large that individual member s can successfully hide Groups of all s trong st dents or all weak students s hould be avoided. If possible, at least one member of each team some additional effort by the instructor, but it can be done and done effectivel y should have experience with the computer tool s to be used to complete the assignments 3. Give clear directions regarding both the assignments and the communication tools.l5 1 Virtual groups may find it particularly frustrating to have to decipher muddy direction s about what to do and how to do it and their frustration could hurt both their motivation and their performance. Give short preliminary assignments that require the team members to demonstrate their mastery of the communication sof tware. 4. Monitor team prog r ess and be available to consult when tea m s are h aving pr o b lems. 15 6 1 The tendency of some students in traditional classes to let groupwork slide in the face of other time demands is likely to be worse when the team members never see each other face-to-face Appoint team coordinators whose respon si bilitie s are to keep their teams on ta s k and to report on progre ss and problems at regular intervals Periodically rotate thi s role among team members. Prompt groups that are not meeting frequently enough and offer guidance if they appear to be stuck 5 Intervene w h e n necess ar y to h elp te a ms ove r come inter p ers on al pro bl ems. l 61 Suggest strategies like active lis tening to resolve conflicts (Each side makes its case, and the other side has to repeat that case to the fust side's satisfac tion without attempting to counter it. When both sides have Refe r ences 1. See for previous FAQ columns. 2 Cooper, J., and P. Robinson Annotated Bibliography on Cooperative Learning ," 3 For descriptions of different types of active and cooperative learning exercises and guidance on how to implement them, see ( a ) Millis B.J ., and P G Cottell Cooperativ e Learning for H igher Education Faculty Phoenix American Council of Education/Oryx Press ( 1998 ) ( b ) Johnson, D W., R.T Johnson, and K.A. Smith, Activ e Learning: Cooperation in the Colleg e Classroom, 2nd ed., Edina MN Interaction Book Co. ( 1998 ) ( c ) Felder, R.M., and R. Brent Cooperative Learning in Technical Courses : Procedures, Pitfalls and Payoffs ," Eric Document ED-377038 (1994 ) 4 Felder, R.M. and R. Br ent, Is Technology a Friend or Foe of Learning ," Chem. Eng. Ed 34 ( 4 ), 326 ( 2000 ) 5. Millis B.J ., "Managing-and Motivating!-Distance Learn ing Group Activities 6. Bailey M.L. and L. Luetkehans Ten Great Tips for Facili tating Virtual Learning Teams ," Distance Learning '98: Pro ceedings of the Annual Conference on Distance Teaching and L earning, Madison WI August 5-7, ( 1998 ) ERIC Docu ment ED-422838 7. Kaufman, D B. R.M Felder and H Fuller "Accounting for Individual Effort in Cooperative Learning Teams, J Engr. Ed., 8 9 (2), 133 ( 2000 ) 0 All of the Random Thoughts columns are now available on the World Wide Web at http://www2 ncsu edu/effective_teaching/ and at http : //che ufl.edu/~cee/ Sprin g 2001 103

PAGE 22

~SQ classroom ) -----1111111-------THE BUSINESS MEETING An Alternative to the Classic Design Presentation JAME S A NEWELL Rowan University Glassboro, NJ 08028 T here is an increasing conse n sus among academics and practicing engineers that effective communica tion skills shou ld be an integral part of an engineer ing education_l 1 31 When engineers who have been out of school for ten years are asked "What courses do you wish you had taken? ", Kranzberl 4 l reports that th e most commo n answer is "English courses ." Both ABETcsi and the rest of the technical communityl 61 recognize that comm un ications are part of a broader package of interpersonal communica tion and teamwork skills that Seat a nd Lord l 71 refer to as "performance ski lls. Many educationally focused programs including the pro grams at R owanl 81 and the University of North Dakota l 9 J have integrated technical communication into their core en gineering curriculum. In many cases however oral commu nication exercises in engineering consist of little more than giving repeated technical Powerpoint presentations to an audience and answering a few brief questions at the end Such an exercise emulates a presentation at a technical con ference but resembles very little else in the business world. There is no doubt that this presentation format is valuable, but it should not be the only experience that an undergradu ate engineering student receives Jim Newell is Associate Pr ofessor of Chemi cal Engineer ing at Rowan University His technical research interests are in high performance polymers and carbon materi als H is pedagogical interests focus on com mun ications and assess m ent of learning out comes He currently serves as Secretary / Treasurer of the Chemical Engineering D ivi sion of ASEE. Conducting a business meeting instead of a final pre se nta tion in a senior plant -d esign course provides an alternative to ANOTHER formal oral pre se ntation In this model s tudent teams plan and conduct a formal busines s meeting with facu lt y and industrial repre se ntative s serving in formalized roles. Details of the process are provided below THE PROCESS Each design team is asked to conduct a bu si ness meeting with the Executive Committee of their company/customer. The Executive Committee consists of the Chief Executive Officer Engineering Dir ector Finance Dir ector Mark e tin g/Sa l es Dire ctor Safety/Environmental Dir ector Proposed Plant Manager Obviously the number of members on the Executive Com mittee and their specific roles can be altered to accommo date the number of faculty and/or industrial representatives attending the presentations Each group make s a formal pre sentation to this committee including a description of the proposed process, relevant design issues an economic analy sis and recommendations This presentation should not ex ceed thirty minutes. During the pre se ntation, the committee limits itself to questions of clarification. Following the formal presentation the member s of the committee will ask questions of the design group Commit tee members may address their questions to the team as a whole, or to specific members. Although there is no time limit to the questioning period, 20 to 25 minutes represents a typic al length of time During t h e presentation, the speaker Copyri g ht ChE Divi s i on of ASEE 2 001 104 Ch em i ca l En gi n ee rin g Education

PAGE 23

stands at th e overhead projector or computer whjle the other group members are se ated facing tbe commjttee. All group members are seated during the que s tioning TEAM ROLES Each member of the design group s hould perform a s pe cific function on the team At lea s t three di s tinct roles that must be filled are The Team Leader This member is responsible for providing the introductory materials and anything dealing with the "big picture." Team-leader responsibilities include making sure that all m e mbers of the group are g iv e n sufficient opportunities to participate in the questioning and that every question receives an adequate answer The Economics Expert Thi s member is responsible for presenting th e economic analysis and fielding detailed questions about economic calculations and other issues. The Engineering Expert This memb er is responsible for presenting the technical aspects of the process including equipment selection, sizing, and pro cessi ng issues. This person shou ld be prepared to justify technical assump tions and othe r process decisions Teams with four member s can divide either the economics or engineering i ss ue s between two m e mber s, but there mu s t be only one team leader. Obviou s l y, the se po s ition s may be further divided or additional roles ma y b e added to accomodate larger teams Student learrung i s di sse rv e d if individual member s of a design team s pend the semester focusing on only a s ingle aspect of the design process To avoid this dilemma the faculty member 's se lection of the engineering expert and the econorrucs expert should be made and announced to the team only 48 hours before the pre se ntation. Using thi s ap proach team member s cannot know which sec tion of mate rial they will be responsible for di sc u ssi n g and are more likely to work on all aspects. The team may pick it s own leader. GRADING An ongoing concern with group proje c t s is how to effec tively account for individual performance in team project s. l' 01 In this business meeting grading can account for both team and individual performances. It is reasonable for s tudents to feel that their grades should not be de stroye d by a weak performance from an unmotivated s tudent. At the s ame time a weak member can negativel y impact the effectiveness of the team pre se ntation. Thu s, a di vis ion between team and individual point s seems appropriate. On the pre se ntation itsel f, the team as a whole is graded on a five-point scale based on the following items: Spring 2001 [J Visual Aids (Clarity; Font Si ze; Usefulness) [J Organization (Appropriate Structure and Flow ?) [J Int roduction (Grabs Attention? Appropriate Content?) [J B ody (Co mpl e t e n ess; Accuracy; Clarity; etc.) [x3] [J Summary (Co n c i se? Covered K ey Points ?) [J Overall Effectiveness (Speake r 's Goals Acco mplished ? ) Total Possible Points: 40 Thu s, each team member receives the sa me s core from these 40 point s. Indi v idual team member s are also evaluated on [J D elivery (Volume; Clarity ; Rat e; etc.) [J P oise and Appearance (Ap propriat e Dr ess? Nervousness? etc.) Total Possible Points: JO Thu s, every team member can receive up to fifty points from the pre se ntation. Forty of the s e points are the same for every member while ten point s vary from member to mem ber. Tru s divi s ion of team and individual grading makes all member s accountable for the success of the team while at the sa me time it maintain s individual distinctions. The que s tioning period also re s ults in a portion of the grade, but the mecharusm i s different for the experts and the team leader. Each expert i s evaluated on the following [J Poi se (Ca lmn ess, Ability to Think on One's Feet") [x2] [J Ability to Answer [x2] [J In teraction with Audience (Eye Contact? Demeanor) Total Possible Points: 25 Thu s, each expert has 25 pos s ible points for his or her role durin g que s tioning. The experts' total for the presentation and que s tioning i s divided by 7 5 to provide a 1-10 grade. The team leader ha s additional responsibilities during the que s tioning so hi s or her sco ring i s more involved It is eval uated on [J Poi se (Ca lmn ess, Ability to Think on One s Feet ") [x2] [J Ability to Answer [x2] [J Int eraction wit h Audience [J Distribution (All Group Memb e rs Used ?) [x2] [J Respon s ibili ty (Questions Suitably Answered?) [x2] Total Possible Points: 45 Each team leader ha s hi s or her total sco re divided by 9 5, resulting in the s ame 1-10 grading as the experts. It is impor tant to note that the team leader doe s not receive more credit than the other team members but that more of the team 10 5

PAGE 24

leader s grade is determined by the questioning A s ample grading sheet is shown in Table 1. Obviously the categories can be expanded altered, or weighted differently to accom modate different priorities of design faculty. SELECTION OF EXPERTS AND TEAM LEADERS Design teams select their own team leaders while experts are assigned by the faculty member in charge with only 48 hours advance notice The team leader is responsible for sending all members of the Executive Committee a brief eTABLE 1 Final Meeting Grade Report ( NOTE : x2 = double-w e ightin g; x 3 = triple weighting ) Ev a luator __ ___ ___ Project ______ ___ Co111111011 Prese11tatio11 Grades: Vi s ual Aid s ( Clarity ; Font Si ze; Usefuln e s s) Org a nization ( Appropri a t e Structure and Flow ?) Introdu c ti o n ( Grabs Attenti o n ?: Appropriat e Cont e nt ?) Body ( Complet e nes s; Accurac y; Clarity ; et c.) [ x3 ] Summary ( Concise ? Cov e r e d K e y Points ?) Overall Eff e ctiv e n ess ( Goal s A cc ompli s h e d ?) D e liver y Poi s e and Appearan c e (Questio11i11g) Poi s e [x 2 ] Abilit y to An s w e r [ x 2] Audi e n ce Int e racti o n Di s tribution [ x2 ] R es p o n s ibility [x2} Individual Totals Team Total Individual T o tal Grand T o tal Score 106 Total Points Team Leader Eco110111ics Tech11ical Group Leader Eco11omics Tech11ical mail that includes Aformal in v itation to th e meeting, including mention of the tim e and plac e A stat e ment id e ntifying th e team l e ad e r and other expert s A brief summary of the topi c to be dis c ussed during the meeting The e-mail must be sent at least 24 hours before the meeting RESULTS The business-meeting format has proven successful at two different universities Students reported that they "felt more like a team" and were less s tressed by the presentation format. Students with internship or other industrial experi ence reported that the format was more realistic and closer to what they experienced in their jobs Overall the students rated the new format a 4 73 out of a possible 5.00 when asked to rate the effectiveness of the business meeting. The faculty have al s o enjoyed this method Because of the group format there was more time for detailed questioning It was also easier to evaluate both group and individual performances Other universities including the Universidad Nacional de Salta in Argentina have expressed interest in this idea and it i s presently being implemented at the Israel Institute of Technology Overall the business meeting pro vided a useful alternative to a classical oral presenttion. REFERENCES 1. Bakos J.D., A Department Policy for D e veloping Commu nication Skills of Undergraduate Engineers ," J. of Eng. Ed. 75 101 ( 1986 ) 2. Elbow, P ., Teaching Thinking b y T e aching Writing ," Phi D e lta Kappan p 3 7 ( 1983 ) 3. Newell J.A. D.K. Ludlow and S P K. Sternberg, Progres sive Development of Oral and Written Communication Skills Across an Integrated Laboratory Sequ e nce ," Ch e m Eng. Ed. 31 ( 2 ), 116 ( 1997 ) 4. Kranzber M ., Educating the Whole Engineer, ASEE PRISM p. 28 November ( 1993 ) 5 En g ine e ring Crit e ria 2000 Engineering Accreditation Com mission, Accredit a tion Board for Engine e ring and Technol ogy Inc ., B a ltimore, MD ( 1998 ) 6 "Manufacturing Education Plan: Phase I Report Industry Identifies Competenc y Gaps Among N e wly Hired Gradu at e s ," Society of Manufacturing Engineer s ( SME ), D e arborn MI (1997 ) 7 Seat E. and S Lord Enabling Effective Engineering Teams: A Program for Teaching Interaction Skill s," J of Eng Ed ., 88 ( 4 ) 385 ( 1999 ) 8. Newell J.A. A.J. Marches e, R.P Ramachandran B. Sukumaran and R. Harvey Multidisciplinary Design and Communication: A Pedagogical Vision ," Int e rnat J Eng Ed ., 15 (5) 376 ( 1999 ) 9. Ludlow D K. and K.H. Schulz Writing Across the Cur riculum at the Univer s ity of North Dakota, J of Eng. Ed ., 83 ( 2 ), 161 ( 1994 ) 10 Kaufman D.B. R.M Felder and H Fuller "Accounting for Individual Effort in Cooperative Learning Team s J of En g Ed. 89 ( 2 ), 133 ( 2000 ) 0 Ch e mi ca l E ng in ee rin g Edu ca tion

PAGE 25

.,~. 111 51111iii3.._1_e_tt_e_r._s_to t h e e d _i_ to r __ ) Editorial Note: The "Class and Hom e Probl ems" section on pages 366-368 of the Fall 2000 issue of CEE presented Erich A. Muller's article, "A Thermodynamics Pr oblem with Two Conflicting Solutions." In it, tanks A (isothermal) and B (adiabatic) are filled with an ideal gas and connected by pipes and a valve Initiall y, P A > p 8 If the valve is opened and equilibrium attained, will it have been necessary to add ( or remove) heat from tank A? Prof esso r Mull e r s a rticl e ha s elicited the following two l etters. His reply is also appended. We appreciate the interest that Pr ofesso r Muller 's problem has generated, and request that any further corres pond e nc e on this problem be e -m ai l ed to him at emuller@usb.ve To the Editor: The recent article by MUller ( 1 J presents an intere s ting di s cussion of pedagogically important issue s. We wish to com ment on two aspects of the article. First we b e lie ve that it i s pedagogically more so und to tre a t MUiler's two conflicting so lutions as ( non-conflicting ) so lution s to diff ere nt prob lems that arise from two different equilibrium models of th e s ituation, as implied in hi s comments. Second we believe that his "Comments on the Equation for the Uniform State Uniform Flow Model can be improved regarding the ba s ic assumptions underlying u se of the un s tead y-s tate energy balance equation for a control volume and it s general appli cation in first law analysi s We elaborate on both these point s in the followin g. Concerning the analysis of the s ituation de sc ribed in the article we note that hi s Solution # l relates to a model in which it is s tated that tank B i s adiabatic"; th a t i s, ther e i s no heat transfer to or from tank B ( Q = 0) at any time to any other body although thi s doe s not preclude exchange of energy via flow of matter through the connecting line and valve. Practically s peaking the equilibrium sta te for the contents of tank B is a partial equilibrium s tate with respect to the contents of tank A: mechanical but not thermal equilibrium. Regardless of where the control surface i s placed ( around tank A alone or around tank s A and B together ), the conclusion reached i s as MUiler s tate s : Q A > 0. Solution# l is the solution to the problem ari s ing from one particular model of the situation. His So l ution #2 relate s to a different model of the si tua tion in which it is s tated that there is "a heat transfer be tween the tanks" (presumably through the connecting line and valve) In this case tank B evidently has an adiabatic enclosure with a (small?) diathermal hole in it. This changes the equilibrium aspect of the model to be a ddre sse d to one allowing for both mechanical and thermal equilibrium with Spring 200 1 respect to the contents of both tanks Thi s also changes the conclusion reached for the resulting problem to as MUiler also s tate s, Q A = 0. We thu s believe that it is pedagogically better to treat the two cases as two differ e nt model s of the s ituation and to compare the re s ult s of a first-law analysis of the resulting problem s, rather than to pre se nt the result s as two conflicting so lution s of the s ame problem. MUiler cannot on the one hand s tate that tank B is adiabatic" and on the other s tate that there i s "a heat tran sfer between the tanks ." Thermody namic s require s pr ecise, rather than "s hrewd, s tatements of model s and sys tematic an a ly s i s of resulting problems. Concernin g hi s Comment s on the Equation for the Uni form Stat e, Uniform Flow Model ," we feel that MUiler 's ju s tification of hi s s tartin g point for so lution #1 as a conse quence of a general first-law analysis for a control volume, can be s trengthened Thi s s trengthening is pedagogically import a nt to enable s tudent s to appreciate points at which approximations are m a de to exact equations. Hi s "ge neralized energy balance, Eq (7), should be re placed by (we also change the sign of W in accordance wit h recommended practice ) d [ ()] m u +e +e = dt sys sys k,sys p ,sys Q+w+I, m(t)[h(t)+e k( t)+i\(t)] inlets I m(t)[ii(t)+ ek( t)+ ep( t)] (A) exus In Eq. ( A) u, ek, er, and h deote specific internal energy kinetic energy, potential energy, and enthalpy, respectively, and a tilde C) denote s an appropriately defined intensive 10 7

PAGE 26

quantity. Thus for a property within the control volume (sys) ( ) J u(z ,t) p(z ,t) dY ( ) U sys t V U sys 1 =-msy s (-t) =--'--~J-p(~z-,t~)d_V_ (B) V and similarly for ek ,s ys and ep,sys. In Eq. (B), dV is a vol ume element, p is density and z denotes a point within the control volume. Correspondingly for a property at an inlet or exit f h(x t)p(x t)un(x t)dA h t = H(t) = A () m(t) f p(x ,t) u 0 (x t)dA A (C) and similarly for ek(t)and ep(t). In Eq. (C), dA is an area element of an inlet or exit area, x denotes a point on the area, and un is the flow velocity normal to dA. Eqs. (A) to (C) must be supplemented with the mass-conservation equation dm sys -d -= I 111(1)I 111(1) t inlet s ex it s (D) The validity of Eq (A) rests on two generally accepted concepts not introduced by Mi.iller: the continuum h y poth esis and a local eq uilibrium h ypothesis The former allows integration of point properties over volumes and areas, as in Eqs. (B) and (C), and the latter allows calculations using macroscopically based property relationships. Equations (A) and (D) are differential equations. As in some introductory texts, l 2 31 it is tempting to deal instead with their integrated forms, between times t 1 and t 2 say, m 2( u 2 + ek 2 +ep,2)-m1(u1 +ek I +ep 1) t 2 =Q 12 + w 1 2 + I f 111(1)[ii(1)+ek(t)+ eP(t) ]ct1m1 ets 1 1 1 2 I f 111(1)[ii(1)+ek(1)+ ep( 1)]ct1 (E) ex it s t 1 m 2 m 1 = L mi L m e (F) inlet s exits Equations { (A),(D)} and { (E),(F)} are exact. Equation (E) is only a formal result and may not always be useful however. This form is deceiving since it implies neglect of any inter dependence of the left and right sides of Eq. (A). Simplification of Eqs. { (A),(D)} or { (E),(F)} involves invoking appropriate approximations for special cases of the spatial and temporal dependence of the properties at the inlet s and exits and of the system. Important special cases are 10 8 uniform flow, for which the properties at an inlet or exit are independent of po sition x (giv ing ii(t)= h (t)) (or for each phase of the flow) uniform state, for which the propertie s of the system are independent of po s ition z (giving ii sys (t)= U sys (t)) (or for each phase within the system) steady-property flow, for which the properties at an inlet or exit are independent of time t steady flow, for which m at an inlet or exit is indepen dent of time t (stea dy flow u s ually implies stea dy property flow, but the converse i s not nece ssar ily true) steady state, for which the properties of the system are independent of time t; this entails the vanishing of the left si de of Eq. (A) (steady state usually implies steady flow and steady-property flow) The uniform flow (UF) assumption at inlets and exits (incorporated without comment by Miiller in hi s Eq. 7) and the uniform s tate (US) assumption for the syste m are often u se d in the absence of any information concerning spatial dependence of the propertie s. (The former is consistent with a plug-flow assumption and the latter with a well-stirred vessel assumption.) Together they form part of the basis for an unsteady-state flow model referred to by Miiller as the Uniform-State Uniform-Flow (USUF) model. This desig nation by itself is misleading however, si nce thi s model includes a third assumption that corresponds to the steady property flow assumption defined a bove As essentially pointed out by Miiller, these three assumptions (together with neglect of kinetic and potential energy terms) allow Eq. (E) to be simplified to MUiler 's Eq. (1), hi s "working equa tion" of the USUF model. More generally, for unsteady-state flow proce sses, the steady-property flow assumption does not hold, and the USUF model is invalid. We do not believe that it should be empha s ized pedagogically s ince it severely restricts the first-law analysis to rather special cases, such as the discharge situa tion described by MUiler in hi s solution #1 and filling a vessel from a constant-property s ource/reservoir. We recom mend instead that a first-law analysis deal directly with the differential equations (A) and ( D) as such. This approach handles all situations (including the USUF model as a spe cial case), and is consistent with the approch of some intro ductory textsr 4 51 and recent pedagogical articles .l 6 71 References R.W. Missen University of Toronto W.R.Smith University of Guelph 1. Millier E.A ., "A Thermodynamic s Problem with Two Con flicting Solutions," Chem. Eng. Ed., 34 (4), 366 (2000) Chemical Engineering Edu ca tion

PAGE 27

2. Sonntag R.E. C. Borgnakke, and G J. van Wylen Funda m e ntals of Th e rmodynamics 5th ed. Wiley, New York NY pp. 163-173 ( 1998 ) 3. Qengel, Y.A. and M.A. Boles, Th e rmod y namics, 3rd ed. McGraw-Hill, New York, NY, pp. 222-229 ( 1998 ) 4. Elliott J.R., and C.T. Lira Introductory Chemi c al Engi neering Th e rmodynamics, Prentice-Hall PTR Upper Saddle River, NJ pp. 72-77 ( 1999 ) 5. Sandler, S.I., Chemical and Engin ee ring Th e rmod y namics, 3rd ed., Wiley, New York, NY pp. 30-36 ( 1999 ) 6. Wisniak, J., Discharge of Vessels: Thermodynamic Analy sis ," J Ch e m. Ed 74, 301 ( 1997 ) 7. de Nevers, N., Non-Adiabatic Container Filling and Emp tying, Ch e m Eng. Ed. 33, 26 ( 1999 ) 0 To The Editor: In the Fall 2000 Class and Home Problems Column, E.A. Mtillerl 1 l proposes a thermodynamics problem designed to demonstrate that two seemingly correct but incompatible solutions can be found from the thermodynamic analysis of a particular process, and furthermore that such incompatible solutions provide an opportunity to improve one s under standing of thermodynamic analysis. Millier proposes the following: Consider two tanks, A and B, connected with a valve and initially filled with (ideal) gas at the same temperature but the pressure in A is greater than the pressure in B Tank B is well insulated (adiabatic) but tank A is maintained at constant temperature by thermal contact with a heat source or sink. Mtiller asks: "If the valve that connects both tanks is opened and equilibrium is attained, will it have been neces sary to add (or to remove) heat from tank A ?" (Denoted as QA ) For this problem it is clear that tanks A and B will be at the same pressure at the end of the process. But Mi.iller clearly intends that tanks A and B are also at the same temperature when equilibrium is attained. For tanks A and B to reach the same temperature at equilibrium would require that tanks A and B be in thermal contact. Clearly, the contra diction is that tank B cannot be well insultated (adiabatic) and in thermal contact with tank A. This contradiction ap pears in both solutions presented in the paper. Solution #1 is obtained by considering an energy balance on a control volume around tank A and shows that QA > 0. Muller subsequently argues that this solution is incorrect by considering an energy balance on a control volume around tank B; for this system, the paper (correctly) shows that energy must be removed from tank B if the temperature of tank B is unchanged. Since Mtiller is treating the tempera ture of tank B to be the same as tank A (and the temperature of tank A is unchanged), energy must be removed from tank B, which violates the requirement that tank B be adiabatic. Spring 2001 In fact, since tank B is well insulated the energy balance on tank B in the paper correctly shows that the temperature in tank B will increase at equilibrium Solution #2 is obtained by considering an energy balance on a control volume around both tanks and the connecting piping, so that the change in internal energy must equal the heat transfer to tank A (Q A ). Since Mtiller intends the tem peratures in the two tanks to be equal at equilibrium, the internal energy i s unchanged, and Q A = 0. As discussed earlier the temperature in tank B actually increases during the process so the internal energy of the system increases andA A >0. Another way to s how Q A ,;: 0 is to consider a system such as the contents of tank A after equilibrium is attained. Now, suppose Q A = 0. The contents of such a system could then be considered to undergo an adiabatic reversible expansion (since Q A = 0). Note however that (oT/oP) s > 0 for all gases (real and ideal ) Therefore when the pressure in tank A decreases, the temperature in tank A also decreases-but this is a con tradiction s ince tank A must be maintained at a constant temperature. Therefore Q A cannot equal 0. Irrespective of the difficulties expressed above Muller's point is well made that one s understanding is improved by resolving the dispute between seemingly incompatible ther modynamic analyses. Reference Thomas 0. Spicer University of Arkansas 1. MUiier, E.A., A Thermodynamics Problem with Two Conflicting Solutions ," Chem. Eng. Ed., 34(4), 366 (2000) Author's Response to Letters to the Editor I have received many comments personally and publicly, on the problem I presented in the Fall 2000 issue of CEE. As with Levenspiel's original thermo problem each and every comment is different, ranging from You chose the wrong answer" to "Send me another one of these problems." The main message of the paper is that if you use equations straight out of a book and apply them to a problem without fully understanding the assumptions behind the equations, you have a chance of coming to a false conclusion. Never theless, I think some readers missed the point," and I be lieve further discussion is in order. The initial problem is clearly stated, especially with regard to the final state : "equilibrium is attained." In a simple system such as this, thermodynamic equilibrium requires the 109

