Front Cover
 Table of Contents
 Chemical Engineering at the University...
 Bill Koros of Georgia Institute...
 A Student-Centered Approach to...
 A Case Study Representing Signal...
 Sermons for Grumpy Campers
 The Catalytic Pellet: A Rich Prototype...
 Letter to the Editor
 A Course on Energy Technology and...
 Fostering an Active Learning Environment...
 Teaching Population Balances for...
 Computing Liquid-liquid Phase Equilibria:...
 Back Cover

Chemical engineering education
http://cee.che.ufl.edu/ ( Journal Site )
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Permanent Link: http://ufdc.ufl.edu/AA00000383/00172
 Material Information
Title: Chemical engineering education
Alternate Title: CEE
Abbreviated Title: Chem. eng. educ.
Physical Description: v. : ill. ; 22-28 cm.
Language: English
Creator: American Society for Engineering Education -- Chemical Engineering Division
Publisher: Chemical Engineering Division, American Society for Engineering Education
Publication Date: Summer 2007
Frequency: quarterly[1962-]
annual[ former 1960-1961]
Subjects / Keywords: Chemical engineering -- Study and teaching -- Periodicals   ( lcsh )
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Numbering Peculiarities: Publication suspended briefly: issue designated v. 1, no. 4 (June 1966) published Nov. 1967.
General Note: Title from cover.
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Table of Contents
    Front Cover
        Front Cover
    Table of Contents
        Page 153
        Page 153a
    Chemical Engineering at the University of California
        Page 154
        Page 155
        Page 156
        Page 157
        Page 158
        Page 159
        Page 160
    Bill Koros of Georgia Institute of Technology
        Page 161
        Page 162
        Page 163
        Page 164
        Page 165
        Page 166
    A Student-Centered Approach to Teaching Material and Energy Balances 2. Course Delivery and Assessment
        Page 167
        Page 168
        Page 169
        Page 170
        Page 171
        Page 172
        Page 173
        Page 174
        Page 175
        Page 176
    A Case Study Representing Signal Transduction in Liver Cells as a Feedback Control Problem
        Page 177
        Page 178
        Page 179
        Page 180
        Page 181
        Page 182
    Sermons for Grumpy Campers
        Page 183
        Page 184
    The Catalytic Pellet: A Rich Prototype for Engineering Up-Scaling
        Page 185
        Page 186
        Page 187
        Page 188
        Page 189
        Page 190
        Page 191
        Page 192
        Page 193
    Letter to the Editor
        Page 194
    A Course on Energy Technology and Policy
        Page 195
        Page 196
        Page 197
        Page 198
        Page 199
        Page 200
        Page 201
    Fostering an Active Learning Environment for Undergraduates: Peer-to-Peer Interactions in a Research Group
        Page 202
        Page 203
        Page 204
        Page 205
        Page 206
        Page 207
        Page 208
    Teaching Population Balances for ChE Students: Application to Granulation Processes
        Page 209
        Page 210
        Page 211
        Page 212
        Page 213
        Page 214
        Page 215
        Page 216
        Page 217
    Computing Liquid-liquid Phase Equilibria: An Exercise for Understanding the Nature of False Solutions and How to Avoid Them
        Page 218
        Page 219
        Page 220
        Page 221
        Page 222
        Page 223
        Page 224
    Back Cover
        Back Cover
Full Text

chemical engineering education

Bill Koros

S.. of Geoigia Institute of Technology


Arce. Oyanader, Whitaker
STeaching Population Balances For Chie Students: Application to Granulation Processes (p. 2091
0 Bucala. Piha

c Student-Centered Approach To Teaching Material And Energy Balances 2. Course Delivery. Assessment (p. 167)
3 Bullard, Felder
Te A Course on Energy Technology and Policy (p. 195'g
T ecRandom Thoughtsi Sermons For Grumpy Campers (p. 183)
o Bucal. Pia

u BulFelder
SA Chemical Engineering at the University of California, Santa Barbara (p. 1 54
) E Gray. Leal. Seborg
c Q
r c Fostering an Active Learning Environmentfor Undergrads: Peer-to-Peer Interactions ina Research Groupp. 202)
o U
(D 4.- Long. Matthews.Thompson
SComputing Liquid-liquid Phase Equilvbria: Understand the Nature of False Solutions and Avoid Them (p. 1151
SGOlaya. Ibarra. Reyes-Labarta. Serrano Marcilla
7D Bill Koros of Georgla Institute ofTechnology (p. 161)
E - Paul
c c
c U A Case Study Representing Signal Transduction In Liver Cells As A Feedback Control Problem (p. 1 77
U b Singh, Jayaraman, Haln

SUniversity of California, Santa Barbara

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

Tim Anderson

Phillip C. Wankat

Lynn Heasley

James O.Wilkes, U. Michigan

William J. Koros, Georgia Institute of Technology

Nicholas Rosinia


John P.O'Connell
University of Virginia

E. Dendy Sloan, Jr.
Colorado School of Mines

Kristi Anseth
University of Colorado
Thomas F. Edgar
University of Texas at Austin
Richard M. Felder
North Carolina State University
H. Scott Fogler
University of Michigan
Carol K. Hall
North Carolina State University
Steve LeBlanc
University of Toledo
Ronald W. Rousseau
Georgia Institute of Technology
C. Stewart Slater
Rowan University
Donald R.Woods
McMaster University

Vol. 41, No. 3, Summer 2007

Chemical Engineering Education
Volume 41 Number 3 Summer 2007

154 Chemical Engineering at the University of California, Santa Barbara
Tom Gray, L. Gary Leal, and Dale E. Seborg
161 Bill Koros of Georgia Institute of Technology
Donald R. Paul
183 Sermons For Grumpy Campers
Richard M. Felder

177 A Case Study Representing Signal Transduction In Liver Cells As A
Feedback Control Problem
Abhay Singh, Arul Jayaraman, and Juergen Hahn

185 The Catalytic Pellet: A Rich Prototype for Engineering Up-Scaling
Pedro E. Arce, Mario Oyanader, and Stephen Whitaker

195 A Course on EnergyTechnology and Policy
Thomas F. Edgar

167 A Student-Centered Approach To Teaching Material And Energy
Balances 2. Course Delivery And Assessment
Lisa G. Bullard, Richard M. Felder
202 Fostering an Active Learning Environment for Undergraduates:
Peer-to-Peer Interactions in a Research Group
Christopher E. Long, Michael A. Matthews, and Nancy S.Thompson
209 Teaching Population Balances For Che Students: Application
to Granulation Processes
Veronica Bucala and Juliana Pina

115 Computing Liquid-liquid Phase Equilibria: An Exercise For Under-
standing the Nature of False Solutions and How to Avoid Them
Maria del Mar Olaya, Isabel Ibarra, Juan A. Reyes-Labarta,
Maria Dolores Serrano, and Antonio Marcilla

194 Letter to the Editor

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 � 2005 by the Chemical Engineering Division, American Society for
Engineering Education.The statements and opinions expressed in this periodical are those ofthewriters 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 and for 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 (USPS 101900).


Author Guidelines for the



The laboratory experience in chemical engineering education has long been an integral part
of our curricula. CEE encourages the submission of manuscripts describing innovations in the
laboratory ranging from large-scale unitoperations experimentsto demonstrationsappropriate
for the classroom. The following guidelines are offered to assist authors in the preparation of
manuscripts that are informative to our readership. These are only suggestions, based on the
comments of previous reviewers; authors should use their own judgment in presenting their
experiences. A set of general guidelines and advice to the author can be found at ourWeb site:

c Manuscripts should describe the results of original and laboratory-tested ideas.
The ideas should be broadly applicable and described in sufficient detail to
allow and motivate others to adapt the ideas to their own curricula. It is noted
that the readership of CEE is largely faculty and instructors. Manuscripts must
contain an abstract and often include an Introduction, Laboratory Description,
Data Analysis, Summary of Experiences, Conclusions, and References.
* An Introduction should establish the context of the laboratory experi-
ence (e.g., relation to curriculum, review of literature), state the learning
objectives, and describe the rationale and approach.
* The Laboratory Description section should describe the experiment in
sufficient detail to allow the reader to judge the scope of effort required
to implement a similar experiment on his or her campus. Schematic dia-
grams or photos, cost information, and references to previous publica-
tions and Web sites, etc., are usually of benefit. Issues related to safety
should be addressed as well as any special operating procedures.
SIf appropriate, a Data Analysis section should be included that concisely
describes the method of data analysis. Recognizing that the audience
is primarily faculty, the description of the underlying theory should be
referenced or brief.The purpose of this section is to communicate to the
reader specific student-learning opportunities (e.g., treatment of reac-
tion-rate data in a temperature range that includes two mechanisms).
*The purpose of the Summary of Experiences section is to convey the
results of laboratory or classroom testing. The section can enumerate,
for example, best practices, pitfalls, student survey results, or anecdotal
* A concise statement of the Conclusions (as opposed to a summary) of
your experiences should be the last section of the paper prior to listing

rj[ =department
---- U s_____________________________________

Chemical Engineering at

the University of California,

Santa Barbara

This Young Department Has Built a National Reputation Through
Timely Recruiting and a Stress on Interdisciplinary Activities

It wasn't so long ago that mention of UC Santa Barbara
in the engineering world might get a response like "UC
what?" Until 1961, this University of California campus
located on the scenic coast sometimes called California's
Riviera did not even have an engineering school. It took
some time after that for the school and its chemical engineer-

ing program (established in 1966) to get noticed. But by the
usual academic standards, their rise to national prominence
was lightning-fast.
Brad Chmelka, now a professor in the ChE department
at UCSB, was scouting for his first faculty position in 1992
after earning his doctorate at UC Berkeley and spending two
� Copyright ChE Division of ASEE 2007
Chemical Engineering Education

years in post-doctoral work at the Max Planck Institute for
Polymer Research in Germany. He recalls visiting UCSB
almost as an afterthought. He already had decided that he
would go to either Caltech or the University of Minnesota.
When he was choosing Ph.D. programs a few years earlier,
he had judged UCSB's engineering programs to be promising
but still obscure.
But what he saw at Santa Barbara changed his plans. "I was
shocked," he says. "I had no idea what had happened since
I had looked at it last." A once-obscure school was now an
academic powerhouse attracting national notice.
So what did happen to put UCSB's young ChE program on
the map so quickly? Probably the best answer is that several
factors converged in the right place at the right time. One
was a strategic decision in the mid-1980s by the University
of California Regents to make the Santa Barbara campus
into a major research center. Another was a pool of talented
scientists and engineers made available by the downscaling
of corporate research labs. Yet another was the talent already
in place or just arriving. One of UCSB's most distinguished
ChE faculty members is Jacob Israelachvili, a fellow of the
National Academies of Science and Engineering, who came
to the department in 1986.
Leadership from forward-looking deans and departmental
chairs played a role, as did the near-perfect climate and the beauty
of the university's ocean setting. So did the culture of collabora-
tion and interdisciplinary research that was emerging at UCSB.
The university's emphasis on cross-disciplinary teamwork has
attracted corporate and academic researchers eager to move
beyond the restrictions of traditional academic boundaries.

The progress that so struck Chmelka 15 years ago has
continued to this day. The ChE department at UCSB is not
the largest ChE program in the nation, but it may have the
highest concentration of top-flight talent. Its strong standing
is signified by the ninth-place ranking among ChE graduate
programs in the latest survey by U.S. News and World Report.
A 1999 study by the Korean Advanced Institute of Science and
Technology ranked it first based on "research impact factor per
ChE faculty member." In 2003, Chemical Engineering News
ranked the department first based on citations per publication;
it also noted that the department's percentage of National
Academy of Engineering (NAE) members was the highest of
any ChE department in the country. Currently, seven of the
department's 17 senior faculty members share this honor.
Additionally, seven of its professors are fellows of AIChE or
the American Physical Society (APS), and one, Israelachvili,
is a fellow of the Royal Society (U.K.) as well as a member
of the National Academies of Science and Engineering.
A number of ChE faculty at UCSB also have won prestigious
awards in recent years. Glenn Fredrickson, a member of the

NAE and anAPS fellow, won the APS Polymer Prize in 2006.
Bud Homsy, who is also an NAE member and anAPS fellow,
won the APS Fluid Dynamics Prize in 2005. Israelachvili won
the 2004 Materials Research Society Medal. The department
chair, Gary Leal, won the APS Fluid Dynamics Prize in 2002.
Mike Doherty won the both the Clarence G. Gerhold and the
Alpha Chi Sigma awards in 2004 from the AIChE. Joe Za-
sadzinski won the 2004 American Chemical Society Award
in Colloid Science. Samir Mitragotri received the Allan P.
Colburn Award in 2005 from the AIChE. Sanjoy Banerjee
won the AIChE's Donald Q. Kern Award in 2006.

The ChE program started in 1965-66 with the arrival of the
first faculty member, Bob Rinker and the first department
chair, Jack Meyers, who had been a faculty member at Pur-
due for 16 years. (Bob now has emeritus status and Jack died
in 1994) Three other faculty members who are now emeriti
(Orville Sandall, Duncan Mellichamp, and Owen Hanna)
were hired in quick succession.
The subsequent recruitment of the current ChE faculty is
summarized in the sidebar, at end. In 1969 the department's
nuclear engineering degree program was initiated. The nuclear
engineering program was subsequently discontinued in 1995,
yet its impact remains: Four of the department's current fac-
ulty were originally hired as nuclear engineers.
By necessity, the early years of the ChE department were
concerned with building the department by developing in-
structional programs, constructing laboratories, and initiating
research programs. Several faculty members also provided
leadership of the campus and the University of California
(UC) System during critical periods. In particular, Duncan
Mellichamp was elected head of both the campus Academic
Senate and the UC Academic Council, unusual honors for an
engineering professor. The pioneering efforts of the initial
complement of faculty provided the basis for the department's
subsequent growth and enhanced reputation. By 1981, the
ChE program had nine faculty positions, 195 undergrads, and
33 graduate students. Hired during those years were current
ChE faculty members Dale Seborg (1977), Gene Lucas
(1978), and Banerjee (1980).
Meanwhile, the university as a whole had established
strong programs in biology, chemistry, and especially phys-
ics, as well as distinguished institutes in marine sciences and
theoretical physics.
The elements were in place for UCSB's next big leap, to the
status of a full-fledged research university, with the College
of Engineering and the ChE department playing key roles in
the university's rise to national prominence.
Under Dean of Engineering Robert Mehrabian, the fo-
cus at the College of Engineering initially was on materials.
Fredrickson, who came to UCSB in 1990, says Mehrabian

Vol. 41, No. 3, Summer 2007

was hired in 1983 "with orders to create a world-class materi-
als department." He proceeded to do so, with an impact that
went well beyond one discipline. As Fredrickson (who has a
joint appointment in ChE and Materials) explains, Mehrabian
filled the Materials Department with people who had worked
in corporate settings such as Bell Labs and who had gained
high visibility in academia by publishing extensively. A
number of them were given joint appointments in chemical
or mechanical engineering, and their experience in industry
had accustomed them to working in cross-disciplinary project
teams. These factors "had the effect of breaking down bar-
riers between different parts of the College of Engineering,"
Fredrickson says. "It created a research and education experi-
ence different from almost any university I know of." Three
current ChE faculty members came to UCSB during this era:
Theo Theofanous (1985); and Israelachvili and Zasadzinski
(both hired in 1986).
The ChE program's rise in reputation and visibility within
the chemical engineering community continued with the
recruiting, in 1989, of Gary Leal and Henry Weinberg from
Caltech. Leal became the department chair and remains in that
post today. Weinberg was on the ChE faculty until 1996, when
he left to become chief technology officer with the Silicon
Valley firm Symyx Technologies. Fredrickson, recruited from
Bell Labs, was Leal's first hire. He was followed by current
faculty members Eric McFarland (1991), Chmelka (1992),
and Ed Kramer (1997).
The strategy behind these and later hires, says Leal, was
simply to find the best people. "We always seek to hire the
best candidate regardless of his or her particular research in-
terests, the type of person who comes along every few years
at one of the other top departments," he says. "We do not seek
to hire people in a specific research area." But it also helped
reinforce the department where it already was strong, in areas
such as process control and chemical kinetics, while building
strength in emerging areas such as materials. Frederickson,
whose focus was on polymer theory when he came to UCSB,
says there also "was a drive to strengthen the theoretical and
computational side of the department. I was hired in part to
help meet that objective." In the characteristic UCSB way, the
new recruits opened up new avenues for collaboration.
To take just one example, the polymer theorist Frederickson
found his experimental counterpart in Kramer. They have
done a number of projects together, to the benefit of their
shared students. Recently, they have been working with
UCSB Chemistry Professor Craig Hawker to develop a
new generation of nanoscale computer chips based on self-
assembling polymers.
The rapid growth of the department and research programs
since 1981 has also benefited the educational programs by
allowing a broader range of elective courses. Also, many
influential textbooks were written by department faculty
during this period.

Collaboration across academic disciplines and departments
is a UCSB trademark. It is impossible to give an accurate
picture of the ChE department without including the depart-
ments and research groups, both in and out of Engineering,
with which its faculty is affiliated. Most of its professors
have joint appointments, including eight with the Materials
Department of the College of Engineering. The ChE faculty
also includes the dean of the College of Engineering, Matt
Tirrell, who is also a professor of Materials. (Tirrell, who
came to UCSB from the University of Minnesota in 1999,
has received the Allan P. Colbur, Charles Stine, and Profes-
sional Progress awards from AIChE, as well as delivering its
Institute Lecture in 2001.)
Another department colleague is UCSB Executive Vice
Chancellor Gene Lucas. Chancellor Henry Yang also has
engineering ties -he is a professor of mechanical engineering.
These connections suggest the importance of engineering,
including ChE, at UCSB. As Seborg notes, it is "very rare
for a nonengineering university" to have the engineering
disciplines so well represented in its top leadership.
The opportunities for collaborative research and educa-
tion in ChE extend beyond academic departments and well
beyond UCSB. ChE faculty play key roles in government-
and industry-financed research groups. Fredrickson is as-
sociate director of the Materials Research Laboratory, an
NSF-funded institute that brings researchers together from
physics, chemistry, biology, materials, and biochemistry as
well as chemical engineering. The MRL also includes ChE
faculty members Tirrell, Homsy, Israelachvili, Kramer, and
Leal. Fredrickson is director of the Mitsubishi Chemical
Center for Advanced Materials (\ 1C-CAM) and the MRL's
Complex Fluids Design Consortium (CFDC), which also
includes Banerjee.
Frank Doyle is the associate director of the Institute
for Collaborative Biotechnologies (ICB), an Army-funded
research organization led by UCSB in collaboration with
MIT and Caltech. Its mission is to develop revolutionary in-
novations in bio-inspired materials and energy, biomolecular
sensors, bio-inspired network science, and biotechnological
tools. Most of its more than 60 researchers are from UCSB
science and engineering departments. In addition to Doyle, the
ChE faculty members associated with ICB include Chmelka,
Patrick Daugherty, Fredrickson, Israelachvili, Mitragotri,
Tirrell, and Zasadzinski.


The department's research interests have evolved over the
years along with the larger trends in science and the economy.
Zasadzinski says he was working on enhanced oil recovery
when he arrived at UCSB in 1986, and he has seen his own
interest shift toward "biologically relevant materials." He is
Chemical Engineering Education

UCSB Department of
Chemical Engineering
leadership, pictured left
to right: Brad Chmelka,
Gary Leal, and Dale

now involved in research aimed at developing tiny nanode-
vices to deliver drugs or diagnostic agents to specified
targets in the human body. Doyle and Seborg are applying
their expertise in process modeling and control to develop
control strategies for diabetes patients, in collaboration
with medical researchers. But energy-related research has
become increasingly important in recent years. Chmelka,
the department's vice chair for graduate affairs, says new
Ph.D. students are as eager to explore challenging prob-
lems related to energy as they are to study bio-engineering
topics. Chmelka is involved in energy-related research
along with ChE colleagues Eric McFarland and Susan-
nah Scott. In one project, funded by the U.S. Department
of Energy, Scott and Chmelka are designing materials for
catalysts that can be used to produce fuels such as biodiesel
from plant oils.

The department research activities also include traditional
areas of chemical engineering, such as reaction engineering,
thermodynamics, and transport phenomena, in their modem
forms; Leal says it is particularly strong in the thermo and
transport areas. It also is strong in materials, especially com-
plex fluids and "soft materials," as well as in research that
links materials and colloid science with biological applica-
tions. Israelachvili's lab does important work in the surface
force measurements of biological binding strengths and
biological lubrication phenomena. Leal lists other strengths
-process design and control (including systems biology) as
well as surface chemistry, catalysis, and surface physics-and
states that the department has "one of the strongest theory and
simulation activities in the country."

