Chemical engineering education ( Journal Site )

Material Information

Chemical engineering education
Alternate Title:
Abbreviated Title:
Chem. eng. educ.
Physical Description:
v. : ill. ; 22-28 cm.
American Society for Engineering Education -- Chemical Engineering Division
Chemical Engineering Division, American Society for Engineering Education
Place of Publication:
Storrs, Conn
Publication Date:
annual[ former 1960-1961]


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


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-

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Source Institution:
University of Florida
Rights Management:
All applicable rights reserved by the source institution and holding location.
Resource Identifier:
oclc - 01151209
lccn - 70013732
issn - 0009-2479
lcc - TP165 .C18
ddc - 660/.2/071
System ID:

Full Text


Chemical Engineering Education
Department of Chemical Engineering
University of Florida Gainesville, FL 32611
PHONE and FAX: 352-392-0861

Tim Anderson

Phillip C. Wankat

Carole Yocum

James O. Wilkes, U. Michigan

William J. Koros, University of Texas, Austin


E. Dendy Sloan, Jr.
Colorado School of Mines

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

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

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

96 A Supercritical Extraction Experiment for the Unit Operations
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

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

112 Thermodynamic Properties Involving Derivatives: Using the Peng-
Robinson Equation of State, R.M. Pratt

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



... of The University of Texas at Austin

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.

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
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)

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


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.


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.

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


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.

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
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



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
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

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

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

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
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.

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.

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.

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.

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.

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,
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-
8. Wankat, P.C., "Learning Through Doing: A Course on Writ-
ing a Textbook Chapter," Chem. Eng. Ed., 27(4), 208 (1993)

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




For the Unit Operations Laboratory

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.

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

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.


- Micro-metering

Spring 2001



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.

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-

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
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.

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
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.

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.



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)

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...



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

... w-Orkin
togeffier in



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,
(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 and at

% -1classroom


An Alternative to the Classic Design Presentation

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.

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.

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
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

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?
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.

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-

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



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


Poise and Appearance

Poise [x2]
Ability to Answer [x2]
Audience Interaction

Distribution [x2]
Responsibility [x2}

Individual Totals

Group Leader Economics


Team Total
Individual Total
Grand Total


mail that includes
A formal invitation to the meeting, including mention
of the time and place
A statement identifying the team leader and other
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.

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.

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


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

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)

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

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 _(t)- (B)______
msys(t) Jp(z,t)dV (B)
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

h(t)= t p(x, u(x,t)dA (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

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
=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

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
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
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

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

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

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:

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:, Chemical Engineering Department,
University of Michigan, Ann Arbor, MI 48109-2136.



Using the Peng-Robinson Equation of State

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.

Using the Peng-Robinson equation of state, calculate the

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

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

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
v-b v(v+b)+b(v-b)
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

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
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



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

A aP /(RT)2
For an N-component fluid with composition, {w }, we
calculate the mixture parameters, a and b, from the empirical
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
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


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

(az )


tion for the mixture is a mole fraction weighted average of
the pure component values, i.e.,
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

CID =141.376J/mol-K

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

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
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
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

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


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
Using Eq. (10), we now obtain Cv=132.436 J/mol-K.
We will use an equation analogous to Eq. (10) to calculate
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
or c=179.586m/s=646.5km/hr

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

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.

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




Demonstrating the Quantitative Accuracy

of the Bernoulli Equation

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
To demonstrate the value of a rigorous computer

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.

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

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
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 {
The mechanical energy balance (Bernoulli equation in-

Figure 1. Schematic of the experimental apparatus.

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)
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
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
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.



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


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
= 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.









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.

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).


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.

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.

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.

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>
7. Keffer, D., "AWeb 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) 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




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
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.

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)
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
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)
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

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

Cl C2

Figure 1. Idealized adsorption isotherm.
Spring 2001

picted in Figure 2: high concentrations moving ahead of low
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
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 ...........-------- ------------------ ----- ___

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. 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.


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-

*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.

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





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




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

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
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

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




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).



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



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.

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.

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

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)



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)
heat of adsorption (J/mol)
packing porosity
gas constant
adsorbent's apparent density

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


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


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


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


A- 15i qA -qA)
t rp

Energy balance

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


Spring 2001 12


Student-Performance Enhancement by



A Case Study in Bioengineering and Process Modeling

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.

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 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- 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

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.

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-

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

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
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


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

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

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


2 and A
3 and A
4 and B
5 and B

Taking Taken

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.


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


Food Intake Blood Insulin

+ P Blood Glucose

+ P


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

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


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




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

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
0 50

10 1

ao 10 1

0 --'- 0
) 0 4 8 12 16 20 24

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

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,

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. exchange of ideas
12. exchange of knowledge
13. technical support

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




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
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.

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.

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.

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.,
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
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




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
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.

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

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

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
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
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)

dC 0 (2)
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

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(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

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


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.

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.

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

E 400
s o



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.

-250 *
200 0
150 ** *
50 o "

0 100 200 300 400 500 600 700 800
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

5.100 o
v9, ^ oa
o50 e
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.
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.





Part 3. Evaluation

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.

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
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

am i


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


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.

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-
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

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-
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

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
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
We found retention was higher during the
sophomore year for spiral-taught students 98-99C
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
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

ion I
e Ch


ons 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.


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.

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.

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
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
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.

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.

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 ')

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,
4. Linek, V., V. Vacek, and P. Benes, Chem. Eng. J., 34, 11
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
10. Rushton, J.H., Chem. Eng. Prog., 47, 485 (1951)
11. Calderbank, P.H., Trans. Instn. Chem. Engrs., London, 36,
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



Clarification of Some Concepts

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.

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

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)


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 -= 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

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)


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


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

Thus, we see that
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).


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.
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

0.4 Im Figure 2.
0.2 Nyquist plots for
r a)
(-1,0) Re GLI(S)= 2( 1)
-0.2 2(s-1)
-1.5 -1.0 -0.5 0.0 0.5 b)
GL2(S) =
(s- 1)
The dotted (---)
portion is for
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-
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).

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.

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
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



What Do Students Really Need?

University of Wisconsin-Madison Madison, WI 53706-1691
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

MAA Curriculum Foundations Workshops

Physics and Computer Science
Bowdoin College Maine Oct. 28-31, 1999
William Barker:
Interdisciplinary (Math, Physics, Engineering)
USMA West Point Nov. 4-7, 1999
Don Small:
Clemson University South Carolina May 4-7, 2000
Susan Ganter:
Health-Related Life Sciences
Virginia Commonwealth University May 18-20. 2000
William Haver:
Technical Mathematics (at two sites)
Los Angeles Pierce College California Oct. 5-8, 2000
Bruce Yoshiwara:
J. Sargeant Reynolds Community Col. Virginia Oct. 12-15, 2000
Susan Wood:
Mary Ann Hovis:
Grinnell College Oct. 12-15, 2000
Thomas Moore:
Business. Finance and Economics
University of Arizona Arizona Oct. 28-29, 2000
Deborah Hughes Hallett:
William McCallum:
Mathematics Education
Michigan State University Michigan Nov. 1-3, 2000
Sharon Senk:
Biology and Chemistry
Macalester College Nov. 2-5, 2000
David Bressoud:
Mathematics Preparation for the Major
Mathematical Sciences Research Institute Feb. 9-11, 2001
William McCallum:

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


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

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?

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
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.

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
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


rim A

ssor o

e Pro
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
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
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.

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.

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


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

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


FALL 2001


Deadline is June 1, 2001

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