PAGE 28

simultaneous achievement of three conditions: homogeneity of pressures (mechanical equilibrium) homogeneity of tem perature (thermal equilibrium) and homogeneity in chemi cal potential (diffusive equilibrium); i.e. onl y if all three conditions (P A = P 8 T A = T 8 and A = 8 ) are simulta neously met can we affirm that the system will not change in time if left alone Solution #1, as Missen and Smith note pertains to the achievement of mechanical equilibria but as is also noted in the original article, leaves a temperature gradient among tanks A and B Given enough time, mass diffusion must take place, transferring energ y from tank B to tank A So, even though tank B has adiabatic walls and thus no heat transfer to the surroundings it does transfer energy due to a tempera ture difference. In hindsight the phrase "Given enough time this tempera ture gradient will produce a transfer between the tanks" should read Given enough time, this temperature gradient will produce a mass transfer and con s equent energy transfer between the tanks in order to be unambiguous It is clear, however that there are not two solutions to the problem even if the catchy title implies so Only one solut.A.-6 111111 3._b_o_o_k_re _v_ie_w ________ ) Advanced Transport Phenomena by John C. Slattery Publi s h e d b y Cambrid ge Uni ve r s i ty Pr e s s, Th e Edinbur g h Buildin g, Cam bridg e, UK ; 7 34 pa ges ; a va il a bl e in p a p e rba c k a nd hard cove r Reviewed by David C. Venerus Illinois Institute of Technology Advanced Transport Ph e nomena is a new textbook writ ten by Professor J.C. Slattery that represents a revision of an earlier text by the same author: Momentum, Energ y and Mass Transfer in Continua (1981 ) Tran s port phenomena i s a fascinating and interdisciplinary subject that is covered by at least one required course in all graduate chemical engi neering programs and remains an active area of research. Like its predecessor, the new book is intended for graduate students in engineering. The text is organized into three topics according to the main subjects of transport phenomena: momentum energy and mass transfer. In addition, there are two shorter topics that are covered ; kinematics (coming before the three main topics) and tensor analysis (an appendix) Each of the three main topics is divided into three sub-topics that can roughly JJO tion is possible. Any argument attempting to set solution #1 as the correct one must fir s t di s prove solution #2-an im possible task Many students and teachers (and Spicer s note is a clear example) apply the textbook equations directly to a problem without further thought on the problem It is in this sense that I totally agree with the second point noted by Missen and Smith. I believe that one s hould teach the general energy balance and for each particular case simplify it accordingly The point of the original class problem is that if one starts directly with Eq (2) one may elude some of the assump tions behind its derivation. One should always start with a generalized equation such as Eq (7 )* and integrate it accord ing to the given problem Categorizing systems as steady s tate uniform flow, etc. and stating formal equations in each case only entices the student to learn a myriad of equations making things more difficult and prone to error s. Erich A. Miiller Uni ve rsidad Simon Bolivar Equation ( 7) is identical (with the exception of the arbitrary s ign given to the work ) to Eq ( A ) o fMi s sen and Smith not to Eq. ( E ) a s s tated in their comment. be described as the formulation, application and reduction of transport balance equations. This matrix style of organi zation where the column s are the main topics (momentum, heat and mass) of transport phenomena and the rows pro vide the components and applications for each topic, is simi lar to that used in the classic text Transport Phenomena by Bird Stewart, and Lightfoot (BSL) and allows the instructor/ reader the flexibility to cover the topics by column or by row. The style and teaching philosophy of the author are re vealed in Chapter 1 (kinematics) where concepts such as motion, velocity and phase interfaces are introduced. Vari ous transport theorems are developed and used to derive the differential mass balance, or continuity equation and the jump mass balance from the mass conservation postulate. Hence the approach taken here and throughout the book is to start from general postulates about the physical world and to convert these postulates into useful conservation equations using formal mathematical tools The sub -topi c structure is itself instructional in that the reader is forced to recognize the similarities (and differ ences) between momentum, heat and mass transfer In Chap ters 2 5 and 8 (Foundations for ... ) differential forms of the conservation equations and their corresponding two-dimen sional forms Uump balances) are derived simultaneously. Ch e mi c al Engin ee ring Edu c ation

PAGE 29

CALL FOR PAPERS Fall 2001 Graduate Eduction Issue of Chemical Engineering Education We invite articles on grad uate educatio n and re searc h for our fall 200 1 issue. If yo u are interested in contributing, please se nd us yo ur name, the subject of the contribution, and the tentative date of submission. Deadline is ,lune 1. 2001 Respond to: cee@che.ufl.edu This is followed by rather lengthy developments on the behavior of materials where the most widely used (classi cal) constitutive equations are eventually presented. In Chap ters 3, 6, and 9 (Differential Balances in ... ), various trans port problems are formulated using the conservation and constitut iv e eq u ations derived in preceding chapters. These problems which range in complexity from one-dimensional, steady-state problems to two-dimensional problems that in clude boundary-layer theory, are solved using both analyti cal and numerical techniques. Chapter s 4, 7 and l 0 (Inte gral Averaging in ... ) are devoted to deriving reduced forms of the differential balance equations: time-averaged (turbu lent flows), area-averaged, local volume-averaged (pseudo continuous media), and global volume-averaged ( macro scopic balances). Appendix A provides a comprehensive review of tensor analysis and includes operation s in both rectangular Carte sian and curvilinear coordinate sys tem s. Scattered throughout each chapter are several worked examples, and each chapter ends with a se rie s of exercises (for which a so lution manual is available). At the end of each "Foundations of..." chapter there i s a summary sub section where the reader will find table s with the conserva tion eq u ations expressed in rectangular Cartesian cylindri cal, and spherical coordinate sys tems. There is no question that Advanced Transport Phenom ena is a comprehensive and carefully prepared textbook. The use of material volumes and transport theorems (rather than stationary differential volumes, as i s BSL) to derive differential conservation equations i s appropriate for gradu ate-level courses. Significant attention is given to the be havior of materials and to the entropy inequality and its use in the formulation of constitutive equations. Another positive aspect of this book is the utilization of jump balances to derive boundary conditions. Jump bal a nce s are rarely covered in modern texts on transport phe nomena but are invaluable in situations involving free and/ or moving boundary problems I particularly like the tables in Chapter 2 where the jump mass and jump linear momen tum balances are given for several special surfaces in the three main coordinate systems. Where the optimal balance is between being mathemati cally rigorous and comprehensive while also developing Spring 2001 phy s ical insight on tran s port problem s is, of course, a mat ter of preference. Many readers of this book might find that there i s too much emphasis on the first two at the expense of the third. As I read through certain portion s of the book, I so metime s found myself leafing through page after page of derivation to find the punch lin e (From my own rough estimate, there are on average a little more than seven equations per page or in the 700-page book a total of about 5000 equations!) For example, in sec tion 5.3 roughly ten page s are used to tran sfo rm so me general postulates about the thermal behavior of material s into u se ful results (i .e., viscosity and thermal conductivity are positive, Fourier 's law internal energy can be expressed in terms of density pre ss ure temperature and a heat capacity). Unfortunately, di sc u ssio n about the phy s ical implication s for the different constitutive assumptions used in the development is scant. Another comment is that the book i s almost comprehen sive to a fault. For example readers may find the results from the integral averaging chapters of marginal value, either because the s ubject i s too complex to be developed at an advanced level (e.g., turbulence and pseudo continuo u s media ), or because it was too simple and therefore inappro priate for a graduate-level text (e.g., macroscopic balances). Also, it is unlikely that one will find a situation that calls for the macro sco pic moment-of-momentum balance or the jump entropy inequality. These portion s of the book could have been better used to provide more physical insight or to analyze moving boundary problems which are so prevalent in material s science and engineering. Having said that, edu cators and researchers in thi s field will be glad to have a s ingle book where the equations needed to handle such a wide variety of transport problem s can be found Advanced Transport Ph eno mena i s a comprehensive text book that provides systematic coverage of a challenging s ubject. It can be used as a primary text for a first-year graduate course on transport phenomena ; st ud ents with prior expos ur e to the s ubje ct at the l evel provided by BSL will have a sufficient background It co uld also serve as a so lid reference book for more advanced graduate co ur ses on fluid mechanic s or on heat and mass transfer. My overall impres sion of the book is positive; I recommend it to those with an interest in teaching graduate-level transport phenomena or to those interested in learning advanced topics in this im portant and fascinating field. 0 I II

PAGE 30

k35 class and home problems ) The object of this column is to enhance our readers' collections of interesting and novel problems in chemical engineering. Problems of the type that can be used to motivate the student by presenting a particular principle in class or in a new light or that can be assigned as a novel home problem, are requested, as well as those that are more traditional in nature and that elucidate difficult concepts. Manuscripts should not exceed ten double-spaced pages if possible and should be accompanied by the originals of any figures or photographs. Plea se submit them to Professor James 0 Wilkes (e-mail: wilkes@umich.edu), Chemical Engineering Department, University of Michigan Ann Arbor, MI 48109-2136. THERMODYNAMIC PROPERTIES INVOLVING DERIVATIVES Using the Peng-Robinson Equation of State R M P RATT The National University of Malaysia Bangi, Selangor, 43600, Malaysia E quations of state are among the marvels of chemical engineering. Though simple and convenient, they may be used to model both liquid and vapor behavior for non-polar and low-polar mixtures 1 1 21 Con se quently such methods are the preferred tools of the hydrocarbon process ing industry. It is not often, especially in thermodynamic s, that you can do so much with so little. In this article, we calc ul ate thermodynamic properties that contain derivatives a topic not normally found in textbooks. There are two motivations for presenting this material. First, the calculations are simp l e, requiring no iteration or trial-and-error solutions. They are however, useful items to add to the engi ne er's toolkit and they require only critical property and ideal-gas heat-capacity data Second, it enables the st ud ent to use some seemingly abstract equations of thermodynamics to directly make numerical calculation s It is rewarding to see these relationships used to make actual calculations and to observe relative magnitudes of various quantities. To illustrate the method s, we use the Peng-Robin son equa tion of state applied to a binary vapor hydrocarbon mixture There is an almost endless number of derivatives that can be calc ul ate d-we will co n sider only a few of the more com monly enco untered ones It is trivial to simplify the ensuing eq u ations for the special case of a pure component or to app l y the equations to any number of components. The equations are valid for both liquid and vapor phases. 112 PROBLEM STATEMENT Using the Peng-Robinson equation of state, calculate the J = (aTJ 1 ) Joule-Thomp so n coefficient, -la p ) H ttaPI 2) Fluid sonic velocity, c = vl ap Js for a binary vapor mixture of n-butane and n-pentane at 390K and 11 bar that consists of 35.630 mole % n-butane. Take k; j for this binary pair to be zero. SOLUTION We will solve thi s problem in three steps. First, we will use the Peng-Robinson equation of s tate to evaluate the three derivatives involving P v, and T i.e., (aP I av )T' (aT I aP)v, Ronald M. Pratt is a lecturer in the engineer ing department at the N ational Universit y of Malaysia He obtained his BS in mathematics and in chemical engineering at the Colorado School of Mines his MS in mathematics at the Fuxin Mining Institute in Liaoning Province China and his PhD in chemical engineering at the Colorado School of Mines. Research inter ests involve molecular dynamics and fractal modeling Copy ri g ht C h E Division of ASEE 2001 Chemical Engineering Education

PAGE 31

and (av/ aT)p. Then we will find the r ea l fluid heat capaci ties, Cv a nd CP and finally we wi ll apply the se results to calculate the two thermodynami c deri vatives indicated above. Solution of the Peng-Robinson Equation of State for (aP / clv)T, (aT I aPt, and (clv / aT)p The Pen gRobin so n equation i s written as P = RT a V b v( v + b ) + b( v b) where R uni ve r sa l gas constant T a b sol ut e temp era tur e v molar vo lum e a ac[1+m[1-,jTtT c ]] a c 0.4572 3553 R 2 T / /P c m 0 .37 464 + 1 .54226 m 0 .26992 m 2 b 0.077796074 RT C /P C T c critical temperature TABLE 1 ( 1 ) P c critical pre ss ur e m pit ze r acentric factor Critical Property Data for a-butane and n-pentane The critical propertie s for the two co mpon e nt s of o ur sys tem are taken from Smith and Van Ne ss ( Table 1 ):13 1 n-butane n-pentane For convenience, the Pen Robin so n equation i s often T c( K ) 425. 1 469 7 P c( bar) 37.96 33 7 0) 0 200 0.252 written in a c ubi c pol y nomial form fo r the compressibility factor z = Pv / RT f(Z)=Z 3 +az 2 + ~z +y=0 w h ere CX=B-1 = A-28-38 2 Y=B 3 +8 2 -AB a nd A= aP / ( RT ) 2 B = bP I RT (2) For a n N-component fluid with composition {w;} we calculate the mixture parameter s, a and b from th e empirical relation s: N N a= LL w;wj,ja;aj (1-k;j) a nd i= l j=I N b=Lw ;b; i = I (3) The binary interaction coefficient, k;j, i s exac tly zero for i=j ; for i;tj k ;j is clo se to zero for h y dro car bon s. Values of k;j for many component pair s are avai lable in the literature, 141 a thou g h for mo s t h ydrocar bon p a ir s it i s safe to take k ij =O W e wi ll h enceforth u se va lu es without s ub sc ript s to refer to Sp rin g 200 1 quantities applied to th e mixtur e as a whole and s ub sc ripted values for pur e compone nt quantities. From Eq. ( 1), we calc ul a t e the pure co mpon e nt parameter s u s ing R=83 14 c m 3 -bar/mol-K: a 1 = 15 91 1115 c m 6 -bar/m o l 2 a 2 = 23522595 c m 6 -bar/mo!2 b 1 = 72 43235 cm 3 /mol b 2 = 90.14847 c m 3 /mol and th e n from Eq. (3), we find that a = 2063 1 852 cm 6 b a r/mo!2 b = 83.836216 cm 3 /mol W e now so l ve Eq (2) for the compressibility factor, Z. Thi s e quation i s easily so l ve d u si n g Newton-Raphson itera tion l5l or b y u s ing th e cubic formu l a. [IJ In eit her case we ca lculate the va por pha se compressibi lit y factor (largest of the three real root s) to be 0. 7794 for the vapor. Conse quentl y, the molar vo lume v of the vapor mixture i s ZRT/P = 229 7 54 cm 3 /mol. With knowledge of the molar vol ume and compressi bilit y, we now calcu l ate the three PVT derivative s, which fo llow directl y from the equation of s tate Knowledge of these quantities i s prerequi si t e to finding mo s t a n y derivative ther modynamic property. W e know th at these three derivatives mu s t sa ti sfy th e cyclical rule ," which may be written as ( t~ )J t;J J ~~ t =-l (4) Therefore once we h ave values for any two of the three PVT d e ri vatives, the third m ay be calculated from Eq (4) We will eval u a te each d eriva ti ve independently however a nd u se Eq. (4) to check our work The first d erivative in Eq. (4) i s found by direct differen ti ation ofEq. (1), ( a P ) RT 2a( v+b ) av T = ( V b )2 + [ v ( v + b) + b ( V b ) ] 2 (5) Sub s titutin g in the va lu es determined above, we find that ( t~ ) T = -0 .0 035459 bar/ ( c m 3 /mo!) The seco nd d e ri va ti ve in Eq. (4) i s al so fo und by direct differentiation of Eq (1) ( ap I R a' aT) v v b v( v + b ) + b ( v b) and is found to be 0.0434866 bar/K. Ther efo re ( t! l = 22.99 558 KI bar (6) The third d erivative in Eq. (4) i s a bit trickier si nce Eq. ( 1 ) i s not readily exp li cit in volume or temperature It i s there fore found implicitly u s ing Eq (2), (7) 1/ 3

PAGE 32

where ( az 1 ( J/a-z)+(~ l (6Bz+2z -3 B 2 -2 B+A-z 2 ) l aT Jr= 3z 2 +2(B-1)z+(A-2B-3B 2 ) ( aB) = -bP aT p RT 2 The derivative term, a =da/dT may be evaluated directly from Eq. (3) as da 1 ( )(jj fifi I a =dT=zL.,.L.,WjWj 1-kij l ~ai + a,""aj) (8) 1 = IJ = l J where (9) The pure component parameters are found from Eq. (9) as a 1 =-25547 0 cm 6 -bar/mol2 K a / =-38460 .2 cm 6 -bar /mo1 2 -K and da/dT for the mixture is found from Eq. (8) to be a =-33543 8 cm 6 -bar/mol2-K. Substituting known values in to Eq. (7) we find that ( l = 12 .26396 cm 3 / mo!K If we multiply the three numbers together we will see that we have satisfied Eq (4). Calculation of the Heat Capacities Cv and CP We fir s t find Cv We will consider this real fluid property to be a sum of an ideal gas contribution and a residual correction for non-ideal behavior: (10) The ideal-gas contribution i s found using heat-capacity data applicable to gases at very low pressures, which are avail able in many thermodynamics textbooks We will use the simple correlation in Smith and Van NessC 3 l c~ = R(A+BT+CT 2 +oT 2 1) (11) which is not recommended for temperatures below 298K nor valid for temperatures over 1500K For n-butane and n-pen tane the coefficients are given in Table 2 The ideal gas contribu114 A B C D TABLE2 n-pentane 1.935 2 .4 64 36.915 X 10 3 45.351 X 10 3 [1.402 X 10 6 14 111 X 10 6 0 0 tion for the mixture i s a mole fraction weighted average of the pure component va lu es, i. e., N C 10 =I_w C 10 V I V i = l I (12) Inserting the known temperature of 390K into the above equations, we calculate for each component CID= 113 050J/mol-K vi and for the mixture cID =141.376J/mol-K v 2 c~D 131.283 J / mol-K To calculate the residual contribution to Eq. (10), we use the standard equation found in many textbooks r 4 6 l for the residual internal energy derived from the Peng-Robinson equation of state UR = _Ta_' -_a fn [-z _+ B-c( )] (13) The value of c~ is calculated from its definition c~ =( a~TR l Evaluation of the partial derivative of Eq. (13) with respect to temperature yields CR = -n --,----=c;Ta" (l z + a(1 + .fi)lj v Z + a( I .fi) (14) with the temperature derivative of Eq. (8) yielding where (16) These equation s appear complicated, but the calculation is straightforward, albeit tedious. Pure component parameters for a" are found from Eq (16) to be a['= 53.2619cm 6 -bar/ mo1 2 -K 2 a2 =80 7496cm 6 -bar/mo1 2 -K 2 and a" for the mixture is found from Eq (15) to be a"= 70 2732 cm 6 -bar/ mo1 2 -K 2 Ch e mi ca l Engine e ring Education

PAGE 33

If doing hand calculations, very little error (us ually les s than 2%) is introduced by using the mole fraction weighted aver age in calculating a". In thi s case, we wou ld calculate a" to be 70.9557 cm 6 -bar/mol 2 -K 2 Substituting the above mixture quantities into Eq. (14) (using ZL =0.779438 ) gives c~=l.152 J/mol-K. Using Eq. (10), we now obtain Cv=l32.436 J/mol-K. We will use an equation analogous to Eq. (10) to calculate Cr, (17) and since cJP =C~ +R, we readily calculate cJP to be 139.597 J/mol-K. The residual contribution ma y be calcu lated from the general relationship between Cv and Cr, C~=C~+T(~;)Ji;t-R ( I 8) The two parti a l derivative s are already calculated above and can be substituted into Eq. (18); we find that C~ =C~+124.85 cm 3 -bar/mol-K and therefore C~=l36.37 cm 3 -bar/mol-K, or 13 .63 7 J/mol-K. Adding the ideal gas and residua] contribu tions according to Eq. (17) yie ld s CP = 153 235 J / molK Calculation of Thermodynamic Properties J andc Now that we have values for the three PvT derivatives as well as the two heat capacities, Cv and Cp, we can calculate a large number of thermodynamic derivatives. We will only evaluate two of the more commonly encountered ones, the Joule-Thompson coefficient, J, and the spee d of so und in a fluid, c. It is simp le to calculate the Joule-Thompson coefficient,(clT/ clP)H, using the working equationl 61 1 =-1 [T( av ) -v] Cp aT p (I 9) since all the required values have been calculated. Substitut ing into Eq. (19), we obtain J = 1.62195 Kl bar The fluid sonic velocity -J(aP / ap ) 8 is calculated from the working equation l 61 Cp aP C = V -Cvl av T (20) All the required values have been calculated. Substituting into Eq. (20) yields c=l47.164 (cm 3 -bar/mol)5 Since the se Sprin g 2001 are unusual ve locity units some unit s conversion is in order. The average molecular weight of the vapor mixture is 67 .152 g/mol and we find that the sonic velocity is ( kg-.!!!. I c2 = 21657 cm 3 -bar I00000 l s 2 ) _m_ 1000g lmol mo! bar 100cm kg 67.152g or ? 3.225l x !0 8 c~ s c=l 79.586m/ s=646 .5km /hr We can compare this result with the low pre ss ure (ideal gas) limiting value CID 05 cm= f 0 RT =185.683(cm 3 -bar/mol) =226.590m/s CV DISCUSSION Calculation of derivative propertie s is easy if there is an equation of state available to model the PVT behavior of the fluid. Two such properties have been evaluated here using the Peng-Robin so n equation of state It is trivial to evaluate a large number of other derivative properties once we know the three PVT derivatives and the two heat capacities. In this age of computers it is worthwhile for the student to develop a sprea d s heet or se t of computer s ubroutines to calculate thermodynamic properties of hydrocarbons and hydrocar bon rnixtures .L7 1 Including these and other thermodynamic derivatives would be very easy, indeed. It is interesting to estimate some of the se derivatives by u sing their finite-difference approximations and to compare these estimates with results u sing the equations di sc ussed above. For example, Cr is approximated by evaluating the enthalpy H=Hm+UR+RT(Z-1) at two nearby temperatures at 11 bar (and same composition) cP =( 1 = 30012 !~=;:;o 5 977 15 3.2361 /mol-K which is essentially the same as the result obtained above, with any erro r due to the finite-difference approximation. REFERENCES 1. Winnick, J., Chemical Engineering Thermodynamics Wiley, New York, NY ( 1997 ) 2 Sandler, LS ., Chemical and Engin ee ring Thermodynamics, 3rd ed., Wiley New York NY ( 1999 ) 3. Smith J.M. H.C Van Ness and M M. Abbott Introduction to Ch emica l Engineering Thermodynamics 5th ed., McGraw Hill, New York NY ( 1996 ) 4. Walas, S M ., Phase Equilibria in Chemical Engineering, Butterworth-Heinimann Boston MA (1985) 5. Carnahan, B., H.A. Luther and J.O. Wilkes, Applied Nu merical M e thods, Wiley New York, NY ( 1969 ) 6. Kyle, B.G., Chemical and Process Thermodynamics Prentice Hall, NJ ( 1994 ) 7. Savage, P.E., "Spreadsheets for Thermodynamics Instruc tion," Chem Eng. Ed ., 29 ( 4 ) (1995) 0 J/5

PAGE 34

.,a_5_3._1a_b_o_r,_a_t_o_r.:.y ________ ) COMPUTER MODELING IN THE UNDERGRADUATE UNIT OPERATIONS LABORATORY Demonstrating the Quantitative Accuracy of the Bernoulli Equation D AVID J KEFFER University of Tennessee Knoxville, TN 37996-2200 T he purpose of this experiment is to demonstrate the predictive capabilities of the Bernoulli equation in determining the time it takes a liquid to drain, under the influence of gravity from a tank and through an exit pipe, as a function of initial tank charge, exit-pipe diameter, and exit-pipe length. The project is comprised of an experi mental component and a modeling component. In the modeling component, predictions of the efflux time are obtained from several different approximate solutions of the Bernoulli equation; in the experimental component, the fl u x time for water draining from a tank through various exit pipes is measured Comparisons between the experimental and theoretical values are then made. The purposes of the comparison are To evaluate which terms of the Bernoulli equation are important To test the limits of applicability of the Bernoulli equation To demonstrate the value of a rigorous computer modeling Descriptions of fluid-flow experiments appear in the lit erature. For examp l e, Hesketh and Slater described an efflux from a tank experiment where students fit height-versus time data, assuming there are no pressure losses within the system.[1 1 In this work, we include head losses due to various friction terms. Hanesian and Perna described an experiment in optimizing pipe diameter with respect to capital and oper ating costs .r2 1 A key difference in the latter experiment is that the system was operating at steady state In the experiment described here, efflux from a tank, there is no steady state, and thus the resulting equations are differential in nature. EXPERIMENT AL SYSTEM Our system is situated inside a cylindrical tank (tank ra dius = R T ) filled with water to height, H The tank has a cylindrical pipe (pipe radius = Rp) of length L extending from the base of the tank (see Figure 1) The length and the diameter of the stainless steel exit pipe are variables depend ing on which of the eight available pipes is used The pipe dimensions are given in Table 1. The experimental apparatus is intentionally kept as simple as possible When the students first see the tank and pipes they frequently smirk and comment that the experiment is too low-tech to teach them anything of value but through this experiment they learn that The best experiment is the Da vi d Keffer has been an Assistant Profesor at the University of Tennessee since January 2000. His research involves the computational description of the behavior of nanoscopically confined fluids. He has transferred the tools of his research-solving algebraic, ordinary and partial differential equations-to the under graduate engineering curriculum by integrat ing modern computer modeling and simula tion tools not only in numerical methods courses but in any engineering course C op yr i g ht C hE Divisi o n of ASEE 2001 116 Ch e mi c al En g in ee ring Edu c ation