One theme runs through all this research-an emphasis on
basic engineering science rather than applied engineering.
"We are a very fundamentally oriented department," Leal

says. It is also an inner-directed program, driven more by
the intellectual curiosity of first-rate faculty than by an
urge to hop on bandwagons. Trends come and go, Leal
explains, but the best minds will always be out in front:
"The basic philosophy is that the hot new topic is always
changing. We want to be in a position to be a leader in
whatever the future brings as well as a leader in the topics
of the present." 0

ChE at UCSB: At a Glance
Web site http://www.chemengr.ucsb.edu
University of California founded: 1868
History Santa Barbara campus joined the UC System: 1944
College of Engineering founded: 1961
ChE Department established: 1966
U.S. News
& World ChE Department: 9th
Report rank- College of Engineering: 19th
Current faculty: 20 (17 full professors,
one associate, two assistants)
Faculty Emeritus and adjunct faculty: 5
statistics and NAE members: 7
honors NAS member: 1
Fellow of the Royal Society (U.K.): 1
Fellows of AIChE or APS: 7

Student Undergraduate: 190 students (30% female,
enrollment 30% minority)
statistics Graduate: 79 students (33% female, 67% have
B.S. degrees from U.S. schools)
UCSB coastline: Approx. 2.5 miles
Distance to Los Angeles: 105 miles
Campus Distance to San Francisco: 333 miles
environment Average January temperature: 52 �F
Average July temperature: 66 �F
Average yearly rainfall: 16.1 inches
Average days of rain each year: 35

Vol. 41, No. 3, Summer 2007

The Chemical Engineering Department at the UC Santa
Barbara currently has 20 faculty-17 full professors, one as-
sociate professor, and two assistant professors. In the order in
which they joined UCSB (and year of arrival), they are:

* Dale Seborg (1977), professor and department vice
chair. Ph.D.: Princeton. Research interests: process
control, system identification, and process monitoring.
Current applications include monitoring and control
strategies for type 1 diabetes patients and monitoring
strategies for industrial bioreactors. Honors and awards:
AIChE Fellow, 2004; Statistics in Chemistry Award
(shared), American Statistical Association, 1994; Educa-
tion Award, American Automatic Control Council, 1993;
Meriam-Wiley Distinguished Author Award (shared),
American Society of Engineering Education, 1990.

* Gene E. Lucas (1978), professor, executive vice chancel-
lor. Joint appointment in: Materials. Ph.D.: MIT. Research
interests: composite materials for aerospace applications,
fusion reactor materials, and radiation embrittlement of
light-water reactor steels. Honors and awards: R.E. Peter-
son Award for Best Paper on the Application of Experi-
mental Mechanics, Society for Experimental Mechanics,
1997; Young Member Engineering Achievement Award,
American Nuclear Society (ANS), 1991.

* Sanjoy Banerjee (1980), professor. Joint appointment in:
Mechanical Engineering. Ph.D.: University of Waterloo.
Research interests: multiphase, complex-fluid, turbulent/
chaotic, and environmental systems. Current projects
range from nanoscale problems to macroscale phenom-
ena such as turbulent transport processes at the air-sea
interface, of importance in global warming. Honors
and awards: Donald Q. Kern Award, American Institute
of Chemical Engineers (AIChE), 2006; Heat Transfer
Memorial Award, American Society of Mechanical En-
gineers, 1999; Danckwerts Memorial Lecture, Chemical
Engineering Science/Institution of Chemical Engineers,
London, U.K., 1991; Melville Medal, American Society
of Mechanical Engineers, 1983.

* Theo G. Theofanous (1985), professor; director, Center
for Risk Studies and Safety. Joint appointment in: Me-
chanical Engineering. Ph.D.: University of Minnesota.
Research interests: risk assessment and management
of complex technological and environmental systems.
Areas of investigation include multiphase flow phys-
ics, issues of uncertainty in risk assessment, interfacial
instabilities in high-speed flows, aero-breakup, explo-
sive dissemination of liquids, defense against chem-bio
weapons, and burnout physics and nuclear reactor safety.
Honors and awards: Elected to National Academy of En-
gineering, 1998; elected to Russian Academy of Science,
Ufa Branch, 1998; E.O. Lawrence Medal, U.S. Depart-
ment of Energy, 1997.

* Jacob N. Israelachvili (1986), professor. Joint appoint-
ment in: Materials. Ph.D.: Cambridge University. Re-

search interests: Intermolecular and intersurface forces
in complex fluid systems; friction and stickiness; using
the Surface Forces Apparatus (SFA) to study interac-
tions between surfaces separated by various liquids,
surfactants and polymers, as well as interactions of
biomembranes and biological macromolecules. Honors
and awards: elected to National Academy of Science,
2004; MRS Medal, Materials Research Society, 2004;
elected to NAE, 1996; Alpha Chi Sigma Award, AIChE,
1991; elected fellow of Royal Society of London, 1988;
elected fellow of Australian Academy of Science, 1982.

SJoseph A. Zasadzinski (1986), professor. Joint appoint-
ment in: Materials. Ph.D.: Univ. of Minnesota. Research
interests: visualization of molecular and supramolecular
ordering in complex fluids and biomaterials; develop-
ment of new techniques to make complex fluids and
biomaterials compatible with high-resolution micros-
copy; creating biologically inspired materials with
potential uses in drug delivery and diagnosis. Honors
and awards: American Chemical Society Award in Col-
loid Science, 2004; fellow of the American Association
for the Advancement of Science, 2000; Burton Award of
the Microscopy Society of America, 1993; Presidential
Young Investigator, NSF, 1986.

SL. Gary Leal (1989), professor, department chair. Joint
appointment in: Materials and Mechanical Engineering.
Ph.D.: Stanford University. Research interests: fluid dy-
namics and rheology of complex fluids (e.g., polymeric
liquids, liquid crystalline polymers, immiscible blends
and emulsions, and colloidal and nanoparticle suspen-
sions); nonlinear and surfactant-induced phenomena in
interfacial flows. Honors and awards: Fluid Dynamics
Prize, American Physical Society (APS), 2002; Bingham
Medal, American Institute of Physics, 2000; William
H. Walker Award, AIChE, 1993; elected to the National
Academy of Engineering, 1987; fellow of APS, 1984; Al-
lan P Colburn Award, AIChE, 1978; Camille and Henry
Dreyfus Foundation Teacher-Scholar Award, 1975.

* Glenn H. Fredrickson (1990), professor; director of
Mitsubishi Chemical Center for Advanced Materials.
Joint appointment in: Materials. Ph.D.: Stanford Univer-
sity. Research interests: analysis of complex fluid and
multiphase polymer systems; study of equilibrium and
dynamical properties of suspensions, polymer solutions
and melts. Honors and awards: Polymer Physics Prize,
APS, 2007; elected to National Academy of Engineer-
ing, 2003; Alpha Sigma Chi Award, AIChE, 1999;
elected fellow of APS, 1998; John H. Dillon Medal,
APS, 1992; Camille and Henry Dreyfus Teacher-Scholar
Award, 1991; Presidential Young Investigator, NSF,

* Eric McFarland (1991), professor. Joint appointment in:
Electrical and Computer Engineering. Ph.D.: MIT (also
M.D., Harvard). Research interests: study of condensed
matter systems with emphasis on developing high-
throughput screening technologies for combinatorial ma-

58 Chemical Engineering Education

trials research; investigating new photocatalytic systems
for energy production. Honors and awards: Special Award
for Outstanding Advances in Nuclear Technology, ANS,
1992; Presidential Young Investigator, NSF, 1990-1995.

SBradley F Chmelka (1992), professor. Ph.D.: UC
Berkeley. Research interests: study at the molecular
level of the fabrication and functions of new catalysts,
adsorbents, optoelectronic materials, porous ceramics,
heterogeneous polymers and biominerals; development
and application of nuclear magnetic resonance imaging
techniques to observe heterogeneous solids. Honors and
awards: Alfred P Sloan Foundation Research Award,
1996; David and Lucile Packard Foundation Award,
1993; Camille and Henry Dreyfus Foundation Teacher-
Scholar Award, 1993; New Young Investigator Award,
NSF Division of Materials Research, 1992.

* Ed Kramer (1997), professor. Joint appointment in:
Materials. Ph.D.: Carnegie-Mellon. Research inter-
ests: microscopic fundamentals of fracture of polymer
glasses, diffusion in polymers, polymer surfaces, and
interfaces. Honors and awards: Maurice Higgins Award,
Polymers-West Gordon Conference, 2001; Swinburne
Award, Institute of Materials (U.K.), 1996; elected fel-
low of American Association for the Advancement of
Science (AAAS), 1994; elected to National Academy of
Engineering; Polymer Physics Prize, APS, 1985; elected
fellow of APS, 1983.

* Matthew V. Tirrell (1999), professor, dean of Engineer-
ing. Joint appointment in: Materials. Ph.D.: Univ. of
Massachusetts, Amherst. Research interests: interfacial
properties of materials used in applications ranging from
coatings and adhesion to lubrication and bioengineer-
ing. Honors and awards: Le Prix D6dale de la Soci6t6
Franqaise d'Adhesion, 2005; Institute Lecturer, AIChE,
2001; elected to National Academy of Engineering,
1997; Charles M.A. Stine Award, AIChE, 1996; Profes-
sional Progress Award, AIChE, 1994; Fellow of the
APS, 1987; John H. Dillon Medal, APS, 1987; Allan
P Colburn Award, AIChE, 1985; Presidential Young
Investigator, NSF, 1984; Camille and Henry Dreyfus
Teacher-Scholar Award, 1980.

SMichael E Doherty (2000), professor. Ph.D.: Cambridge
University. Research interests: process synthesis and
conceptual design of chemical process systems. Topics
of current interest include combining reactions and sepa-
rations, crystallization of organic materials, and systems
with complex chemistry. Honors and awards: Clarence
G. Gerhold Award, Separations Division, AIChE, 2004;
Excellence in Process Development Research Award,
Process Development Division, AIChE, 2004; Alpha Chi
Sigma Award, AIChE, 2004.

SSamir Mitragotri (2000), professor. Ph.D.: MIT. Re-
search interests: developing novel methods of drug de-
livery based on controlling the transport of biomolecules
to desired targets. Strategies include use of external
forces (e.g., ultrasound, chemicals, and high-velocity

jets) as well as new biomaterials with advanced struc-
ture-function characteristics. Honors and awards: Allan
P Colburn Award, AIChE, 2005; Outstanding Pharma-
ceutical Research Award, Controlled Release Society
(CRS), 2004; CRS-Capsugel Innovative Aspects of Oral
Delivery Award, 2004; 3M Young Faculty Award, 2001.

SPatrick S. Daugherty (2001), associate professor. Ph.D.:
U. Texas, Austin. Research interests: elucidating protein
interaction principles in biological systems; developing
biotechnologies that apply molecular and cellular engi-
neering to diagnosis and treatment of disease. Honors
and awards: Camille and Henry Dreyfus Foundation
Teacher-Scholar Award, 2006; NSF Career Award, 2005.

SG.M. (Bud) Homsy (2001), professor. Joint appointment
in: Mechanical Engineering. Ph.D.: U. Illinois. Research
interests: fluid mechanics and transport, with particular
focus on interfacial flows, polymer and viscoelastic fluid
mechanics, porous media flows and microgravity fluid
mechanics. Honors and awards: Elected to National
Academy of Engineering, 2006; Fluid Dynamics Prize,
APS, 2004.

SFrank J. Doyle III (2002), professor and associate
director of the Institute for Collaborative Biotechnolo-
gies (ICB). Ph.D.: California Institute of Technology.
Research interests: nonlinear model-based control of
complex nonlinear and distributed processes; applica-
tion of systems engineering tools to problems in biology.
Honors and awards: Alexander von Humboldt Research
Fellow, 2001; Ray Fahien Award, American Society for
Engineering Education (ASEE), 2000; Office of Naval
Research Young Investigator Award, 1996; National
Young Investigator Award, NSF, 1992.

* Susannah L. Scott (2003), professor. Ph.D.: Iowa State
University. Research interests: chemistry and physics
governing interactions and reactions of molecules at solid
surfaces; applications in heterogeneous catalysis, electronic
materials and advanced materials. Honors and awards:
Union Carbide Innovation Recognition Award, 1998-1999;
John Charles Polanyi Prize in Chemistry, 1994.
* Todd M. Squires (2005), assistant professor. Ph.D.:
Harvard. Research interests: physical effects in micron-
scale systems. Current topics of focus include "pore-
scale engineering" techniques for analytical separations,
microfluidic manipulation for potential use in portable or
implantable devices, active microrheology to character-
ize a material's response, and the fluid mechanics of
the inner ear. Honors and awards: NSF Career Award,
2007; named one of four "Rising Stars" by Chronicle of
Higher Education, 2005.
* M. Scott Shell (2007), assistant professor. Ph.D.: Princ-
eton. Research interests: protein structure prediction and
sequence design; protein stability, dynamics, and inter-
molecular association; the glass transition and dynamics
in rough energy landscapes; anomalous behavior in com-
plex liquids and mixtures; robust simulation algorithms
for free energy calculations. 1

Vol. 41, No. 3, Summer 2007 15

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IChemE 1957-20 07/////
heart of the process Jubilee of the Royal Charter
160 Chemical Engineering Education
160 Chemical Engineering Education

--- - ^ K.___________________________-

Bill Koros

of Georgia Institute of Technology

The University of Texas at Austin * Austin, TX 78712
The court of public opinion often holds that university
professors fall solidly and completely into one of two
extreme categories. One (the bad guys) is the group
that lives to do research and has a visible disdain for teaching
and for students. The other (the good guys) really loves teach-
ing and students but must do research or fall victim to the old
adage "publish or perish." Personally I have never believed
that this extreme view correctly characterizes most of us. Case
in point: William J. (Bill) Koros, who loves both teaching
and research, perhaps equally, and has excelled at both while
never slighting one for the other. Indeed, it is fair to say that
Bill would say research is teaching and vice versa.
I first met Bill in the fall semester of 1968 when he enrolled
in an undergraduate elective course on polymer engineering

that I was teaching during my second year as a new faculty
member at the University of Texas at Austin. Over the course
of that semester it became apparent this fellow had more talent
and enthusiasm than most undergraduates I had met to that
point. Having Bill in my class was the beginning of going on
40 years of being close friends and colleagues. What a bonus
for teaching a class!

Bill was born in Omaha, Neb., in 1947. He spent most of
his youth in Houston, where his father was actively engaged
during the booming growth of the oil and gas industry. After
high school Bill entered the University of Texas at Austin and
studied chemical engineering-intending a similar career in
the oil and gas industry. Instead, upon receiving his bachelor's
in ChE in 1969, he found work with E.I. DuPont Co. in a
polymer processing group. This move into the emerging

� Copyright ChE Division of ASEE 2007

Vol. 41, No. 3, Summer 2007

polymer area was significant. Bill has noted that the polymer
course where we first met (in fall '68) was an important fac-
tor in broadening his vision of what "chemical engineering"
could mean. His four years at DuPont were divided between
assignments in Wilmington, Del., and Camden, S.C. It was
while working for DuPont that Bill met his wife-to-
be, Ann-then a newly arrived schoolteacher
from Massachusetts who wanted to explore
life outside New England.
What Bill learned in those pivotal
years at DuPont shaped much of his
subsequent professional life; one. ,I
the most important things he learned
was that professional life would bl
a lot more fun and rewarding with
a Ph.D. Thus, in fall 1973 he re-
turned to UT for graduate school.
It so happened that at that time
I had a new grant from the
National Science Foundation
to study the peculiar aspects
of gas sorption and diffusion -,
in glassy polymers, and Bill
decided to work on the project
with me; this intersection of
events shaped both our lives r
for decades to come.
To put Bill's Ph.D. dis-
sertation on "Sorption and
Transport in Glassy Polymers"
into perspective, it is impor-
tant to know that the 2-liter
poly(ethylene terephthalate)
soft drink bottle was being
commercialized in this time
frame and that modern hollow
fiber gas separation membrane
were actively being research. d
(although not commercialized uuil
a few years after Bill completed In,
Ph.D. in 1977). Thus the experiniui.iI
techniques and theoretical frame 1i k, h 1
data analysis that were developed dII uni
Bill's Ph.D. research were very pcitunclit to
these new technologies, and as a result his work
garnered a great deal of industrial attention and has
continued to do so.
At about the time Bill was finishing his Ph.D., I learned
of and alerted Bill to an opening for an assistant professor
at North Carolina State University. The selected applicant
would collaborate with the expanding research program of
Professors V.T. Stannett and H.B. Hopfenberg, who were
interested in topics similar to Bill's Ph.D. dissertation. Bill

was awarded this position and began a very prolific period of
research and teaching. He was also very influential in the lives
of many undergraduate students. As a result of his mentoring
and encouragement, many of these students went on to enter
Ph.D. programs throughout the country, beginning a trend
that continues to this day-N.C. State students make
up a notable portion of those choosing UT for ChE
grad school. Many of these students went on to
become leaders in industry and universities.
In 1984, Bill decided to return to his roots
in Texas. He came to UT Austin as a pro-
fessor of chemical engineering and was
a key figure in establishing a program
F: of research on membranes as part of
St the Separations Research Program
, that was just beginning under the
leadership of Professor J.R. Fair.
His 17 years on the faculty at UT
S were an incredible period of growth
for Bill in research, teaching, and
professional leadership.

A In 2001, Billjoined the chemi-
Scal engineering faculty at the
Georgia Institute of Technology
as a result of a very attractive
offer from that growing depart-
ment. Interestingly, Bill and
Professor R.W. Rousseau, chair
at Georgia Tech, were colleagues
at N.C. State years before. Bill
has established a strong research
program at Georgia Tech and con-
tinues to be highly committed to
Research, teaching, and leadership.
One can gain a quick sense of Bill's
impact in research and on people by
examining the list of graduate students,
post-docs, and visiting researchers he
has worked with over his career at N.C.
State, UT, and Georgia Tech, as shown in
Fable 1 (at end). Reflecting Bill's collabora-
ul e nature, a number of the M.S. and Ph.D.
students were co-advised with various colleagues
including Vivian Stannett, Harold Hopfenberg, and
Rich Felder at N.C. State, and Grant Willson, Gary Ro-
chelle, Keith Johnston, and myself at UT Austin.

Above, left: Never one to take himself too seriously,
"Wild" Bill briefly held court as a cowboy in promoting
the General Dynamics Teaching Award in 1992.

Chemical Engineering Education

Bill brings to classroom teaching a genuine interest and
concern for every student, an infectious enthusiasm about
chemical engineering, and a wealth of experiences from
research, his years in industry, and consulting. He spends
countless office hours with students discussing homework,
exams, life, and whatever else needs to be confided to some-
one. I have seen students lined up in the hall patiently waiting
their turn; Bill gives each one his full and undivided attention.
Sometimes when you call him and no one answers the phone,
it may well be because there is a student "in chambers" who
Bill feels cannot be interrupted. Bill is truly concerned about
every individual in his classes, and
he works very hard to ensure that
each one becomes more than they
were before he touched their lives.
It is not uncommon for Bill to iden-
tify a seemingly undistinguished
undergraduate student that he brings
into his fold and nurtures; many of
these have become Ph.D. graduates
with very successful careers. Bill
sees human potential where others
often do not.
He takes the same approach with
graduate students working with him
as he does with undergraduates in
the classroom. He believes every
one is a special individual and
devotes enormous attention to the
development of each. As a result,
he attracts some of the most prom-
ising graduate students. His former
students are major contributors in
industry and academia, reflecting the
excellent guidance Bill gave them.
Their subsequent feedback,
sometimes years later, has ren-
dered the verdict convincingly:
Bill's dedication to students and
their development is greatly ap-
preciated by those he's taught. It
has also been widely recognized
by his peers: Bill has received numerous awards for teach-
ing including two during his time at N.C. State and three
during his time at UT-notably the prestigious General
Dynamics Award in 1990, which is given once a year to a
single engineering faculty member.

Above, right: It seems to be a recurring theme ...
Bill at age 5 in Houston.

Bill's research program has encompassed nearly every as-
pect of membrane science and technology. Beginning with his
Ph.D. dissertation he has had an interest in the fundamental
issues of how small molecules are sorbed into polymers and
transported through them. His early work focused on barrier
materials but quickly evolved into the use of membranes for
molecular separations. Bill has contributed greatly to the un-
derstanding of sorption and permeation properties of polymers
with theoretical models for pure- and mixed-gas sorption
and permeation in glassy polymers. Complementary experi-
mental work by his group has helped clarify which types of
mixed-gas sorption and permeation
behavior are readily predictable by
straightforward extensions of pure-
gas measurements. This work is
important for gas separation using
membranes and provides guidance
on treatment of complex cases that
require accounting for significant
nonlinear interaction factors.
To assist in the analysis of these
.. a more complex cases, he has de-
veloped precise methods to ex-
perimentally measure polymer
volume dilation during gas sorp-
tion. This approach allows simul-
taneous measurements of length,
width, and thickness of a film
after equilibration with a penetrant
gas. His approaches have been
used by researchers in Japan and
Europe to better understand the
complex interactions of pure and
mixed gases in contact with glassy
polymers. These glassy materials
are preferred for the separation of
CO2 from natural gas; however,
they show odd, history-dependent
behaviors under some conditions.
Better understanding of changes in
separation efficiency in the presence
of elevated CO2 partial pressures has
been pioneered by Bill and his research group.
Bill's research group has called attention to the need for
advanced membranes that allow a step change in membrane
performance while maintaining the well-accepted solution
processing method for membrane formation. Bill has identi-
fied concepts to design polymer molecules and composite
structures that circumvent the well-known trade-off between
permselectivity and productivity of conventional membranes.
His group has developed a class of polymers with hyper-rigid
backbones that have extensive flat, packable segments, punc-

Vol. 41, No. 3, Summer 2007

Bill models three decades worth of
hairstyles in: (above) his third year as
an undergraduate, accepting the "Engi-
neering Fellows" mug award for good
grades from UT Austin then-Dean John
McKetta, April 1968; (above right) with
his wife Ann one year before completing
his Ph.D., spring 1976; and (right) with
his research group at N.C. State, having
just enjoyed their regular Friday lunch at
Raleigh's "Two Guys" restaurant,
July 1980.

tuated by regions of highly packed disruptive
units. This complex but highly desirable
morphology provides a periodic "bottleneck"
environment. Ideally, molecular-sieving size
and shape discrimination occurs at the intercon-
nected bottlenecks to permit excellent perfor-
mance relative to conventional polymers.
In addition to the concepts of molecular
design of new polymers mentioned above, Bill
has been a pioneer in developing composite
structures that defeat the selectivity-produc-
tivity trade-off. These consist of inorganic
molecular sieves imbedded in a polymer ma-
trix, or so-called "mixed-matrix" systems.
He has substantially advanced this concept
by demonstrating the importance of properly
matching the transport characteristics of the
two materials and by addressing the need to
bond the two phases together to avoid bypass
channels that can severely compromise this
approach. He is the recognized leader of this
new concept of membrane design, which has
attracted much interest around the world.
Bill's research has gone well beyond materi-
als concepts to include understanding of the

processes by which advanced materials can be converted into membranes of
practical value. He has developed a state-of-the-art hollow fiber spinning facility
and has contributed significantly to the understanding of the issues governing
membrane formation. He has worked closely with industry to advance the state
of membrane art in practice. It is the complete integration of concepts from
the molecular level to practical processing issues and finally into practice that
truly distinguishes the contributions of Bill Koros in the area of membrane
science and technology.
Bill's research has resulted in more than 270 peer-reviewed papers, several
major reports, and 16 patents for novel membrane concepts. He has been invited
to talk about his research at venues around the world. He was among the very
first group of young faculty to receive an NSF Presidential Young Investiga-
tor Award (1984). While at N.C. State he received the Sigma xi Outstanding
Young Scientist Research Award (1980) and the Alcoa Foundation Research
Award (1983). While at UT he received similar recognition for his research and
leadership. At Georgia Tech he received the W.T. Ziegler Award as the Outstand-
ing Chemical Engineering Professor of the Year in 2003. He received the AIChE
Institute Award for Excellence in Industrial Gases Technology in 1995 and the
AIChE Separations Division Clarence Gerhold Award in 1999.
Chemical Engineering Education

Above left, On behalf of ARK (Animal Rights Kinship), Ann (then ARK president) and Bill (then ARK vice president)
receiving a special proclamation from the Austin City Council. Above right, Bill surrounded by some members of his
Georgia Tech research group, August 2006.

Bill has given freely of his time to professional leadership
and service. He served as secretary of the North American
Membrane Society (NAMS) from 1987 to 2004. He was chair
of the 1989 Gordon Research Conference on Membranes. He
has organized and chaired numerous conferences and working
groups. Since 1990, he has served as editor-in-chief of the
Journal of Membrane Science, clearly the premier journal in
this field. Thejournal has grown tremendously under his lead-
ership and now has editors in France (P. Aimar), Korea (Y.M.
Lee), the Netherlands (M. Wessling), and the United States
(A.L. Zydney). Bill has also served on the editorial boards
of Chemical Engineering Education, Journal of Macromo-
lecular Science: Reviews in Macromolecular Chemistry and
Physics, Polymer Contents, and Industrial and Engineering
Chemistry Research.
While at UT, Bill served as associate department chair
(1991-1993) and then chair during 1993-1997. During his
term as chair Bill coordinated significant alumni fund-raising
activities in addition to the usual issues of budgets, teach-
ing schedules, catalog revisions, and recruiting faculty and
graduate students, etc. He spent a great deal of time building
consensus among the faculty for decisions that needed to
be made. Since arriving at Georgia Tech he has gracefully
transitioned to the role of senior statesman-making things
happen behind the scenes and through committees.

Bill considers himself very fortunate to have identified and
pursued his field of research during some of its most pivotal
times, which covered several decades-a fact much in evi-

Vol. 41, No. 3, Summer 2007

dence in his photos from that span. Certainly, Bill's dedica-
tion to the trilogy of academic life-i.e., teaching, research,
and service-has been equally evolved: He has been judged
worthy of an enviable amount of recognition of a broader
nature than that for any single pursuit. In 2000 he was named
a Distinguished Graduate of the University of Texas at Austin
(B.S. 1969, M.S. 1975, and Ph.D. 1977) and was elected to
the National Academy of Engineering. In 2002 he was elected
fellow of the American Institute of Chemical Engineers, and
in 2003 he was elected fellow of the American Association
for the Advancement of Science. He holds the prestigious
Roberto C. Goizueta Chair in Chemical Engineering at
Georgia Tech and has been designated a Georgia Research
Alliance Eminent Scholar. He receives numerous invitations
every year to give plenary lectures or to give advice on some
weighty issue or another.
No matter how busy Bill is, however, I know there is one
person who gets his full attention and devotion, and this is
his wife, Ann. They are a deeply committed couple, to each
other and to doing their part to make the world a better place.
Ann's schedule is as full as Bill's, so it is an uncommon but
always welcome treat to see her accompanying him at con-
ferences. Ann, in addition to being involved in leadership
roles in a number of animal rights/welfare organizations for
nearly 30 years, has used her considerable video production
skills to promote the work of many animal and environmental
groups-causes very close to her heart. In addition, since
moving to Atlanta, she has been teaching videography and
editing in a special program for inner city students. And it
isn't beyond her to ask Bill to take the stand in the name
of a cause, as well: One semester she recruited "Professor

Koros" and a team of his graduate students to lecture and
give science demonstrations at her school. The audience may
have been worlds away from Bill's usual student body, but
Bill noted that the experience was as stimulating and eye-
opening for him and his students as the lessons seemed to
be for the youngsters. So while the jury may still be out on
whether one person can do it all, I confidently rest my case:
All-around educator Bill Koros comes as close to that ideal
as anyone I know. 1

Ph.D., M.S., Post Doctoral and Faculty Visitors
Who Studied with Bill Koros (1977-2006).
Ph.D. and M.S. Degrees Granted.*
Ph.D. Student Institution Year
Gautam Ranade * NCSU 1980
Rey T. Chern NCSU 1983
James L. Osborne* NCSU 1983
Edgar Sanders NCSU 1983
Dyi-Kang Yang * NCSU 1984
Mark E. Stewart * NCSU 1987
Tae-Han Kim UT Austin 1988
Greg K. Fleming UT Austin 1988
Brooks J. Story UT Austin 1989
Susan M. Jordan UT Austin 1989
Mark Hellums UT Austin 1990
Ingo Pinnau UT Austin 1991
Dave Pope UT Austin 1991
Maria R. Coleman UT Austin 1992
James R. Miller UT Austin 1992
Mary Rezac UT Austin 1993
Luiz A. Pessan UT Austin 1993
David R. B. Walker UT Austin 1993
Steven C. Pesek UT Austin 1994
Lora C. Bonser UT Austin 1994
Peter Pfromm UT Austin 1994
Maryam Moaddeb UT Austin 1995
Edward J. Simpson* UT Austin 1995
Egbert Jakobs UT Austin 1996
Vincent Geiszler UT Austin 1997
Scott A. McKelvey UT Austin 1997
Henky D. Kamaruddin UT Austin 1997
David Woods UT Austin 1997
Anshu Singh UT Austin 1997
Mathews Thundyil UT Austin 1998
Dominic Clausi UT Austin 1998
Catherine Zimmerman UT Austin 1998
*Indicates a Ph.D. or M.S. student co-supervised with a colleague at
NCSU or UTAustin as acknowledged in article text.

Rajiv Mahajan UT Austin 2000
Keisha Steel UT Austin 2000
Seth Carruthers UT Austin 2001
De Vu UT Austin 2001
David Punsalan UT Austin 2001
John Wind * UT Austin 2002
Ryan Burns * UT Austin 2002
Ted Moore * UT Austin 2004
Mohammed Al-Juaied * UT Austin 2004
David Wallace * UT Austin 2004
Wen Xu * UT Austin 2004
Shilpa Damle * UT Austin 2004
Fangbin Zhou Georgia Tech 2004
Bill Madden Georgia Tech 2005
Alexis Hillock Georgia Tech 2005
Jason Williams Georgia Tech 2006
Shabbir Husain Georgia Tech 2006
Preeti Chandra Georgia Tech 2006
Raymond Chafin Georgia Tech 2006
MS Student Institution Year
Gary N. Smith NCSU 1980
Clyde J. Patton* NCSU 1980
Ned R. McCoy, Jr* NCSU 1981
Danny Henderson NCSU 1981
Sam-Heng Chen* NCSU 1982
Charles T. Page NCSU 1982
HaithamAl-Hussaini* NCSU 1983
Robert E. Yui NCSU 1984
Lewis R. Iler NCSU 1984
Richard Kollaja NCSU 1985
Michael Moe UT Austin 1987
Chad J. Segura UT Austin 1987
Ronald J. Kuse UT Austin 1987
Michael A. Henson UT Austin 1989
Maria Gou UT Austin 1989
Jay Carnes UT Austin 1993
Brian Price UT Austin 1994
Jennifer Qin UT Austin 1999
Gunaidi Djoekita UT Austin 2000
Maria Towidjaja UT Austin 2001

Post-Doctoral Fellows and Visiting Faculty
Dr. Ron Husk Dr. Thomas Steinhausler
Dr. Kevin O'Brien Dr. Jin Hui Lee
Dr. May-Britt Hagg Dr. Eberhard Staude
Dr. Birgul Tantekin-Ersolmaz Dr. Wulin Qui
Dr. Claudia Staudt-Bickel Dr. Shabbir Husain
Dr. Alan Greenberg Dr. Shan Wickramanayake

Chemical Engineering Education

--- - ^K__________________________-0

A Student-Centered Approach to Teaching


2. Course Delivery and Assessment

North Carolina State University * Raleigh, NC 27695
Lisa G. Bullard received her B.S. in
n the first few days of class we did all the usual ChE from NC State and her Ph.D. in
Sthings-handing out materials, explaining course ChE from Carnegie Mellon. She served
n handing out materials, explaining coue in engineering and management posi-
procedures (see Appendix 1A in Part 1), and talking tions within Eastman Chemical Co. from
about the importance of the course and the need to keep up 1991-2000. At N.C. State, she is currently
. a teaching associate professor and the
with the work on a regular basis. We also did several things director of undergraduate studies in the
that are not routinely done in engineering classes. Department of Chemical and Biomolecular
On the first day, we took digital pictures of the students in
groups of four holding name tent cards, and later we studied
Richard M. Felder is the Hoechst Celanese
these "flash cards" in our offices and attempted to learn the Professor Emeritus of Chemical Engineer-
students' names. One of us knew all of the students in her ing at North Carolina State University.
He is coauthor of Elementary Principles
section by the second class of the semester; the other is less of Chemical Processes, an introductory . '
gifted as a mentalist, and knew about 90% of his students chemical engineering text now in its third
by the end of the second week. The name tents, which the edition. He has contributed more than
200 publications to the fields of science
students also brought to their problem session, helped the and engineering education and chemical
graduate TAs learn the students' names as well. process engineering, and writes "Random
Thoughts," a column on educationalmeth-
Also on the first day, we asked the students to organize ods and issues for Chemical Engineering
Education. With his wife and colleague, Dr. Rebecca Brent, he co-
themselves into groups of three and four. We then presented directs the National Effective Teaching Institute (NETI) and regularly
them with a fairly extensive material and energy balance offers teaching effectiveness workshops on campuses and at confer-
problem (Problem 8.74 of the course text), and gave them ences around the world.
about five minutes to itemize the information they would need
� Copyright ChE Division of ASEE 2007

Vol. 41, No.3, Summer 2007

This two-part series describes the structure of the stoichiometry course
at North Carolina State University. The course has a variety of learning
objectives, and several nontraditional pedagogies are used in the course
delivery. Thefirst paper outlined the course structure and policies, the
preparation given to the teaching assistants (who play an integral part in
the course delivery), and the course assignments. This one describes the
methods used for classroom instruction and assessment.

and the approach they would take to solve the problem. We
told them the exercise was intended to give them a preview
of what the course was about and a taste of how we would be
conducting the lectures and problem sessions, and we assured
them that while we would collect their outlines, we would
not grade them. At the end of five minutes they signed and
turned in their papers. On the last day of class, we gave them
the identical in-class exercise and then returned their first-day
efforts to give them a tangible sense of how much they had
learned in the course.
The students' first assignment was to submit a one-page
autobiography, using autobiographies of the instructors as
models. Our autobiographies included information about our
families and personal interests as well as our academic inter-
ests, and we encouraged the students to do the same in theirs.
We compiled a portrait of the class from the autobiographies
and shared it as a memo to the students (see Appendix 2A).
Our goals in this exercise were to give the students a sense
of their instructors as somewhat normal and approachable
human beings and to help the class start to develop a sense
of community.
Something we didn't do, but plan to do in the future, is a
variant of an activity our department head, Peter Kilpatrick,
uses when he makes outreach visits to community high
schools. Peter polls the students to get their nominations for
the greatest challenges facing the world today, typically get-
ting responses that include solving dil. v. iv I _' y crisis, reducing
our dependence on nonrenewable resources, curing AIDS
and other diseases, feeding the world's growing population,
and reversing global warming. He then talks about how
engineers in general and chemical engineers in particular
will be essential in efforts to solve those problems. We can
take the additional step of pointing out that whatever form
the solutions to these problems eventually take, material and
energy balances will inevitably play critical roles.
Finally, on the first day of class we advised the students to
read "How to Survive Engineering School"'1 and "A Survival
Guide to Chemical Engineering. "[2

We prepared a series of class handouts that supplemented
the course text and contained a number of questions and
problems, with blank spaces for answers and solutions. The
complete set of handouts can be found at edu/felder-public/cbe205site/handouts.html>. Appendix 2B
shows an illustrative page from one of them.
In a typical lecture session, the class would work through
part or all of a handout in a mixture of lecturing by the
instructor, individual activities, and small-group activities
focused on the questions and gaps in the handouts. The stu-
dents would individually read a passage of text or part of a
problem statement or solution and perhaps briefly discuss it
in small groups to make sure they understood it. When they

reached a gap, one of several different things might happen:
(a) the instructor might go through the solution at the board
in traditional lecture format; (b) the students might be given
a short time (30 seconds-3 minutes) and asked to work indi-
vidually or in small groups to try to fill in the gap; or (c) the
instructor might skip the gap and tell the students to be sure
they knew what went in it before the next exam. The class
was told and periodically reminded that some of the questions
and problem segments in the handouts would show up on the
exams, and they did.
When active learning (individual and group activities in
class) was used, the instructor used a variety of formats.
Sometimes students worked together in pairs or groups of
three or four; sometimes they worked individually; and
sometimes they worked individually first and then got into
pairs, compared their solutions, and tried to reconcile any
differences (think-pair-share). Occasionally they worked
in pairs with one student doing the solving and explaining
and the other asking questions and giving hints if necessary
(ili,, i.I. -.1. i, lJ .. 1r problem solving), with the roles reversing
from one activity to the next. In all of these cases, when the
instructor stopped an activity, he/she would call on several
students for responses, ask for additional responses from
volunteers, perhaps augment or elaborate on the responses,
and then proceed with the lesson.
The approach of using handouts and active learning exer-
cises has several purposes. Students can read straightforward
material much more rapidly than instructors can present it.
Having them read prose descriptions, definitions of terms,
and simple algebraic and arithmetic calculations saves an
enormous amount of class time-enough to cover the difficult
material in lectures and activities and still get through the
complete course syllabus. In addition, people learn difficult
material and develop skills through practice and feedback,
not by being lectured on what they are supposed to know.
Numerous research studies have demonstrated the effective-
ness of relevant activities at promoting learning and skill de-
velopment.[3] We believe that more genuine learning resulted
from those brief activities in class and problem sessions than
from everything else we did in class. (For more information
on active learning, see Felder and Brent.t4])

Most of the weekly homework assignments were completed
by student teams, with the assignments being structured in
a manner that met the five defining criteria for cooperative
I,. . It " 1
1. Positive interdependence. The team members must rely
on one another. If a team member fails to fulfill his or
her responsibilities, the overall team performance evalu-
ation suffers.
2. Individual accountability. Different team members may
take primary responsibility for different parts of the

Chemical Engineering Education

assignment, but each team member is held individu-
ally accountable for the entire assignment content. In
addition, team members who behave irresponsibly (e.g.,
"hitchhikers," who fail to do what they are supposed to
do and often don't even show up) do not get the same
grade as those who perform responsibly.

3. Face-to-face interaction, at least part of the time. Much
of the learning in cooperative learning takes place as
teams discuss and debate conflicting strategies and solu-
tions. This criterion precludes the "divide-and-conquer"
strategy in which different team members complete
different parts of the assignment and simply staple the
parts together, so that each student only knows about
the part he or she did.

4. Development and appropriate use of interpersonal
skills. Team members are helped to develop skills
required for high-performance teamwork, including
leadership, communication, time management, project
management, and conflict resolution.

5. Regular self-assessment of team performance. The
members periodically reflect on what they are doing
well as a team, what they need to improve, and what if
anything they will do differently in the future.

Smith, et al.,[5 Felder and Brent,E6,7 and Oakley, et al.,E81
provide detailed information about cooperative learning
strategies and the research base that supports the effective-
ness of this method, and Felder, et al.,[9,10] describe and assess
an implementation of cooperative learning in a sequence of
chemical engineering courses, beginning with the stoichi-
ometry course.

In the remainder of this section, we summarize the princi-
pal features of the Fall 2005 implementation of cooperative
learning in CHE 205.

Team Formation

Primarily because some students normally drop CHE 205
in the first few weeks of the course, we made the first four
assignments individual, which minimized the number of
homework teams that had to be reformed due to drops. As
is consistently recommended in the cooperative learning
literature, we formed the teams rather than allowing student

Not surprisingly, some students objected to having to work
in instructor-formed teams, arguing that they preferred to
work by themselves or at least to be allowed to choose their
own teammates. We acknowledged their unhappiness and ex-
plained that our primary responsibility as teachers is to prepare
them to be engineers, and engineers work in teams whether
they like it or not, don't get to choose their teammates, and
are evaluated on their ability to work effectively with those
teammates as much as (or more than) on their technical skills.
That explanation may not have made all the protesters happy,
but it went a long way toward calming them down.

All teams had either three or four members. In our expe-
rience, two is too few (not enough diversity of skills and
problem-solving approaches, and no intrinsic mechanism for
conflict resolution) and five is too many (someone in the group
is likely to be left out). There were 14 teams in one section
and 16 teams in the other section. Of the 30 teams, 23 had four
members and seven had three members. Having four members
provides more diversity of ideas and keeps groups from falling
below critical mass if someone drops the course or is fired
from the group (a possibility we discuss later); having some
groups of three accommodates classes in which the number
of students is not exactly divisible by four and enables us to
add team members from groups that dissolve.
Before we formed the teams, we collected information from
all the students including their grades in prerequisite courses,
the hours during the week when they were unavailable for
working on group homework assignments, and their gender
and ethnic background. (They had the option of declining to
provide the latter two pieces of information.) We then formed
the teams using three criteria:
1. Ability heterogeneity. We did not want some groups
composed entirely of A students (which inevitably
form when students are allowed to self-select) and
other groups composed of C, D, and F students. Such
groupings are intrinsically unfair, and teams of all good
students are likely to use a divide-and-conquer strategy
(parcel out the work and not even look at the parts of
the assignment other than their own). When there is a
spectrum of abilities among team members and the team
is functioning effectively, the weaker students get the
benefit of one-on-one tutoring from their stronger team-
mates and the stronger students get the greater depth of
understanding that invariably results from teaching oth-
ers. Grades in prerequisite courses serve as our measure
of ability.
2. Common blocks of time to work on assignments outside
class. If teams are randomly formed, conflicting de-
mands imposed by other classes, extracurricular activi-
ties, and jobs can make it impossible for the members
to find a common meeting time at a reasonable hour
of the day. We do our best to make sure that the teams
we form have a few hours each week when none of the
team members has conflicting obligations.
3. No isolation of at-risk minorities in teams. Studies have
shown that students in minorities historically at risk for
dropping out tend to be marginalized if they are isolated
in student teams. E6 Women and African-American,
Latino, and Native American men are at greater risk for
dropping out of chemical engineering in the first two
years of the curriculum than are men in other ethnic
groups, and so we tried to make sure that no team had
only one member in any of those categories.