PAGE 35

simplest experiment that still ha s enough guts to demon strate the underlying physics of the sys tem. "c 3 J MATHEMATICAL MODEL The mathematical model used to describe efflux from the tank is based on the mass and mechanical energy balances. If we define our sys tem as the dotted line in Figure 1, and if we stop timing the efflux when the water level reaches H ', then the control volume is always full and we have a mas s balance of the form in=vTAT= vT 1tR~= o ut=vpAp vp 1tR ~ (1) assuming an incompressible fluid where vT is the flow average velocity in the tank AT is the cross-sectional area of the tank and RT is the radius of the tank. The subscript P designates analogous variables and parameters of the exit pipe. The average velocity of the fluid in the tank is defined as (2) where tis time. Equation (2) can be s ub s tituted into Eq. (1) to yield an expression for the velocity in the pipe dH R 2 V =-_I_ P dt R 2 p (3) The mechanical energy balance (Bernoulli equation inSystem H' L Figure 1. Schematic of the experimenta l apparatus. Spring 2001 TABLE 1 Pipe Dimensions Length (inches) 30 24 12 6 I 24 24 24 Inside Diameter (inches) 3 /16 3/16 3/16 3/16 3/16 1 /8 1 /4 5/16 eluding friction terms ) ha s the general form g~z + ~v 2 + Af' + I,h = 0 g c 2g c p r (4) where g is gravity, !lz = L+H ', !lv 2 =v /-v/, !lP is the pres s ure drop p i s the den s ity of the fluid and hr are the terms co ntributing to the head lo ss due to friction. Again if we define our sys tem as the dotted line in Figure 1 we have the advantage that the accumulation term within the sys tem over which the material and mechanical energy balance i s drawn i s zero, si nce the sys tem is constantly full of liquid. Thi s result s in a non-zero pressure drop corre s ponding to the height of the water in the tank, less H ', the final height at which we s top the experiment. In thi s sys tem we can consider frictional head loss due to the pipe wall, the contraction, and the tank wall I.h r= h r pipewall +h r contraction+ h r tankwa ll We define each term in the Bernoulli equation Af'= pg(H H') gc (5) (6) The Darcy equation gives the friction head loss for flow in a straig ht pipe ( f PL) v~ h -4 -r,pipewall DP 2gc (7) where fp i s a dimensionle ss friction factor and O p is the diameter of the pipe_ l 4 l If we assume turbulent flow in the pipe we can obtain an estimate of the friction factor, fp, u si n g an empirical relation known as the Blasius equation, applicable to turbulent flow with Reynold s numbers in the range of 4000
PAGE 36

If we combined Eqs (1) through (10) we obtain a me chanical energy balance of the form l 6 1 ( dH ) I. 7 5 [2(0.0791) 0 2 5 LD ? ] -g(L+H)+ dt po .2 sD~ 7 5 + (o 4J ( dH) 2 lo!J1 +l (l 1 O i I J[D} ( ctH)] 2 + 32H ( ctH ) =o dt 2 4 0 2 0 2 dt 02 p dt T P T (11) Equation (11) is a first-order nonlinear ordinary differential eq u ation It has no known analytical solution. If we rely on our engineering intuition to neglect terms of less significance, however, we might omit the kinetic energy term the friction loss due to contraction and the friction lo s s due to laminar flow in the tank. If we make these three assumptions, we will find that we can obtain an analytical solution to the resulting differential equation -[2(0.0791) 0 25 ot 5 ] 4 17 '}_[( H 0 J 317 ( H(t) J 317 ] tg p0 .25 D~ -75 L3 l+ L l+ L (12) where H 0 is the initial height of the water in the tank at time zero Thus, we can find the time it takes for the water level in the tank to fall to a height, H from the initial height H 0 This approximation is what is often used to describe the system in unit operations laboratories solely because it has an analyti cal solution. We will see in the next section, however, that this approximation gives not only quantitatively but also qualitatively incorrect results. 180 160 . The more rigorou s approach is to numerically solve the ordinary differential equation ( ODE) in Eq. (11). We can use a standard numerical ODE-solution technique ( e .g. Euler' s method or a Runge-Kutta method) if we can arrange the ODE into the form dH dt=f(H t) (13) Equation (11) cannot be put in this form Therefore we cannot easily solve for the velocity in the tank DH/dt, at every Euler or RungeKutta time step as is required by those algorithms But for any given time t, for which we know the height H, we can obtain the numerical value of the tank velocity by using a technique to solve a single nonlinear algebraic equation such as the Newton-Raphson method Combining the Newton-Raphson and Runge-Kutta methods is a relatively simple algorithm to implement and involves nesting the iterative algebraic equation s olver inside the routine that obtains the tank velocity for the ODE solver. For the undergraduates in the unit operations laboratory we provide ju s t such a routine written for MATLAB.l 61 The students are familiar individually with the Runge-Kutta and Newton-Raphson techniques and the majority of them di rectly comprehend the combination of the two methods We have integrated the modeling component of this ex periment with the curriculum-wide Web Resource for the Development of Modern Engineering Problem-Solving Skills instituted in the Department of Chemical Engineer ing at the University of Tennessee. Pl This web resource acts as a stand-alone self-teaching module that student s at any level in the program-from sophomores to graduate stu dents-can access to obtain the basic algorithms to solve systems of linear algebraic equations, systems of nonlin ear algebraic equations, systems of ordinary differential D ... -----....... ]18 Figure 2. Efflux time as a fun c tion of exit pipe length for the ex peri mental case, the approximation to the mechanical energy balance with an analytical solution (Eq 12), and for more complete me c hanical en ergy balance solved numericall y (Eq 11). The data are for water at 85 F draining from a six-inch di ameter baffled tank from an initial height of 11 in. to a final height of 2 in. through a pipe with a nominal diameter of 3 / 16 in. 140 u 120 ., ] 100 == ., 80 60 40 0 10 20 D 30 .. .... Cl .... _g 40 D experiment --analytical solution, eqn (12) numerical solution, eqn (11) 50 60 70 exit pipe length {cm) 80 C h e mi ca l En g in ee rin g Edu c ation

PAGE 37

equations, numerical integration, and linear regression and analysi s of variance. EXPERIMENTAL RESULTS In the lab the students examine the effects on efflux time of the initial water charge, the exit-pipe diameter, and the exit-pipe length. Here, we limit ourselves to the effect of the exit-pipe length. In Figure 2 we plot the flux time versus exit-pipe length for the experimental case, for the approxi mation to the mechanical energy balance with an analytical solution (Eq. 12), and for the complete mechanical energy balance, solved numerically (Eq. 11) The data are for water at 85 F draining from a six-inch diameter baffled tank from an initial height of 11 in. to a final height of 2 in. through a pipe with nominal diameter of 3/16 in The water density and viscosity were obtained from the literature.r s i At short pipe lengths, we see that the experimental efflux time decreases with increasing pipe length, because gravity and the hydrostatic pressure term in Eq. (11) create a driving force for flow proportional to (L+H). As we increase L, the driving force increases and the tank drains faster. In contrast, at longer pipe lengths, the experimental efflux time in creases with increasing pipe length, because we have reached a point where skin friction due to the pipe wall is the dominating factor. The approximation to the Bernoulli equation that has an analytical solution (Eq. 12) fails to model this behavior both qualitatively and quantitatively. The trend for Eq (12) is a monotonic increase in efflux time with increasing pipe length. The average relative error of Eq. (12) with respect to the experimental data is 32 6 % The more complete Bernoulli equation in Eq. (11) models the experiment both qualitativelty and quantitatively. The average relative error of Eq. (11) with respect to the experi mental data is 3.1 % Plots have also been generated regarding the dependence of efflux time on pipe diameter and initial water height. Both the analytical solution (Eq 12) and the numerical solution to Eq. (12) model the behavior qualitatively, namely that efflux time decreases as pipe diameter increases or initial water height decreases. But as was the case with the pipe length, the quantitative agreement is substantially better using Eq. (11). CONCEPTUAL LESSONS OF THE EXPERIMENT After the students have collected the experimental data in the laboratory, they take the data to the computer lab and model it using both Eqs. (11) and (12). Additionally, they look at variant models, adding one term at a time-kinetic energy, friction due to contraction, and friction due to the laminar flow in the tank wall. Adding the terms individually allows the student to determine the effect of each term in the Spring 2001 mechanical energy balance on the efflux time. The students can also explore the comparison of experi ment and theory in terms of error analysis. For example they can calculate the Reynolds number at each experimental data point and show that for any given theoretical model the accuracy decreases as the Reynolds number drops and reaches the lower limit of applicability of the expression used for the turbulent friction factor. Finally, the students (primarily juniors) obtain a first-hand demonstration of the quantitative accuracy of the Bernoulli equation. The experience helps them understand the signifi cance, validity, and limitations of the otherwise abstract mathematical expressions with which they are presented in classroom lectures on fluid flow CONCLUSIONS In this work we have described a very simple efflux from a tank experiment, of the sort commonly employed in under graduate unit operations laboratory courses. We have shown that relying only on a simplified analytical solution to the Bernoulli equation not only fails to quantitatively model the experimental results but also qualitatively fails to capture the correct trends. We have provided a more complete me chanical energy balance outlined its numerical solution, and shown that it both qualitatively and quantitatively models the experiment. The inclusion of a computer simulation in the experiment allows the students to demonstrate for themselves the conse quences of over-simplified engineering approximations and the value of a rigorous mathematical model. ACKNOWLEDGMENTS The author would like to thank Professor John Prados in the Department of Chemical Engineering at the University of Tennessee for his aid and encouragement in this work. REFERENCES 1. Hesketh R.P., and C S Slater, Cost Effective Experiments in Chemical Engineering Core Courses ," Proc. of ASEE Ann. Conf Charlette, NC ( 1999 ) 2. Hanesian, D., and A. Perna, Estimation of Optimum Pipe Diameter and Economics for a Pump and Pipeline System ," Pro c. of ASEE Ann. Conf, Milwaukee, WI ( 1997 ) 3. Davis H.T. University of Minnesota, Department of Chemi cal Engineering and Materials Science personal communi cation ( paraphrased ) 4. Perry, R.H., and D Green, Perry s Chemical Engineering Handbook, 6th ed. McGraw-Hill New York, NY (1984) 5. "Flow of Fluids Through Valves Fittings, and Pipes ," Crane Technical Paper No 410, Crane Co. New York, NY ( 1979 ) 6. Keffer D ., ChE 310 Course Website," at 7. Keffer D. "A Web Resource for the Development of Modern Engineering Problem-Solving Skills at 8. Geankoplis, C J Transport Processes and Unit Operations 3rd ed. Prentice Hall Englewood Cliffs NJ ( 1993) 0 119

PAGE 38

2001 ASEE Annual Conference CheJDical Engineering Division Program June 24 27, 2001 Albuquerque, New Mexico Technical Sessions------1 Monday, June 25 I Session 1 3 13 10:30 a .m Capstone Design Issues in Chemical Engineering Moderators: Chris Wiegenstein and David Miller l. "Ca p s tone Chemical Engineering Laboratory Courses at Michigan T ec h A.J. Pintar E.R Fisher, and K.H Schulz 2. Open Be gi nnin g Project s: A Flexible Approach to Encouraging Student Curiosity and Creativity S.S. Moor 3. "A Hand s -On Multidisciplinary De s ign Course for Chemical Eng in ee rin g Students" J.M. Keith D. Charu, J Meyer, and N. Norman 4. "T h e Inclu s ion of Desi g n Content in the Unit Operations Laboratory D. Rid gway, V.L. Youn g, and M.E Prudich 5. "An Introduction to Proce ss Simulation for the Capstone De sig n Course" D. Miller T.N. Roger s and B .A. Barn a 6. "Gra duate Brid g in g and Continuing Eduction in Chemical Engineering via th e Web" R M. Worden D Briedis and C.T. Lira Session 1413 12: 30 p.m. Non-Traditional Topics in Chemical Engineering Moderators: Nada Assaf-Anid and Ann Marie Fl y nn l. Introducing Emerging Technolo g ie s into the Curriculum Through a Multidisciplinary Industrially -S pon so red Research Experience J.A. Newell, S M Farrell, R P He ske th and C.S. Slater 2. Integration and Use of a Novel Semiconductor Pro ces in g Simulator to Teach Stream Re cy cle Issu es to Chemical Engineering Students P. Blowers and E. W e i s m an 3. "A Course on Health Safet y and Accident Prevention A.M. Flynn J. Reynolds a nd L. Theodore 4. "Trai nin g Chemical Engineers in Bioprocessing C. Preston, D. Briedi s, a nd R.M. Worden 5. Biotechnolo gy and Bioproce ss ing Laboratory for Chemical Engineering and Bioen g ine eri n g" S. Sharfstein and P Relue 6. Bacterial Di s infection in the Classroom: Engineering-Based Experimental D es ign N.M. Assaf-Anid Tuesday, June 26 Session 2213 8:30 a.m. Laboratory Automation and Classroom Demonstrations Moderators: Connie H o /L ein and Jim H enry I Laboratory Remote Operation: Features and Opportunitie s" J M Henry 2. "Us ing Web-Based Supplemental Instruction for Chemical Engineering Laboratorie s" C.R. Nippert 3. Virtual Reality Laboratory Accidents" J .T. Bell a nd H.S. Fogler 4 "Exerc ise in Chemical Engineering for Freshmen S.M Farrell and R.P Hesketh 5. "Teac hing Chemical Engineering with Ph ys ical Plant Models K.H Pang 6. "E ngineering Experiments Utilizing an Automated Bre a dmaker R.P. Hesketh, C S Slater and C.R. Flynn 7. "Ut ilizing Experimental Mea s urement s to Introduc e Underrepresented Pre-College Students t o Science a nd Engineering A. Perna and D Hanesian 120 Chemical Engineering Education

PAGE 39

Session 2565 2:30 p m. Math R e quir e men ts in the Chemical Engi n eeri n g Curric ulum Mod e rators: Anton Pintar and J en na Ca r penter I. Mathematics and C h emical Engineering Education" A. Pint a r F. Carpenter M. C utlip M Graham, and J. Pu szy n sk i 2. Mat h e mati cs in C h e micaJ Engineering: From the Ball-Park t o the Lap-Top "' R Toghiani and H. Toghiani Ses s ion 26 1 3 4:30 p m. A Galax y of Stars Mod erators: Da vid Kauffman and Melani e McN e il Senior chem i caJ e n gineering faculty w h o hav e been l eade r s in the anaJysis development and dissemination of educational technique s will be members of a p ane l t o discuss the c urr e nt s tate of c h emical e n g ineering educatio n and how it ha s progres se d o r di g r essed, over the past three decades and h ow it wi ll c h a n ge in th e co min g d ecades They wi ll introduce rising s tar s" in th e fi e ld, who wil l aJ so participate in th e pane l discussion. Se ni o r p a n e l m e mb e r s include Ri chard Fe ld er, James Stice, an d Bill y Crynes. I Wednesday June 27 I Session 32 1 3 8:30 a.m The Lat est in Pedago gy in C hemical Eng ineerin g Mod era tor s: J oe Shaeiwi tz and Walla ce Whiting I. The R ole of H omework" P. Wankat 2. "Usi n g Cr iti cal EvaJ u ation a nd P ee r-Review Writin g Assignments in a Chemical Engineering Process Safety Course D K Ludl ow 3. "C riteri o n-B ased Grading for Learning and Assessment in the Uni t Operation s Laborator y" V.L. Yo un g M.E Prudi c h and D.J. Goetz 4. Mid -Se m es t er Fee db ack E nhan ces S tud e nt Learning R Wickramasinghe a nd W.M Timpson 5 D eve l op m e nt and Impl e mm e n ta ti on of a Co mput er-Based Learnin g System in Chem i cal Engineering N .L. B ook, D K Ludlow and 0 C. Sitton 6. Evaluation of IT Tool s in t h e Classroom" S. Soderstrom a nd C. Loren z Sess i on 34 1 3 1 2:30 p.m The Master as the First Professional De g r ee Moderator : Da vid Kauffman Ther e i s a great deaJ of discu ss ion co ncerning the need for a more-than -fo ur-ye ar program for th e first profes s i o naJ le ve l in engineer in g. A p a n e l of ex p erts wi ll g i ve background information and discus s is s u es ra i sed by the a udien ce. Panelist s in c lu de Thoma s H an l ey Gera ld May, and P au l Pe n field. Session 35 1 3 2:30 p m. Computers and Computation in the Chemical E ngin eer in g C urriculum Mod era t ors: Anneta Ra za t os and Donald Visco I Temp l ateB ased Pro gramm in g in ChemicaJ Engineering Cour s es D L. Silver s tein 2. "SeaJing Ana l ysis-A Valuable Technique in Engineering Teaching and Practice" E.M. K o p aygorodsky W.B Kr an t z, a nd V.V Guliant s 3. I s Pro cess Simulation Effectively Uti l ized in C h emicaJ E n gi n eering Courses?" M.J. Save l ski K.D. Dahm a nd R P H esketh 4. Scientific Visualization for Teaching Thermodynamics" K.R. Jolls 5 Integratin g Best Pra ctice P edagogy w ith Computer -A id ed Modelin g and Sim ul ation to Imp rove Undergraduate C h emicaJ E n g in ee rin g Education J .L. Gossage, C.L. Yaws D.H. Chen, K Li T.C H o J. Hopper and D L. Cocke Society-Wide Picnic Sunday, June 24, 5:00 p m. National Atomic Museum Meet the ASEE Board Breakfast Tuesday, June 26, 7:00 a.m. Spring 2001 ChE Division Lectureship Monday, June 25, 4:30 p.m. Moderator: Doug Hirt Speaker to be announced ChE Division Business Luncheon Tuesday June 26, 12:30 p.m. ChE Division Awards Banquet Monday, June 25, 6:30 p.m. Albuquerque Petroleum Club Speaker to be announced ASEE Annual Reception and Awards Banquet Wednesday, June 27, 6:00 p.m. 12 1

PAGE 40

.t3 .. h-3._1a_b_o_r._a_t_o_r.:.y ________ ) USING IN-BED TEMPERATURE PROFILES FOR VISUALIZING THE CONCENTRATION-FRONT MOVEMENT P AULO CRUZ, ADELIO M ENDES, FERNAO D. MAGALHA.ES University of Porto 4200-465 Porto, Portugal P urification of gas streams through adsorption in a packed column is an important process in chemical engineering. The experimental study of such systems involves determination of breakthrough curve s for the ad sorbable components in the column. Both theoretical and practical implementations of this process are common in undergraduate courses but students do not readily assimilate some of its aspects. The retention of a concentration front in an adsorbent bed and its implications on the formation of shock waves, for instance, are not easy to visualize mentally especially when experimental information concerns only the out l et concentration history In our senior undergraduate laboratory we have devel oped an experiment that has been successful in helping stu dents grasp the concepts of concentration-front movement in fixed beds Due to the structure of the curricular program, most students actually take this lab course before the ad vanced separation course in which the theory associated with these processes is detailed This does not seem to im pair the students ability to interpret and understand the experimental results and theoretical concepts however. In addition to the measurement of the outlet breakthrough curve a set of thermocouples within the bed allows for the indirect visualization" of the advancement of the concen tration front. A process simulation program, developed for this purpose, also lets students gain sensitivity for the relative importance of the different operation parameters and physical proper ties. This easy to-use software is available for downloading at http://raffje.up.pt/~lepae/simsorb.html In this paper we start by briefly describing the Solute Movement Theory, which is a basic tool for interpreting this kind of process, and the mathematical model used in the 122 software s imulation, which involve s a more detailed de scription. Later we will illustrate how student s can us e both in the interpretation of experimental re s ult s THEORETICAL BACKGROUND A certain ga s, A diluted in an inert carrier gas s tream travels in a column packed with a non adsorbent solid at the same velocity as the carrier. If, however, the s olid adsorbs gas A, then it s velocity will be lower than the carrier' s. Simply put the gas i s retained by the s olid i. e., it cannot proceed along the column while the adsorption sites are not filled. Thi s idea i s more-or-le ss simple and intuitive. Things become a bit more complicated, though when one tries to interpret phenomena s uch as the formation of differ ent kinds of concentration-front waves. Thi s i s when the Solute Movement Theory ( SMT) comes in handy It predict s (for simplified but meaningful conditions) the solute veloc ity as a function of concentration. Its main result states that an infinitesimal element of solute with concentration c A will travel the column at a velocity u , which depends (inversely) on the slope of the ad s orption isotherm for c A (dCIAldc A) V u =----.,..-s 1dq A l+p ---dcA (l) Paulo C r uz is a PhD student in Chemical Engineering at the University of Porto, Portugal He received his degree in chemical engineering from the same University in 1998 His research interests are in multicomponent mass transport and sorption in porous solids and membranes Ade li o M ende s received his licentiate and PhD from the University of Porto Portugal where he is currently Associate Professor. He teaches chemical engineering laboratories and separation processes His main research interests include membrane and sorption gas separations. F ern ii o Magal h iies is Assistant Professor of Chemical Engineering at the Universi t y of Porto Portugal. He received his PhD from the University of Massachusetts in 1997 His research interests involve mass transport and sorption in porous solids and membranes Co p yr i g ht C hE Divi sio n of ASEE 2 001 C h e mi ca l En g in ee ri ng Edu c ati o n

PAGE 41

where v i s the interstitial velocity of the inert carr ier gas, E is the packing poro s ity, p is the absorbent's apparent den si ty and q A i s th e concentration of A a d sorbe d in th e solid, in equilibrium with cAThe reader can find the detail s of our approach for deriving Eq (1), ba se d on a differential ma ss balance to the column, at http://raffje.up.pt/~lepaelsimulator html For other approaches see, for example, the book b y Wankat. [ 'l SMT implies of course, a series of s impli fy ing assumption s, the m ajor being 1 local adso rption equilibrium 2. plu g flow in gas phase 3 negligible pressure drop along the column 4. isothermal operation 5. lo w adsorbate conce ntra t i on As s umption s 4 and 5 imply that the inter s titial gas velocity can be assumed constant. It i s quite clear, from Eq. (I), that stro n ge r adsorption ( higher dq A /dc A) implies s lower so lute movement (lower u ) On the other h a nd if there is n o adsorption, then u = v, and the so lute move s at the same s peed as th e inert carrier gas. Let u s now consider that th e column, initiall y without so lute i s s ubject to an inlet concentration s tep of magnitud e c 2 Suppo se that two well-defined linear regions, as s hown in Figure 1 compose the adsorption isotherm for thi s so lut e Solute elements with concentrations b etwee n O and c, will, acco rding to Eq. (1), ha ve a velocity V u =---~-s l (1-E) qi l+p -E c 1 (2) On the other hand for so lute elements with co ncentr a tion s between c 1 and c 2 the velocity i s V u s 2 = ----(--~) 1 -E q 2 -qi l+p ---'------'-E (c2 -c,) (3) Velocity u i s lower than u 2 Due to the particular s h ape of the i so therm hi g h concentrations tend to m ove fas ter than low ones. Thi s would apparently l ead to the sit u a tion deFigure 1. Idealiz ed adsorption i so th er m Spring 200 1 picted in Figure 2: high concentrations mo v ing ahead of low co ncentr a tion s! This is obviously a phy s ic a l impossibility. High concen trations cannot exist without th e lower ones What actually occurs is the formation of a s hock wave. The concentration front s hown on the left in Figure 2 pre se rve s its s hape as it mo ves along the column, with a velocity intermediate be tween u 1 and u 2 Thi s velocity can be derived from a mass balance to the s hock wave the re s ult being V u =----s l l-Eq 2 +p --E c 2 (4) As will be s hown later di s per s ion effects (not accounted for in SMT) ca u se the concentration front to develop some di s tortion as it moves along the column. And what will happen in the case of desorption i. e when ass umin g the s ame isotherm a ne gat ive concentration step i s app li ed at th e column entrance (Fig ure 3)? On ce agai n th e higher co ncentration s ( between c, and c 2 ) tend to move faster. But no w these ca n ac tually move ahead of th e lo wer ones, causing a pro gressive deformation of the originally s harp concentration front. We have then, a dis per s ive or diffu s ive wave.[1 1 This di sc u ss ion can b e easily ex tended to the analysi s of more realistic sys tem s, where the a d so rption equilibrium i s d escri bed by say, a Langmuir-type i so therm Such isotherms w h ere dq/dc decre ases w ith increasing c, are called favor a bl e isotherms. It i s easy to under s tand that in the opposite case i.e. for an unfa vora ble i so th erm, the conditions di cussed h ere for th e formation of s hock and diffu se waves would be reversed. The way SMT describe s adsorption in a packed column is quit e s impli s tic. More reali s tic considerations, s uch as axial z Figure 2. Hypothetical progression of a step in co n ce ntra tion, correspo ndin g to the isotherm s h ow n in Fi g ur e 1. This is the basis for the formation of shock waves. ------------------~~ z Figure 3. Hypothetical progression of a n eg ative step in concentratio n correspo ndin g to the isoth er m shown in Figure 1. This wo uld b e a dispersive wave. / 23

PAGE 42

dispersion, intra-particular mass transport resistance, and non-isothermal behavior, can be added if one establishes a more complex mathematical model for this process. The differential mass and energy balances of our "complex model" (CM) are presented in the Appendix. Students are expected to be able to interpret each term in the balance equations, even though the resolution of a sys tem of partial differential equations is beyond their abilities. For that we supply our homemade software simsorb which uses finite difference discretization of the spatial coordinate (routine PARSET from package FORSIMVI) and performs the time integration with routine LSODA. It use s a MS Excel interface for inputting the data and for plotting the results. This software is available for downloading at http://raff.fe up pt/~lepae/simsorb.html The input spreadsheet already contains the set of physical parameters and operating conditions used in simulating our experimental results. The adsorption isotherms (of the type Langmuir-Freundlich) were experimentally measured at our lab and the Peclet number (axial dispersion) estimated from an available correlation .r2 1 Values for the global heat-transfer coefficient and the intra-particle diffusion coefficient were not measured directly They were obtained by fitting the model to experimental results This is done previously by the class tutor, so when the students run the simulator for the first time they observe a good agreement between the model s output and their experimental results. Student s can later run the simulator with other input data and analyze its effects on the system's performance. An example of this is given later in this paper. INTERPRETING EXPERIMENT AL RESULTS The previous theoretical introduction is es sentially the first contact that students have with Solute Movement Theory. Even if they seem to understand it relatively well, the sedi mentation of concepts demands a more tan gible i.e. experimental, approach. Ideally it would be possible to directly observe the evo lution of a concentration front within a packed column This is of course, not the case. Only inlet and outlet concentrations are, in prin ciple accessible. By measuring the tempera ture at different points in the column s axis, however one can obtain indirect informa tion on the behavior of the concentration front along it. can be obtained between the applicability of SMT and an on-line visualization of the progress of the concentration front, as we shall see. For our lab course we use the adsorbate/adsorbent pair CO/activated carbon Carbon dioxide was chosen since, in addition to being quite safe to work with and having a low cost it has a high heat of adsorption in activated carbon We used activated carbon from Chemviron Carbon in the form of extruded pellets (6.3 mm x 3 6 mm). Our setup is shown schematically in Figure 4 The column is 250 mm long and 50 mm in internal diameter. Seven evenly spaced holes were drilled in its side to allow for insertion of the thermocouples. The column is placed inside an oven. This has a twofold purpose: to keep the surrounding temperature constant (the oven is set to a temperature slightly above room temperature) and to allow for complete regen eration if necessary. Actually we noticed that for this sys tem (CO/activated carbon) high-temperature regeneration is not needed; pure helium flow at operation temperature suffices for removing the adsorbed CO 2 (within the sensor's detection limit). The inlet flow rates of helium (the carrier gas) and carbon dioxide are controlled with two needle valves and monitored with electronic flow meters The outlet con centration of carbon dioxide is measured with an infrared CO 2 sensor. The inlet feed concentration can be checked before starting a run by directing the feed into the sensor through a column by-pass. A data-acquisition system con nected to a computer allow s for continuous visualization and if desired, storage of all data (flow rates tempera ture, composition). Students are asked to perform two breakthrough experi ments: Swap t;HC~heO'"cl-k ...o,i,c:J--ll valve valve One may point out that the existence of measurable thermal effects is certainly con trary to the SMT' s original hypothesis of iso thermal operation Nonetheless, as long as these are not excessive a good compromise Figure 4. Experimental setup for breakthrough experiments with in-bed temperature measurement. 124 Ch e mical Engin ee ring Education

PAGE 43

I. Response to a positive concentration step at the inlet (from pure helium to about 5 % molfraction CO 2 ) 2. Response to a negative concent ration step at the inlet (from 5 % CO 2 back to pure helium) after stage I has reached steady state. Complete execution time is about 1.5 hours, leaving enough time for the students to plot the data in the computer and start analyzing the results. As an example, we next provide so me typical plots ob tained for the operating conditions listed in Table 1. The breakthrough curve (i.e. the history of the CO 2 con centration measured at the column's outlet) obtained for a positive concentration step is shown in Figure 5. As discussed previously SMT predicts for a po s itive inlet step and a favorable isotherm, the formation of a shock wave (a sharp vertical front). On the other hand the experimental curve shows a notorious tilt and rounded edges. It is actually noticeable-a pronounced tailing as the front approaches the steady-state concentration. This departure from "idea ity" is associated with dispersion effects that oppose the compressive nature of the front, such as axial dispersion intra-particular mass transfer resistance, and non isothermality Students are asked to identify and discuss these phenomena. By using the software sim ulator, they will actually be able to identify the predominant di s persive effect in this case. Operation TABLE 1 Operating Conditions Ambient Operation Helium Temperature Pressure Pressure Flowrate ( O C) (Pa) (Pa) (m 3 (PTN)/s) 38.1 1.00 X 10 5 2.60 X [0 5 4.35 X J0 5 1 200 400 600 800 1000 Time(s) Carbon Dioxide Flowrate (m 3 (PTN)/s) 2 .4 8 X 10 6 1200 1400 Figure 5. Breakthrough curve (exit CO 2 mo] fraction as a function of time) for a positive conce ntration step at the inlet. The solid line refers to the fit of the complex model. The dashed line is the result from Solute Movement Theory: an ideal shock wave with breakthrough time computed from Eq. (4). Sprin g 2001 Figure 6 shows the corresponding temperature historie s along the column Data from the la st thermocouples are not s hown since they are placed at the beginning and at the end of the packed bed where heat is being dissipated through the column's inlet and outlet flanges. This effect masks the temperature information provided by the two thermocouples Thermocouples 2 and 6, on the other hand depict quite well the progress of the concentration front along the column. The observed increase in temperature is associated with the exothermal adsorption of CO 2 at the concentration front. The significant amplitude of the temperature increase (about 7 C), as well as the long length of time that it takes for cooling down, usually surprises the students. It is a good way to make them s tart questioning the validity of the isothermality hypothesi s, often applied without proper re flection in chemical engineering problems A more s ubtle observation is associated with the s ucces sive broadening of the temperature peaks along the column or, more clearly visible, the decrea se in the temperature maximum measured in each thermocouple. Note: the second peak s hown in Figure 6 was recorded with a slightly differ ent thermocouple and therefore it has a different response time Aside from this deviation from the general trend one may then conclude that this broadening is associated with the increasing di s persion of the concentration front as it travels along the column. Eventually, the dispersive and compressive effects compensate each other at so me point in the column and the s hape of the front stabilizes. This is the so -called constant pattern regime .[1 1 Despite the clear evidences of non isothermality and dis persive effects, students are asked to use SMT (more ex actly Eq. 4) to predict the time it takes for the shock wave to reach each thermocouple and to compare this with the experi mental results, u s ing the maximum temperature in each peak as a reference for the passage of the concentration front. Note that (for s uch a comparison to be meaningful) we have 44 [ 43 e 42 g_ 41 E 40 39 38 37 0 100 200 300 400 500 600 700 800 900 1000 Time(s) Figure 6. Temp erat ure histories obtained at evenly spaced points inside the column for a positive concentration step at the inlet. The solid lines refer to the fit of the com plex model. 125

PAGE 44

to assume that the temperature front travels in combination with the concentration front. Under so m e conditions ( m ain l y for adiabatic sys tem s), the temp erat ur e front ma y le a d the co nc e ntration front Y 1 Th e rea so n a bilit y of our assumption is reinforc e d by comparing s imul ate d concentration and tem perature profiles. In addition, as ca n b e seen from T a bl e 2, there i s a go od agreement between the SMT estimations and the ex perimental result s. It i s r e markable that the s impl e SMT model s till see m s to ha ve some pr e dictiv e va lue und er the se operating conditions. In relation to the de so rption s t ep, tb e resulting break through curve i s s hown in Figure 7. SMT p redic t s th at a negative concentration s tep assoc i a ted with a favorable i so therm lead s to a diffus e wave. Th e presence of other di s p er s ion phenomenon adds to thi s effect causing the experimen tal concentration front to hav e a very pronounced tilt. Figure 8 s hows the temperature hi story profile s The peaks are n ow inverted s ince de sorptio n is an endothermic pro cess. Now there is a clear broad e nin g of the peak s as the front tra ve l s along th e co lumn ag r eei n g w ith its disper s i ve nature (i n a ddition to the aforeme ntioned di s p e r s ion phenomena ). Th e qu a litative differenc es b etwee n the results obtained from the positive and ne gative s t e p s are quite evident to the s tudent s and contain a lot of material for di sc us s ion The quantit a tive analysis in t er m s of SMT is a l so quite int eres in g In ad dition s tud e nt s are asked to run the si mul at ion pro gra m and to compare it s re s ult s to the experimental data (see Figures 5 to 8 and Table 2) The com pl ex model by co n sidering seve ral di spersion effects and non-isothermality i s a ble to reproduce quite nic e l y th e s hap es of the br eak through c ur ves and temp erat ur e peaks. Stud e nt s are encouraged to run th e si mulator with ot h er input parameters and therefore ga in se nsitivity to how the se affect the results. It i s particularl y interesting to s tud y those TABLE2 Time for the Concentration Front to Reach Each Thermocouple Position Th e ex p e rim e ntal tim e r e f e r s t o th e tim e w h e n th e maximum t e mp e ra tur e i s r e a c h e d th e th eo r e ti c al t im e fr o m SMT us e s Eq (4 ), and th e th eo r e ti c al tim e fr o m CM u ses th e r e sult s from th e c ompl ex m o d e l s imulations Thermocouple Experimental Theoretical Theoretical position time time from SMT time from Cm ( m ) ( min ) ( min ) ( min ) 0 0.0 0 0.042 3.0 2.1 2.3 0.083 4.8 4.2 4 .2 0.125 6.6 6.3 6.2 0.167 8.4 8.4 8.3 0.208 10.3 10.4 10.5 0.250 12.1 12.5 12.5 126 200 400 600 800 1000 1200 1400 Tlme(s) Figure 7. Breakthrough c urve (exit CO 2 mo] fraction as a function of time) for a n e gative concentration step at the inlet. The so lid lin e refers to the fit of the complex model; the dashed lin e is the result from Solute Movement Theor y, wit h breakthrough times for eac h conce ntration comput e d from Eq (1) 39 38 37 0 .... 36 !! :, 35 Cl. E 34 .... 33 32 31 0 m = = = = = Tlme(s) Figure 8. Temperature histories obtained at ev e nly spa c ed points inside the c olumn for a n e gativ e c oncentration st e p at the inlet. The solid lin e s refer to the fit of the complex model. S r----------, 0 0 3 "#h = 7 W/(m2 K) h = 700 W/(m2 K) 200 400 600 800 1000 1200 1400 Tlme(a) Figure 9. Breakthrough curv e s obtained with the c omplex mod e l for two diff e r e nt valu e s of th e global heat-transfer c oeffici e nt, h Th e value h= 7 W l (m 2 K) is the on e used in fitting the experimental data (Figures 5 to 8) Th e valu e h=700 W {m 2 K} on the other hand is e quival e nt to assum ing that h eat transfer to th e exterior is instantaneous. Ch e mi c al Engin ee rin g Edu c ation

PAGE 45

parameter s that are probab l y more difficult (o r impo ss ible ) to change experimentally, such as the g lobal external heat transfer coefficient the heat of s orption or the intra-particu lar ma sstransfer coefficient. For example, increa s in g the global heat-tran sfe r coefficient gives ri se to a quite differ e nt breakthrough curve (see Figure 9). The o utlet concentration front i s now much clo ser to a pe rfect sig moid approaching s teady state much more rapidly. Thi s see m s to indicate that heat accumulation in s ide the column i s the major cause for the tai l ing of the breakthrough curve. As the front pa sses, the temperature rise s s ignificantly and the amount adsorbed is lower than for i s othermal operation. A s the column cools down again, the adsorptio n equilibrium i s s hifted toward the adsorbed s tate and more CO 2 is retained in the column. The consequence is that the outlet co nc e ntration w ill take lon ger to reach steady s tate In addition to complementing th e discussion of th e results, using the s imulation program has an extra pedagogic pur pose : it shows s tudent s how proce ss modelin g in general can be u se ful in helping to understand and optimize a real sys tem. CONCLUDING REMARKS The experimental s tudy of adsorption i n packed bed s can be complemented if in addition to me as uring the outlet breakthrou g h curves one obtains the temperature hi s tori es in diff e rent point s along the bed Such an experimental se tup is quite simple and economic a nd provides val uable qualita tive and qu a ntitative information that students can proce ss without major difficultie s. Solute Movement Theory is a b s ic tool for that anal ys i s In addition, u s in g a sof tw are s imul a tor ba se d on a more detailed mathematical model pro v ide s a better description of th e proces s and allows s tudent s to perf orm "v irtual experiments and under s tand ho w different factors APPENDIX The main assumptions of the model are: temperature ): influence the behavior of the adsorption sys tem ACKNOWLEDGMENTS The authors wish to thank the Chemical Engineering De partment for pro vi din g financial s upport for the setup of thi s experiment. NOMENCLATURE c A co n ce ntr a ti o n of A in th e int erparticul ar gas phase ( mol/m 3 ) Cp 8 h eat ca p ac it y of gas (J/ mol/K ) Cp h eat ca p acity of adsorbent ( J/k g /K ) D ax axia l di s p ersio n coeff icient ( m 2 /s) D ; intra-particle di f fu sio n coefficient ( m 2 /s) h overa ll heat-tr a n sfer coeffic ient (J/m 2 /K/ s) P pressure ( P a) q A conce nt ratio n of A a d sor b e d in th e so lid ( mol/k g) q A average co nc e ntr at i o n of A adsorbed in th e so lid ( mol/kg ) R b bed radi u s ( m ) r P particle radius (m) t time (s) T temperature ( K ) u interstitial so lut e ve l oc it y (mis) v int ers titial ca rri er gas ve l ocity ( mi s) z axial coor dinat e ( rn ) Greek L e tter s D. H h eat of a d so rpti o n ( J/mol ) packing porosity ':R gas co n s t a nt p a d sorbe nt s apparent density REFERENCES 1. Wank.at, P ., Ra te-Cont r o ll ed Separations, El se vier Applied Science London pp 239-251 ( 1990 ) 2 Edwards, M.F. and J F Rich ar dson "Gas Di s p ersio n in P acked Beds, Ch e m Eng Sci 23 109 ( 196 8 ) 3. Yang, R.T Gas S e paration by Adsorption Processes, Impe rial Co ll ege Pr es L ondon, pp 161-165 ( 199 7 ) 0 1. Plu g flow w ith axia l dispersion 2. Negligible r ad i a l grad i ents 3. Negligible pr essure drop av v aT + D T a ( 1 aT I l aT + ':RT 1 E a = 0 az T az ax az T2 az ) T at P p a t (Al) 4. Variable interstitial ve lo city 5. Instantan eous t h e rmal equilibrium between stationary and mobile phases 6. Neg li g ibl e thermal ax ial dispersion 7. Constant heat ca pa c iti es 8. Intra-parti cular mass transport de scribed b y linear driving force mod e l 9. Negligible film mass transfer resistance JO. Helium do es not absorb 11 No h eat accumulation at the wa ll Global ma ss balanc e (w h ere the total concen tration ha s already been rewritten as a fun tion of tot a l pre ss ure assumed constant and Sp rin g 2001 Inter-particular so lut e ma ss balance a(vcA) _D a 2 c A + ac A + 1a q A =0 az ax az 2 at p at (A2) Intra-particular so lute ma ss balance ( u s ing the linear driving force model) (A3) Energy balance r aT [ r ] aT aq 2 h E ':RT vCp g az + E ':RT Cp g + p ( l -E)Cp 5 at D. H p ( lE)at + R;;-(T-T a )-0 (A4) 1 27

PAGE 46

(.3 11111 ij 111111 3..._c_l_a_s_s ,-, o_o_m _________ ) Student-Performance Enhancement by CROSS-COURSE PROJECT ASSIGNMENTS A Case Study in Bioengineering and Process Modeling G-OLNUR BrnoL, lNANQ BrnoL, A.Lr QINAR Illinois Institute of Technology Chicago, IL 60616 A wide range of practical industrial and medical ap plications has increased the demand for bio related" courses in the university curriculum. Stu dents from biology, chemical engineering, and electrical e ngineerin g departments, all with different interests and ex pectations enroll in these courses Due to the diverse nature of the population in s uch classes a variety of educational approaches and tools are neces sary, both for accumulating knowledge and for implementing the theory The typical undergraduate student take s four or five courses per semester, but for many students this load may become too dificult to handle because of all the assignments projects, and midterm examinations. From time to time this necessi tates a trade-off among the tasks in the to-do list." This need led u s to initiate a cross-course platform that offered a joint term project to tho se students taking the "Introduction to Bioengineering" (IB) and "Process Control" (PC) co ur ses. With this initiative, we tested the hypothesis that integrating cross-course concepts in bioengineering and process control co ur ses through a unified project could provide a stimulat ing learning environment. The integrated project would a l so challenge the students to think beyond each co u rse in an isolated manner. BACKGROUND Biotechnology/biomedical engineering courses at the un dergraduate and graduate levels are offered regularly in the Chemical and Environmental Engineering Department at the Illinois Institute of Technology Among the undergraduate le vel courses, "Introd uction to Bioengineering provides an introductory knowledge of biotechnology and biomedical Copyright ChE Di v i s i o n of ASEE 2001 1 28 engineering from a chemical-engineering point of view. One half of the semester is spent on biomedical engineering, while the other half is used for biochemical engineering Topics covered in the course are listed in Table 1. Typically, two-thirds of the IB class population has a strong interest in biomedical engineering, while one-third is interested in biotechnology. The department offers a bio medical specialization program and students interested in Giilnur Biro/ holds BSc MSc, and PhD degrees in chemical engineering from Bogazici Univer sity Istanbul She was a senior research associ ate at I/T's Department of Chemical and Environ mental Engineering She is currently a research professor in Northwestern University s B iomedi cal Engineering Department. Her research inter ests include glucose-insulin interaction in human body metabolic pathway analysis and modeling and monitoring of bioprocesses Inane Biro/ received his BSc and MSc degrees in El ectricalEle ctronics Engineering and PhD degree in Physics all from Bogazici University Istanbul and is currently a senior research as sociate at the Illinois Institute of Technology His current research interests include study of com plexity via autocatalytic reactions model order reduction and web-based programming. Ali <;inar received his BS degree in chemical engineering from Robert College, Turkey (1970) and his MEngng (1973) and PhD (1976) de grees from Texas A&M University. His teaching and research interests are process modeling and control statistical process monitoring and fault diagnosis, and use of knowledge -based systems for real-time process supervision and control Chemica l En g in ee rin g Edu c ation

PAGE 47

... we tested the hypothesis that integrating cross-course concepts in bioengineering and process control courses through a unified project could provide a stimulating learning environment. careers in medicine and in the medical industries are ex pected to take thi s course. Many undergraduate students who take the 1B course register concurrently for the PC course since it i s a senior-year core course. Some stu dents take the PC in their six th semester to avoid poten tial conflicts in their schedules. Table 2 s how s the con tent of the PC course. There are ro u ghly 10-15 students w h o register for the 1B course each semester, while 25-35 students register for the PC course. In both courses, homework assignments are u su ally given on a weekly ba sis and form 20 % of the course grade. Students are encouraged to discuss the problems and to exchange ideas with the in str uctor s and teaching assis tants. Since the number of students i s relatively low it gives them an opportunity to interact with the course in str uctor s on a one-to-one ba s is. In the IB course, th e homework assignments are theory intensive and can be so l ved using a calculator or an Excel worksheet, while in the PC course, homework problems are computation-intensive and knowledge of Matlab is required to so lve them In order to have a uniform st udent profile in Matlab competence, the instructor tutors introductory topics in a computer-laboratory environment, hold s office hour s in a computer lab and assigns study hours under the supervi sion of the teaching assistant. Furthermore, s upplementary web-based tutorial material about Matlab and a trouble shooting service on the source codes are provided through the Internet. SCOPE We wanted to form a cross-course platform where stu dents co uld use their knowledge from two different fields bioengineering and process control--emphasizing the use of common tools from process dynamics differential equa tions, and comp ut er simulations. Concentrating on a unified project students would then have an opport un ity to analyze the results from a wider perspective To that end, glucose-insu lin interaction was chosen as the model system to be investigated. Its dynamic behavior is interesting for process modeling and control, and the unique interactions taking place in various organs in the body are of importance in bioengineering. The choice of this model sys t em turned out to be a very attractive proj ect in both co ur ses Students were quite interested in the project, b ot h b eca u se of its academic impact and be cause of the c h allenges that it offered in investigating a real-life problem. All of the bioengiSpring 2001 TABLE 1 Course Contents: "I ntroduction to Bioengineering" [] Part I : Biomedical Engineering Th e Hi s tory of Biomedicine : A Brief Review Overall Description of the Human Body Phy s ical Chemical and Rheological Properties of Blood Modeling th e Body as Compart m e nt s, Sources, and Streams Transport through Cell Membranes Artificial Kidney Devi ces Artificial Heart-Lung De v ic es [] Part II: Biochemical Engineering Re v iew of Microbiology and Chemicals of Life Kinetic s of Enzyme-Catalyzed Reaction s Kinetics of Key Rate Processes in Cell Cultures D esig n and Analysis of Biological Reactors Transport Phenomena in Bioprocess Systems TABLE2 Course Content: ''Process Co ntrol [] Incentives for c h emica l process co ntrol design aspec t s, a nd control hardware [] Analysis of the dynamic behavior of chemical processes Fundamental models input-output models, state space models Linearization of nonlinear systems Laplace tr a nsform s, transfer functions Dynamic behavior of firstand higher-order systems Time delay inver se response Empirical model s from plant data [] Analysis a nd design of feedback control systems Feedback control (PID contro l time-domain criteria, internal-model co ntr o l ) Stability analy s is, root l oc u s analysis Frequency response technique s, Bode diagrams Performance of feedback control [] Enhancements of single-loop control (cascade feedforward, inferential contro l ) [] Model predictive contro l [] Multivariable proce sses: int eractio n multi loop control, muiltivariable contro l [] Process contro l d esign 1 29

PAGE 48

TABLE3 Summary of Student Profiles and Project Descriptions (VG-U nder graduate: G-Graduate) Students Courses (T heir background s, special Project ChEIB ChEPC interests specifications, etc.) ID Taking Taken UG Biology UGChE 2 UGChE 2 and A UG ChE, Biomedical Program 3 a nd A UG ChE, Biomedical P rogram 3 UGChE 3 UG ChE Biomedical Program 4 UGChE 4 and B G ChE Intere s t in Transport Phe. B G ChE Interest in Biotechnology 5 and B UG ChE Attended Medical School C UGChE C UGChE D neering stu dents and one-fourth of the process control students volunteered to work on this project. PROJECT DESCRIPTION The purpo se of this project was to analyze the dy namic behavior of glucose-insulin interaction in a healthy person and/or in a diabetic patient. A pharma cokinetic model of diabetes mellitus originally devel oped by Puckett [ 1 l had been used previously and an MS s tudent who was working on this project at IIT wrote Matlab codes for it. 121 T hese codes were given to the st udents so they could spend their time and energy in under s tanding the fundamental phenomena involved in the glucose-insulin interaction rather than writing and debugging co de. A s ummary of the student pro files in both courses performing a project along with the project topic, is given in Table 3. Students were grouped by taking into account their background s and the sta tu s of their course registrations. In the 1B course we tried to match students so that at lea s t one of them was concurrently taking or had a lread y taken, the PC course. In the process control course, we rearranged them so that if all the group member s were taking both 130 Figure 1. (a) Block diagram representing the pancreas as a PID contro ll er and th e human body as a multi-input-output process ; (b) The effect of food intake on blood gl u cose and insulin regulated by pancreas. Project # ID Project Topic Students Comprehensive review of g lucose-insulin interactions ChE 2 Effect of food on gl u cose insulin interactions 2 1B 3 Gluco se in sul in int eractions in a healthy man 3 4 Effect of exercise on g lu cose insulin interactions 2 s Stud y ing metabolic pathways of li ver ChE A Modeling pancreas of a h ea lthy man 2 PC B Modeling metabolic pathways of liver to control glucose l evel in blood 3 C Effect of daily activities on dosage of insulin 2 D Optimal timing and do sage of in s ulin Food Intake ~----~ Blood Insulin P~s: ~ ( ~ntro ll cr) Blood Glucose (a) 250 .----------------~ 80 C: .!! 200 c !l c: 8 150 51 E o0 a ,oo "O g iii 50 Upper Limit ... .. :-':. ..... -: ... ... ....... .. .. .. .. Lower Limit / 70 C: 0 60 c 50 !l C: :::40 8 ,E : 30 ii! .5 20 0 iii 10 0 +-------,~--~---~----+ 0 0 (b) 2 Time (hr) 3 4 Chemical Engineering Education