When we first began to use cooperative learning, we had
the students fill out a one-page information sheet with the
information needed to form teams using those criteria, and

Vol. 41, No.3, Summer 2007

then sorted the students into teams manually. For the last, two
years we have used an online instrument called "Team Maker"
developed by Richard Layton at the Rose-Hulman Institute of
Technology."11 The students enter the requested information
into a database, the instructor specifies the sorting criteria,
and Team Maker does the sorting. We have found that the
instrument sorting is more reliable than our manual efforts
ever were and takes much less time to implement.
Individual Accountability
We used several methods to hold students individually
accountable for all the assignment content (not just the parts
they focused on) and for fulfilling their responsibilities on
the team:
- The midterm andfinal examinations were all taken
individually and covered all of the content and skills
involved in the homework assignments. If students did
not participate in solving the homework problems or if
they participated but did not understand all of the solu-
tions, their test grades would be likely to suffer and they
would get low course grades. In addition, students had
to get an average individual test mark of 60 or better to
pass the course, regardless of their homework scores.
- The 205 students were warned about the dangers of the
divide-and-conquer strategy (discussed previously), of
simply working out solutions ...,, i, , at group meet-
ings, and were advised to outline the solutions to every
problem individually before working out all the details
in the group. In divide-and-conquer, each student truly
understands only the problem solution he or she ob-
tained, and in group sessions, the strongest team mem-
bers tend to outline and begin every problem solution,
so that the weaker students may never get practice in
either activity before the exams. On the first few assign-
ments, we had the students sign and turn in individual
outlines with the final team solution. The outlines were
logged in but not graded-unless they were not done, in
which case points were deducted.
- Peer evaluations of team citizenship were conducted
using an online rubric called the Comprehensive As-
sessment of Team Member Effectiveness (CATME),
developed by Matthew Ohland ofPurdue University and
colleagues at several other institutions.E61 The students
used the rubric to rate their teammates and themselves
in the categories of contributing to work, interacting
with teammates, keeping the team on track, and expect-
ing quality. The rubric was explained shortly after the
students began working in teams and was completed
three times during the semester. After the first adminis-
tration, the ratings were released to the students so that
they could see how their individual ratings compared
to the team's average rating and discuss reasons for any
low ratings that may have been given. (The students
were not told how each teammate rated them.) The rat-
ings from the second two administrations were used to
adjust each student's average team homework grade for
the period since the prior administration. The adjust-
ment algorithm is outlined in Reference 12.

Before we formed the teams, we collected in-

formation from all the students including their

grades in prerequisite courses, the hours during

the week when they were unavailable for work-

ing on group homework assignments, and their

gender and ethnic background (optional).

- Students who were hitchhikers (who chronically missed
team i. .. o,, and/or failed to do what they were sup-
posed to do prior to the m,. , i,, i could, after several
warnings, be fired by unanimous consent of the rest of
the team. Students who repeatedly received no coop-
eration from their teammates could quit after several
warnings. Students who were fired and students who
quit had to find teams of three willing to accept them for
the remainder of the course, otherwise they would get
zeros for the remaining assignments. In practice, both
firings and quittings are relatively rare. In fall 2005, two
students were fired and none quit.

Positive Interdependence
Several features of the course implementation promoted
mutual reliance of team members on one another:
- We encouraged the students to distribute primary
responsibility for working out different problems among
the team members, balancing this advice with the mea-
sures listed in the preceding section to discourage the
divide-and-conquer approach.

- We defined four team roles that rotated with each as-
signment-coordinator (to arrange meeting times and
delegate responsibilities), monitor (to check each team
member's understanding of problem solutions), recorder
(to produce the final version of the complete assign-
ment), and checker (to check the final solution for errors
and turn it in when it was due). On teams of three, the
coordinator also functioned as monitor. If a team mem-
ber failed to fulfill his or her role, the assignment grade
would likely suffer.

- On two of the midterm tests, we offered a bonus of three
points to all members of teams with average test grades
of 80 or higher. (The test averages were generally in
the low 70s.) This offer encourages the best students in
each group to try to get the highest grade possible and
it also encourages tutoring, as the stronger students try
to help their weaker teammates maximize their grades
to help raise the average above the criterion level. We
did not require all team members to get above 80, which
would have put unrealistic and sometimes impossible
demands on the weakest members.

Face-to-Face Interaction
The main thing we did to encourage face-to-face interac-
tion was to make sure the members of the teams we formed

Chemical Engineering Education

had common blocks of time to meet outside class. The steps
described above to discourage divide-and-conquer also had
the effect of promoting interaction.

Regular Self-Assessment of Team Functioning
Every three weeks the homework assignment included a
question that asked the team to specify (a) what they were
doing well as a team, (b) what areas needed improvement,
and (c) what, if an ihlinig. would they try to do differently in
future assignments.

Development of Teamwork Skills
- Shortly after the teams were formed, we had them
complete a team expectations assignment in which they
wrote and signed off on team rules and expectations,
made copies for each member, and submitted a copy to
the instructor. When they completed peer ratings, we
suggested that they refer back to the rules and base their
evaluations in part on how well the team members were
meeting the agreed-upon expectations.

- C.. -q, i-, t, the CATMEpeer evaluation rubric was an
important step in the students' acquisition of teamwork
skills. The rubric identifies well-established characteris-
tics of members of highly effective teams and provides
students with detailed feedback on how well or poorly
they are displaying those characteristics. Having to
complete the rubric for practice two weeks after the
teams began to work together helped the students under-
stand what was expected of them, and doing it twice
more with the outcomes affecting individual homework
grades reinforced their understanding.
- Periodic self-assessment of team fi .. i.. -1n11, provided
further opportunities for students to reflect on the
behaviors that were helping and iA1 in,, their perfor-
mance as a team.

- Several times during the semester we conducted 10-
minute mini-clinics in class to help students figure out
methods for dealing with common problematic situa-
tions.E' We would describe a situation (e.g., the pres-
ence of a hitchhiker on the team) and ask the students
to work in small groups and brainstorm possible team
responses. We listed their suggestions on the board and
added our own if we had ideas none of them thought of
(which didn't usually happen). Then we had the groups
try to reach consensus on the best initial team response
to the problem teammate, the best next response if the
first one didn't work, and the best last-resort response.
(Most groups suggested either firing the student or leav-
ing his/her name off subsequent assignments). We listed
those suggestions, and then went on with the lesson.
The students left with excellent strategies for dealing
with the situation under discussion, and the miscreants
were put on notice that their irresponsibility would
probably have unpleasant consequences in the future.
- We used-and taught the students how to use-active
listening1 for conflict resolution. On several occasions,
a conflicted team reached an impasse and required

intervention. The first of the two conflicting sides made
its case, and someone on the opposite side repeated it
verbatim without responding to it, with people on the
first side making corrections until the second side got it
right. Then the second side made its case, and the first
side had to repeat it without attempting to refute it. Af-
ter that, the two sides worked out a resolution. Doing so
was relatively easy once each side understood the other
side's case well enough to articulate it.

Team Dissolution and Reformation
Early in the semester, the students were told that a month
after the teams were formed, they would be dissolved and
reformed unless every member of a team stated in writing
that he or she wished to remain with the same team members,
in which case the team could stay together. One team in each
section chose not to remain together, and we distributed their
members among existing teams of three.
In the past, only the most dysfunctional teams have not
elected to remain together, and we have never had to dis-
solve more than two of them. Some of the teams that remain
together encounter interpersonal conflicts, but with or without
our help they work through them- one of our primary course


In the traditional deductive approach to teaching, basic facts
and methods are taught and illustrated, and later- sometimes
much later, if at all-the students are introduced to applica-
tions of the methods to real-world problems. The alternative is
inductive teaching',. in which students are first presented with
a challenge of some sort (e.g., a question to be answered, an
observation to be explained, or a problem to be solved), and
the relevant principles and methods are presented in the con-
text of addressing the challenge. Prince and Felder[13,14] outline
and compare various forms of inductive teaching-including
inquiry-based learning, problem- and project-based learning,
case-based teaching, and Just-in-Time Teaching-and sum-
marize the research attesting to the effectiveness of these

While we did not use a purely inductive approach in CHE
205, the instruction had a strong inquiry-based flavor in that
questions and problems provided the context for much of the
teaching. The students were told on the first day of classes that
they could not count on being shown explicitly in lectures how
to solve all their homework problems, but they were assured
that extensive guidance would be provided in the text, the
course handouts, and by the instructors and TAs during office
hours. The first-day exercise, in which we had the students
outline what they would do to solve a complex problem taken
from the course text, is a classic inductive activity. Once we
had begun discussing material balances early in Chapter 4, all
new topics (recycle and bypass, reactive systems, gas laws,
phase equilibrium relations, etc.) were introduced as logical

Vol. 41, No.3, Summer 2007

extensions of the type of analysis the students were already
accustomed to.
The computer played a central role in the course. We used
it to demonstrate instructional software tools, communicate
with students, create assignments and tests, maintain class
records, archive student team peer ratings and use them to
adjust team homework grades for individual performance, and
post student handouts, assignments, study guides, the course
syllabus and policies, and old exams. The TAs demonstrated
software in the problem sessions and maintained spreadsheets
with assignment and test grades and problem session atten-
dance records. The students worked through the instructional
tutorials and used other resources on the text CD, e-mailed
questions to instructors and TAs, viewed and downloaded
assignments and various resources posted on the course Web
site, and used Excel and E-Z Solve on homework problems.
The department does not yet offer CHE 205 in a distance
education format, but given the current extent of our use of
instructional technology, the transition to a distance offering
in the future should be straightforward.
Most computer instruction in CHE 205 took place in the
weekly two-hour problem session. A brief introduction was
given to E-Z Solve (which is user-friendly to an extent that
almost precludes the need for instruction), and then half of
the first four problem sessions was spent teaching Excel using
an instructional CD we developed with basic instructions for
key operations and worked-out examples from the course text.
The students worked individually and in pairs on their own
laptops or on laptops checked out from a department cart.
Starting in 2006, the university began requiring all N.C. State
students to bring their own laptops, which will eliminate the
need to maintain the cart.
A technology-based resource that we do not use in CHE 205
is PowerPoint, since we believe that anything we might use it
for can be done better with a combination of handouts, board-
work, and occasional access to Web-based resources. For the
reasoning behind this decision, see Felder and Brent.[151

Study Guides and Tests
There were three midterm exams and a comprehensive final
exam in the lecture section, and two computer quizzes (on E-Z
Solve and Excel) in the problem session. (See edu/felder-public/cbe205site/tests.html> for sample exams.)
The midterms and final exam were open-book, but the students
could not refer to their lecture notes or worked-out homework
solutions. The computer quizzes were closed-book. The stu-
dents were strongly advised to use tabs or some other system
to mark locations of important text material so they wouldn't
waste a lot of time hunting for things during the open-book
tests. They were also advised to read "Tips on Test Taking"[16]
before the first midterm exam.

One of the lecture sections met in three 50-minute periods
per week and the other met in two 75-minute periods, which
made it difficult to give the two sections equivalent in-class
exams. Partly to avoid this difficulty and partly to minimize
speed as a major factor in test performance, common midterms
were given to the combined sections in two-hour blocks on

A technology-based resource that we do not use

in CHE 205 is PowerPoint, since we believe that

anything we might use it for can be done better

with a combination of handouts, boardwork,

and occasional access to Web-based resources.

Friday afternoons. The midterms were designed to be com-
pleted by the students in about an hour (which meant that the
instructors could work through the solutions in less than 20
minutes). Each section took its own three-hour final exam.
One to two weeks before each exam, we posted study guides
on the course Web site ( cbe205site/guides.html>) that listed the terms and concepts
the students might be asked to explain and the types of things
they might be asked to do (calculate, formulate, derive,
troubleshoot, brainstorm) on the exam-which is to say, we
announced our learning objectives for the course. The class
period before the exam was designated as a review session and
the students were encouraged to come prepared with questions
about the test, which they did. In some of these sessions, we
described a system and had the students brainstorm questions
and problems related to it that we might ask on the test. The
tests were composed entirely of questions and problems of
the types listed on the study guides.
Some instructors who hear about this approach for the
first time are skeptical: it appears to them that we are spoon-
feeding the students, eliminating the need for them to study
anything beyond a narrowly restricted body of material. This
is far from the case. The study guides are generic and com-
prehensive, and students who study hard enough to be able
to do everything on them have learned what we wanted them
to learn and deserve good test grades. Moreover, the study
guides and the tests include problems that require thinking
and conceptual understanding at levels considerably beyond
those typically required in stoichiometry course tests. Based
on our past experience in CHE 205, a significant percentage
of the students would get low grades without the explicit
understanding of our expectations that the study guides give
them, and massive curving would be required to keep us from
having to fail most of the class. With the study guides, they
understand that they will have to go beyond rote memoriza-
tion and formula substitution to succeed in the course, and all

Chemical Engineering Education

but 10-15% of them routinely do so. (The grade distribution
for Fall 2005 is given in the next section.) This is not spoon-
feeding-it is teaching.
Course Grading
The absolute grading system outlined in Appendix 1A of
Part 1 was used to determine final course grades, using a
weighted average of the midterm exam grades (40%, with the
lowest of the three grades counting half as much as each of
the other two), the final exam grade (30%), homework grades,
with team grades adjusted based on the peer ratings (20%),
and problem session quizzes and in-class exercises (10%). A
grade of C- or better in CHE 205 is required to move on to
the next course in the departmental curriculum.
The grade distribution for Fall 2005 is shown in Table
1. Grades of S and U (satisfactory and unsatisfactory) are
given to students who choose to take the course on a pass-fail
basis-which only non-majors are allowed to do-and IN
denotes incomplete, a grade given only to students prevented
from completing the course requirements by serious demon-
strable extenuating circumstances.
This grade distribution is typical of course offerings since
we began using the system described in this series of papers,
although sometimes there are fewer C's and more A's and B's.
It is markedly different from distributions commonly seen in
the time before 1990 when the course was taught traditionally.
Then, A's were rare, more students got C's than any other
grade, and as many as 40% got D's or F's or dropped the
course, or if grades were curved, failing exam grades would
be curved up to B's and C's. We are aware that some might
suspect that our higher grade distributions reflect a lowering
of standards. We invite any who have this concern to examine
the study guides and exams on the course Web site and judge
for themselves.
Academic Integrity
The following section is included in the course syllabus:
- Academic integrity. Students should refer to the univer-
sity policy on academic integrity found in the Code of
Student Conduct (found in Appendix L of the Handbook
for Advising and Teaching). It is the instructor's under-
standing and expectation that the student's signature on
any test or assignment means that the student contrib-
uted to the assignment in question (ifa group assign-
ment) and that they neither gave nor received unauthor-
ized aid (if an individual ........ .a i s Authorized aid
on an individual assignment includes discussing the
interpretation of the problem statement, sharing ideas
or approaches for solving the problem, and explaining
concepts involved in the problem. Any other aid is con-

sidered unauthorized and a violation of the academic
integrity policy. All cases of academic misconduct will
be submitted to the Office of Student Conduct. If you
are found guilty of academic misconduct in the course,
you will be on academic integrity probation for the
remainder of your years at NCSU and may be required
to report your violation on future professional school
applications. It's not worth it!

The language in the syllabus was carefully chosen to de-
scribe authorized aid as opposed to listing the behaviors that
constitute cheating (we'd surely leave something out). This
language has evolved due to painful personal experience and
the fact that some of our engineering students must surely
be contemplating a career in law, based on the excuses that
we've heard from them. We spend at least 10 minutes on the
first day of class discussing academic integrity and giving
examples of appropriate and inappropriate behavior, and we
also have someone from the Office of Student Conduct come
to a problem session early in the semester to discuss univer-
sity policies related to cheating. We prefer to spend this time
making our expectations explicitly clear up front rather than
spending it later in Judicial Board hearings. We still catch
cheaters from time to time, but we believe our precautionary
measures significantly reduce the number of attempts at it.
At the suggestion of the director of the NCSU Office of
Student Conduct, we are in the process of shooting a video
with students role-playing specific examples of what does
and does not constitute cheating. In Fall 2006 we premiered
a live version of the skit on the first day of class, which was
well received by the students. Our hope is that the skit, and
later the video, will make abundantly clear to students what
the boundaries of acceptable behavior are when they work on
individual and team homework and when they use the same
computer for assignments involving E-Z Solve or Excel.
Student Evaluations
We collected informal mid-semester student evaluations
and formal course-end evaluations, the latter using the form
prescribed for all courses by the CBE Department.
The midsemester evaluations asked the students to list
features of the course that were contributing to their learning
and features that were hindering their learning. The features
contributing to learning mentioned by more than two students
were (in order of the number of students mentioning them)
the homework, office hours, class handouts, problem session,
group homework, instructors' availability and helpfulness,
lectures, class activities, text, and text workbook. The features
that they felt were hindering their learning were the earli-
ness of the class (8 a.m. for one section, 8:30 for the other

Final Course Grade Distribution
Grade A+, A, A- B+, B, B- C+, C, C- D+, D, D- F S, U, IN
% of Class 18% 36% 27% 6% 9% 4%

Vol. 41, No.3, Summer 2007

one), the rapid pace of the lectures, group homework, harsh
grading of homework, length of the assignments, and lectures
(too much theory, not enough examples, repeating material in
handouts). In response to their comments, we increased the
number of worked-out examples covered in lectures and prob-
lem sessions and eliminated some material from the lectures
so we could slow the pace down. In response to a complaint
from one of the students, we also cautioned one of the TAs to
avoid sarcastic remarks when grading homework
In the final course evaluations, the course and the instruc-
tors were ranked well above average for all departmental
undergraduate courses. The only systematic complaints had
to do with the heavy workload, the problem session (which
some students did not find particularly helpful), and the earli-
ness of the class.

This two-part series of articles outlines an approach to
teaching the stoichiometry course that incorporates a variety
of instructional methods designed to maximize learning and
skill acquisition. The methods include writing learning objec-
tives and using them to guide the design of both instruction
and assessment; sharing the objectives with the students in
study guides for exams; and using forms of active, coopera-
tive, and inquiry-based learning. Although the course tests
included more high-level thinking questions than CHE 205
exams normally contain, the students performed substan-
tially better than they normally do when the course is taught
We did not carry out a control study to confirm the last
observation, mainly because there was no need to do so. Our
objective was not to validate the methods we were using: the
literatures of cognitive science and engineering and science
education are filled with demonstrations of the effectiveness
of those methods.[3,,13,17-19] Moreover, one of us used many
of the same pedagogical methods in a sequence of chemi-
cal engineering courses including the stoichiometry course
and demonstrated that the performance and attitudes of the
students in his classes were consistently superior to those of
a traditionally taught comparison group.[9,10]
This is not to say that every instructor of the stoichiometry
course should immediately try to do everything we have
described in the paper. We would never presume to suggest
such a thing even if we believed it to be sound advice, which
we don't. Different teachers have different teaching styles,
personalities, teaching philosophies, levels of experience,
competing demands on their time, and levels of comfort
with different teaching methods. For an instructor to launch
full-scale into a pedagogical approach with which he or
she is unfamiliar and/or uncomfortable is a prescription for
likely disaster.
Instructors considering these approaches may be concerned
about the time requirement. Teaching a course for the first

time will involve an enormous time commitment whether
the course is taught traditionally or in the manner outlined in
these papers. The most time-consuming activity in our imple-
mentation was preparation of the handouts, but this was done
over a period of about five years. Now that the coursepack
containing the handouts is in place, almost no time is required
to prepare lectures. At steady state, the instructors and the six
teaching assistants each spend approximately 10 hrs/week
between lecturing, office hours, and grading.
What we suggest is that instructors consider a gradual
movement toward the style of teaching we have described.
For example, if you are an instructor preparing to teach the
stoichiometry course:
- Consider doing several .1-,,,, at the beginning of
the course to help establish a sense of the class as a
learning community, such as learning as many of the
students' names as you can as quickly as you can and/
or sharing .. ... l,,,, of yourself with them .1 ..,- ,1 an
introduction or biography and >. iin, them to do the
same for you.
- If you have never written formal learning objectives,
try i,* , i, them for one section of the course and
-. i1,, them in a study guide for the test covering that
section. 20
- If you have relied exclusively on traditional lecturing
in the past, consider introducing some short small-
group activities that call on the students to do the
same .-,,,,, they will be called upon to do in assign-
ments and tests.'4
- Instead of always lecturing on principles, then il-
:i, i, .1,,, problem solution methods in class, and then
assigning similar problems, use some inquiry-based
learning in which students are first given challenges
(e.g., questions to answer, realistic problems to solve,
or experimental observations to interpret) and the
principles and methods to be taught are introduced in
the context of addressing the challenges.t13141
- Instead of only assigning homework problems of
the "Given this and this, calculate that" variety,
add problems that call for students to improve their
higher-level .-1,,,i,,,, skills, such as asking them to
think about why measurements might differ from val-
ues they calculate, or to think of as many ways as they
can to measure a physical property described in the
course, or to interpret familiar phenomena making use
of concepts taught in the course.
- Once you have gained a reasonable level of comfort
with those methods, you might move toward balancing
individual work with cooperative learning, assign-
ing problem sets to student teams but taking care to
hold individual team members accountable for all the
knowledge and skills required to complete the assign-
ments.f5 81
As these methods become more familiar, you can continu-
ally increase their use, always seeking the optimal blend of
pedagogical effectiveness and your own comfort level.
Chemical Engineering Education

We acknowledge with gratitude the numerous and signifi-
cant contributions to CHE 205 of the TAs (especially Adam
Melvin) and Paul Cousins, director of the N.C. State Univer-
sity Office of Student Conduct.