PAGE 49

courses they sw itched member s to ensure that no s tudent did exactly the sa me project in both co ur ses Introduction to Bioengineering The proj ects were assig n ed after the in s tructor covered the topic s in the course, and the s tudent s were allowed five weeks t o work on th e project s. At th e end of thi s p e riod s tud e nt s presented their findings in a ten-minute pre se ntation sess ion as a final project wort h 20% of their ,---------OLUCOSE ( a ) () r UDPO~ CO~ OLUCr .. ,._ OLUCO~OOEN 1 FRIJCTOSE ._p OLYCfAAL tHYOf ....... ...:.AOIYACET"' P~ f ACYL-CoA CILYC-P ,-----+----PHOO_.._PH1PYAUYATE + J r---, I I I I I I I .. "' 1 1rn9(hll PYRUVATE....,.. ACTYL -C oA MAL.ATE._. OltALOACETATE ___,,..CITIIATE crnuc ACJO CYCLE co, Liver Tissue Plasma ,j [SJ 0 .!0 100 1 na lhl> i: ~ F 0 i-~ 0 50 a:, : me (hr) a,~ -----~ 00 (b) .. : ffl9(hr ) ,a, ,0 t irN {ho "" : n {h r ) 1 00 0 .!0 100 t rrwl hrl ,00,--------, l"" '"' ,oo \. '--' --------' ,oo 0 oo Figure 2. (a) A simp li f i ed metabolic pathwa y network of the li ver; (b) Concentration profiles of intermediate metabolites for several sample runs. Spring 200 1 course gra de A varie t y of s tudent s from differ e nt background s participated : there was o n e grad u ate stu d e nt with biote c hnolog y as hi s area of interest, sev en chemica l engineering und ergrad u ate students, and one biol ogy under gra duat e s tudent. There were also fo ur gra duat e s tud e nt s a uditin g th e co ur se w ho did not prepare a project but participated in the wo rk by g ivin g feedback during the pre se ntation s. Four of the undergraduate s tudent s were regi s tered in the Bio medical Engineerin g Program and were goi n g to continue their e ducation in medicine The biology s tudent was registered in th e Biotechnology Cer tificate Pro gra m. A s ugge s t e d timeline fo r the se project s was f) Lit erature review ( 1 week): Students were given a brief description for each of the projects and were asked to make a literature s ur vey to provide ba ckgrou nd mat e rial on the specific topic of inte r est. f) Mathematical Model ( 1 week): A mathematical model in Matlab code was provided and the s tudents were ex pected to spend a week on understanding the code and using it efficiently under the supervision of both the instructor and the graduate student who wrote the co d e f) Modification of the M odel(] week): Dep endi n g on the pr oject description, some modifications in th e Matlab code were needed. Students mad e such c h anges to the o r ig in a l code f) Testing and Validating the R esults ( 1 week): The numerical results after the necessary modifications have been produced an d va li dated against the availa bl e lit e r ature data .fl 3 4 l f) Pr epa rin g the R eport ( 1 week): Students we r e given a week to wr it e their detailed final r e port s and to pr epare their oral presentations. This enha n ced their ab ili ty to sup p ort their wo rk and ideas and provided immediate feedback on wha t the students learn ed from this experie n ce. The s tudent from the Biolo gy Department carried out a compre h ensive review on glucose-insuli n in teractio n s in the human bod y, wit h an e mpha s i s on the interaction s in different organ s. The thr ee Bio medical Pro gram s tudent s concentrated on glucose in s ulin interactio n s in a healthy per s on and tried to under s tand the underlying mechani s m s (see Figure 1 ). The graduate s tudent put her efforts i nto s tud ying the metaboli c pathw ays of the li ver u s ing metabolic e n gi neering concepts, initiatin g a promi s ing re sea rch topicf 51 (see Figure 2). Other s tud e nt s worked on 1 3 1

PAGE 50

investigating the effects of exercise or food intake on glucose-insulin interaction s in a diabetic pa tient (see Figure 3). Pro cess Control In the process control course, students were asked to work for two weeks on the project and to report their findings through project reports and presen tations. This would account for two homework assignments and 4% of their overall grade. The description of a suggested project on the control of glucose level in blood was In healthy people, the pan c reas controls the glucose level in blood. When the pancreas does not function properly, the person is diagnosed as a diab etic patient, and his blood glucose level is co ntrolled by insulin injections. Such a patient has to be careful about his diet as well as his exercise. Inv es tigate different cases on a model human body: a health y p e rson a patient under nominal conditions, the food intake of a patient, and the exercise of a patient. 180 2000 UpperLimil 160 1500 120 1 00 I 80 1 000 60 Lower Llmi1 500 40 20 0 0 (a) 0 4 8 12 16 20 24 Time(lr) 60 70 50 60 E 50 :i 40 C 40 30 E 30 g 20 20 iii 1 0 10 0 0 (b) 0 4 8 12 16 20 24 Tirre(tr) Figure 3. A typical blood glucose and insulin concentration profile for repetitive intake of food 13 2 E :i C 0 ii E E E ;; E Test closed-loop and open-loop contro llers on the model equat ions Involve tasks such as finding the parameter subspace where the system works in a healthy r eg im e, determine the appropriate dosage of insulin injection for a patient and find the food and exercise tolerance limits for a patient The other project titles in the PC course were "Search for a Power Law," Internal Model Control ," "Complex Systems," and "Popula tion Dynamics. Student groups were told to select one of these topics or to come up with their own project proposal s. More than one group was allowed to select one title but all groups were expected to work separately and to pursue different tasks. Students in the 1B course were invited to select the Control of Glucose Level in Blood" project. Apart from the four students in IB, TA B LE4 Project Q u estionnaire low-High I. What wa s yo ur level of co mpet ence u s in g Matlab before the project ? I 2 3 4 5 2. What i s yo ur level of competence using M at l ab af t er th e project? I 2 3 4 5 3. What i s the difficulty level of thi s project compared to other course project s? l 2 3 4 5 4. Whal i s th e r e lev a nc e of yo ur project title to your a re a of interest? 5 H ow would yo u rate th e c hallen ge of the proj ec t ? 6. Overall, how would you rate this project ? 7 H ow many hours did you spend on this project ? 8. Are yo u t aking Intr oduction t o Bioengineering Are you taking Process Control 9. Facilities/tools at IlT were okay. I 0 If I had more tim e, I would pr epare a better project. No Yes No Yes I r eceived h elp deali11g with the project from the instru c tor a11d TAs . 11. ... as excha n ge of ideas 1 2 ... as exchange of know l edge 1 3 .... as t ec hnical s upport I received help deali11g wit h the project from m y frie11ds ... 14 . .. as exchange of ideas I 5 .... as exchange of knowledge I 6 .... as technical s upport 17. This project was a u seful learnin g t ool for me 1 8 It is easi ly app lic able to other areas. I 9. The goa l s were rea so nable 20. I u sed my knowledge from other courses 2 I. I would consider engaging further research in this field 2 3 4 5 2 3 4 5 I 2 3 4 5 I 2 3 4 5 I 2 3 4 5 I 2 3 4 5 I 2 3 4 5 l 2 3 4 5 I 2 3 4 5 I 2 3 4 5 I 2 3 4 5 I 2 3 4 5 I 2 3 4 5 I 2 3 4 5 I 2 3 4 5 I 2 3 4 5 Chemical Engineering Education

PAGE 51

future improvements in this cross-course four more students picked this topic, signify ing the appeal of biomedical topics among the students. They formed a valuable "control group" simi l ar to 1B students involved in the project who were not taking PC, which gave us the opportunity to monitor cross-course interactions. Studen t interest in this t opic was also evi de n ced by the co n trib u tio n of o t her class mem bers duri n g project presentations. Two of the eight students performing a project on this topic were gra du ate students with interests in bio technology and transport phenomena. One of the undergraduate students had previously at tended m edical school and provided valuable perspective on the subjects ... The project played an important role in triggering the scientific curiosities of the students and project assignment. The choice of the project topic turned out to be an attractive one due to the popularity of biomedical engineering in education and re s earch. The project played an important role in triggering the scientific curi osities of the students and providing an oppor tunity to adapt their knowledge to different fields. As a follow-up, we developed addi tional educational software in order to help students to explore many case studies. Some of the PC students were assigned the task of devising a control mechanism centered providing an opportunity to adapt their knowledge to diffe r ent fields. The cross-course project approach to teach ing bioengineering and process control de scribed in this paper directly benefited fo u r students taking both courses concurrent ] y T h e other four who had taken the process control class in the previous semester found that the on different organs, such as the pancreas and the liver, as well as investigating the timing and dosage effects of insulin injections. Other students considered projects on topics other than the glucose-insulin interaction After the oral presentations in both classes students were given a questionnaire to provide feedback to the instructors. They were carefully informed that the questionnaire (see Table 4) would be used only for course enhancement and educationa l research purposes and that it would not have any effect on grading. Evaluation of the returned questionnaires indicated that all students showed improvement by at least one level in their competence in Matlab, accounting for an average increase of 70 % Although they find this project difficult (4 15 out of 5.00) and challenging (4.40) with respect to other class projects, t h ey found it quite relevant to their own area of interest (3.50) a n d were willing to engage in further re search in the field (3.47). Most of them reported that they needed more time to deliver a better project (4 20), which is an indication of their interest and willingness to be involved in it. The students tended to receive help from instructors and TAs (3 60) rather than their peers (2 50). They found it a useful learning tool (3.75) with quite reasonable goals (3.45) although they were near-neutral to the applicability in other areas (3.35). Overall the students rated the project an average of 3.90 The fact that they have used their knowledge from other classes (3.70) suggests that the initiation of a cross-course platform may become a very useful learning tool, supporting our hypothesis. CONCLUSIONS AND FUTURE DIRECTIONS Diversity of interests, technical abilities, and states of knowledge among students provided unique feedback for Sprin g 2001 project helped them integrate their acquired knowledge in process control to a bioengineering project. Hence, eight out of nine bioengineering students were served by this cross-course initiative As a result of this experience, we are looking forward to offering such a cross-course plat form in future courses ACKNOWLEDGMENTS The Fall 1999 students in the Introduction to Bioengineer ing and Process Control courses are gratefully acknowl edged. Special thanks also go to F Ceylan Erzen for provid ing the Matlab codes. REFERENCES 1. Puckett, W R. Dynamic Modeling of Diabetes Mellitus," PhD Thesis, University of Wisconsin-Madison ( 1992 ) 2 Erzen F.C G Biro!, and A. Cinar, "Glucose-Insulin Inter action: An Educational Tool," Proceedings of the World Con gr e ss on Medical Physics and Biomedical Engineering, Chi cago, Illinois, July ( 2000 ) 3 Pehling G ., P. Tessari J E Gerich M.W Haymond, F.J. Service, and R.A Rizza Abnormal Meal Carbohydrate Dis position in Insulin-Dependent Diabete s," J Clinical Invest ., 74 985 ( 1984 ) 4 Sorensen J T A Ph y siologic Model of Glucose Metabolism in Man and Its Use to Design and Assess Improved Insulin Therapies for Diabetes, PhD Thesis MIT Cambridge, MA ( 1985 ) 5. Kizilel S. R. Kizilel, G. Biro!, I. Biro! and A. Cinar, "Glu cose-Insulin Interaction in a Healthy Human Body: Investi gation of Stimulating Different Metabolic Pathways of Liver," World Congress on Medical Physics and Biomedical Engi neering Chicago IL July ( 2000 ) 6 Erzen Fetanet Ceylan, Gulnur Biro! and Ali Cinar, "Simu lation Studie s on the Dynamics of Diabetes Mellitus Pro ceedings of the IEEE International Bioinformatics and Bio medical Engineering ( BIBE ) Symposium Washington, DC, November ( 2000 ) 7. Erzen, F.C. Giilnur Biro!, and Ali Cinar An Educational Simulation Package for Glucose-Insulin Interaction in Hu man Body ," AIChE Annual Meeting, Los Angeles, CA, No vember ( 2000 ) 0 133

PAGE 52

.,~ 5-3._l_a_b_o_,-,_a_t_o_r.:.y ________ ) DEVELOPING THE BEST CORRELATION FOR ESTIMATING THE TRANSFER OF OXYGEN FROM AIR TO WATER W AYNE A. B ROWN McGill University Montreal, Quebec, Canada H3A 2B2 T he study of engineering is usually carried out in a defined sequence. Students are first taught a set of basic tools that includes, for example, mathematical concepts and solution procedures along with the various conservation laws. They then apply these concepts to el ementary problems associated with their chosen discipline In the final stages of the educational process the simple concepts are extended to allow the students to apply them to multifaceted engineering problem s Due to the complexity of syste ms of practical interest, theory developed around simple systems cannot normally be applied in the form derived Often the theory is used to identify the set of governing variables, and a relationship between these variables is then established empirically. To generalize these solutions over a number of experimental co n ditions, variables are often gathered into dimension l ess groups. Although the number of independent dimensionless groups is governed by Buckingham's Pi theorem, [ I I a num ber of useful groups have already been defined. These di mensionless groups represent ratios of competing effects, expressed in terms of experimental variables Thus devel opment of an empirical relationship depends so m ewhat on the experience of the engineer or researcher. If particular effects are not identified as being important in the primary analysis, then they cannot be reflected in the final solution. It i s imperative that students be taught the following re garding prob l em analysis: There are man y differ ent design equations that can be developed, depending on what assumptions are made. Th ese assumptions are choices and are Left to the judgment of the process e n g in eer. The engineer should always use the applicable set of data to formulate a process design. More than one approach to a given problem may Lead to a reasonable answer. The best approach is to consider many different methods of achieving a solution, but emphasis should be placed on the solution achieved by u s in g th e set of data most applicable to the probl em at hand. It is often not possible to verify the results of an estimated param ete r since a pra ct ical and accurate alternative measurement method may not exist. Thus, one may have to accept the r esults of an empi ri ca l co rr e lation We developed, and describe here a laboratory exercise in an attempt to convey some of the above messages It is based on the experimental determination of the overall mas s -tran s fer coefficient describing the transfer of oxygen to water in an agitated tank OBJECTIVES OF THE LABORATORY The objectives of the laboratory exercise were to Analyze a problem involving the transfer of o xy gen to water and fo rmulat e a set of mathematical equations to adequatel y des c ribe the process Fit the developed equations to experimental data to deterWa yne A Bro wn has held the position of Assistant Professor in the Department of Chemical Engineering at McGill University since 1999 Prior to that he worked for five years in the oil sand industry first as a pro cess engineer and then as a research scien tist. He received his formal training at McGill receiving his BEng (1989) MEng (1991) and PhD (1998) from the Department of Chemical Engineering. Copyright ChE Divi sio n of ASEE 2001 1 34 C h e mical Engineering Edu c ation

PAGE 53

On a practical level, the lab deals with benign materials. As such, there are no fume hood requirements or disposal problems. The lab can easily be extended to examine the effect of other variables, such as temperature, oxygen partial pressure, and liquid v olume. mine the mass-transfer coefficient Study the influence of the measuring device on estimates of the mass-transfer coeffic ient D eve lop the semi empir i cal equations first put forth b y Ri c hards to es timate the mass-transfer coefficient Compare experimental results with estimates obtained from the Richards equation "Tailor" the Ri c hards relation so that it makes the most use of the data collected EQUATION DEVELOPMENT Mass Transfer Coefficient from Experimental Data The transfer of oxygen from a gas to a liquid phase can be divided into a number of transfer resistancesY 1 The set of eq uation s that describes the transfer of oxygen from a gas phase to water in a batch system is dependent on the assump tions app lied Some of the issues to be considered are: The c hang e in concentra tion of oxygen in. the air ove r the residence time in the liquid phase The transfer of in e rt co mpon ents from the air in addition to oxygen. The composition of the particular gases used The change in gas holdup with tim e The mixing c hara cte ristics of the gas phase The mixing c har acte ri s ti cs of the liquid phase Th e pr esence of additives in the liquid phase Th e change in volumetric gas flow rate due to the transfer of matter from the gas t o liquid phases The resistan ce to mass transf e r across the gas -liquid interface Th e influence of surface aeration The implications of various assumptions on the resulting differential equations are discussed elsewhere 9 l For the current experime ntal setup, the following assumptions are assumed reasonable: Th ere is negligibl e change in. oxygen co n centration in the gas phase. The gas holdup stays constant wit h time The concentrations of oxygen in the gas and liquid phases are in equilibrium at th e gas-liquid interfa ce. The liquid is well mixed. These assumptions lead to the following eq uation s for the gas and liquid phases: Spring 200 1 where KLa is the volumetric mass-transfer coefficient. These equations ca n be integrated subject to the conditions CL(O) = O and Ca(O) = C~ to y i eld CL(t) = C~(l -e-KLat) C 0 (t)=C~ (1) (2) initial (3) (4) The problem is further complicated when the measure ment method is considered in the analysis. One of the most common and convenient methods for measuring dissolved oxygen is through application of a dissolved oxygen elec trode. To make a measurement, oxygen dissolved in the surrounding fluid must diffuse to the probe membrane, across the mt>mbrane, and finally through the probe s olution to the active electrode tip. A number of approaches have been applied successfully to model this process such as Fick's second law _l 9 l However if the bulk sol uti on in the tank is not viscous, transport through the electrode membrane can be treated as a first-order process described by an equation of the form (5) Here, the diffusion through the probe solution is neglected. Substituting Eq. (3) into Eq. (5) and integrating the result subject to the initial condition (6) an expression relating the overall mass-transfer coefficient to the probe outp ut can be derived ( K a k k I C (t) =C l l+ L e p t_ P e-KLatj (7) p L k -K a k -Ka p L p L Using this equation, the overall liquid mass-transfer coef ficient can be determined directly from the probe output. To determine the probe time constant, Eq. (5) is solved, s ubject to the conditions given by Eq. (6) and Eq (8): CL(t) = C ~ (8) In Eq (8), c~ is a constant for a given oxygen partial 135

PAGE 54

pressure and system temperature. Using Eqs. (6) and (8) Eq (5) can be integrated to yield Cp(t) = ct.(t-e -k pl) Generalized Correlation of Oxygen-Transfer Data (9) The volumetric mass-transfer coefficient, KLa is a complex function, dependent on the system geometry the properties of the liquid, and the process operating conditions In terms of basic variables, the function can be expressed as KLa= KL a( di ni hi wi ,Ii dT hL ns, w 8 ,Pr r crr Do 2 N, Vs v 1 ,g) (IO) In developing his correlation, Richards considered KL and a" separately For geometrically similar vessels, dimensionless groups related to geometry do not vary. In this particular situation the overall mass-transfer coefficient per unit trans fer area, KL associated with the transfer of oxygen from a gas phase to a Newtonian fluid is expected to be a function of the variables (11) From Buckingham's Pi theorem, three dimensionless groups can be created. Thus, as suggested by Rushton ,f 1 the relation ship can be written KLd = Ki ( Ndf Pr y x (___Ei__ ) ~ Do z l r ) D0 2 Pr (12) Here K 1 is a constant that accounts for the geometry of the particular system For convective mass transfer between spheri cal particles and a liquid a has been shown empirically to have a value in the range of 0.4:=; a :=;0.6 1 11 In his derivation, Richards used a value of a =0.5. Thus, for constant diffusivity and fluid properties, and assuming that the gas consists of spherica l bubbles, Eq. (12) reduces to (13) Richards development is completed by noting that the inter facial area for mass transfer is correlated adequately by Calderbank's equation 1111 (14) As shown through the dimensional analysis performed by Rushton, et al. P a is itself a function of a subset of the variables introduced in Eq (10) 11 21 For the assumption of constant fluid properties applied above the Richards correla tion for the overall mass transfer coefficient is obtained by multiplying Eqs. (13) and (14) to yield K a K (P IV )0.4 v0N0 5 L 4 G L s (15) Data from a number of different systems have been correlated 136 using the relation developed by Richards.[1 3 1 4 1 In applying the Richards equation, data on the power requirements of the gassed system are not always readily available. Therefore, as part of the current development, it is useful to express the correlation in terms of the more commonly measured variables as they appear in Eq (10) Useful for this purpose is the empirical correlation put forth by Michel, et al., c i si ( p 2 Nct 3 10.45 PG= K 5 l Q0 56 1 ) (16) Note that this equation is not dimensionless, and thus care should be taken when extrapolating outside the range in which the data was collected. An estimate of the ungassed power requirements can be obtained from the dimension less relationship based on the Rushton's power number. 11 21 For geometrically similar vessels function is of the form p ( d 2 Npr V(ct N 2 )"" Po= 3 5 = K6l-'--J -'= fn(Re, Fr) N d;Pr r g (I 7) The Froude number (Fr) is only important if a vortex is formed. As most systems are baffled, the dependence of the power number (Po) on Fr is usually not considered, and Eq (17) reduces to a function of Re only This function is often expressed graphically. Since the dimensionless groups E r lenmeyer w l thwater C1 M1 M2 S1 S2 Speed controller To vent To data acquisition (D/A) board Figure 1. Experimental apparatus. Temperature (TI) pres sure (PI), gas flow rate (FI} and dissolved oxygen (DO}, wer e measured continuously Only the signal from the dissolved oxygen probe was sampled by the data acquisi tion board however Solenoid valves S1 S2 and S3 were used to choose th e source of th e gas added to the fermen tor, while valve Vl was used to adjust the flow rate. Valve Cl was used to purge the Erlenmeyer flask with nitrogen for determination of the probe time c onstant. Details of the procedure can be found in the text. Ch e mi c al En g in ee rin g Education

PAGE 55

related to geometry have not been included, however a single curve for each impeller configuration is required. Thus, using Eqs. (I 5) through (17), an estimate of the mas transfer coefficient can be obtained. EXPERIMENTAL Apparatus A 4-L tank was used for all experiments (see Figure 1 ). The vessel was 13 cm in diameter and had a height of30 cm. No baffles were installed All experiments were performed using 2 L of distilled water, re s ulting in a liquid depth of approximately 15 cm. A flat-blade propeller was used that was 6.5 cm in diameter from tip to tip. The propeller had 4 blades and was located 2 cm from the bottom of the vessel. Air was introduced into the bottom of the tank through a s parger that consisted of four equally s paced hole s, directed radially outward. The temperature was controlled by mean s of a 300-W heater connected to a controller (Omega Model BS5001Jl). Dissolved oxygen was measured using a dis solved oxygen electrode (Ingold DL-531) in conjunction with a digital meter equipped with an analog output (Cole Parmer Model O 1971-00). Data from the meter was logged on a personal computer by means of a data-acquisition board and bundled data-acquisition software (LABTECH notebook for Windows). Experiments were run over a range of gas flowrates (2-4 L mjn 1 ) and stirring s peeds (I 00-1200 rev min 1 ). Prior to each set of experiments, the probe was calibrated u s ing nitrogen and oxygen saturated solutions of water. All experiments were performed at 30C and at atmospheric pressure Determination of Probe Time Constant The dissolved oxygen probe was placed into a flask of ....)00 0 !:t 80 :, C. 8 60 .. ..Q e CL 40 -c ., !:j .; E 20 0 z 0 0 50 100 Tim e (s) 150 200 Figure 2. Fit of Eq. (3) (dotted line) and Eq. (7) (thick solid line) to experimental data (thin solid line). Experimental data were generated at an air flowrate of 3 L min 1 and a stirring speed of 1100 rev min 1 In calculating KLa by Eq. (3 }, only data between 30 and 98% saturation were consid e red as described in the text. Spring 2001 water that had been purged to sa turation with nitrogen (see Figure 1). After a reading of 0% had been established, the probe was quickly immer se d into the vessel containing 2 L of water sa turated with oxygen to 100%. Under these condi tions, the dynarrucs of the probe are described by Eqs. (5), (6), and (8) To facilitate the determjnation of the probe constant, a linearized form of Eq. (9) ( c 1 fol Ci. _L Cp) = kpt (18) was used From Eq. (18), a plot of fn( C~ / ( C~ CP)) ver sus t should yield a straight line with a slope of k P. The slope of the be st-fit line was determined by linear regresion. Determination of K& The vessel was first purged with nitrogen until the dis so lved oxygen probe s tabilized at a value of 0 %. The purge gas was then sw itched in s tantaneou s ly to air through means of a series of so lenoid valves (see Figure 1). An estimate of the mass-transfer coefficient was then obtained by fitting Eq. (7) to the data collected. As the model function cannot be linearized a nonlinear regression algorithm was used to extract the best estimate of K La from each data set. RESULTS AND DISCUSSION As a preliminary exercise to the laboratory students were asked to develop the appropriate equations with which to estimate K La. It became apparent to the s tudent s during thi s exercise that the set of equations generated depends on the assumptions that were made with respect to specific aspects of the problem. For instance if it was assumed that the rate of mas s transfer from the gas to liquid i s s mall compared to the dynarruc associated with the probe, then { I/ KL a) 'tp, and the effect of the probe is negligible. Under these circum stances, the rate of mass transfer can be calculated adequately from Eq. (3); but if trus i s not the case, then the probe dynarrucs must be taken into account.l 161 Thus a function s uch as Eq. (7) is required. The probe constant was calculated by each group of stu dents using a graprncal approach. Typical values obtained for 'tp were between 14 and 17 s. From Eq (5) the probe output s hould attain a value of 63% sa turation when t = 'tp. From the experimental data used to determine 'tp trus con dition was verified (data not shown). Therefore, Eq (5) proved to be an adequate representation of the dynamics of the probe. Typical data obtained by the students for calculation of KLa is shown in Figure 2. It has been shown that truncating data collected early in the experiment can minjmize the effect of the probe on the estimate of KLa.(1 71 Therefore, under appropriate conditions, reasonable estimates of KLa can be obtained from Eq. (3) and knowledge of the probe dynamics is not required Even when these conditions are 137

PAGE 56

met however due to the exponential nature of Eq. (3) th e best estimates of KLa are obtained from Eq. (3) using data collected at times on the order of the time constant, t= 1 / KL a. As such, it is recommended that data above 30% sa turation never be discarded. r I 71 For the current exercise, when neglecting the effect of the probe, only data between 30 and 98% sa turation were con sidered when determining KLa using Eq (3). When the probe dynamic s were considered, however, Eq. (7) was applied and all of the data collected were used. Using the data s hown in Figure 2, Eq. (3) and Eq. (7) yield KLa estimates of 134 h 1 and 285 h ', respectively. Therefore, serious errors re s ult if the probe dynamics are not considered. This is to be ex pected since the dynamics of the mass-transfer proces s and the probe are on the same order for these data. Thus, the concept that the measuring device is an integral part of a process is reinforced. From Figure 2 it is apparent that Eq. (7) adequately repre sents the data, where Eq. (3) doe s not. In addition, for two first-order processes in series, the s um of the time constants of each process should equal the time at which the overall process achieves a value of 63 %. For the data presented a value of 63% is achieved at approximately 30 s. The sum of the time constants, t + l / KL a, i s equal to 29 s. Therefore the assumptions that Pied to the development of Eq. (7) ap pear to be appropriate-other formulations could also fit the data as well or possibly even better however. For in sta nce unsteady-state diffusion to the active element in the probe could h ave been solved using the appropriate form of the diffusion equation. l 7 l The so lution to thi s problem can then be fit to the data to determine the probe time constant. The range over which the dynamics of the probe can be neglected was studied by comparing estimates of K La ob tained using Eqs. (3) and (7) (see Figure 3). From this figure, it can be seen that the two estimates deviate at relatively low values of K La Quantitatively it i s apparent that the impact of the probe becomes important when the probe time con stant is 20% of the time constant associated with the transfer proces s, 1/K.La This rule of thumb has also been s uggested by others.l I 71 The data generated by the students was then compared with the Richards equation This was accomplished by plot ting the KLa estimates obtained by the students on the same axes as the data used to generate the relationship in the original work by Richards (see Figure 4). When originally presented, KLa was quoted in units of mML 1 1 atm 1 _l 1 31 This selection of units was most probably related to the sodium sulphite oxidation method that was used to generate the data. Data generated using this technique are often displayed as H'K La, where H is Henry 's constant.r I 81 To facilitate com parison with the data generated by the s tudents data used to generate the original correlation were divided by Henry 's constant at 30C (see Figure 4). In the laboratory exercise, 138 axes complete with the data used by Richards were handed out in printed form to each lab group. Thus, the comparison exercise nece ssitated that the points be plotted by hand. Therefore the students were forced to critically exami ne the deviation of the experimental values from the Richard s equa tion. The data generated sca tter s within the bound s of the original data sets. This scatter is rather large, however. For instance KLa values of between 75 and 250 h 1 correspond to a value of 300 on the abscissa. Thus estimates by the corre500 2 0 0 ., e 400 .. 1 5 C: >, 0 ,, ., .c 300 0 ";" Q. yo:;:0 1 0 .... O> =0 0. : .... 200 ., c, ., C: 0 5 "' 100 a a a a 100 200 300 400 500 KL a considering probe dynamics (hr 1 ) Figure 3. Comparison of estimates of K L a obtained by considering (Eq. 7) and neglecting (Eq. 3) the probe dy namics. Closed circles represent the K L a estimates, while open circles represent the ratio of the probe time c onstant to the time constant of the transfer process w h ere t =I/KL a The solid lin e indicates a perfect correspondence between the two estimates of K L a 500 450 0 400 . 350 . ~-300 / ~ .c 250 ; '!, ;,: 200 0 150 ~ -"' .. 100 ... .. 50 a a 100 200 300 400 500 600 700 800 (Pc,NL)" 4 (Vs)" 5 Figure 4. Assessment of the applicability of the Richards equation to experime ntal apparatus. The ordinate has the units indicated while the abscissa has units of (HP/1000 L}4 (cm / minf 5 (RPM) 0 5 Black (Richards 1 3 1 } and gray (Coo per 1181 ) circles represent the data originally used by Richards to assess his corre lation. Results were divid ed by Henry's consta nt at 30 C as described in the t ext. The solid line represents the best fit to thes e data, as suggested by Richards. Open circles represent data generated as part of the curre nt laboratory exercise. The dotted lin e represents the results of Eq (19) Chemical Engin e e ring Education

PAGE 57

lation are on the order of %. This finding is often diffi cult for many students to accept as critical analysis of em pirical correlations on thi s le ve l is new for them. The correlation developed by Richard s underestimates the data generated by the students in almost all of the cases (Figure 4). There are two plausible explanations for thi s result. First, the original development of the correlation was meant to apply to geometrically simjJar vessels. 11 31 There fore, it is possible that the consistent offset from the Richard s correlation is related to geometric differences between the systems used to generate the various data sets. The Richards equation can be tuned for a specific geom etry as follows: For the experimental system at hand only N and Qare varied; furthermore, for Reynolds numbers associ ated wit h all stirring speeds, it can be shown that Po is constant in Eq. (17). 1141 Thus Eqs. ( 15) through (17) can be reduced to (19) This equation ha s one adjustable parameter (K 7 ) that ac counts for geometry and the fluid properties of the system As a first step to improving the correlation, K 7 was deter rruned using only the student data. The resulting equation was plotted on Figure 4. Because only data specific to the system under study was used Eq (19) is a better representa tion of the system used in the study, as is evident in the superior fit. A second plausible explanation to account for the differ ences noted between the Richards correlation and the experi mental data is related to surface effects. In its development the Richards correlation assumes that the tanks are well 450 -~400 0 C ~ 350 "' ~300 0 0 0 0 e 25o 0 e :; 200 .! 8 1150 ~100 0 "' 0 i 50 .i 0 0 50 100 150 200 250 300 350 400 450 Mea s u r ed K L a (h 1 ) Fig u re 5 Ability of various corre lation equations to fit the experimental data Black circles represent results of the Richards correlation as originally presented (Eq 15). Open circles represent the Richards correlation tailored for the geometry of the experimental system (Eq 19). Grey circles represent the equation resulting when surface effects are considered through inclusion of the Froude number (Eq. 22) Spring 2001 baffled 11 3 1 As a result s urface effects are negligible and no dependence on the Froude number is expected. The Froude number was also not considered in application of Eq (17) for the same reason The experimental apparatus used by the students had no baffle s. Thus, a dependence of the K L a on the Froude number is expected especially for larger values ofN To address this s hortcoming in the original derivation the Richards correlation is further modified to account for pos sible surface effects The Froude number is defined as Fr= ( di: 2 ] (20) The desired equation can be obtained from Eqs. ( 19 ) and (20), and ha s the general form of KLa = K 7( i r N 2A+ I.76Q0.4 (21) Although the value of 'A is not known it is recognized that Eq. (21) i s also a function of N and Q only. The specific value of 'A could be deterrruned through regression using the ex periment a l data collected. In the resulting equation, the exponent of N would be tailored to the data collected by the s tudent s, whlle the functionality of Q would be dictated by the data sets originally u sed by Richards Therefore, a more reasonable approach is to tailor all exponents to the experi mental data generated by the students. The result of this exercise is the equation (22) The ability of this equation to capture the relevant features of the experiment i s readily see n in Figure 5. While the Richards equation repre se nts the data well the best fit re sults when the equation is tailored to the experimental data collected. Thus, whlle an adjusted correlation coefficient, r2 of 0.8 I is associated with the fit of Eq. ( 19), this value increa ses to 0 98 when Eq (22) i s applied. Thls result may seem obvious as Eq. (22) ha s three adjustable parameters while it appears as if Eq. (19) ha s only one. In actuality, however, both equations have three adjustable parameters The difference is that the exponents in Eq. ( 19) were ob tained from correlations fit u s ing other se t s of data, whlle those in Eq. (22) were fit to the data obtained with the current system only The difference among the three approaches becomes readily apparent at this point. As the equations are further tailored to the experimental data the mathematical form better fits the data Thu s, the spectrum of po ss ibilitie s associated with proce ss de sig n can be elucidated. When no data are avail able the engineer mu s t rel y hea v ily on data generated from dimen s ionally si milar sys tems Thi s approach is only justi fied however in the absence of reliable data associated wit h the system of i n terest. As data become available, the pre -------------Continued on page 147. 1 39

PAGE 58

[!t9Q curriculum ) ------------A PROJECT-BASED SPIRAL CURRICULUM FOR INTRODUCTORY COURSES IN ChE Part 3. Evaluation DAVID DIBIAsm, LISA CoMPARINI,* ANTHONY G. DixoN, AND WILLIAM M CLARK Worcester Polytechnic Institute Worcester, MA 01609 T his sen es reports on the development delivery and assessment of a project-based spiral curriculum for the first sequence of courses in chemical engineer ing. The program represents significant restructuring of the introductory chemical engineering curriculum Traditionally, a compartmentalized course sequence designed to build a conceptual foundation is taught during the sophomore and junior years, followed later by more integrated projects. Our new curriculum requires students to learn and apply chemi cal engineering principles by completing a s eries of open ended design projects starting during their sophomore year. The new curriculum is spiral in that students understanding of basic concepts is reinforced by revisiting them in different contexts with ever-increasing sophistication. A more detailed explanation of the concepts, curriculum design, and implementation behind this effort was described in the first two part of this series.c 1 2 1 Part 1 described the curriculum design and Part 2 detailed the implementation In this paper we present the details of the assessment design describe the results of our assessment and draw conclusions about the success of the new curriculum. BACKGROUND The background describing the need for the new curricu lum, the published research upon which it was based, and the philosophy behind our approach was presented in the first paper of this series.l 11 In this section we summarize the literature upon which our assessment plan was based. An extensive array of literature exists regarding assess ment of student learning. An excellent bibliography is avail able from the Department of Education C 3 l and two good resources are available from the National Science Founda* Current Address: School of Famil y Studi e s Univ e rsity of Conn e cticut, Storrs CT 06269-2058 140 tion _c 4 5 l There are al s o a number of references that outline the details of asses s ment plans aimed at continuous im provement.f 6-91 Most of the philosophy and techniques de scribed in those articles are adaptable to individual educa tional research and curriculum reform efforts Assessment tools are generally categorized according to the types of methods and when they are applied during an educational project. There are two broad classes describing the timing of assessment. Formative assessm e nt refers to periodic data collection and evaluation prior to project completion. It is used to improve the intervention during the project and helps answer the question "Is it working?" Summative assessment concerns data collection and evalua tion at project completion. It is u s ed to make conclusions about project retention alteration or elimination and nor mally answers the question Did it work?" There are two general classes of assessment types QuantiDav i d D I B i asio is Associate Professor of Chemical Engineering at WP/ He received his BS MS and PhD degrees in chemical engineering from Purdue University His educational work focuses on active and cooperative learning and educational assessment. His other research interests are in biochemical engineering specifically biological reactor analysis. L i s a Compar i n i is a post-doctoral fellow in the Depattment of Family Studies at the University of Connecticut. She received her PhD in Develop mental Psychology from Clark University where she focused on issues of language communication culture and development. While her primary area of interest is in communicat i ve practices within the family context her interest in issues of development and communication extend to other interactive contexts including the classroom Anthon y G Dixon is Professor of Chemical Engineering at WP/. He holds a BSc degree in mathematics and a PhD degree in chemical engineering from the University of Edinburgh. His research has included development of interactive graphics software to aid in teaching process design and mathematics to engineers. Will/am M Clark is Associate Professor of Chemical Engineering at WP/ He holds BS and PhD degrees in chemical engineering from Clemson U n iversity and Rice University respectively, and has thitteen years of experience teaching thermodynamics unit operations and separation pro cesses His educational research focuses on developing and evaluating computer-aided learning tools. Co p yr i g ht C h E Di v i s i o n of A SEE 2001 Ch e mi c al En g in ee rin g Edu c ati o n

PAGE 59

tative methods are those familiar to most engineers. They include exams (s tandardized course exams, comprehensive, oral); surveys with statistical analysis (particularly pre/post); database analysis; written reports (laboratory, design, or re search project); graded oral presentations ; and graded port folios These methods are generally performance-based and measure what students can rely on traditional tests for nontraditional interventions; and develop in-house instruments when validated ones are availableJ 1 3 1 Because any single assessment method has advantages and disadvantages triangulation (the use of multiple meas urements) is a key to valid assessment. Evalua actually do Within a disciplines pecific con text it is relatively easy to evaluate student performance, but the design of the tool itself may be problematic. These methods can be used to evaluate both team and individual per formance Performance-based tools (authentic evaluation) were pioneered at Alverno Col lege .1101 O Conner 1111 described a design competition approach to performance assess ment, and Miller et al r 121 present a com prehensive assessment plan involving mul tiple types of evaluations. The new tion events that occur during and after the inter vention are also important. When multiple mea surements taken at different time points con verge on common results one can confidently draw conclusions about the observed process or curriculum is spiral in that outcomes. students understanding of basic concepts METHODS Our assessment plan was designed to probe student learning in basic chemical engineering and students' ability to demonstrate learning in both team and individual contexts. We also ex amined attitudes, satisfaction, and confidence about chemical engineering. For longitudinal data we looked at individual student perfor mance in follow-on courses in the junior and senior years. Our overall plan combined forma tive and summative measures and employed both qualitative (interviews, open-ended question naires videotaping of st udent group work) and Qualitative method s typically involve analy sis of text and visual information. They in clude videotaping, audiotaping, direct obser vation, portfolios, self-reports, open-ended sur veys, interviews, focus groups, performances and journals. Engineers have been somewhat slow, however in finding productive ways to adopt these methodologies that are used in de velopmental psychology and cognitive science is reinforced by revisiting them in different contexts with everincreasing sophistication. Most of the methods involve qualitative analysis that is unfamiliar to technologists. The main advan tage of methods such as videotaping is that they record actual work-not student interpretations of what was asked of them in a survey By observing students doing chemical engineering, we can probe how and why they learn. This can yield rich information about the learning process. Sometimes this information i s quantified but usually the results are qualitative. MarcusP 3 l summarized the main features of good and poor assessment plans The keys to a good assessment plan are: use of both control groups and target groups to minimize variation, including control for contaminating elements; mul tiple measurements using multiple tools ; a mix of formative, summative, quantitative and qualitative tool s; and use of an external evaluator. Good plans define measurable objectives and design the assessment method s directly from those ob jectives They implement continuous feedback for improve ment, use preand post-measurements and include longitu dinal studies when possible The evaluation plan s hould uncover program flaws as well as attributes. Poor assessment plans overemphasize one set of outcomes (for example, affective rather than cognitive) or one type of measurement (all quantitative); vaguely define the perfor mance criteria; do not link data collection to the program ; Spring 2001 quantitative ( pre/post s urveys, standard course evaluation s urvey s, individual exams, and team problem-solving competitions) tools External consultants were used extensively throughout the project. Intervention and Comparison Coho r ts At the beginning of each implemention year we randomly se lected a cohort of incoming so phomores to participate in the spiral curriculum. During the first implementation year, this was about one-third of the class In the second imple mentation year, half of the incoming class was randomly selected. Selecting half in the second year meant we elimi nated class size as a variable in our analysis. Students not selected were taught in the traditional fashion in a separate section and repre se nted our comparison cohort. Each year we made minor adjustments (prior to the start of the aca demic year) to insure demographic simi larity between the intervention and comparison groups. We also examined grades of each cohort in their first year at WPI. There were no significant differences in first-year performance between the two cohorts Since participation in the spiral curriculum was vol u ntary, students could withdraw at any time during the academic year and move into the comparison section Only one stu dent did that during the two years of implementation No s tudents were allowed to self-select into the experimental sectio n. In the following discussion we will refer to the 141

PAGE 60

intervention group as the spiral-taught cohort and the tradi tionally taught students (the control group) as the compari son cohort. Spiral-taught thus refers to all the components of the new curriculum, not simply just the spiral topic structure. We did our best to control contaminating variables. Both cohorts were taught essentially the same material, using the same textbooks Both cohorts met for the same number of class periods each week and, as schedules allowed during the same class hour each day. When scheduling did not allow the latter, we avoided vastly different meeting times For example, if the comparison group was scheduled at 11 :00 a.m we scheduled the spiral-taught section for close to that hour and avoided times such as 8 : 00 a.m or 4:30 p.m. Pro b lem Solving Co m petitions: Team and Individual Team At the end of each implementation year, we held a team-based problem-solving competition All sophomores were invited to participate. Spiral-taught students were placed in teams and comparison students were placed in separate teams Most students were teamed with others with whom they had not previously worked. We constructed teams with a mix of abilities Uudged by grade records) and gender. All participants were paid, and the winning teams from each cohort were awarded additional prize money. This structure meant that from the student standpoint, they were competing only with peers (not comparison groups versus spiral groups). The participation rate was 75 % for the first year and 90 % in the second year Teams were given an open-ended chemical-process prob lem to solve and had two hours to develop their solution. The problem involved a simple reaction/separation process for the production of formaldehyde from the decomposition of methanol. Students were given the reaction and the desired production rate They had to develop the process flowsheet, make reactor and material-balance calculations, and choose and design a separation scheme. Each team selected one group member to present its solu tion. These ten-minute presentations were videotaped The presentation videotapes and written student work were sent to three external experts in chemical engineering Judges were given the problem solution some guidelines for rating student work, and a form for reporting their analysis of each team's solution The judges ranked all teams from best-to worst on the basis of the technical work not on the presenta tion quality. The highest ranked spiral team and the highest ranked comparison team were each awarded prize money. We were interested in the comparative rankings of spiral versus comparison teams. Judges were volunteers from academia and industry and had no knowledge of whether the teams were spiral-taught or comparison teams We also vid eotaped each team during it s two-hour working sessions to help us understand something about the process of solving chemical engineering problems. 142 Individual At the end of the second implementation year we held an individual exam competition Students were given an exam that tested four basic areas of chemical engineering. The exam was open-book and was designed at about Bloom levels 3-4: application and analysis Again, all sophomores were invited and paid to participate. The participation rate was 61 % of the total sophomore class. We offered the exam to juniors to probe long-term retention of basic knowledge. Only four participated however yielding too small a sample to draw conclusions We blind-graded each individual exam using a numbering system that preserved student anonymity. To promote conscientiou s participation we offered more cash to students scoring above 70 % on the exam. Questionnaires. Surveys. Interviews We contracted developmental psychologists from the Frances L. Hiatt School of Psychology at Clark University for our external consultants. Kevin O'Connor and Lisa Comparini were the consultants with Comparini being with us for most of the project. All questionnaires and surveys were designed by the consultants, and all interviews (in person or electronic) were conducted by Comparini. Both O'Connor and Comparini were intimately involved in the design of the competitions described above. Comparini con ducted the analysis of the questionnaires and surveys. RESULTS The results from the major assessment measures are sum marized below. In all cases the results were positive regard ing the success of the spiral curriculum project. Assess ment design allowed u s to probe program effects from a variety of different views. The converging results clearly demonstrate the superior educational benefits the new curriculum provided Team Problem-Solving Competition Spiral taught student teams were judged signifi cantly higher than c omparison teams in both years of the team c ompetition. In the first year, all three judges ranked the spiral teams as the top three of the six participating teams by a wide margin In the second year, spiral-taught teams were unanimously ranked as the top two of eight total and four of the top five teams were spiral-taught groups. This clearly demonstrates the ability of spiral-taught students to perform at higher levels than comparison students on open-ended problems In general, the judges' comments indicated that spiral taught teams demonstrated better overall problem analysis than comparison teams A more global systems-oriented approach was taken by higher-ranked teams. Spiral-taught teams also showed more progress in generating a flowsheet completing material balances and handling equilibrium con version calculations. Poorer team solutions (primarily com parison groups) were characterized by incomplete flowsheets Ch e mi c al Engin ee rin g Edu c ation

PAGE 61

trouble handlin g reaction product s, and an inability to com pletel y couple the reaction and se paration portion s of the proce ss. Very often, comparison te a m s focused too much on one particular as pe ct a nd failed to d e m o n stra t e knowledg e of th e big pictur e Thi s performance assessment was a major milestone in our evaluation. Since o n e of our objectives was to improve s tudent s' abilities to so lve open-ended problems in team situations, the results were very encouraging. Our evaluation plan was not designed to probe individual effects. For ex ample we did not run a sec tion that had topic s piraling and no cooperative learning We stro ngly belie ve, howe ver, that repeated exposure to s piraled topic s (a critical mechani s m in improving knowledge retention ) coupled with s ub s tanti ve team work i s a major re aso n for the results. Individual Exam Competition Spiral-taught students performed better, as indi v iduals on ba sic chemical engineering prob lems. W e were not able to conduct thi s co mp e tition in the first implementation year, but we did co nduct it at the end of th e seco nd implementation year. Twenty st udent s participated ten from each co hort. The results are s ummarized in T a ble 1 a nd Figure 1. As a group, the s piral-taught s tudents s how e d better under s tandin g of chemical engineering. The average sco re was higher for s piral-taught st udent s and more of them sc ored above the 50 % and 70 % le ve l s. Figure 1 s how s that s piral-taught st udent s perform e d the same or better than co mpari so n s tud e nt s in thre e of the fo ur areas te s ted Tho se four areas were material b a lan ces, classi cal thermodynamic s, stage d equilibrium se parations and so TABLE 1 Average Total Scores for Individual Exam Competition ( T otal possible points = 40) Average # Scores # Scores Cohort Score > 50 % >70% Spiral-Taught 21.7 5 3 Comparison 18. 8 3 2 10 8 0 (,) 6 "' Q) tn ca 4 ... Q) > ct 2 0 lution thermodynami cs. A clear difference in learning mate rial balanc es was s hown. Spiral-taught s tudent s were con tinuou s l y u si n g thi s material in different contexts throughout the so phomo re year. A simi lar difference though not as dramatic was see n for classical thermod y namics. It i s s ig nificant that for the case of s taged se paration s, the s piral taught s tudent s had been exposed to the s pecific material te s ted ( ba sic McCabe-Thiele calculations) several months prior to the exam The comparison students were enrolled in th e tr a ditional course concerning thi s material at the time of th e exam Spiral-taught s tudent s did not do as well on the so lution thermod y namic s problem. Thi s area was the most di ffic ult to build into the s piral curriculum and we recognize th at it i s one area of the curriculum needing improvement. A typical c ritici s m of coo perati ve learning is that so me s tudent s will be carried b y their group. The individual exam results and the longitudinal data s hown below serve to dis prove that notion in our case. Again the combination of topic s piraling repeat e d exposure to open-ended problems and extensive gro up wo rk was s ucce ssfu l in improving indi v idu a l s tudent learnin g. Longitudinal Effects Spiral-taught students received higher gra d es than compa ri son students in follow-on junior and senior -l eve l c h emica l e n gi n eeri n g cou rs es We tracked s tudent s throu g hout their academic programs to under s tand how participation in the new curriculum corre lated with later performanc e Examination of grades in our unit operations laborator y s howed th a t team s comprised of two or more s piral tau g ht s tudent s generally recei ve d hi g her report and oral pre se ntation gra de s than team s comprised Material Bal. Classical Staged Sep. Solution Figure 1. Average score of eac h co hort on individual problems. Maximum score p er probl e m w as 10 points Spring 2001 Thermo. Thermo. solid = spiral-taught open = comparison 1 43

PAGE 62

Examination of grades in our unit operations laboratory showed that teams comprised of two or more spiral-taught students generally received higher report and oral presentation grades than teams comprised mostly of comparison students. mostly of comparison students WPI' s upper-level program is heavily project-ba sed It makes sense that students experienced in project-based learn ing would show higher level s of performance in similar academic activities as they became juniors and seniors These projects are similar to se nior-level research (BS thesis) project s done at other sc hool s The first cohort of s piral taught s tudents graduated thi s year Contaminating factors s uch as mixing of s tudent s among spira l-taught and com parison cohorts and upper-level project grade inflation (80% of these project s receive A 's) made this analysis uninforma tive. Of the nine graduating se nior s who received awards for outstanding project work, however five were from the s pi ral-taught curriculum For that class, only a third of the graduates were in the spiral-taught cohort. An alternative to probing project performance is to com pare grades of comparison and s piral-taught s tudent s in up per-level courses. These courses represent the core knowl edge of the discipline and include : fluid, heat and mas s transport; kinetics and reactor de sig n; two proce ss de s ign courses ; and two unit operations lab courses. A variety of faculty members course format s, and teaching method s are u se d in thi s mix : large lecture group work, laboratories and team-based capstone de s ign WPI awards only four letter grades ( A, B, C and NR)-there is no D grade The NR (No Record) grade, typically covers the traditional D-F range and i s a "fai ure grade that re s ult s in no course credit. In all cases s piral-taught st udent s received a higher per centage of A's and a lower percentage of C s than compari so n students. For the cla ss of 2000, spiral-taught s tudent s represented 33 % of the class yet they accounted for 40 % of the A 's and only 22 % of the C 's, from a total of eight core juniorand senior-level courses. For the class of 2001, s pi ral-taught students represented 50 % of the cla ss and ac counted for 64 % of the A 's and only 29 % of the C 's, from a total of five core juniora nd se nior-level courses. For both cohorts over two years of dat a, a total of 35 failing grades were earned in all courses examined. Only three of tho se were from spiral-taught students, and the same s tudent earned all of them. This data demonstrates the ability of s piral-taught students to perform at higher le ve l s de s pite different course formats and variable teaching s tyle s and s tandard s in their upper level courses. 1 44 Attitudes About the Curriculum, the Discipline, and the Faculty Spiral-taught students showed more positive at titudes about c hemi c al e ngin eer in g and higher c onfidence in the major than com parison stu dents. Student course evaluations are required for all WPI courses A sta ndard form is used that primarily examines st udent sat i sfac tion with the instructor. We examined the aggregate responses from all sop homore-lev e l chemical engineering courses for sections taught by all instructors. There were no significant differences between s piral instructor s and other faculty. In fact the percent of positive student response s for the spiral curriculum instructors as a group, was equal to or higher than that for instructor s in the traditional sections (i.e., those teaching the co mparison cohort). When the project started, we planned to implement pre/ po s t s urveys during each year. During the first implementa tion year we observed that results from the se s urveys gave little information particularly for the time inve s ted adminis tering them to each cohort. We also made a philosophical deci sio n that s urvey s with closed wording, forced-choice responses, and fixed topics were not appropriate for our project. We felt this type of evaluation tool which restricts s tudents responses to predetermined question s, did not allow us to probe a range of po ssi ble topic s and responses from the s tudent s' perspective s Hence we u se d open-ended ques tionnaires for the remainder of the project. All so phomore s were given a que stio nnaire at the end of each implementation year Students were asked about their TABLE2 Results from End-of-Year Questionnaire [Numb er of students responding eac h ye ar is in()] Po sitive comment s Number of topic s Negative comments Number of topic s Spiral-Taught 97-98 98-99 (11=14) (n=IS) 45 61 19 19 22 38 12 14 Confidence in c hoic e of major Po s iti ve change 12 12 Negative change 0 No change 0 2 Comparison 97-98 98-99 (n=l8) (n=II) 20 27 9 15 22 33 14 16 2 10 5 l 6 0 Chem i ca l En g in ee rin g Educatio n