1. Felder, R.M., "Howto Survive Engineering School,"( I,... i , / .
37(1), 30 (2003), Surviving-School.html>
2. Bullard, L.G., "A Survival Guide to Chemical Engineering," www.ncsu.edu/felder-public/Papers/CHE_Survival_Guide(Bullard).
3. Prince, M.J., "Does Active Learning Work? A Review of the Research,"
J. Eng. Ed., 93(3), 223 (2004), Prince_AL.pdf>
4. Felder, R.M., and R. Brent, "Learning by Doing," Chem. Eng. Ed.,
37(4), 282 (2003), Active.pdf>
5. Smith, K.A., S.D. Sheppard, D.W Johnson, and R.T. Johnson, "Pedago-
gies of Engagement: Classroom-Based Practices," J. Eng. Ed., 94(1),
87 (2005)
6. Felder, R.M., and R. Brent, "Cooperative Learning in Technical
Courses: Procedures, Pitfalls, and Payoffs," ERIC Document Repro-
duction Service, ED 377038 (1994), public/Papers/Coopreport.html>
7. Felder, R.M., and R. Brent, "Effective Strategies for Cooperative
Learning," J. Cooperation & Collaboration in College Teaching,
10(2), 69 (2001), CLStrategies(JCCCT).pdf>
8. Oakley, B., R.M. Felder, R. Brent, and I. Elhajj, "Turning Student
Groups into Effective Teams," J. Student Centered Learning, 2(1),
9 (2004). paper(JSCL).pdf>
9. Felder, R.M., "A Longitudinal Study of Engineering Student Perfor-
mance and Retention. IV. Instructional Methods and Student Responses
to Them," J. Eng. Ed., 84(4), 361 (1995), felder- public/Papers/long4. html>
10. Felder, R.M., G.N. Felder, and E.J. Dietz, "A Longitudinal Study of
Engineering Student Performance and Retention. V. Comparisons with
Traditionally Taught Students," J. Eng. Ed., 87(4), 469 (1998), ncsu.edu/felder-public/Papers/long5.html>
11. Cavanaugh, R., M. Ellis, R. Layton, and M. Ardis, "Automating the
Process of Assigning Students to Cooperative-Learning Teams,"
Proceedings of the 2004 ASEE Annual Conference, Salt Lake City,
(2004), See for information
about obtaining and using this instrument
12. Ohland, M.W, M.L. Loughry, R.L. Carter, L.G. Bullard, R.M. Felder,
C.J. Finelli, R.A. Layton, and D.G. Schmucker, "The Comprehensive
Assessment of Team Member Effectiveness (CATME): A New Peer
Evaluation Instrument," Proceedings of the 2006ASEEAnnual Confer-
ence, Chicago (June 2006), Information about CATME may be found
13. Prince, M.J., and R.M. Felder, "Inductive Teaching and Learning Meth-
ods: Definitions, Comparisons, and Research Bases," J. Eng. Ed., 95(2),
123 (2006), pdf>
14. Prince, M.J., and R.M. Felder, "The Many Faces of Inductive Teaching
and Learning," J. Coll. Sci. Teaching, 36(5), 14 (2007), edu/felder-public/Papers/Inductive(JCST).pdf>
15. Felder, R.M., and R. Brent, "Death by PowerPoint," Chem. Eng. Ed.,
39(1), 28 (2005) PowerPoint.pdf>
16. Felder, R.M., and J.E. Stice, "Tips on Test-Taking," edu/felder-public/Papers/testtaking.htm>
17. Bransford, J., A.L. Brown, and R.R. Cocking, (Eds.) How People

Vol. 41, No.3, Summer 2007

Learn: Brain, Mind, Experience, and School (Expanded edn.),
Washington, DC: National Academy Press (2000), edu/books/0309070368/html/>
18. Heywood, J., Engineering Education: Research and Development in
Curriculum and Instruction, John Wiley & Sons, New York (2005)
19. McKeachie, WJ., McKeachie's Teaching Tips, llth Ed., Houghton
Mifflin, Boston (2002)
20. Felder, R.M., and R. Brent, "How to Teach (Almost) Anybody (Almost)
Anything," Chem. Eng. Ed., 40(3) 173 (2006), felder-public/Columns/ T, I. 11,,,,. z i 11l


Dear students,
Learning about you from your biographies has been an enjoyable,
educational, and humbling experience. We wanted to share a little of
what we learned so that you can get a sense of the impressive group
of people that you are.
You're mostly Southerners, many from small towns and farms,
but there are also quite a few Yankees and international students
from all over the world. In the class are speakers of Spanish, French,
Chinese, Hindi/Bengali, and a West African dialect that the writer
didn't name. Most of you are single, some are engaged, a few are
married, and one of the latter has a son "who is four and well on his
way to becoming an evil genius."
Some of you were influenced to choose your current majors by
charismatic family members or teachers, many chose them because
they were good at chemistry and math in school, and some were
motivated by a desire to help people (biomedicine) or protect the
environment (environmental science). Some have worked in industry
and have a feeling for what engineers do; most have not and are
hoping they've made a good decision and afraid that their friends
who question it may be on to something. ("What's your major?"
"Chemical Engineering." "Wow, are you crazy?") They probably
have made a good decision-there's almost nothing you can think
of that skilled professionals do that you don't find engineers doing,
and N.C. State is an outstanding place to learn to do it. Some people
claim that engineering students are all narrow-minded geeks who
have no interests outside of their classes, but you collectively make
liars out of them. For one thing, you can write-and I'm not just
talking about the one who got a degree in English literature before
coming back to get an engineering degree. Many of your essays were
stylishly and entertainingly written, including a beautifully crafted
piece that talked about how much the author hated having to write.
Your interests are all over the place, including working on and rac-
ing cars, reading, music (we have several pianists, violinists, and
drummers, as well as a banjoist and a concert-level French hornist),
debate, the outdoors, and sports. Among you is a commercial pilot
and flight instructor, an army chemical operations specialist, an
expert in outdoor power equipment technology (which apparently
is a competitive field-one of you placed first in the state and 11th
nationally in it), a personal fitness trainer, a paralegal, an actor, a
firefighter, and jewelry maker.
You are a very athletic crowd. Collectively you're into tennis,
backpacking, biking, basketball, baseball/softball, football, running,
golf, dance, rock climbing, kayaking/canoeing, volleyball, , .. ' II ,.
cheerleading, competitive horseback riding, skiing/snowboarding,
swimming (one of you does mini-triathlons), surfing, karate, discus/
shot put/high jump, wakeboarding, skateboarding, fishing, hunting,


hockey, and lacrosse... and there are enough of you who play soccer
at a very high level to put together a team that could probably wipe
out every other department in the college. You also include a num-
ber of fanatic Wolfpack football followers, and one brave soul who
admits to being a big Tarheel fan. (No, I won't reveal names.)
You are also well developed spiritually. Many of you spoke of the
importance of your faith in your life, some mentioning being active
in your church, campus faith-based organizations, and mission work.
Among you are volunteers for Habitat for Humanity, the SPCA, the
Durham Rescue Mission, the Appalachia Service Project, the Red
Cross, the March of Dimes, and several local hospitals.
In short, you are a diverse, talented, and generally splendid group of
people. We feel privileged to be your teachers this semester, and look
forward to getting to know you better as the semester progresses.
Lisa Bullard and Richard Felder


* Internal energy table
(a) Choose a reference state (phase, T, P) for a species, at which
U is set equal to 0. (Example: Liquid water at the triple point, used
in Tables B.5-B.7)
(b) Determine AU for the change from the reference state to an-
other. Call the result i of the species at the second state relative to
the reference state. Repeat for many states, and tabulate U.
(c) Thereafter, calculate AU for a specified change of state (to
substitute into the energy balance equation) as Ufinal -U ml, substitut-
ing values from the table for both internal energies.
If you chose a different reference state, the numbers in the table

would all be different but the difference between the values for any
two states would always be the same. The two internal energy tables
shown below for carbon dioxide at 1 atm illustrate this point.

Ref: C0,(g, 1 atm, 0 oC) Ref: CO,(g, 1 atm, 100 oC)
T(oC) U (kJ/mol) T(�C) U(kl/mol)
0 0.00 0 -3.82
100 3.82 100 0.00
200 8.00 200 4.18
300 12.50 300 8.68

Exercise: A table of specific internal energies of nitrogen at P = 1
atm contains the following entries:

T(oC) T(kl/mol)
0 -0.73
25 0.00
100 2.19
200 5.13

(a) What reference state was used to generate this table?
(b) Q: What is the physical significance of the value 2.19 kJ/mol?
A: It is for the process AU N2(_, _ atm, �C) -- N2(_
_ atm, _C)
(c) What is AU for the process N2(g, 1 atm, 200 oC) -- N(g, 2 atm,
100 �C)?
(d) Calculate the heat required to cool 2.00 mol N2 from 200 �C to
100 o�. a

Chemical Engineering Education

--- - ^ K.___________________________-

A Case Study Representing


As a Feedback Control Problem

Texas A&M University * College Station, TX 77843-3122
systems research has undergone significant changes in
recent years due to the inclusion of new applications for � . Abhay Singh is a Ph.D. student at Texas
control--e.g., microelectronics manufacturing or drug A&M University, College Station. He re-
S:ceived his B.E. in chemical engineering
dosage adjustment for biomedical applications -and the use from Panjab University, Chandigarh, India
of systems concepts in new areas such as systems biology. in 1998. Afterward, he joined Indian Pet-
Srochemicals Corporation Ltd. (IPCL) as a
As the results from research tend to influence what is taught b production engineer (Chemical) for four
in a classroom and vice versa, it is very important to have years. His research interests include sensor
illustrative examples that can easily be presented location, soft sensor design, and systems
access to illustrative examples that can easily be presented biology. He is a recipient of the CPC 7 Out-
to undergraduate students without requiring an advanced F standing Contributed Paper Award.
background in the systems area. Arul Jayaraman received his B.E. (Hons)
There are many applications in the field of drug infusion in chemical engineering and M.S. (Hons) in
physics from BITS Pilani, India, in 1992, his
control[13] that have been developed and used in classroom M.S. from Tufts University in 1994, and his
example problems. The selection of examples from the field Ph.D. from the University of California, Irvine,
in 1998, both in chemical engineering. He
of systems biology, however, is much more limited. This is joined Harvard Medical School as instructor
despite it being widely recognized that feedback loops are in bioengineering in 2000. He joined Texas
common to many cellular functions.[4-8] This paper addresses A&M University, College Station, as an assis-
tant professor in 2004. His research interests
these points as it investigates a signal transduction pathway include systems biology, molecular bioengi-
involved in the body's response to inflammation or injury, neering, and cell-cell communication.
Juergen Hahn received his degree in en-
one of many areas of interest to systems biology. While the gineering from RWTH Aachen, Germany,
described system is of interest to the biomedical community, in 1997, and his M.S. and Ph.D. degrees
it is simple enough to be presented in an undergraduate class in chemical enginin g from the University
of Texas, Austin, in 1998 and 2002, respec-
and contains feedback regulation of the signal transduction tively. He joined Texas A&M University,
pathway. Additionally, the system can be appropriately de- College Station, as an assistant professor
pathway. Additionally, in 2003. His research interests include
scribed using block diagrams and transfer function models process modeling and analysis, systems
for perturbations around a steady state. biology, and nonlinear model reduction. He
has published more than 30 articles and
The outline of the paper is as follows: Section 1 is an in- book chapters.
production. Section 2 presents the biological significance of
� Copyright ChE Division of ASEE 2007
Vol. 41, No.3, Summer 2007 17

the system and describes the model representing the signal
transduction pathway. A block diagram representation of
the signal transduction pathway is developed in Section 3.
Section 4 presents the transfer functions that describe the ef-
fect concentrations of some proteins in the pathway have on
other proteins in the pathway and investigates the dynamic
behavior of the signal transduction pathway. Furthermore,
the dynamics of cells in which the regulatory mechanism
does not function properly, as is often associated with certain
types of cancer,t61 are investigated based upon the developed
transfer function model and compared to the behavior of the
original system. Section 5 presents how this model was used
within an undergraduate process dynamics and control class
taught at Texas A&M University, and Section 6 presents
some conclusions.

Cell signaling refers to the process by which cells sense
their environment, including communication with other cells.
Signaling in cells is initiated by extra-cellular molecules that
activate an intracellular signaling pathway, which ultimately
leads to the formation of proteins involved in basic cellular
processes like regulation of cell growth and division or expres-
sion of other, secreted proteins. This entire process
in which biological information is transferred
from extra-cellular signals into changes
inside a cell is referred to as signal
transduction. As malfunction of sig-
naling pathways can be associated
with some diseases, e.g., certain 7
types of cancer, cells usually have
regulatory mechanisms built into
signal transduction pathways.
The system under investiga-
tion in this paper deals with
signaling pathways involved SOCS3-mRNA .
in a body's response to burn-
injury-induced inflammation.
The injured cells release cyto-
kines, one of which is interleukin SOCS3mRNA
6 (IL-6), to the bloodstream. These
cytokines are sensed by hepatocytes
in the liver, and they activate the acute
phase response (APR). The acute phase
response up- or down-regulates the expres-
sion of certain plasma proteins that take part
in the body's response to the burn-injury-induced
inflammation. Investigating cell signaling in hepatocytes
stimulated by inflammatory agents is of crucial importance
to understanding the mechanisms underlying the APR.
The specific topic of this paper is the development of a trans-
fer function model of the JAK (Janus-Associated Kinases)/
STAT (Signal Transducers and Activators of Transcription)
signaling pathway in hepatocytes stimulated by IL-6.[910] Sig-


naling through the J \ K N I \ I pathway is regulated by SOCS3
(Suppressors Of Cytokine Signaling 3) proteins. These pro-
teins are induced by the JAK/STAT signaling pathway once
the signal emanating from the cell surface reaches the nucleus
of the cell. SOCS3 regulates further signaling from the cell
surface to the nucleus of the cell by inhibiting the activation
of STAT3, a process that is usually taking place as a result of
binding of IL-6 to the receptors on the cell surface.

The system under investigation is based upon the JAK/
STAT pathway of the model presented in Singh, et al.,[11] and
is shown in Figure 1. The model of the J \IK N I \1' pathway
consists of 33 ordinary differential equations, in which each
state corresponds to the concentration of a particular protein
or protein complex in either the cytosol or the nucleus. It is as-
sumed that the cytosol is "well-mixed" and, separately, that the
nucleus can also be viewed as "well-mixed." The differential
equation for a particular component (A) is written as:

where vA represents the rate of production/consumption of species
Ain aparticularreaction. It should be noted that these reac-
tions can also include formation and degradation of
a specific protein/protein complex.
While the availability of the detailed
model can have advantages for ana-
lyzing the dynamic concentration
profiles of some specific compo-
nents of the system, e.g., dynam-
ics of phosphorylated STAT3
outside of the nucleus, it is not
Always required, nor is it neces-
sarily always feasible, to model
every single component of the
system. Instead, it is important
to know the dynamic profiles of
certain key components and the
effect a change in the concentra-
tion of one component has on oth-
ers present in the system. This type
of cause-effect relationship can be
conveniently represented in a block dia-
gram. If the relationships between inputs
and outputs can be appropriately described by
linear ordinary differential equations, then transfer
functions can be derived that capture the input-output behav-
ior of the individual components of the system.
These transfer functions are determined by investigating
individual cause-effect relationships in which step inputs are

Figure 1. (above) JAK/STAT signaling pathway induced
by IL-6 in hepatocytes.
Chemical Engineering Education

Figure 2. Block diagram representation of signaling pathway implemented in Simulink.

used to excite the system. It is then possible to derive the transfer function by numerically determining parameters, such that
the difference between the response of the nonlinear model and the transfer function model is minimized.
The following dynamic relationships were identified as important for describing signaling through the JAK/STAT pathway:
D Effect ofIL-6 concentration on the receptor complex concentration
- Effect of changes in the concentration of the receptor complex on concentration of STAT3 in the nucleus
- Effect of concentration of nuclear STAT3 on concentration of formed SOCS3
D Effect of concentration of SOCS3 on the receptor complex concentration that can participate in cell signaling
The last of these four dynamic relationships is responsible for the feedback effect in the pathway. An illustration of the block
diagram can be found in Figure 2.
It should be noted that an increase in IL-6 concentration will lead to an increase in receptor complexes that participate in
signaling, and an increase in the number of receptor complexes will also lead to more signaling and a larger amount of nuclear
STAT3. More nuclear STAT3 will lead to increased transcription and translation of the plasma proteins involved in the APR,
while at the same time it leads to the formation of higher levels of SOCS3. SOCS3, on the other hand, has a negative effect on
the activity in the pathway as it prevents phosphorylation of STAT3 by binding to the receptor complexes.
The concentration of IL-6 is used as the input for the system and the concentration of nuclear STAT3 is used as the output of the model.
In order to identify the transfer functions, the cell is assumed to be at steady state with a constant input of 3.0E-4 nM of IL-6,
resulting in a concentration of the phosphorylated receptor complex (IL6-gp80-gpl30-JAK*)2 of 6.973E-4 nM, a concentra-
tion of SOCS3 of 0.1047 nM, and a concentration the nuclear STAT3 dimer (STAT3N*-STAT3N*) of 0.1048 nM. The cell is
perturbed from the steady-state by a step change of �10% in the concentration of IL-6, which serves as the input to the system.
The obtained output trajectories are used for identification of the following transfer functions:
(IL6- gP80- gP130- JAK)2 5.45
G, =
IL - 6 1.65s + 1

STAT3N* - STAT3N* 320.92

- IL6 - gP80 - gP130 - JAK") -0.03462s2 +0.4462S+ 1

G SOCS3 e06�
STAT3N* - STAT3N* 1.08s +1

(IL6 -gP80 -gP130- JAK* )2 0.0019
SOCS3 1.2s
SOCS3 1.2s +1

Vol. 41, No.3, Summer 2007

Steady State
input IL-6


/ Nonlinear
S--------- Linear

6 \ %

0 5 10 15 20 24
Time (hr)

Figure 3. Dynamic response of (IL6-gp80-gpl30-JAK*)2
complex for �10% step change in the IL-6 concentration
around the steady state (0.5 pMIL-6 concentration).

Figure 4. Dynamic response of STAT3N*-STAT3N*
complex for �10% step change in the IL-6 concentration


0.06 r

0 5 10 15 20 24
Time (hr)

Figure 5. Dynamic response of SOCS3 for 10% step
change in the IL-6 concentration about the steady state
(0.5 pM IL-6 concentration).