PAGE 63

expectations for the year and whether or n ot they were met. They were asked abo ut their choice of major an d their confi dence in pur s uin g chemical e n gi n eer in g. We aske d what were the 2 to 3 mo s t-valuable a nd the 2 to 3 l east-val uabl e a s pects of their s ophomore-year classes. Additional que s tion s included estimates of work effo rt qualit y of teaching assistants, and an y ge neral comme nt s A su mmar y of th e content analysis of the results is s hown i n Table 2. We s hould keep in mind that the se responses were taken from a fairly open-ended questionnair e The numb ers in a particu lar category do not nec ess aril y repre se nt re s pon ses to th e sa me que s tion s They repre se nt relatively s pontan eo u s num ber s of mentioned topics, rather than re s pon ses to forced choice que s tion s. The overall re s ult s show that s piral-taught s tudent s were more sa ti s fied with their academic ex p erie nc e and more confident with their choice of major than th eir peers in th e comparison sec tion we re Ther e we r e about twice as many po s itive comments made b y s piral-t a u g ht st ud e nt s on a broader number of topic s than b y comparison s tudent s The po s itive comments included topic s s uch as group wo rk lab work interaction with the profe ssors, and the projects Many of the negative comments m a de b y s pir a l-tau g ht s tud e nt s were about problem s that the y reported impro ved durin g th e year (s uch as kink s" in early course organization a nd chang ing professor s) and were generally not about the qualit y of their overall learnin g experience. Negative s tudent co mment s were parti c ul ar l y revealing. Spiral-taught s tudent s co mplained most abo ut their hi g h workload and a bout the teaching assistants. The co mpari so n s tudent s' complaints were often s tat e d in terms of a de ficit ( not enough application, not enough material covere d not enough group work not enough project s, not enough indi vidual attention not being in th e s piral class) a nd were mor e s uggestive of a dissatisfaction with their overall experience. Retention in CM retention in the traditio n al courses was significa ntl y lower than normal while spiral s tudent retention was maintained a t 80%. We interviewed many of the students w h o l eft the spira l c urri c ulum and found that reasons were typically r e lated to lea vi n g engineering for one of the sc i e nce s (c h e mi s try bio c h emistry). An int e re s tin g an ec dot e is that one s tudent w h o le ft l ate in the year said s h e remained in the spiral curricu lum so long only because s h e liked it so much-eventually it became clear that c hemi cal engineering was not her pr efe rr e d di scip lin e and s h e swi tch ed to civil engineering. The Process of Learning Chemical Engineering We are c urr ently involved in a d etai l ed analysis of the problem -so l vi n g sess ion vi d eo tape s taken during the team co mpetiti o n. The se are th e two-hour tapes of eac h team that were not u se d for jud g in g team so lution s. The tape s have all been tr a n scri b e d and are b ei n g analyzed u s in g technique s similar to Linde, et al. 1141 to s tudy th e problem-solving pro cess in spiral-ta u g ht and compariso n teams. Our m et h o dol ogy for thi s analysis combines the expertise of a de ve lop mental psychologist with that of a c h e mi cal e n g ineer. C 151 Preliminary results indicate that the spira l-t a ught team s exhib it ed s i g ni fica ntl y di fferen t teamwork ski ll s than did th e comparison teams Since spiral-ta u g ht teams presented b e ter so lution s, we are interested in characterizing their pro cess a nd co nne ct in g it to o ur c urriculum de s i g n We o b served th at spira l -ta u g ht teams behaved mor e lik e practicing chemical eng in eers attacking a problem w hil e comparison teams b e h aved lik e students of c h emica l e n gi ne ering We 've o b serve d sig ni fica nt di ffe r e n ces in the u se of tools of the profession (a uth ority figures, textbooks, pub li s h ed d ata etc.) that point s to a mod el of teamwork so m e w h a t di fferen t than th e traditional e n gineeri n g model. None of the teams (com pari so n or s piral) ex hibit e d a n y evidence of team dysfunction due t o typical p ro bl ems s uch as domi nant individuals (either intellectually or personality-based) ge nd er bia s, lack of participation, or l ack of Spiral-taught students showed higher retention rate s in the major than did c ompari so n students. TABLE3 motivation Successful teams as rated by external judges, had a greater a bility to con str uct a framework for so lvin g the problem. Unsuccessful teams s tru gg led to do so, and s uch teams we r e un a bl e to move toward a framework even when individual memb e r s see m ed capab l e of starti n g the process. We are currently artic ul ati n g th e theoretic a l ba s i s for th ese o b serva tion s a nd formulating an in-d e pth description of the model and its relation to the new c urri c ulum Retention is a key issue when new cur ricula are implemented We are probabl y s imilar to mo s t department s in that the bi gest lo ss of st udent s from the ma jo r occurs during the sophomore year. Hi s torically our retention rate i s about 80 %, meaning that 20% of the s tudent s enrolling in the first chemical engineering course leave the major by the end of their s ophomore year We found retention was higher during the s ophomore year for s piral-taught s tudent s compared to the comparison cohort. Table 3 s how s the retention data Note that in 98-99, Spring2001 Retention Data for Sophomore ChE Students Total Students Ac ademi c Year P e rc e nt at and Section Retain e d Year E nd 96-9 7 No separate sections 80 62 97-98 Compar i son 80 32 Spiral taught 88 14 98-99 Comparison 68 17 Spiral-taught 80 16 Areas Needing Improvement De s pite the s ucce ss of the curricu lum as de scri bed a bo ve, we are aware of three aeas w her e improvement is n ee d ed. We attempted to incorporate writing into the c urri c ulum to 145

PAGE 64

exploit the writing-to-learn philosophy. But our efforts lacked consistency and due to time taken to deliver the new cur riculum we could not implement all we had envisioned Although spiral-taught students had multiple writing oppor tunities, a concerted program to improve writing was not possible Some anecdotal evidence from upper-level writing samples supports the notion that we did have so me positive impact on spiral-taught st udent s' writing a bilities We s truggled with spiraling the concepts associated with solution thermodynamics This is so me of the most difficult material that sophomores encounter. In fact, many sc hool s do not teach it until the junior year The optimal time and location in the curriculum for introducing some of these theoretical concepts is not known. We made improvements from the first to the second implementation year, but our sense is that more work is needed to sort out how st udent s may best understand the se concepts The final project, for both implementation years was a significantly different and more complex project than any of those earlier in the year We asked students to design a project that could be used in future course offerings. The technical material involved some topics of chemical engi neering (transient material and energy balances) that are not normally a part of the sophomore year. We believe that students s howed mastery of the technical material, but they could not translate that knowledge sufficie ntly into the con text of the project. Hence they developed mediocre-to-poor projects regardless of the team There appears to be a general intellectual limit to their ability to integrate concepts from earlier in the year and extrapolate them to new s ituation s. We are currently examining that limit by analyzing our evaluation data from those projects. SUMMARY We believe our assessment results clearly s how the ben efits of all the educational act ivitie s implemented in the spiral curriculum In fact, we were quite s urprised that dif ferences between spiral-taught and comparison cohorts were so dramatic in so many different areas. Results from a vari ety of measurements and analysis converged upon a consis tent answer. Compared to traditionally taught st udent s, s piral-taught students displayed equal or better understanding of basic chemical engineering principle s, were better in teams at solving open-ended problems had higher satisfaction level s with their academic experience had higher retention rates, performed better in upper-level courses, and were more con fident about their choice of chemical engineering as a major. Although our evaluation plan could not delineate effects of individual curricular improvement s, we believe that frequent open-ended project experiences built around a s piral topic structure were the major reasons for project success. 146 After extensive discussions the WPI chemical engineer ing department voted to permanently adopt the curriculum described in thi s series of three papers for all our sophomore st udents beginning in the fall of 2001. ACKNOWLEDGMENTS The authors would like to thank the Department of Educa tion for s upport of this work under th e Fund for the Improve ment of Post-Secondary Education (FIPSE) Award No. Pl16B6051 l. REFERENCES 1. Clark, W.M., D. DiBia sio, and A.G. Dixon A Project-Based, Spiral Curriculum for Introductory Courses in Chemical Engineering: 1. Curriculum D es ign ," Chem. Eng. Ed ., 34 ( 3 ), 222 ( 2000 ) 2. Dixon A.G. W M Clark and D. DiBiasio, A Project-Based, Spiral Curriculum for Introductory Courses in Chemical Engineering: 2 Implementation ," Chem Eng Ed. 34 ( 4 ), 296 ( 2000 ) 3. Marcus, D ., "Notes on Evaluation Design ," Fund for the Improv ement of Postsecondary Education Department of Education, web site, a ccessed August, 1996 at http :// www .ed. gov / offices / OPE/FIPSE/biblio html updat ed January 9 ( 1998 ) 4. Frechtling J. editor User-Friendly Handbook for Proj ec t E va luation N a tional Science Foundation, NSF 93-152 ( 1996 ) 5. Frechtling J ., L.S. Westat eds. Us e r-Fri e ndly Handbook for Mi xed M e thod Evaluations, National Science Founda tion, NSF 97-153 ( 1997 ) 6 Olds B.M. and R.L Miller A Measure of Success ," ASEE Prism p. 24. December ( 1997 ) 7. Rogers G ., EC2000 and Measurement : How Much Preci sion is Enough?" J. Eng Ed ., 89 ( 2 ) 161 ( 2000 ) 8 DiBiasio D. Outcomes Assessment: An Unstable Process? Ch e m. En g. Ed. 33 ( 2 ), 116 ( 1999 ) 9. Rogers G ., Outcomes Assessment : Opportunity on the Wings of Danger, Ch e m Eng. Ed. 33 ( 2 ), 106 ( 1999 ) 10. Mentkowski M. and G. Loacker Assessing a nd Validating the Outcomes of Colleg e," in Ass e ssing Educational Out comes: New Dire c tions for Institutional Research Jossey Bass (1985 ) 11. O Connor, K., Overcoming Obstacles to Boundary Crossing in Multi-Institution Product Realization Projects ," proceed ings of the Technology Reinvestment Project Grantees Con ference NSF ( 1997 ) 12. Miller, J ., D. DiBiasio J Minasian, and J Catterall, More Students Learning Less Faculty Work ? -The WPI Davis Experiment in Educational Qu a lity and Productivity ," in Stud e nt Assisted Tea c hing and L e arnin g : Strategi es, Mod e l s, and Outcom es," M Miller, J. Groccia, and J. Miller Anker Publishing ( 2001 ) 13 Marcus, D. Evaluation for Second and Third Year and Beyond ," Annual FIPSE Project Director 's Meeting, Wash ington D .C October ( 1997 ) 14. Linde C. J. Roschelle and R. Stevens, Innovative Assess ment for Innovative Engineering Education: Video-Based Interaction Analysis ," Report to the NSF Synthesis Coali tion, Institute for Research on Learning Palo Alto CA ( 1994 ) 15 Clark W. L. Comparini D DiBiasio and A Dixon "The Process of Learning Chemical Engineering : What Works and What Doesn 't," ASEE meeting, St Louis MO, June ( 2000 ) 0 Ch e mi ca l Engin ee rin g Education

PAGE 65

Estimating the Transfer of O xy gen Continued from pa ge 139. ferred approach is to tailor the functional form derived from existing correlations in an attempt to maximize the use of the specific information available. The laboratory exercise also has secondary benefits. First, the exercise bridges the gap between biotechnology and classical chemical engineering. Students are often under the impression that the area of biotechnology represents a radi cal departure from the chemical engineering principles ap plied to other industries. This laboratory serves to demon strate that the high tech fields have been developed on the same set of principles as the mature industries. On a practi cal level, the lab deals with benign materials. As s uch there are no fume hood requirements or di s po sal problems The lab can easily be extended to examine the effect of other variables, such as temperature, oxygen partial pre ss ure and liquid volume. CONCLUSIONS When faced with a design problem the chemical engineer often must tum to empirical expressions generalized through the application of dimensionless groups. But as data become available that are specific to the system of interest the ba s ic proven empirical expression s hould be tailored to reflect these data. Extracting the relevant parameters of interest (i.e KLa) from experimental data generated for this purpose is subjective, based heavily on the assumptions made by the engineer. Although many approaches may be adequate, oth ers may lead to erroneous results. A key variable to consider when analyzing the problem is the influence of the measur ing element on the resulting data set. NOMENCLATURE a area available for mass transfer per unit vo lum e of ungassed liquid ( m 2 m 3 ) C G concentration of oxygen in the gas pha se ( mot L 1 ) C~ concentration of oxygen in the gas pha se at t=O ( mo! L 1 ) CL concentration of oxygen in the liquid (mot L 1 ) C~ concentration of oxygen in the liquid in equilibrium with the gas pha se ( mot L 1 ) CP concentration of oxygen in the l.iquid, as measured b y the di sso lved oxygen probe ( mot L 1 ) d i impeller diameter (m) '4 tank diameter (m) Do 2 diffusivity of oxygen in water (m 2 s. 1 ) g acce l eration of gravity (m s 2 ) h i height of impeller from bottom of tank ( m ) h L height of l.iquid ( m) I i length of impeller blade s ( m ) H Henry s constant for oxygen and water ( mmol L 1 atm 1 ) K i empirica l constant KL overa ll mass-transfer coefficient per unit transfer area, Spring 2001 based on the liquid phase (m s 1 ) KL a volumetric mass-tran sfe r coefficient, based o n the liquid volume (hr" 1 ) k p (!!tp)(s 1 ) n 8 number of baffles n i number of blades on impeller stirring speed (rev s 1 ) P power input into un gasse d liquid (W) P G power input into gassed liquid ( W ) v 5 s uperficial gas velocity, based on cross sec tion of vesse l (m s 1 ) v, terminal ri se velocity of a gas bubble (m s 1 ) w 8 width of baffle s ( m ) w i width of impeller blade s ( m ) Q gas flow rate (L s 1 ) time (s) Greek symbols a,~. y, ').._ exponents in Eqs (12), ( 17 ) a nd (21) t p time constant of the dissolved oxygen probe (s) t time constant of the transfer process (1/KLa)(s) f liquid viscos it y (cp) Pr liquid density (kg m 3 ) cr r su rface ten s ion at gasliquid interface ( mN m 1 ) REFERENCES 1. Geankoplis C .J ., Tran sport Proc esses and Unit Op e rations Prentice-Hall, Inc ., NJ ( 1993 ) 2 Bailey J.E. and D F. Ollis Bio chemical Engineering Fun damentals, 2nd ed. McGraw-Hill, Inc. New York, NY ( 1986) 3. Linek, V., J. Sinkule, and P. Benes Biote c hnol. Bioeng., 38 323 ( 1990 ) 4. Linek V., V. Vacek and P Benes, Chem. Eng. J ., 34 11 ( 1987 ) 5. Benedek, A. and W.J. Heideger, Biotechnol Bio eng., 13 663 ( 1971 ) 6. Sheppard J.D ., and D G Cooper, J. Chem. T ec h. Biot echnol., 48 325 ( 1990 ) 7. Ruchti G., I.J. Dunn and J.R. Bourne Biot echnol. Bio eng., 23 277 ( 1981 ) 8. Chang, H.N ., B Halard and M Moo-Young, Biote c hnol Bio eng., 34 1147 ( 1991 ) 9 Wernau W .C., and C R. Wilke Biot echnol. Bioeng. 25 571 ( 1973 ) 10. Rushton, J H ., Chem. Eng. Prag ., 47 485 ( 1951 ) 11. Calderbank, P H. Trans lnstn. Chem. Engrs., London 36 443 ( 1958 ) 12. Rushton J H ., E W Costich, and H J Everett Chem. Eng Prag ., 26 395 ( 1950 ) 1 3. Richards, J W ., Prag. Ind Microbial. 3 143 (1961) 14. Kargi, F ., an d M. Moo-Young in Vol 2 of Th e Principl es of Biot ec hnology, Engineering Considerations, C.O. Cooney and A.E. Humphrey, eds; in Comprehensive Biotechnology: The Principl es Applications and Regulations of Biotechnology in Industry Agriculture and Medicin e, M Moo-Young, ed., Pergamon Press New York, NY 15. Michel B.J ., and S.A. Miller, AIChE J., 262 ( 1962 ) 16 Tribe L A., C.L. Briens, and A. Margaritis, Biot ec hnol Bio eng 46 388 ( 1994 ) 17. Merchuk, J .C., S. Yona, M.H. Siegel, and A.B Zvi Biotechnol Bioeng ., 35 1161 ( 1990 ) 18. Cooper, C.M., G.A. Fernstrom, and S.A. Miller, Ind. Eng. Chem 36 504 (1944 ) 0 147

PAGE 66

.,~ .. 111 ij 11111111 .._c_l_a_s_s_r o_o m ________ __,,) UNDERGRADUATE PROCESS CONTROL Clarification of Some Concepts R .RAVI Indian Institute of Technology Kanpur Kanpur 208 016, India T eaching undergraduate process control can be an en joyable experience for an instructor given the wide range of quality chemical engineering textbooks that are now available. C 1 61 After teaching the course a couple of times however I felt there was still a need for clarification of some fundamental concepts especially in the areas of frequency response and stability. In this article I hope to achieve such a clarification through some simple, yet illus trative, examples FREQUENCY RESPONSE : ONLY FOR STABLE SYSTE M S ? In the context of process control the frequency response is usually associated with the response of a linear, time invari ant (constant coefficient) system to a sinusoidal input. In the most common way of deriving" the frequency response result the output response is shown to be a sinusoidal func tion of the same frequency ( m) as the input, once the tran sients have died out. Further, the ratio of the amplitude of the output to that of the input called the amplitude ratio (AR) is shown to be equal to IG(jm )I, while the phase difference ( (j>) between the output and the input is shown to be arg(G(jw)] where G(s) is the transfer function representation of the system of interest and jd-1. Thus the frequency response calculation is reduced to the calculation of the magnitude and phase of the complex num ber, G(jw), as a function of the frequency. This information is usually represented in the form of a Bode diagram or a Nyquist plot. The key point of our discussion is the condition "once the transients have died out Clearly, this happens if the system is stable, i.e if all the poles of the transfer function G(s) lie in the left half (of the Pres e nt addr e ss : Indian Institute of T e chnology Madras Madras 600028 India 148 complex) plane (LHP). Thus it might appear that frequency response makes sense only for stable systems. But we do find Bode diagrams and Nyquist plots for the pure capacity (G(s)=A/s) and the PI controller, G (s) = [ K c (-r 1 s + t)]/-r 1 s both of which are (open-loop) unstable. Do these diagrams mean anything then? In the case of the pure capacity system, one can show that the response to a sinusoidal input is bounded and is a superposition of a con stant and a sinusoidal function whose amplitude and phase are in fact provided by G ( jm), as for a stable system (It should be noted that a s ystem with a zero pole is to be regarded as unstable in spite of a bounded response to a sinusoidal input. Recall that the step response of such a system grows with time.) But what about a system with a pole in the right half plane (RHP) for which the response to a (bounded) sinusoidal input will have a time-growing component arising out of the unstable pole? Does the Bode diagram (or the Nyquist plot) for such a system obtained from the corresponding G(jm) have any meaning? The answer to the last question is yes. The common way of deriving the frequency response re sult is only a method of measuring the frequency response for stable systems and does not constitute a fundamental R. Ra v i obtained his BTech from the Indian Institute of Technology Madras in 1984 and his PhD from Purdue University in 1991. His research interests are in applied statis tical mechanics and process control For the past few years his abiding passion has been the understanding of the origins of thermodynamics and fluid mechanics. C opyri g ht C hE Divi s i o n o f ASEE 2 001 Ch e mi c al En g in ee ring Edu c ation

PAGE 67

definition of it. The fundamental definjtion is provided b y a basic re s ult of linear systems theory P 1 There exists a peri odic so lution for a linear time invariant sys tem s ubjected to a periodic forcing; thi s periodic solution ha s the sa me fre quency as that of the input forcing and it s amplitude and phase at the particular frequency are determined (as ex plained above) from the complex number G(jro) Thjs result hold s whether the sys tem is stable or not. In general, the re s pon s e of a linear sys tem to a periodic forcing will be the s uperpo s ition of the periodic so lution and a non-periodic component, and th e frequency response is defined with re s pect to the periodic component. Thu s, th e Bod e diagram for an unstable sys tem make s se nse in that it represents the same relationship between the periodic com ponent of the (outp ut ) response and the input periodic forc ing as it does for a s table system. This point i s not of minor significance as it gives unjver sa l s tatu s to Bode diagram s or Nyqui s t plot s as s i g nature s of systems they represent, be they s tabl e or unstable The open loop method of mea s uring the frequency re s pon se (after waiting for the tran s ient to die out) will not work for un stab l e sys tem s ( pure capacity being an exception). In the next sec tion we point out two po ss ible method s o f measuring the freq u ency response of unstable s y s tems-one an open-loop method and the other a clo se d-loop method. Although both methods are valid in principle the latter is more practicable The rea so n s are outlined belo w. Frequency Response of Unstable Systems We illustrate the procedures through a si mple sys tem with one unstable pole Open-Loop Method K G 0 (s)= -( -) s-a ( I ) For the Open-Loop Method we consider a si nu soi dal input u(t) = Au s in(rot +u) (2) The response of the sys tem to thi s input can be s hown (fo r instance, by a straightforward Laplace in ve r s ion ) to be S prin g 200 1 u .. _K_ 5-0 After teaching [undergraduate process control] a couple of times I felt there was a need for clarification of some fundamental concepts, especially in the areas of frequency response and stability. In this article I hope to achieve such a clarification through some simple, yet illustrative, examples. () KA 0 (roco s<)> 0 +asin<)> 0 )ea 1 y t = ---~--a2 +w2 +Au IG 0 (jro)ls in{rot +cp 0 +arg[G 0 (jro))} (3) Thi s s ug ges t s a way of "sta bilizin g" the re s pon se by choos ing u s u c h that rocos<)> 0 +a s in<)> 0 =0 (4) so that only the stable p eriodic component of the solution remain s, enabling the determjnation of it s amplitude and pha se. In practice thu s, one i s left to choose a unique value of u ( b e tw ee n O and 21t) for each w; thls can be problem atic g i ve n that the va lue of the un s table pole a is not known a priori. Hence we di sc u ss a more practicable method in vo l v ing closed-loop sta bili zatio n Closed-Loop Method We co n s id er the same first-order un s table sys tem It i s easy to s how that the sys tem can be s tabilized in a feedback loop u s ing a proportional controller of gain K c greater than a/K (F igure 1 illustrates the sc heme ). In fact y(s) K c K = G (s) r( s) s + b CL w h ere b=K c K -a > 0 (5) If a si nu so idal variatio n i s give n in th e reference s ignal r i.e. r(t) = Ar s in rot (6) then we can s how that ( by Laplace inversion, for instance) y j .. Figure 1. An open-loop un stab l e system in a fee dba ck loop wit h a proportional co ntroll er. 1 49