A comparison of the response of the original nonlinear
system and the one obtained from the transfer function model
is shown in Figures 3, 4, and 5. It can be concluded that the
linear transfer function model can adequately represent the
behavior of the original (nonlinear) system. It should be noted
that this first set of simulation experiments was performed
for the sole reason of determining the quality of the fit of the
transfer function models to the response generated by the
nonlinear system. It is also important to keep in mind that
the linear approximation, resulting from the use of transfer
functions, will only be able to represent the original nonlinear
system for excitations near the conditions for which the linear
model was derived.
A second experiment was run using the identified transfer
function model. For these simulations, it was assumed that
the effect of SOCS3 on the phosphorylation of STAT3 had
been removed from the cell, as shown in Figure 6, and in the
block diagram, shown in Figure 7. This effect is similar to a
SOCS3 knockout cell where SOCS3 is not produced, which
has medical significance associated with certain types of
cancers. The only difference between a SOCS3 knockout cell
and the behavior simulated here is that the feedback part is cut
open after the formation of SOCS3 instead of before.
It can be observed from Figure 8 and Figure 9 that the
signal is not down-regulated due to the absence of the effect
of SOCS3 on the system. The receptor complex (IL6-gp80-
gpl30-JAK*)2 (Figure 8) and the nuclear STAT3 dimer

Figure 6. JAK/STAT signaling pathway induced by IL-6
in cells where the effect of SOCS3 on phosphorylation of
STAT3 has been removed.

Chemical Engineering Education

-""...... Linear

....------- --.



10 15 20 24
Time (hr)


0.16 ... ...... ....................................

0.14 /

---- ------ Linear


0 5 10 15 20 24
Time (hr)

A Figure 7. (above) Block diagram of the "open-loop"
signaling pathway implemented in Simulink.

4 Figure 8. (left) Dynamic response of (IL6-gp80-gpl30-
JAK*)2 complex for �10% step change in the IL-6 concen-
tration around the steady state (0.5 pM IL-6 concentra-
tion) in SOCS3 knockout cells.

V Figure 9. (below, left) Dynamic response of STAT3N*-
STAT3N* for +10% step change in the IL-6 concentration
around the steady state (0.5 pM IL-6 concentration) in
SOCS3 knockout cells.

(STAT3N*-STAT3N*) (Figure 9) show a larger deviation
from the steady-state value when compared to the closed-
loop responses shown in Figures 3 and 4. Moreover, the
comparable open-loop response from the nonlinear and the
transfer functions indicate that cell behavior can, locally, be
adequately described by the transfer function model.

The presented model has been used at several points
throughout the Process Dynamics and Control course taught
in the chemical engineering department at Texas A&M
1) It is used during the first week of the semesters when
different systems that include feedback control are
introduced to make the students aware of how often they
come in contact with such systems.

2) The model is revisited when the material about deriv-
ing linear transfer functions from data is covered. In
this specific case the data is generated by the original

Vol. 41, No.3, Summer 2007

Steady State output


nonlinear model whereas the linear transfer functions
represent the model to befit to this data.

3) Since the model contains 11 ,,1. ' feedback regula-
tion, it is also used when the effect of i~. ,.,1 I feedback
control on a system is discussed.

Using the same example throughout the semester allows
students to participate in several steps of modeling and model
validation, rather thanjust performing individual tasks. Also,
this model describing a signal transduction pathway is used
alongside models teaching traditional chemical engineering

This paper presented a case study in which a signal transduc-
tion pathway was represented as a block diagram, and linear
transfer function models were identified in individual blocks
for perturbations of the model around a steady state.
The system behavior was broken up into four components,
and each part represented the effect a change in the concen-
tration of one component has on others present in the signal
transduction pathway. This was illustrated in how SOCS3
serves as an inhibitor of the signal transduction pathway,
and how the effect SOCS3 has on the signaling activity can
be appropriately described by negative feedback in the block
diagram representation of the system.
Also shown was how the identified model correctly repre-
sented the behavior of the original system for the three key
components chosen. Simulation studies have been performed
on SOCS3 knockout cells, which can be compared to the
"open-loop" behavior of the system, as there is no effect of
SOCS3 on the signal transduction pathway. It was found that
our identified model appropriately described the behavior of
the SOCS3 knockout cell in this way.

The presented case study can serve as an example for il-
lustrating feedback regulation in cell signaling for process
control education.

The authors gratefully acknowledge partial financial sup-
port from the ACS Petroleum Research Fund (Grant PRF#
43229-G9) and from the National Science Foundation (Grant
CBET# 0706792).

1. Parker, R.S., and FJ. Doyle, "Control-Relevant Modeling in Drug
Delivery," Advances in Drug Delivery Reviews, 48, 211 (2001)
2. Rao, R.R., C.C. Palerm, B. Aufderheide, and B.W. Bequette, "Auto-
mated Regulation of Hemodynamic Variables," IEEE Engineering in
Medicine and Biology Magazine, 20(1), 24 (2001)
3. Hahn, J., T. Edison, and T. E Edgar, "Adaptive IMC Control for Drug
Infusion for Biological Systems," Control Engineering Practice, 10(1),
45 (2002)
4. Asthagiri, A.R., and D.A. Lauffenburger, "A Computational Study of
Feedback Effects on Signal Dynamics in a Mitogen Activated Protein
Kinase (MAPK) Pathway Model," Biotechnology Progress, 17, 227
5. Bhalla, U.S., and R. Iyengar, "Emergent Properties of Networks of
Biological Signaling Pathways," Science, 283, 381 (2001)
6. Freeman, M., "Feedback Control of Intracellular Signaling in Develop-
ment," Nature, 408, 313 (2000)
7. Kholodenko, B.N. "Negative Feedback and Ultrasenstivity Can Bring
about Oscillations in the Mitogen-Activated Protein Kinase Cascades,"
Eur. J. Biochem., 267, 1583 (2000)
8. Sontag, E.D., "Some New Directions in Control Theory Inspired by
Systems Biology," IEE Proceedings Systems Biology, 1, 9 (2004)
9. Heinrich, PC., I. Behrmann, G. Muller-Newen, E Schaper, and L.
Graeve, "Interleukin-6-type Cytokine Signaling Through the gpl30/
JAK/STAT Pathway," Biochemical Journal, 334, 297 (1998).
10. Heinrich, PC., I. Behrmann, S. Haan, H.M. Hermanns, G. Muller-
Newen, and E Schaper, "Principles of Interleukin (IL)-6-type Cytokine
Signaling and its Regulation," Biochemical Journal, 374, 1 (2003)
11. Singh, A.K., A. Jayaraman, and J. Hahn, "Modeling Regulatory Mecha-
nisms in IL-6 Signal Transduction in Hepatocytes," Biotechnology and
Bioengineering, 95, 850 (2006) 1

Chemical Engineering Education

Random Thoughts...



North Carolina State University

n workshops, I push teaching methods such as active and
cooperative learning that make students more responsible
for their own learning than they are when instructors
simply lecture.1, 2] I believe in truth in advertising, though,
and make it clear that the students will not all be thrilled with
the added responsibility and some may be overtly hostile to
it."�3 If you use those methods, you can expect some of your
students to complain that you're violating their civil rights
by not just telling them everything they need to know for the
test and not a word more or less.
When you use a proven teaching method that makes stu-
dents uncomfortable, it's important to let them know why
you're doing it. If you can convince them that it's not for
your own selfish or lazy purposes but to try to improve their
learning and grades, they tend to ramp down their resistance
long enough to see the benefits for themselves. I've developed
several mini-sermons to help with this process. If any look
useful, feel free to appropriate them.

Student: "Those group activities in class are a waste of time.
I'm paying tuition for you to teach me, not to trade ideas with
students who don't know any more than I do!"
Professor: "I agree that my job is to teach you, but to me
teaching means making learning happen and not just putting
out information. I've got lots of research that says people
learn through practice and feedback, not by someone telling
Vol. 41, No. 3, Summer 2007

them what they're supposed to know. What you're doing in
those short class activities are the same things you'll have to
do in the homework and exams, except now when you get
to the homework you will have already practiced them and
gotten feedback. You'll find that the homework will go a lot
more smoothly and you'll probably do better on the exams.
(Let me know if you'd like to see that research.)"

S: "I don't like working on homework in groups- why can't
I work by myself?"
P: "I get that you're unhappy and I'm sorry about it, but I've
got to be honest with you: My job here is not to make you
happy-it's to prepare you to be a chemical engineer. Here's
what's not going to happen in your first day on the job. They're

Richard M. Felder is Hoechst Celanese
Professor Emeritus of Chemical Engineering
at North Carolina State University. He is co-
author of Elementary Principles of Chemical
Processes (Wiley, 2005) and numerous
articles on chemical process engineering
and engineering and science education,
and regularly presents workshops on ef-
fective college teaching at campuses and
conferences around the world. Many of his
publications can be seen at edu/felder-public>.

� Copyright ChE Division of ASEE 2007

not going to say 'Welcome to the company, Mr. Jones. Tell
me how you like to work-by yourself or with other people?'
No. The first thing they'll do is put you on a team, and your
performance evaluation is likely to depend more on how well
you can work with that team than on how well you solve dif-
ferential equations and design piping systems. Since that's a
big part of what you'll be doing there, my job is to teach you
how to do it here, and that's what I'll be doing."
S: "Okay, but I don't want to be in a group with those morons
you assigned me to. Why can't I work with my friends?"
P: "Sorry-also not an option. Another thing that won't hap-
pen on that first day on the job is someone saying 'Here's a
list of everyone in the plant. Tell me who you'd like to work
with.' What will happen is they'll tell you who you're work-
ing with and you won't have a vote on it. Look, I can show
you a survey in which engineering alumni who had been
through extensive group work in college were asked what
in their education best prepared them for their careers.[4] The
most common response was 'the groups.' One of them said
'When I came to work here, the first thing they did was put
me on a team, and you know those annoying teammates back
in college who never pulled their weight-well, they're here
too. The difference between me and people who came here
from other colleges is that I have some idea what to do about
those guys.' In this class you're going learn what to do about
those guys."

S: "I hate these writing assignments and oral reports you keep
making us do. One reason I went into engineering was to get
away from that stuff."
P: "I'm afraid there's no getting away from it-quite the
contrary. Let me give you an example. A few years ago an
engineer who was on campus interviewing students for jobs
and summer internships came in to talk to an engineering
class that was getting frequent communication assignments
and complaining bitterly about it. He started by writing on the
board a list of everything he did on his job, from designing
and pricing process equipment to writing reports and memos
and talking to people. Then he had the students get in groups
and speculate on what percentage of his time he spent on each
of those activities. They all thought 90% of his time went to
the technical stuff but it was actually more like 10%. He said
that in fact about 75% of his time was spent on writing and
speaking-to coworkers, his boss, people reporting to him,
people in other divisions, and customers and potential custom-
ers -and that his advancement on the job depended heavily
on how effectively he communicated with those people.
He also said-and this was what really got the students'
attention-that the main thing he was looking for when he

interviewed students for jobs was the ability to communicate
effectively. Most industrial recruiters we bring in here will tell
you the same thing. Since communication skill is something
you'll need to get ajob and succeed in it, you'd better acquire
it while you're here, and you will in this class."

And that's that. My suggestion is to put your own spin on
those sermonettes and trot them out when the right occasion
presents itself. While I don't guarantee that they will immedi-
ately convert all students into believers-in fact, I guarantee
they won't-my experience is that at least they'll keep student
resistance down enough to enable the teaching methods we've
been talking about to achieve their objectives.
Let me give you one more encouraging word about student
resistance to learner-centered teaching methods. My colleague
Lisa Bullard uses cooperative learning in both an introductory
sophomore engineering course and the capstone senior design
course. She once told me that she has always had problems
with group work in the sophomore class but never with the
seniors until one semester, when she got the Design Class
from Hell. The students complained constantly about having
to work in groups, many teams were dysfunctional, and things
generally went the way they always had in the sophomore
class only worse.
Lisa wracked her brains trying to figure out what was differ-
ent about the design class that semester and couldn't think of
a thing-and then she got it. Up until that year the seniors had
previously been in her sophomore class and so were accus-
tomed to group work. She had not taught this group of seniors
before, however, and so she was experiencing the headaches
that normally come when students first encounter active and
cooperative learning. So if you find yourself experiencing
those headaches, remember two things. First, you're equip-
ping students with skills that will serve them well throughout
their careers, whatever those careers may be. Second, you're
making life much easier for yourself or colleagues who teach
those students in subsequent courses using the same methods.
It's worth a few headaches.

1. Prince, M.J., "Does Active Learning Work? A Review ofthe Research,"
J. Engr. Education, 93(3), 223 (2004), public/Papers/PrinceAL.pdf>
2. Smith, K.A., S.D. Sheppard, D.W. Johnson, and R.T. Johnson, "Pedago-
gies of Engagement: Classroom-Based Practices," J. Engr. Education,
94(1), 87 (2005)
3. Felder, R.M., and R. Brent, "Navigating the Bumpy Road to Student-
Centered Instruction," College Teaching, 44(2), 43 (1996), www.ncsu.edu/felder-public/Papers/Resist.html>
4. Felder, R.M., "TheAlumni Speak," ( b....I.. i , 1,t..,,... 34(3), 238
(2000), 7

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

Chemical Engineering Education

--- - ^ K.___________________________-


A Rich Prototype for Engineering Up-Scaling

Tennessee Tech University * Cookeville, Tennessee
Universidad Cat6lica del Norte * Antofagasta, Chile
University of California * Davis, California
Jn many widely used textbooks in chemical reaction
n n u s Pedro E. Arce is a professor and chair of the chemical engineering
engineering courses, such as Fogler,�11 Levenspiel,[2] and department at Tennessee Tech University. His interests in engineering
Carberry,[3 the derivation of the conservation equation for education are in active and collaborative engineering learning environ-
the species in a gas mixture, either a pore or pellet domain, ments. His research interests are centered on electrokinetic-hydrody-
the species in a gas mixture, either a pore or pellet domain, namics with applications to soft materials, high oxidation methods, and
is conducted by a "global" approach-where many assump- applied and computational mathematics.
tons and processes are hidden. These assumptions carry
tons and processes are hidden. These assumptions carry Mario A. Oyanader is an associate professor of chemical engineering
significant concepts associated with engineering scaling that at the Universidad Catdlica del Norte in Antofagasta, Chile. His interests
(if properly used) offer a powerful learning environment to in engineering education are in introducing "real world problems" to
students and bringing them into research at early stages of their ca-
train students in engineering scaling. This training is useful reers. His research interests are focused on chemical environmental
in handling current chemical engineering problems and it processes with applications to electrokinetic soil cleaning, contamina-
enhances student readiness to find solutions to these practical tion control, and water management.
situations. In fact, an educational environment that introduces Stephen Whitaker is professor emeritus at the University of California,
scaling as an effective learning tool leads to an excellent Davis. His interests in engineering education are in introducing students
to the fundamentals of science and engineering using a sequential
understanding of processes at the nano-, micro-, and macro- and calculus-based approach, and using up-scaling principles to
scales in students. This, in turn, offers an economical training derive engineering equations. His research interests are in transport
phenomena in porous media, volume-averaging methods, and transport
for students as they learn both fundamental principles and and reacting systems.
up-scaling simultaneously.

� Copyright ChE Division of ASEE 2007
Vol. 41, No.3, Summer 2007 18.

The catalytic pellet has several aspects that make an engi-
neering description of the fundamentals very challenging for
untrained readers, i.e., students. Concepts based on transport
phenomena are coupled with gas-solid (heterogeneous) cata-
lytic chemical reactions, in addition to geometrical parameters.
Students do not seem, however, to have much difficulty in
describing (conceptually) the physical chemistry as it happens
in the system at the microscale. Chemical engineering students
are familiar with hydrodynamics, diffusion, and chemical
reactions from freshman and sophomore courses. Thus, a
microscopic (and even a molecular) description is a logical,
and fairly simple, first step for students when describing the
physics of transport with chemical reactions inside a catalytic
pellet. On the other hand, the development of a description
at the macroscopic level is problematic. In fact, identifying
the proper mathematical language for a useful global or mac-
roscopic description sometimes becomes a bottleneck in the
learning process. This aspect, perhaps, led educators in the
past to "simplify" the mathematical and physical description
so that students are confronted with a simple model. This
approach, however, stifles the sequential and evolutionary
process of student learning. Instead, a macroscopic descrip-
tion may be easily achieved when the problem is viewed
from an up-scaling point of view. Basically, the connection
between micro and macroscopic description is an integration
of the former in a physical or geometrical domain (see further
description, below). This approach will produce a mixture of
"averaged" quantities and "point" variables. In order to close
the problem description, a connection between the two is
required. These concepts are rooted in general principles of
scaling and engineering approximations that are the subject
matter of this contribution. A byproduct of the approach is
that concepts from freshman and sophomore mathematics
courses become relevant and of enormous practical value
for the students. This leads to a successful marriage, rather
than to a divorce, between mathematics and physics for the
engineer in training.

An analysis of the literature shows that heterogeneous
reactions and catalysis are very popular subjects. Traditional
textbooks such as Levenspiel[4] introduce students to models
using an intuitive approach (see more below) that allows
them to compute concentration profiles and effectiveness
factors. Other textbooks with more sophisticated mathemat-
ics concentrate on an a priori analysis with implications to
practical aspects5 8]; within this framework, Aris[9] reported
useful techniques for obtaining information from reaction-
diffusion equations without actually solving such equations.
The spectrum of contributions could accommodate all levels
of trained readers between these two limits, and it would ap-

pear that there is nothing to be added from the expert point
of view.

Nonexperts, however-the students-may fare less well.
They may wonder how a complicated problem in two phases
with reaction on the walls may be modeled as a domain with
homogeneous reactions (see section below) by a simplistic and
intuitive approach. Those more mathematically gifted may
explore a more sophisticated description, but will not survive
the mathematical machinery in Aris.[10] Therefore, despite
expert contributions on the subject of transport and reaction in
heterogeneous media, there is a need for a systematic approach
to introducing nonexperts to the subject. This approach must
be based on first principles, must conclude with the overall
or macro-transport equations, and must be followed by the
complete and logical sequence of steps at the heart of the
scaling process. These concepts are so important in training
the future engineer, from both fundamental and practical
points of view, that disguising them does not seem to be a
useful and effective strategy.
The classic and intuitive approach to up-scaling used in
the literature for a porous domain (e.g., Levenspiel[41) usually
leads to confusion concerning homogeneous and heteroge-
neous catalytic reactions. This approach is based on a global1
balance for species A in an incremental volume of the pore
domain. If this balance is applied to Cartesian geometry,"111
then the result leads to the following differential equation
after the limiting process is invoked:

-VN + R (c A)

Eq. (1) in one dimension yields the following result after a
vague reference to Fick's law with an effective diffusivity,
D f

= Deff -d -- - RA (2)
at 9z az
In many cases, a first order consumption is considered and
Eq. (2) reduces to:
9cA _ 9 90%
- = Deff - - avkcA (3)
at Iz Oz
This equation should describe, according to the traditional
approach, a diffusion process with a heterogeneous cata-
lytic reaction in a pore domain. In many cases, a modified
constant is defined as k' = a k. Students in mass transfer
courses, however, have found an equation that closely
mimics Eq. (3):

d DC =z -k'cA (4)
9t Oz Oz

SThe word global is frequently used to hide the actual scalingprocess in
deriving the macrotransport or up-scaled equation for the domain under
Chemical Engineering Education

The pseudo-similarity between Eqs. (3) and (4) is obvious
because untrained students are not usually concerned with
specific details at this point; learning problems appear as soon
as students begin to compare the two equations. Eq. (4) has
been derived for the case of homogeneous reactions taking
place in the entire volume and with molar concentrations,
cA, expressed per unit of the entire volume. This is a remark-
able contrast with the situation in a catalytic pore domain, in
which reactions are heterogeneous, i.e., located on the surface
and not within the bulk of the domain. In addition, we face
two types of concentrations of species A-surface and bulk.
Obviously, if what a student has learned in the case of Eq.
(4) is correct, something else must be playing a role in Eq.
(3). One conclusion is obvious: Eq. (3) is totally misleading
since, from the point of view of the untrained reader, we
have a chemical reaction homogeneously distributed in the
domain and with concentrations of species A per unit volume
of such volume. No surface reaction, surface concentration,
and connection with bulk concentration are identified at this
point in the learning process.
In order to highlight the reasons why Eq. (3) is mislead-
ing, an analysis of the chemical and physical situation at a
catalytic cavity or pore (see Figure 1) is performed at the
microscopic2 level. We consider here a two-phase system
consisting of a fluid phase, identified as the y-phase, and a
solid phase, identified as the x-phase. The analysis founda-
tions of diffusion and reaction in this two-phase system call
for the use of the species continuity equation in the y-phase
and the species jump condition at the catalytic y-x interface.
The species continuity equation for this system, in the form

Figure 1. Sketch and basic nomenclature of the pellet
and pore domain.