PAGE 68

(7) where C 1 = ~ 2 ~;:; A Y =ArlocL(jro)I; y =arg[ocL(jro)) (8) The signal u(t) = Kc[r(t)-y(t)] can be expressed as u(t) = -K c C1e bl + Au sin (rot+ u) It is possible to show that (9) i.e. the amplit u des and the phases of the "input" and the "output" signals of the unstable system, Go(s) are related as before by the complex number G 0 (jro). The stabilization effect is noted in the b term (note: b > 0) in both y and u in contrast to the open-loop case where we get the time-grow ing term, e", in the output (for the same input Ar s in rot). For concreteness and simplicity, we illustrate the above result with a numerical example_c si We choose 2 G 0 (s)=1 s(! 1) It is easy to see that a unity gain (~ = 1) proportional controller stabilizes the above system in a feedback loop. In fact y( s ) 2 r(s) =s+T If we choose the input to be r(t) = 0.5 sin 2t then we can show that y(t)=e 1 +(0.2)11 2 sin [2t-1.ll(rad)] Further u(t)= r(t)-y(t)= ~ 2 e 1 +0 5 sin [2t+0.93(rad)] and IG 0 (2j)I= F5 and arg[G 0 (2j)]=-2.04rad Thus we see that and (12) (13) (14) (15) (16) (I 7) Of course the above analysis is based on a given system transfer function. This is not known a priori and, in fact, the purpose of the frequency response experiment is to deter mine the transfer function. But what one has to do is to tune the proportional controller to obtain a stable system Then for a known sinusoidal input, r ( t), at various frequencies one would have to measure the amplitude and phase of both 150 u(t) and y(t) (after the transients die out) to construct the transfer function, Go(s). FREQUENCY RESPONSE AND STABILITY CRITERIA We now turn to another aspect of frequency response and stability the famou s Nyquist stability criterion The Nyquist criterion helps one to infer the stability of a feedback control system from the Nyquist (polar) plot of the loop transfer function GL(s) which is the product of the tran s fer functions of all the elements in the control loop The advantage of stability criteria based on frequency response is their ability to deal with non-polynomial GL(s) that the Routh-Hurwitz criteria cannot treat rigorously. This advantage is particu larly relevant to chemical engineering systems that often contain a time-delay element. Most chemical engineering textbooks on process control do not give as much prominence to the Nyqui s t criterion as they do to the Bode stability criterion which is easier to use. An exception is the Luybenr 2 1 book where a detailed discus sion with illustrative examples can be found It is to be noted that the Bode criterion is not general and specifically cannot be applied in cases where the Bode diagram for GL(s) is not monotonically decreasing It is our objective here to high light the potential sources of error in the application of the Nyquist criterion It is not uncommon to find s pecial state ments of the criterion that might work in many cases but fail to yield the correct result for at least some systems. Often these special statements are not accompanied by the conditions under which they hold. Thus it is desirable to always use the general form of the criterion that is given below Let N be the number of net rotations of the Nyquist plot of GL( s) ( 00 < ro < oo ) about the point ( -1 0 ). This i s the net angle traced out by the line segment from ( -1 0 ) to the Nyquist plot as the frequency changes from oo to oo. The sign convention is a positive value for N if the net rotation is in the counter~ clockwise direction and negative if it is in the clockwise direction. Let PR be the number of poles of 1 +GL (s) (note that this is the same a s the number of poles of G L(s) ) in the RHP. Then (18) where ZR is the number of zeros of I +G L(s) in the RHP. Hence, ZR i s the number of roots of the characteristic equa tion l+GL ( s ) =0 that lie in the RHP. Clearly Z R must be zero for a stable system It is not our objective here to give a proof of the above s tatement ( see, for instance Ref. 9), but we illustrate its proper use through a simple example In our opinion the following points are crucial: While the portion of the Nyquist plot from 00 to 0 is Ch e mi c al Eng in ee rin g Edu ca tion

PAGE 69

(a) 0 .4 Im Figure 2. 0.2 ,-, Nyquist plots for f \ a) o.o Re I (-1,0) Gu (s) = 2( s -l) 0.2 and -0.4 b) 1 5 1.0 -0.5 o.o 0 5 2 GL 2(s) = (sI) The dotted{---} (b) portion is for =
PAGE 70

f-ih=i curriculum ) ----------THE INTERFACE BETWEEN ChE AND MATHEMATICS What Do Students Really Need? MICHAEL D. GRAHAM University of Wisconsin-Madison Madison, WI 53706-1691 SUSAN L. GANTER Clemson University Clemson, South Carolina T he Mathematical Association of America (MAA) through its Committee on the Undergraduate Pro gram in Mathematic s (CUPM), i s conducting a Cur riculum Foundations Project, a major analysis of the under graduate mathematic s curriculum. The goal of the project i s to develop a curriculum document that will assist college mathematics departments as they plan their programs for the next decade Historically, CUPM curriculum recommenda tions have had a significant influence on the de s ign of undergraduate mathematic s program s. These important and influential guidelines were la s t revised in 1981. There fore, the CUPM curriculum guidelines need to be recon sidered; such a review and the resulting recommenda tions are likely to have widespread impact on the teach ing of undergraduate mathematics. Given the impact of mathematics instruction on engineer ing the sciences, and the quantitative social sc iences (espe cially instruction during the first two years) significant in put from these partner discipline s is needed to inform the MAA curriculum document. The CUPM s ubcommittee on Calculus Reform and the First Two Years (CRAFTY) gathered much of this neces sary information between Fall 1999 and Spring 2001 through a series of invita tional disciplinary workshops funded and hosted by a wide variety of institutions (see Table 1) Each workshop is focused on a particular partner disci pline or on a group of related di sc ipline s, the objective being a clear, concise statement of what students in that area need to learn in their first two years of college mathematics The workshops are not intended to be dialogues between math ematics and the partner disciplines but rather a dialogue among representatives of the discipline under consideration, with mathematician s there only to listen to the discussion s and to provide clarification on questions about the math ematics curriculum. For this reason almost all of the indi viduals invited to participate in each workshop are from the partner disciplines. The major product of each workshop is a report or group of reports summarizing the recommendations and conclu sions of the workshop. These are written by the representa tives from the partner disciplines, with the mathematics community as the primar y audience, and they address a se rie s of questions formulated by CRAFTY (see Table 2). Uniformity of style i s achieved across the reports by using the same basic questions for each workshop. Having a com mon list of questions also aids in compari n g t h e reports of different workshops The questions are simply designed to guide the workshop discussions, however, and t h erefore are Mik e Graham received his BS from the Univer sity of Dayton in 1986 and his PhD from Cornell University in 1992 both in chemical engineer ing and did postdoctoral work at the University of Houston and Princeton University His re search interests encompass instabilities and nonlinear dynamics in flows of complex fluids, molecular and multiscale simulation of polymeric liquids, and interfacial and multiphase flows Susan L. Ganter is Associate Professor of Math ematical Sciences at Clemson University She has directed several local and national evalua tion studies, including a recent residency at the National Science Foundation in which she inves tigated the national impact of the calculus reform initiative and helped to develop the evaluation plan for the Institution-wide Reform Program in the Division of Undergraduate Education Copyright C hE Divi s ion of ASEE 2 001 1 52 Che mi cal Engineering Edu c ation

PAGE 71

intentionally vague In addition workshop participants are asked to focus primarily on the first question category "Un derstanding and Contents, with the other questions being of secondary importance The reports from each workshop are then widely circu lated within the specific disciplines, as well as in the math ematics community, in order to solicit a broad range of comments. At the completion of this process in the spring of 2001, the reports will be published and used in the formula tion of the MAA curriculum document. A curricu lum con ference that includes invitees from all disciplines will be convened in Fall 2001 to synthesize the workshop findings and begin writing the MAA curriculum document, sched uled to be published in 2002. In addition to providing input into the larger CUPM re view, the reports serve as valuable resources for initiating discussions at individual institutions between mathematics departments and partner disciplines Some mathematics de partments h ave a lr eady begun using the reports to stimulate TABLE 1 MAA C urr ic ulum Foundations Workshops Physics and Computer Scie n ce Bowdoin College Maine Oct. 2 8 3 I 1999 William Barker : barker @ bowdoin.edu Interdisciplinary (Math. Physics. Engineering) USMA WestPoint Nov 4-7 1999 Don Small: ad57 l2 @ usma.edu En,:inee rin g C l emson University South Carolina May 4-7 2000 Susan Ganter : sganter @ clem s on edu H ea lth-Related Life Sciences Virginia Commonwealth Univ e rsit y Ma y 18 20 2000 William Haver : whaver @ atla s. vcu .e du Tech11ical Mathematics (at two sites) Los Ange l es Pierce Co ll ege California Oct. 5-8 2000 Bruce Yoshiwara: byoshiwara @ hotmail.com J Sargeant Reynolds Community Col. Virgini a Oct. 12-15 2000 Susan Wood : swood @ jsr.cc va u s Mary Ann Hovi s: hovisma @ lt c. t e c oh u s Statistics Gri nn ell College Oct. 12-15 2000 Thomas Moore: mooret @ math.grin.edu Business Fi nan ce a n d Eco11omics University of Arizona Arizona Oct. 28 -29 2000 Deborah Hughes Hallett : dhh @ math arizona edu William McCallum: wmc@math.arizona edu Mathematics Educat i on Michigan State University Michigan Nov 1-3 2000 Sharon Senk : senk@pilot.msu.edu Biology a11d Chemist r y Macalester College Nov. 2-5 2000 David Bre s soud : bressoud @ macale s ter.edu Mat h ematics Preparation for the Maior Mathematical Sciences Research In s titute Feb 9-11 2001 William McCallum: wmc @ math.arizona.edu Spring 200 1 interdepartmental discussions Such discussions, as well as those at the CRAFTY workshops, generate good will be tween mathematicians and colleagues in partner disciplines. In general colleagues from partner disciplines value math ematics and welcome the opportunity to state their views about mathematics education, provided their opinions are taken seriously Promoting and supporting informed discus sions with the partner disciplines may ultimately be the most important outcome of the MAA Curriculum Foundations Project. THE CRAFTY ENGINEERING WORKSHOP AT CLEMSON UNIVERSITY One of the CRAFTY workshops was sponsored and hosted by Clemson University on May 4-7 2000. It focused on the needs of engineering from the first two years of college TABLE2 MAA Curriculum Fo undati o n s Works hop Questions U11de r sta ndillg and Co11tent What co n ce ptual math e m a ti c al prin c ipl e s mu s t s tudents master in th e fir s t tw o y ear s? Wh a t m a th e mati ca l pr ob l e mso l v in g sk ill s mu s t s tud e nts ma s ter in th e fir s t t wo y ear s? Wh a t broad math e mati c al to pi cs must s tudent s m as ter in the fir s t two y e ar s? What pri o riti e s e xi s t between thes e topic s? What i s the desired balan ce between th e or e ti c al und e rstandin g a nd co mputational s kill? H o w i s thi s balance a chiev e d ? What are the math e mati c al n ee d s o f diff e r e nt s tud e nt populati o ns and how ca n the y be fulfilled ? Technology Ho w d oes t ec hn o l ogy affec t wh a t mathematic s s hould be learned in th e fir s t two y ear s? What math e mati c al t ec hnol o g y s kill s should students master in the fir s t two years? What diff e rent mathematic a l technology skill s are required of diff e r e nt s tud e nt populati o n s? fll structional foterconnections What impact doe s math e mati cs e du c ati o n r e f o rm have on in s tru c ti o n in y our di sc iplin e? H o w s h o uld e du c ati o n refo rm in yo ur di sci plin e affect mathemat ic s in s tru c tion ? How c an dial og u e on educational is s ue s between your discipline and mathematics best be maintained? fll structional Techniques What ar e th e e ff ec ts of diff e r e nt in s tru c ti o nal m e th o ds in m a thematic s on s tudent s in y our di s ciplin e? What in s tructional method s b es t d eve l o p th e math e mati c al co mpr e h e n s i o n needed for y o ur di s cipline ? What guidance does e du c ation a l resear c h provide concerning mathematical training in your di s cipline ? 153

PAGE 72

mathematics instruction The workshop h a d thirty-eight in vited participant s, with roughly equal repre se ntation from each of four area s in engineering (c hemi ca l civil, e lectrical, mechanical ) and mathematic s. Th e workshop r es ulted in four documents one for each of the four engineering areas, addre ss ing the MAA question s s pecified a t the outset of the workshop. Thi s p a per focuses on the recommendations of the chemi cal engineering group It i s not intended to b e a definitiv e document, but rather a working paper that generates discus sion among chemical engineers in order to provide addi tional feedback for the mathemati cs community. Therefore the authors welcome comments and additional ideas REPORT OF THE CHEMICAL ENGINEERING GROUP The Chemical Engineering group member s are li s ted in Table 3. What Chemical Engineers Do Since this report was originally written for mathemati cians, an appropriate introduction i s to di sc uss what chemi cal engineers do, why mathematic s is needed and how it i s used A reason a bly broad definition i s that chemica l eng n eers design materials and th e pro cesses by which mate rials are mad e Traditionally chemical engineers have been associated with the petroleum and large-scale chemical indu s trie s, but (especially in recent years) chemical engineers have also been involved in pharmaceuticals foods, polymer s and ma terial s, microelectronics and biotechnology The core s ub ject s that underlie and unify this broad field are thermody namic s, chemical reaction proce sses, tran s port processes (i e., the s patial and temporal distribution of mas s, momentum and energy) and proces s dynamic s, de s i g n and control. On top of this fundamental framework, a central emphasis of chemical engineering education is model building and analysis. A go od chemical engineer brings together the funthe proce ss described b y the mathematic s, rather than the s p ec ific closed form (or numeric a l ) result. Her e i s an example: A s tarting point for under s tanding any process is writing down the conservation law s that the sys tem or proces s sa tisfie s ... for conserved quantities accumu lation = input output. Depending on the level of detail of the model thi s equation mi g ht be for example, a large set of linear algebraic e quation s that determine the relation s hips between fluxes of chemical s pecie s throughout the process (a s pecie s balanc e), or it might be a set of parabolic partial differenti a l equations governing the temperature and compo s ition of the fluid in a chemical reactor. In the thermodynamics of multipha se sys tems energy is conserved but takes on a variety of forms; a good knowledge of multivariable differen tial calculus i s essential here to keep track of everything. Mathematics for Chemical Engineering The purpo se of the original report was not to prescribe the math e matic s curriculum-chemical engineers do not want mathematic s instruction to provide only what students can "ge t by with knowing. Nor is it appropriate to come down on either side of the traditional vs. "refo rm debate-it is likely that both sides are right to an extent. Instead, some general thoughts on subject matter and emphasis are pre se nted h ere. Pr eca l cu lu s Foundations By foundations, we mean Ba sic kn ow l edge of families of functions (po l ynomical, ex p onentia l ... ) in t e rm s of data, graphs, words and eq uations basi c trigonometric identiti es and geometry, properties of lo ga rithms e t c Equations, in e qualiti es Basic lo gic and algorithms Small lin ear systems of eq uations Coordinate systems Ba s i c a rithm etic and manipulation skills damentals to build and refine a mathematical model of a pro cess that will help him or her understand and optimize it s per formance. To be good at model building and analysis, s tudent s must have at hand the math ematical background to under stand and work with the core scientific areas, as well as to find sol ution s to the final model that they build In thi s context, the "so lution to a mathem a ti cal problem is of ten in the un derstanding of the behavior of TABLE3 Ma s ter y of the above ar eas i s crucial. Probably the mo s t important thing the mathematics community can do here i s to actively investi gate the pedagogy of K-12 education-to help sort out which reforms" are produc tive from those that are merely "fa ds and to encour age sc hool s not to neglect the education of the more math ematically inclined students by focusing the curriculum too narrowly on the average performer. Another impor1 54 Chemical Engineering Group Members [J Jenna P. Carpenter Int er im Academic Director, Chemical E n g in ee rin g, Civ il E n g in ee rin g a nd Geosciences L o ui s ian a Technological University [J Michael B. Cutlip Professor of Che m ica l E n gineeri n g and Director of th e H o nor s P rogra m University of Connect i c ut [J Michael D. Graham Assoc iat e P rofesso r of C h em i ca l E n gi n eering University of Wisconsin-Madison (disc u ssio n l eader/ r eco rd e r ) [J Anton J. Pintar Assoc i a t e P rofessor of C h e mi ca l Engineering Michigan Technological U niv e r s ity [J Jan A Puszynski Prof esso r of Chemistry and Chemical Eng in ee rin g South Dak o t a School of Min es and Technology Chem i cal Eng in ee rin g Education

PAGE 73

tant ro l e her e is to provide program s that help K-12 math ematics tea c h e r s und ers t a nd some applications of the math e m atics th at they teach (e n gineering faculty s hould do much mor e her e). Lin ear Mathematics Students interested in gra duate sc hool s hould be enco ur aged b y their mathematic s profe ssors, as we ll as their engi neering advisors, to take additional mathematic s courses. A final general comment: st udent s s hould h ave some idea of the power of a theorem but for engineers, concepts are more Chemical engi n eeri n g st ud ents wo uld benefit from earlier ex p os ur e to the b asics of linear sys tem s in R N, particularly The geometry of lin ear spaces Vector algebra ( especially in 3D) Ax = b ( existence and uniqu eness, Gausian elimination, geometric interpre tation, over and und erdetermined sys t ems, a nd l east squares problem s) ... [the] discussions ... generate good will between mathematicians and colleagues in partner disciplines. In general, colleagues from partner disciplines value mathematics and welcome the opportunity to state their views about mathematics education, provided their opinions are taken seriously. Ax = Ax ( characteristic pol ynomial and diagonalization, Jordan form, range and nullspace of A, geometry) At the University of Wiscon s in-Madison for example, there is a co ur se o n lin ear mathematic s" that introduces these notion s and ap pli es them to systems of ordinary differential equations (see n ext sect ion ). Many c h emica l engi n eering s tudent s tak e this in li e u of the traditional differential equa tion s class. Calculus and Diff erential Equations The importance of visualization in calculus cannot be overemphasized, especia ll y as a guide to differential and vector calculus in multiple dimensions plotting (e.g what function i s lin ear on a l ogl og plot? ), working in cyli ndri cal and s pherical coordinate sys tem s, a nd converting between coordinate sys tem s. Somewhat le ss time co uld be spent on technique s for eva lu a tin g co mpli ca ted int egra l s, with the time s pent instead on, for example, visualizing the applica tion of the c h ai n rul e in multiple dimen s ion s Understanding of truncated Taylor se ri es fo r l ocal approximation of func tion s is ve r y important and sho uld be seen early and often. In differ e ntial equations, a thorou g h knowledge of lin ear con s tant coefficient systems ( initial value problem s and bound ary va lue problem s; see previous section) is preferable to emphasis on ex i s t e n ce th eory a nd series sol uti ons for non constant coefficient problems Some qualitative theory for nonlinear syste m s is also desirable. Pr obability and Statistics Alumni s ur veys typically s h ow that this is the mo s t com mon application of math e m at ic s for the practicing chemical engineer with a bachelor 's de gree, in ad d ition to th e exte n s iv e u se of s pre a d s h eets. Key issues here include parameter estimation experimental design sampli n g, a nd the origins and properti es of various distribution fun ctio n s. Spring 2001 important than proofs In other words, it is appropriate for chemical engineeri n g students to l earn mathematical fac t s without always see ing the associate d proofs. Technique and Technology A fair amou nt of the di sc u ss ion at the MAA e n gi n eeri ng workshop, within the chemical engineering group and o th ers, centered arou nd the u se of technology in the m a th ema t ics courses for engineers. In the di sc us s ions technology" meant a number of different thing s, from numerical methods to gra phing calculators to sy mbolic manipulation packages. We'd like to emphasize here some point s to be kept in mind when thinking of the introduction of the se tools into math ematics courses. We do thi s in the form of respo n ses t o two questions, representing both sides of the iss u e (admitted l y, these questions are straw men): "My laptop can do that. Why should I learn to do it b y hand?" Sense of form of mathematical expressions, under stand in g of what manipulations are available, facility with these manipulations Fluency in the language of mathematical concepts Appreciation and recognition of mathematical rigor Di scipli n e, maturity, confide nce of ma stery Closed form results are best, if availab l e R ecognition of limitations of closed form results, where things get difficult Kno wledge of what computers do "Use of computers dumbs down the mathematics course why use them?" Solution of r ea listi c ( complex) problems, many of which involve numerical solutions. In upper-level courses, extensive use is made of programs such as MATLAB, O ctave (avai labl e at ) MathCad, Mathematica and Pol y math 155

PAGE 74

Efficient exploration of solution and design spa c e Visuali z ation, especially in multidimensional and vector calculus Relief from tedium Confidence in results derived by hand Ultimately, the technology should take a back seat in mathematics courses until it becomes necessary for solving interesting problems. For example, in a linear algebra course students should be able to do LU decomposition of a 3x3 system by hand before they are shown that a computer algebra system can complete the process with one com mand. At the same time it is useful to point out the relation ship between numerical techniques and exact ones (e.g., a Riemann sum can be evaluated numerically to approximate an integral). Students should have a solid understanding regarding limitations of numerical methods and their accu racy. They should clearly see the power of analytical solu tions when such solutions can be found. A Suggestion for Coupling Mathematics and Engineering Education One set of issues that arose repeatedly in the MAA engi neering workshop discussions was the concern that students do not see connections between mathematical tools and con cepts and the wide utility of these in engineering. A rela~ed concern was the time lag between exposure to mathematics and its application to the solution of real engineering prob lems. The notion of just-in-time learning was discussed and the suggestion was made that mathematics courses be more applicationor example-driven and be more evenly spread through the curriculum, rather than "front loaded into the first two years. The chemjcal engineering group shared these concerns, but also thought that J) Part of the beauty and power of mathematics is that it is example-independent-calculus applies to econom ics just as it does to mechanics 2) The time spent developing the background for engi neering applications is time not spent on mathematical principles and tools 3) A straightforward just-in-time approach will not satisfy all engineering majors ( e.g., electrical engi neers do not need Laplace transforms at the same time as chemical engineers). An alternative structure can be considered for addressing these concerns which are essentially about how to connect mathematics and engineering in the students minds Spe cifically the college mathematics curriculum could include discipline specific supplements, especially in the calculus sequence These could be workbooks or web pages contain ing, for example, Engineering background material, e.g ., some basic 156 thermod y nami c s and how s pecific mathematical principles and/or tools ( such as total differentials and partial derivatives in several dimensions) are used Exercises or proje c ts integrating mathematics and engineering Additional disciplin e -specific emphases, e g trigono metric identities and manipulations for e lectrical engineering students. These could be used independently by the students, or used in a one-credit course running in parallel with the calculus courses, or simply be resources for mathematics instructors wisrung to gain perspective on engineering appli cations or bring engineering applications into the mathemat ics classroom Thjs is perhaps overambitious but certainly worth considering. It was suggested that, witrun chemical engineering, CACHE (Computer Aids for Chemical Engi neering ) could play a role in studying trus possibility in conjunction with MAA CONCLUDING REMARKS It is clear that the application of mathematical concepts and the generation of mathematical solutions to engineering problems are essential to the educational programs of all undergraduate engineering students Enhanced cooperation between mathematics faculty and engineering facu l ty can lead to a better experience for our students Without excep tion the participants felt that the workshop was a very pro ductive way to promote dialogue between the mathematics and engineering education communities and encouraged the organization of more workshops of trus type Another venue that mathematicians can explore is the American Society for Engineering Education which has a math ematics division On the other hand, it may be productive for engineering educators to attend MAA meetings Perhaps most importantly mechanisms need to be imple mented to promote interaction between engineering and math ematics faculty within individual universities-good rela tionshlps at this level will enable mathematics faculty to understand what material the engineering faculty would like to see reinforced and emphasized, as well as enabling engi neering faculty to gain a better understanding of the issues s urrounding mathematical preparation of entering freshman engineering majors. ACKNOWLEDGMENTS We are grateful to Professors J.B. Rawlings and W.H. Ray (Uruversity of Wisconsin-Madison) and J.F. Brady (Califor nia Institute of Technology), and to Sangtae Kim (Yice President and Information Officer Eli Lilly) for their critical reading and insightful comments on an earlier version of thl s paper. Thjs document reflects the joint efforts of the entire chemical engineering working group. 0 Chemi c al En g in ee ring Education

PAGE 75

AUTHOR GUIDELINES This g uide is offered to aid authors in preparing manu scr ipt s for Chemical Engineeri n g Education (CEE), a quarter l y journal published by the Chemical Engineering Division of th e American Society for Eng ine ering Education (ASEE). CEE publishes papers in the broad field of chemical engineering education. Papers ge nerall y describe a course, a laboratory, a ChE department, a ChE ed u cator, a ChE curriculum, research program, machine computation, specia l instructional programs or give views and o pini o n s on vario u s topics of interest to the profession Specific suggestions on preparing papers TITLE Use specific and informative titles. They s hould b e as brief as possible consistent wit h the n eed for d efi ning the s ubj ect area covered by the paper. AUT HOR S HIP Be consistent in authors hip designation Use first name second initial, and surname. Give complete mailing address of place where work was conducted. If current address is different include it in a footnote on title page. ABSTRACT: KEY WORDS Include an abstract of less than seve nty-five words and a li st (5 or less ) of keywords TEXT We request th at manuscript s not exceed twelve double-spaced typewritten pages in length Longer manuscripts may be returned to the author(s) for revision/shortening before being reviewed. Assume your reader is not a novice in the field Include o nly as much hi story as is needed to provide background for the particular m ateria l covered in your paper. Sectionalize the article and insert brief appropriate headings. TABLES Avo id t a ble s and grap h s which involve duplication or superfluous data. If you can use a graph, do not include a table. If the reader needs the table, omit the grap h Substitute a few typical results for l engthy table s when practical. Avoid computer printouts NOMENCLATURE Follow nomenclature style of Chemical Abstracts ; avoid trivial name s. If trade names are used, define at point of first u se. Trade names should carry an initial capital only with no accompanying footnote Use consistent units of measurement and give dimensions for a ll terms. Write a ll equations and formu l as clearly, and number important eq uati o n s co n secutively. ACKNOWLE DGMEN T Include in acknow l edgment o nl y suc h credits as are essential. LITERATURE CITE D Reference s s h ould be numbered and listed on a se parate sheet in the order occ urrin g in the text. COPY REQUIREMENTS Send two legible copies of the typed (double-spaced) manuscript on standard letter-size paper. Submit original drawings (or clear print s) of grap h s and diagrams on separate s heets of paper, and include clear glossy prints of any photographs that will be used. Choose graph papers with blue cross-sectional lines; other colors interfere with good reproduction. Labe l ordinates and abscissas of gra ph s a lon g the axes a nd outside the grap h proper. Figure captions and legends will be set in type and n eed not b e lettered on the drawings Number a ll illustrations consecutive l y Supply a ll cap ti ons and l egends typed on a se parat e page State in cover letter if drawings or photographs are to be returned Authors s h ou ld a l so include brief biographica l sketc he s and recent photographs with the m a nu script. Send yo ur manu sc ript to Chemical Engineering Education, c/o Chemical Engineering Department University of Florida, Gainesville, FL 32611-6005

PAGE 76

CALL FOR PAPERS FALL 200 1 GRA D UATE EDUCATI O N ISSUE OF CHEMICAL ENGINEE R ING E D UCATION