2The term microscopic here is used in the sense of continuum mechanics,
i.e., local means a point in the finite domain of analysis.
Vol. 41, No.3, Summer 2007

of molar fluxes[12]), can be written as:

-V NA + RA

A=1,2,3,....,N (5)

This equation, however, fails to identify the species velocity
as a crucial part of the species transport equation. To avoid
confusion about the mechanical aspects of multicomponent
mass transfer, Eq. (5) is suggested to be written in the fol-
lowing form11"1:

- V. (CA VA) + RA

A=1,2,3,....,N (6)

Eq. (6) needs boundary conditions, and, when surface trans-
port�141 can be neglected, the jump condition takes the form:


( CaVA n + As, at the - r int erface,

A= 1,2,3,....,N (7)
This equation can be easily written in terms of the molar
flux by recognizing that N = cAy v . Furthermore, Eq. (7)
can be derived by a shell balance around the interfacial re-
gion,a13 14] and the jump condition can be viewed as a surface
transport equation that forms the basis for various mass
transfer boundary conditions that could take place at the
phase interface.[151
At this point, several observations are in order. First, the
microscopic transport and reaction model presented in terms
of Eq. (5) or, alternatively, Eq. (6) and Eq. (7) implies and
describes a very different situation with respect to the one
that seems to be implied by Eq. (3), which has obvious dif-
ferences with respect to Eq. (4). Second, a reaction term
in the microscopic model is located in the jump condition
given by Eq. (7) and therefore implies a reaction located at
the fluid-solid interface. An additional reaction term is also
present in the species continuity equation. Third, there are two
different types of concentrations in the model, i.e., a surface
concentration (moles per unit area), cA,, is used in the jump
condition of Eq. (7) while a bulk concentration (moles per
unit volume), cA , is used in the species continuity equation.
A similar pattern has been used for the two reaction terms,
one in Eq. (6) and the other in Eq. (7).
The dilemma, for students or apprentices, becomes clear by
comparing the so-called global approach and the microscopic
approach presented above. While the microscopic approach
seems to capture the essential physicochemical situation in the
pore domain, it leads to a very different description than one
based on the global approach. This description, however, is
consistent with the physical chemistry involved in the process.
On the other hand, the global approach seems to arrive at an
equation that fails to capture the key aspects of the transport
and reaction process. The objective of the next section is to
reconcile these two results by introducing a process of up-
scaling the microscopic model to arrive systematically and

Figure 2. Different scales associated with a catalytic reactor.

without confusion at the correct macro transport equation for
the pore domain.

In this section, we present two of the different scales in-
volved in a catalytic process. Students are usually familiar
with the reactor scale that produces a given chemical, but
may not be aware of other scales also associated with this
process. Figure 2 shows the rich spectrum of scales associ-
ated with packed-bed reactors, i.e., the five-level hierarchy
involved in a catalytic process. Level I is the packed-bed
reactor scale, and a closer look inside the reactor domain
reveals a Level II scale, associated with the different regions
in the reactor domain. These regions could be different ei-
ther in their morphology or in their function (see Arce and
Ramkrishnal161), although in many cases they are considered
uniform (see Froment and Bischoff171]). An analysis of these
different regions shows they are made of individual catalyst
pellets, i.e., Level III is the catalyst pellet. Level IV is the
one associated with the structure of individual pellets, i.e.,
the domain of the micropores. Finally, each micropore could
be actually different and, therefore, Level V constitutes the
individual pore domain. The flow of information goes from
the smallest length scale to the largest length scale. In other
words, the process of up-scaling starts at Level V and finishes
at Level I, the packed-bed reactor. In this contribution we will
show how to proceed with the up-scaling only with Level V,
i.e., the pore domain, and Level IV, i.e., the catalytic pellet
domain. Other considerations on up-scaling can be found in

Whitaker[181 and Arce, et al.["]
In order to accomplish the
up-scaling process in a rigorous
manner, without confronting all
the geometric complexities, we
will consider the catalytic pellet
made of a capillary bundle.[19 21]
This capillary bundle is as-
sumed to be made of cylindrical
tubes 2L long, with a radius, ro,
and within a pellet of a square
section b2 (see Figure 3). This
pellet domain therefore has a
porosity given by rr 2/b2.
The first step in the scaling
analysis of the model pellet de-
scribed above is to identify the
microscopic description of the
transport and reaction process
taking place at the pore (capil-
lary) level. This description is
based on the capillary model
described above and is restricted

to the case of dilute solutions of
species A. Since the pore domain is "sealed" at one end,
convective transport can be neglected and the general species
continuity [Eq. (5)] takes the form:
0ces 1 D( &cr 2c
-CA D D ri- + z ' in the - phase (8)
at r Or Oz Oz2

Eq. (8)3 also assumes that a homogeneous circumferential
distribution of catalyst is on the internal surface of the pore
domain and therefore a symmetrical condition on the angular
direction can be assumed. Also, there is no homogeneous
reaction, i.e., Ry = 0. In addition, Eq. (8) requires bound-
ary conditions that can be obtained from the jump condition
given by Eq. (7). This condition implies, for the different
boundaries, that:

CA, = cA,�

CA= 0

-D = kcas
LCAr 0





The initial condition is not stated, but could be any sym-
metric concentration distribution present initially within the

3For the steady-state version of this equation, using the concept of mo-
lecularflux, NA, one can write Eq. (13) as V A - 0. This is a similar
looking equation to the incompressibility condition in fluid mechanics, V v
SO, where v is the hydrodynamic velocity of the fluid (see, for example,
Chemical Engineering Education

pore domain. Eq. (9) assumes very good mixing at the
pore mouth with the implication that the mass transfer
coefficient, k , or alternatively, the Sherwood number,
is very large. Eq. (10) represents a symmetry condition
associated with a capillary tube of length 2L. Eq. (11)
clearly captures the interfacial nature of the boundary,
as we observe both type of concentrations cAy and cAS
playing a role in the equation.
The microscopic model described in Eqs. (8)-(12) is
a rigorous description of the physical chemistry pro-
cess taking place at the pore domain, and students can
identify this type of model successfully and without
confusion. Students can apply the knowledge acquired
in physical chemistry and engineering mathematics to
successfully achieve the model.
The next step in the up-scaling process is to recognize
what geometrical dimensions are most relevant to de-
scribe the pore domain in less detail. For example, the
change of the concentration, along the axial direction, z, is
important information needed to describe the performance of
the pore domain. From this point of view, the "local" variation
of the concentration related to the cross-sectional area may be
averaged. This approach has been inherently associated with
an integration of the microscopic model to reach a macro-
scopic model in the domain. In short, the student is looking
to achieve an elimination of the explicit presence of some of
the independent variables to obtain a less detailed description
of the domain.4 The process mimics closely the concept of
average values of a function, as opposed to the point or local
values for such a function. This is another concept already
used by the students in applied mathematics or statistics
courses. Thus, students are once more introduced to the notion
of an average value of a function, f(x) - a concept encountered
previously in calculus. In addition, averaging approaches and
the connection between averaging and integrals is reviewed,
as well as the relation between macroscopic description and
integrals. The connection between micro, differential, and
local concepts is also discussed. By the end, students are
well aware that a microscopic-level model is connected by
integration, i.e., by up-scaling, to a macroscopic-level model
that applies to the domain, i.e., the control line, surface, or
volume that is of interest.
Now, the following definition of area-average for the con-
centration is useful:
1 r=ro
=-- 21rcC dr (13)

Eq. (13) is a useful averaging tool5 to conduct an integration
of the species continuity in Eq. (8). The procedure involves
algebraic steps where students have the chance to apply what
4This process is related to the homogenization of the porous medium.1t2"
SThe equation may be viewed, in fact, an integral operationfor thefunc-
S. thatyields an averaged value, (cA ), ofsuch function in the cross
sectional area.
Vol. 41, No.3, Summer 2007

Figure 3. Cylindrical pore domain and its nomenclature.
they learned in the supporting mathematics courses of the
engineering curriculum (see Arce, et al.,[10]). The final result
is the following area-averaged equation:
S(c.A 0 (c ) 2k
at D 2 0 AS (14)
In arriving at Eq. (14), the use of the boundary condition
given by Eq. (11) was invoked and, therefore, the heteroge-
neous reaction present in this equation has been integrated
with the governing differential equation. The process just
described has led a heterogeneous reaction to look like a ho-
mogeneous-type reaction, given in Eq. (4). The omission of
this aspect of the analysis is a crucial learning failure for the
students and will undoubtedly lead to confusion. The up-scal-
ing approach used above successfully highlights the source
of the reaction term in Eq. (14). The process of integrating
boundary conditions with differential equations to produce
area-averaged or macro-transport equations is typical of all
transport process in multiphase systems.
If students wish to solve Eq. (14), they will encounter dif-
ficulty because the equation shows two types of variables,
i.e., the area-averaged bulk concentration, (cA )Y, and the
surface concentration, c . Therefore, we need to find a
relation between these two variables. Otherwise, the up-
scaling approach would fail and we would need to return to
the original microscopic model in pore domain. In fact, the
approach would fail without a method of closure. There are
several options to implement such a method. [24 28 We will use
a rather elementary approach here based on approximations
that enhance the student's engineering training.
By using the flux boundary conditions at the interface of the
pore domain, the following estimation can be made:

D [A 0 r = O (kcA r=o) (15)

This equation can be rearranged into the form:

CA 0 C c~A r- o = hO- (16)
CA ro Di
From this result, it is possible to identify certain limiting
situations. If kro/D <<1, then the following result would

(CA) CAS (17)
Therefore, in the limiting situation, one could use (cA} )7r
CAs6 to obtain the area averaged equation given by:

(cA ) 0 (CAI) 2k
D -c ( at 9Z2 ro
If the condition kr /D <<1 fails, other closure procedures are
available (see Payne, et al.,[29] and Oyanader & Arce[301).
We are now in a position to offer several useful observations
from the student learning point of view. First, a comparison
between Eq. (18) and Eq. (3) highlights several differences.
Eq. (18) is in terms of area-averaged concentrations and Eq.
(4) fails to identify this important difference. Second, equation
(18) is only valid for certain cases, i.e., slow reactions, and
therefore has limitations. It is also not of a general validity as
Eq. (3) seems to indicate. This limitation is the same type of
constraint found, for example, in the case of the well-mixed
model for CSTR. It is only valid if this particular limit holds,
and many practical situations need a more realistic type of
reactor model (see, for example, Levenspielf21). Third, the
reaction term in Eq. (18) is a source term rooted in the het-
erogeneous, catalytic reaction present at the wall of the pore
domain, as was clearly captured by Eq. (11). An up-scaling
procedure located this reaction term in the macro-transport
Eq. (18). For example, if other homogeneous reactions were
also present in the y-phase, they would appear in Eq. (18) after
originally being captured by Eq. (8). The rate coefficient for
these reactions would differ from that of heterogeneous pro-
cesses. For example, the rate coefficient 2k/ro in the reaction
term identified in Eq. (18) shows the pore radius indicating
that this coefficient is something other than a true homogenous
rate constant. Fourth, by introducing an up-scaling approach
and avoiding misconceptions, we have created a very rich
learning environment for the students where approxima-
tions, closure procedures, and limitations of the resulting
up-scaled or macro-transport equations are all transparent to
the students. Moreover, all basic mathematical skills learned
in courses required as prerequisites for the engineering cur-
riculum are now of practical use, and no mathematical skills
beyond these are necessary!

6This type of approximations is very popular in cases of reaction engineer-
ing problems in homogenous systems such as the "well-mixed" model
for the CSTR that educators have used widely. Unfortunately, the same
approach seems to have been overlooked in multiphase systems.

Moreover, all basic mathematical skills learned
in courses required as prerequisites for the en-
gineering curriculum are now of practical use,
and no mathematical skills beyond these are

Once we have up-scaled the smallest level, V (the pore
domain), it will be useful to show how this information can
be used in up-scaling the system to the next level, IV (the
catalytic pellet domain). We realize the porosity of the pellet
is a parameter that plays an important role and the intrinsic
averaged, scaled-up Eq. (18) is perhaps not the most useful
from a reactor design point of view, since the reactor term
S(C,,) is the unit volume of the fluid phase. In the de-
scription of transport and reaction processes of real porous
systems, 3133] it is traditional to work with the reaction per
unit volume of the porous medium since the ratio of the fluid
volume to the volume of the porous medium is the porosity,
i.e., E =V / V; V=V +V in the notation of Figure 1. By using
the porosity in Eq. (18), one can find the reaction rate per unit
volume of porous media: 121
R = (CA (19)
Eq. (19) represents the usual reaction term found in the reac-
tion design literature. 3134] If one identifies 2e ro as the unit
surface area per unit volume of the porous medium (catalysts
phase) and denotes it by a , Eq. (19) can be written in the usual
form, Ry = a k (CA )Y. Another important quantity that appears
in the process of up-scaling is the diffusivity modified by the
porous medium. The diffusive flux of "A," per unit volume
of porous media for the z-direction of the porous domain of
Figure 1, can be written as.J121

N -D d(c) (20)
Traditionally, a tortuosity factor, T,14 is included to accom-
modate the geometry of the porous medium. Thus, Eq. (20)
is expressed as:

D d(cA) (21)
T dz
The term D /T can be defined as an effective diffusivity of
the medium, Dff, that leads to the usual equation for the flux
in a porous medium:

N = -D d(A)' (22)
By using Eq. (19), written in terms of a , and Eq. (22), Eq.
(18) leads to the up-scaled version of the conservation equa-

Chemical Engineering Education





Physical Picture
Figure 4. Pedagogical sequential steps associated with up-scal

tion for the catalyst pellet (porous medium) usually seen in
textbooks: [135,361

(cA )

D,, 2 avk(c
0 2 ACA), ) -
D f-- avk(Ca )"

Eq. (23) has been derived by a very systematic and pro-
gressive-learning up-scaling approach based on the species
continuity equation and a microscopic description of the
transport and reaction processes at the pore and pellet domain
levels. The approach followed methods well-rooted in a sound
pedagogical environment (see section IV, below) and used a
level of mathematics originating in courses engineering stu-
dents are required to take. In fact, students are surprised by
the level of usefulness of the concepts used in the up-scaling
approach outlined in this section. Comments and discussion of
the pedagogical aspects are presented in the section below.

The concept "Principal Objects of Knowledge," or POK's,
was introduced in the Colloquial Approach l . ii-,, ii,,,.i -1
to enhance student learning and promote a more efficient
study habit in engineering students, in order to master dif-
ficult concepts. The tool was extended to include a variety of
'u111i. I' I in fluid mechanics, mass and energy balances,
and continuum theory. The role of the catalyst particle or
pellet as a rich example of POK for students interested in
learning about transport in porous media and heterogeneous
reactions is identified in this contribution. Principle Objects
of Knowledge are learning enhancers, at an intermediate level
of complexity, that help students by building blocks of knowl-
edge. By looking at Figure 2, catalytic pellets are located at a
level (IV) within the spectrum of scales. Studying transport
and reaction at this level allows students to work efficiently at
all levels. In fact, if packed-bed reactors are assumed uniform,

level IV (the macro-transport equation of the catalytic
pellet) becomes the prototype-design equation for the
packed-bed reactor.'"1
The catalytic pellet is an incubator of learning for
many situations relevant in current chemical reacting
systems. For example, the macroscopic equations
derived in Section III, may be viewed as the design
equations of a micro-reactor housed in the pellet
domain. This has obvious implications for processes
that inherently have associated many scales ranging
from the molecular-, nano-, and micro-scale processes,
such as in transcellular transport, tissue engineering,
pharmaceutical, environmental, and microelectronic
applications. Examples of porous domains related
to these applications may include soils, membranes
in separation and purifications, fuel cells and high
ing. performance batteries, biological porous and fibrous
media (such as human tissues and materials in drug
delivery), and air-cleaning devices. In other words, the
catalytic pellet is a multiscale-domain environment that offers
a powerful prototype for efficiently studying many multiphase
and multicomponent systems (see, for example, Arce 401 and
Arce, et al.,"11). Today, these applications are very relevant to
many engineering majors - including chemical, biomedical,
and environmental engineering. In short, the catalytic pellet
becomes a very flexible POK to help students learning in many
multiphase and multiscale systems of practical interest.
Therefore, appropriate student training in up-scaling vari-
ous scale levels identified in a catalytic process (see Figure
2) gives them a sound background to attack problems within
a wide range of multiphase systems. In short, by following
this up-scaling approach, students will learn about connecting
physics and mathematics, understanding the role of differ-
ent scales, and realizing that the new and frontier chemical
engineering applications of today's technology are not so far
from the classical ones - when viewed from an up-scaling
The sequence identified in Figure 4 represents a sound
pedagogical environment that follows a systematic and pro-
gressive approach41,42] to derive engineering equations in a
catalyst pellet that can be up-scaled to yield macrocoscopic
equations. This approach is more efficient and yields much
less confusion than those currently used in textbooks based
on a more "unit-operation" point of view.
General concepts at the microscopic level of the porous
domain dominate the first two steps of the sequence identi-
fied in Figure 4, as it was illustrated in Sections II and III of
this contribution. Specific microscopic details related to the
pore domain are addressed in the next step (the engineering
equation 38,421) of the sequence. The last step of the sequence
is focused on the up-scaling process. The engineering model
becomes a rigorous mathematical description of the physi-
cal and chemical processes taking place in the domain. This

Vol. 41, No.3, Summer 2007

model is clearly valid at every point of the domain and,
therefore, is undoubtedly connected with the idea of a mi-
croscopic level of the physical system. Solution approaches
should not be emphasized here, just the correct description
of the physics and chemistry taking place is enough. The last
step deals with possible ways to obtain information from the
engineering model.
What is interesting and useful, from the pedagogical
point of view in the sequence of Figure 4, is that students
in engineering majors are quite comfortable with describing
(conceptually) basic or microscopic physical aspects of a
problem, and identifying a mathematical model afterward
that mimics closely the physics that they have visualized.
For example, it is quite rational to introduce students to geo-
metrical and physical chemistry concepts in a pore domain,
within a catalytic pellet, where diffusion and (heterogeneous
catalytic) reactions take place. Heterogeneous reactions and
catalysis must, of course, be introduced separately from the
kinetic concepts, as they usually are in physical chemistry
courses. Diffusion is present as the only transport mechanism
inside the pore cavity, so that reactants can travel from the
bulk to the surface of the pore domain only by gradients of
concentrations. Since the reaction is catalytic, students have
no problem recognizing it is located at the walls of the pore
domain and, therefore, no reaction is present in the bulk of
such pore, unless by-products of the process are present. These
could be produced by homogenous reactions.
Furthermore, students who are familiar with thermal surface
sources can trivially associate the transport and reaction situa-
tion in the pellet with a process at the boundary of the domain
where conductive fluxes and sources (i.e., reaction) must be
involved. In other words, the catalytic pellet is the equivalent
situation to that of the heat conduction and heat generation
with heterogeneous sources (see, for example, Whitaker[43]),
a concept already introduced in the heat transfer course. In
fact, students who have already taken the proper heat and
mass transfer courses usually find the pore and pellet situation
a simple variation of the examples they already encountered
in these subjects. Moreover, the analysis and study of the
catalytic pore and pellet by following the sequence listed in
Figure 4 reinforces the concepts previously learned.
Aris[9] stated that there are many useful ways to extract
information from a model without actually solving the model
equations. In the case under analysis, up-scaling approaches
are an effective way to accomplish this. Although the detailed
solution of the model is not achieved in the process of up-
scaling, students learn a great deal about the system behavior
by implementing the approach. Another important point to
make is that the mathematics required in the process are of
the same level learned in undergraduate-level courses. Thus,
a marriage between mathematics and physics has been born
in students' minds. This connection fosters an excellent in-
tegration of otherwise divorced components or pieces of the
engineering curriculum.

The qualitative assessment, based on the feedback from
students on the implementation of up-scaling approach in
two different courses at the FAMU-FSU College of Engineer-
ing, has shown a very promising trend. The students have
been able to clearly perform better in exercises that involve
conceptually the identification of quantities related to bulk
parameters - such as averaged concentrations, as opposed to
local concentration values - in a fluid phase interacting with
a solid phase through a catalytic reaction. Also, students learn
sequentially about effective diffusivity in a porous domain
and its differences with respect to molecular and Knudsen
type diffusivities.
Student interviews at the end of the course have confirmed
they mastered the concepts and achieved, in general, a deeper
understanding of the different aspects in a heterogeneous
system with diffusion and reaction. A similar outcome was
observed in the kinetic courses taught at Tennessee Tech.
Students felt very comfortable obtaining the description of
the system and identifying boundary conditions for the model.
In addition, they welcomed the discussion of the closure pro-
cess and the implication to the approximations involved in
applying the results of the model. Furthermore, the platform
of knowledge developed seems to be a very good tool to at-
tack other more sophisticated systems, such as a collection
of pores in a catalytic particle. In addition, students have
expressed their satisfaction in using concepts of engineering
mathematics to develop applied or engineering models that
are efficient in handling complex situations in transport and
reaction. One aspect useful to determine is how much the
approach has increased their ability to handle systems with
transport and heterogeneous reactions, and with several scales
involved such as those in biological systems. This aspect will
be a subject matter for future assessment.

This contribution presents an analysis of the importance
of a pellet as an environment where multi-scale transport
processes take place, and introduced a systematic and progres-
sive approach to derive differential models of the up-scaled
or macroscopic type in a pore domain and catalyst pellet. The
up-scaling approach promotes the explicit use of methods
rooted in scaling concepts, and avoids unit operation views
followed in many classical textbooks. The same approach
can be extended to include engineering equations valid for
the entire reactor (see, for example, Whitaker"181).
Once this approach has been introduced, the student can
extend the analysis from one-single porous cavity to a com-
plete pellet. The procedure enhances the student's ability to
understand how a macroscopic type of description can be
used as a useful approximation for describing the process
of diffusion and reaction that takes place in a heterogeneous
Chemical Engineering Education

domain at the microscopic level. Furthermore, students do
not seem to show any confusion about the assumptions and
limitations of the macroscopic model once they have followed
a systematic approach for the derivation and averaging of the
microscopic model.

Some of the key benefits introduced by the approach pre-
sented here, from the student's point of view, include:
a. A realistic description of the physics and chemistry of
the process.

b. A clear identification of the role of the molecular diffu-
sion and surface reaction, and the need for identifying
an effective diffusivity.

c. A chance to reinforce concepts already learned in previ-
ous engineering and chemistry courses.

d. The opportunity for the students to apply mathemati-
cal concepts learned in the engineering math courses

e. A clear opportunity for building blocks of knowledge in
a sequential approach.

f Avoiding the use of "hidden" up-scaling arguments to
derive macroscopic engineering equations directly, i.e.,
without using the micro-scale description for chemical/
physical processes.

The up-scaling approach also allows students to find
things out.[441 In fact, based on what we saw in our courses,
the process of connecting basic physics with mathematical
description creates a powerful learning environment that
helps the students to become confident and alert life-long
learners. In all instances, the mathematical level required
does not go beyond the one reached by students in under-
graduate mathematics courses, quite contrary to what many
educators claim.

1. Fogler, S., Elements of ChemicalReactions Engineering, Prentice-Hall,
Englewood Cliffs, NJ, (1992)
2. Levenspiel, O., Chemical Reaction Engineering, 3rd Ed., John Wiley
& Sons, N.Y. (1999)
3. Carberry, J.J., Chemical and Catalytic Reaction Engineering, McGraw
Hill, N.Y. (1976)
4. Levenspiel, O., Chemical Reactor Omnibook, 1st Ed., John Wiley &
Sons, N.Y. (1981)
5. Aris, R., Introduction to Chemical Reactors, Prentice-Hall, Englewood
Cliffs, N.J. (1969)
6. Aris, R., Diffusion and Reaction in Heterogeneous Catalysis, Oxford
University Press, N.Y. (1975)
7. Aris, R., Mathematical Theory of Diffusion and Reaction in Permeable
Catalysts, 2nd Ed., Clarendon Press, Oxford (1975)
8. Aris, R., Mathematical I! .. i...i Techniques, Pitman, San Francisco
9. Aris, R., "How to get the Most Out of an Equation Without Really
Trying," Chem. Eng. Ed., 10(3), 114 (1976)
10. Aris, R. "The Theory of Diffusion and Reaction: A Chemical Engineer-
ing Symphony," Chem. Eng. Ed., 20(1), 20 (1974)
11. Arce, PE., M. Quintard, and S. Whitaker, The Art and Science of

Vol. 41, No.3, Summer 2007

Upscaling, Chapter 1 in Chemical Engineering: Trends and Develop-
ments, eds. M.A. Galan and Eva Marin de Valle, John Wiley & Sons,
Ltd., England (2005)
12. Bird, R.B., W Stewart, and E.N. Lightfoot, Transport Phenomena,
2nd Ed., John Wiley & Sons, New York (2001)
13. Ochoa-Tapia, A., J. del Rio, and S. Whitaker, "Bulk and Surface
Diffusion in Porous Media: An Application of the Surface Averaging
Theorem," Chem. Eng. Sci., 48, 2061 (1993)
14. Whitaker, S., "The Species Mass Jump Condition at a Singular Surface,"
Chem. Eng. Sci., 47, 1677 (1992)
15. Slattery, J. C., Interfacial Transport Phenomena, Springer-Verlag, N.
Y. (1990)
16. Arce, P and D. Ramkrishna, "Pattern Formation in Catalytic Reactors:
The Role of Fluid Mixing," AIChE Journal, 37(1), 98 (1991)
17. Froment, G.E and K.B. Bischoff, ... ..i-. ..I State Behaviour of
Fixed Bed Catalytic Reactors Due to Fouling," Chem. Eng. Sci., 16,
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Cassano (Eds.), Gordon and Breach Publishers, N.Y. (1986)
19. Zanotti, E, and R.G. Carbonell, "Development of Transport Equations
for Multiphase Systems-I," Chem. Eng. Sci., 39, 263 (1984a)
20. Zanotti, E, and R.G. Carbonell, "Development of Transport Equations
for Multiphase Systems-II," Chem. Eng. Sci., 39, 279 (1984b)
21. Zanotti, E, and R.G. Carbonell, "Development of Transport Equations
for Multiphase Systems-III," Chem. Eng. Sci., 39, 209 (1984c)
22. Whitaker, S., Introduction to Fluid Mechanics, Krieger Publishing
Company, Melbourne, FL (1991)
23. Hornung, U., Homogenization in Porous Media, Springer, N.Y.
24. Crapiste, G.H., E. Rotstein and S. Whitaker, "A General Closure
Scheme for the Method of Volume Averaging," Chem. Eng. Sci., 41,
227 (1986)
25. Quintard, M. and S. Whitaker, "Transport in Ordered and Disordered
Porous Media: Volume-Averaged Equations, Closure Problems, and
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Multicomponent, Mass Transport in Porous Media" Chem. Eng. Sci.,
61, 2643 (2006)
27. Wood, B. D.M. Quintard and S. Whitaker, "Jump Conditions at Non-
Uniform Boundaries: The Catalytic Surface" ( ...i.. i 55, 5231
28. Whitaker, S., The Method of Volume Averaging, Kluwer Academic
Press, Dordrech, The Netherlands (1999)
29. Paine, M.A., R. Carbonell, and S. Whitaker, "Dispersion in Pulsed
Systems-Heterogeneous Reaction and Reversible Adsorption in Capil-
lary Tubes," Chem. Eng. Sci., 38, 2061 (1983)
30. Oyanader, MarioA. and P Arce, "Role Of Geometrical Dimensions In
Electrophoresis Applications With Orthogonal Fields," Electrophoresis,
31. Satterfield, C. and T. K. Sherwood, Role of Difusion in Catalysis,
Addison Wesley, MA (1963)
32. Whitaker, S., "A Simple Geometrical Derivation of the Spatial Averag-
ing Theorem," Chem. Eng. Ed., 18, Winter (1983)
33. Whitaker, S., "Mass Transport and Reaction in Catalyst Pellets,"
Transport in Porous Media, 2, 269 (1987)
34. Satterfield, C., Mass Transfer in Heterogeneous Catalysis, MIT Press,
Cambridge, MA (1970)
35. Dullien, E A., Porous Media: Fluid Transport and Porous Media, 2nd
Ed., Academic Press, Orlando, FL(1992)
36. Davis, R. and M. Davis, Fundamentals of Chemical Reactions Engi-
neering, Mc Graw Hill, N.Y. (2003)
37. Arce, P, "The Colloquial Approach: An Active Learning Technique,"
Science, Education & Technology, 3(3), 145 (1994)
38. Arce, P, "POK in ColloquialApproach Environments," ASEE Annual

Conference I .. ..-..., , 2,,,,
39. Arce, P and M. Oyanader, "The Catalyst Pellet: A Very Rich POK in
Progressive Learning Approaches for Transport and Reaction," ASEE
Annual Conference Proceeding (2003)
40. Arce, P., "Topics in Transport and Reaction in Multiphase Systems,"
Chem. Eng. Ed., 28(4), 224 (1994)
41. Arce-Trigatti, M., and P. Arce, "The Parallel between the Sport
Coaching and the Engineering Instruction," ASEEAnnual Conference

Proceeding (2000)
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Equations, and Models," ASEE Annual Conference Proceedings,
43. Whitaker, S., Fundamental Principles of Heat Transfer, Krieger Pub-
lishing Company, Melbourne, FL (1983)
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Cambridge, MA, (1999) 1

letter to the editor

The recent article "Turning New Faculty Members into Quick Starters"'11 made a lot of sense to me on a first reading.
New faculty members are under immense pressure and they need all the help they can get, but if I may be allowed to
sound a note of criticism, the article contains no mention whatsoever of industry.
The great pioneers of chemical engineering education such as Donald F. Other had strong links with professional
practice but in recent decades the academic community in chemical engineering has developed its own culture which
has grown away from that of industry. This column"ll gives the impression that young engineering faculty are expected
to perform in the same way as their scientific and mathematical colleagues in terms of lectures and supervisions, pub-
lications and grants. Industrial contacts and practice, however, can provide many educational and research benefits. [2]
Such contacts should be encouraged among our "quick-starting" young faculty members, despite the pressures on
their time.

Malcolm Baird
McMaster University
Hamilton, Canada

1. Brent, R and R.M. Felder, "Turning New Faculty Members into Quick Starters", ( ..... i i.' 41(1), 51-52 (2007)
2. Baird, M.H.I., and S.W Marcuson, "Industry/Academic Collaboration-Challenges and Rewards," CIMMagazine, 2(9), 3-7 (Feb. 2007) 1

Chemical Engineering Education

--- - ^ K.___________________________-



University of Texas * Austin, TX 78712

Rarely a day goes by that we do not read or hear a news
item about energy issues. In April 2005 I was plan-
ning to teach a fall elective course on optimization (a
course definitely oriented toward left-brained ChE students). I
decided, however, that it was time to teach something different
and introduce our students to the subject of energy from the
chemical engineering perspective. Thanks to the flexibility
of our department chair, I was allowed to change the course
offered since both courses were electives. I also did a market
survey of about 60 seniors who were enrolled in my process
control class-to provide some stealth publicity (as it would
be a new elective) and also find out how they would react
to enrolling in such a course. While I received quite a few
affirmative responses ("yes, I would be interested, but I am
graduating in May"), there was useful feedback on items such
as numbers of reports, exams, and presentations, as well as
subject matter. I launched the course in fall 2005 and taught
it again in fall 2006. It was an extremely positive experience
for me, and, based on student evaluations, they liked the
less-structured, more individualized course in contrast to the
typical core ChE course.
Teaching an energy course was not a new experience for
me, as I taught a course called '. i.,.. ' Policy and Technol-
ogy" in 1974 during the "first" energy crisis. One of my
former students in that class (who rose to the position of VP
at Amoco and BP) sardonically redubbed it ' i,,. r' Policy,
Technology, and Communism," as I was a "more liberal than
average" professor at the University of Texas then, arguing

that the free market would not provide adequate policy solu-
tions to the looming energy crisis.
Now we are embroiled in the second energy crisis (or as
someone suggested, the "second coming" of llt .In i ,_'y crisis),
but in many ways not much has changed about the proposed
technological solutions to the energy challenge. I did want to
make this second course offering more technical in nature, so I
reordered the course title to I n r.t' Technology and Policy."
Initial enrollment was 25 students, about half of whom were
graduate students. One year later, enrollment grew to 40,
including 10 graduate students, largely due to the popularity
of the first offering. There was an interdisciplinary flavor to
both classes, as several students from electrical, mechanical,
and petroleum engineering were enrolled. This resulted in a
broadening experience for the class because students brought
different perspectives on subjects such as diesel engines,
semiconductors, oil, and gas.

Thomas F. Edgar is the Abell chair in the
Department of Chemical Engineering at the
University of Texas, where he has been a
S faculty member for 35 years. His research
interests are in the areas of process model-
S ing, control, and optimization.

� Copyright ChE Division of ASEE 2007

Vol. 41, No.3, Summer 2007

I selected a book that was not written by engineers or
scientists, but would instead give more insight into the non-
technical (economic/environmental/sociopolitical) aspects
of the course, thus complementing the technically focused
lectures. The End of Oil by Paul Roberts11l offers excellent
insights on Middle East politics and history, at least from the
oil and gas perspective. The author also makes some interest-
ing observations (ca. 2004) about why the liberation of Iraq
should be viewed in strategic energy terms (vs. weapons of
mass destruction). In The End of Oil, Roberts presents a bal-
anced point of view on most different energy alternatives,
although he does not present many details on biofuels. He
makes three major proposals for energy policy changes:
(1) Boost natural gas supplies as a 30-year bridging fuel.
(2) Implement a carbon tracking system to facilitate coal
,, iti. .1r1.. and carbon sequestration.
(3) Iff,.... i,, ,,,,, i. .,t f:. -.'reduce oil and gas con-
sumption in the United States.
Roberts also does not believe the laws of supply and demand
will be an orderly solution to energy shortages, although I
know some economists would disagree (but those are equi-
librium rather than dynamic market viewpoints). He does
not over-hype some of the new energy alternatives, and his
views on the potential "hydrogen economy" are sound ones,
in my opinion. He also provides some calculations designed
to estimate the true cost of various fuels vs. nontraditional
alternatives. One other advantage of this book was its inex-
pensive price of $10 (paperback). This gives
students a break from the $130 books offered
by mainstream publishers that I impose on
them in courses such as process control and
1. U.S. Ene
As it appears the second energy crisis will Occurrence
last longer than a few years (probably forever),
2. Oil Expl
a number of new books that have been pub-
lished recently were subsequently added to the 3. Coal Ext
reading list for the second offering in fall 2006. ification, Li
Other books, such as References 2 and 3, are 4. Fuel Cel
4. Fuel Cell
possible principal textbooks, but their level of Sustainabil
presentation was not a good match for chemical 5. Recover
engineers as they are more oriented to nuclear
power and fossil fuels than desired. Another 6. Energy
key reference is Coal Processing and Pollution 7. Nuclear
Control,41 a book I wrote in 1983. Because this
book is out of print, I scanned six chapters and 8. Solar En
posted them on the Web, much in the spirit of
the Google library project (less controversial 9. Biomass
because I am the author). It is interesting that 10. Energy
much of the coal technology presented in this 11. Climate
book is still appropriate today, although much Utilization
of the economic information is no longer mean- 12. Energy

ingful in terms of absolute costs. This book was published
shortly after the end of the first energy crisis, a victim of bad
timing. It is still, however, a useful resource today.
Other recent books that have appeared include those by
Smil15s and Tester, et al.,[61 published by MIT Press, and a
book on the methanol economy"1 that covers a broad range of
topics. All of these books have certain strengths that could be
valuable in an energy course for chemical engineers depend-
ing on the technical emphasis of the course. For example, the
Tester, et al., book would be suitable for a graduate course on
energy and sustainability.

Table 1 gives a list of the topics covered in the course.
The breadth of energy alternatives is one reason the course
is appealing to chemical engineers. Because of my previous
involvement in creating synthetic fuels from coal, I had a pre-
disposition toward covering that material, but several student
evaluations at the end of the course indicated that they wanted
less coverage on coal (perhaps because they do not subscribe
to coal as the main answer to the current energy crisis). One
advantage to teaching an energy course on the University of
Texas campus is that there are quite a few energy experts in
fields of interest to chemical engineering. Guest lecturers on
geology of oil and gas, the oil business and extraction tech-
niques, energy projections (from a formerAssistant Secretary
of the U.S. Department of the Interior), solar energy, nuclear
power, and energy and the environment (climate change) were
scheduled. Private sector presentations included the hydrogen

Energy Course Topics
Guest Lecturer/Affiliation
rgy Supplies/Origin and L. Long (UT Geology)

oration and Production W. Fisher (UT Geology)
L. Lake (UT Petroleum Engineering)
reaction, Combustion, Gas-
Is, Hydrogen Economy, D. Austgen (Shell Hydrogen)
ity J. Siirola (Eastman Chemical)
y of Oil Shale/Tar Sands
nd Transportation
Power L. Draper (Amer. Electric Power, retired)
S. Biegalski (UT Mechanical Engineering)
ergy, Wind Power G. Vliet (UT Mechanical Engineering)
J. Hoffner (CSG)
Production and Conversion
Change and Energy D. Allen (UT Chemical Engineering)

Policy and Technology

Chemical Engineering Education

Energy Crisis-A True/False Quiz
1. The first energy crisis in 1974 occurred because of a shortage of oil production capacity.
2. The U.S. should sign the Kyoto Treaty (on CO2 emission) even though it treats China and developing
countries more favorably than the U.S.
3. Global warming due to human (anthropogenic) caused greenhouse gas emissions is occurring and its
impact is evident and is measurable today.
4. Hydrogen is the best non-polluting fuel to use (burning it yields HO), so we should convert to a
hydrogen-based economy.
5. Continuing massive oil imports will eventually destroy the U.S. economy.
6. Drilling and producing oil and gas in the Arctic National Wildlife Refuge (Alaska) will significantly
reduce our need for oil imports.
7. Gasoline is more expensive today than in 1975 (in constant dollar terms).
8. The United States has enough fossil fuel supplies (oil, gas, coal, shale) to meet its own energy needs.
9. OPEC controls the price of oil.
10. The invasion of Iraq was partly driven by a need for stability in and access to oil supplies, compa-
rable to other justifications (weapons of mass destruction or Saddam Hussein's reign of terror).
11. At a high enough price for fuel, (e.g., $80/bbl oil) over a 20 year horizon in the future, potential
energy supplies will be plentiful, including solar and biomass.
12. U.S. Government policy should encourage conservation and constrain consumption through in-
creased taxation of gasoline (e.g., $2.00/gallon vs. $.20).
13. Americans will be willing to give up their love affair with personal autos and explore (and use) mass
14. Massive use of hybrid autos and outlawing SUVs are the best near-term solution for reducing oil
15. Fuel cells will largely replace internal combustion engines in autos by 2035.
16. The use of nuclear energy for electric power production in the U.S.A. can increase from 20% to 30%
by 2025.
17. World oil production will reach a maximum in the next four years and then start declining irrevers-
18. A worldwide growth rate of 2% in energy use is small enough that we don't have to worry about
energy supply/demand imbalances.
19. The politically expedient solution to the energy crisis is short-term comfort for ourselves vs. agreeing
to some inconveniences and price increases on behalf of our grandchildren. Would our culture vote for a
candidate who told us we needed to make major sacrifices in our lifestyle and economic well-being?
20. Investment in new energy technology will have the same beneficial impact on the U.S. economy as
information technology and computing in the past 20 years.
21. New advances in technology and engineering ingenuity will increase electrical efficiency, combus-
tion efficiency, and provide a plethora of personal energy sources, thus raising our standard of living
even higher.
22. The next major war will be fought over access to energy supplies.

economy (from a VP at Shell Hy-
drogen), the solar panel business,
sustainability (Jeff Siirola from
Eastman Chemical), and a former
CEO from American Electric
Power (who spoke on the theme,
"would I build a nuclear power
plant today?"). Student evalua-
tions indicated that they enjoyed
hearing from different speakers
rather than just from the course
instructor. I found the speakers
very informative, and engaged
them in discussions and debate
after the typical obligatory Power-
Point presentations. I encouraged
the students to participate in such
discussions, but did not want to
impose a requirement on their
participation (e.g., you have to ask
one question in class every three
weeks). It took a few weeks to get
the fluid, engaged environment I
was seeking, but it did occur. I
added a few more guest speakers
for the second offering, such as in
CO2 sequestration.

One of the effective ways to get
the class talking during the first
week of class was to have them
participate in a true-false quiz
on energy (see Table 2). I have
used this quiz in teaching several
older adult groups with success,
and have found that participants
immediately react and share their
viewpoints and impressions with
others in the class. A number of
questions are loaded with a politi-
cal viewpoint, so the true or false
answer depends on your politics.
Because the students do not for-

mally take the quiz and submit the answers, this
is not too threatening, even in the home state of
President Bush. As each question can lead to a sepa-
rate discussion, I find that we are unable to cover
all of the questions in the first class meeting, and
some questions are saved for later in the semester.
In these discussions it is interesting to gauge how
well-informed students are on energy matters, since
very few of them read a daily newspaper.
The grading structure for the course is given in
Table 3. As mentioned earlier, it is a course where

Vol. 41, No.3, Summer 2007

Grading Policy-Energy Technology and Policy
(1) Two written reports plus literature portfolio (40%) - specific topics selected by
(a) research on selected energy technology
(b) government-regulatory issues
(2) Two ten-minute oral reports presented by each student (10%) based on the above
written reports
(3) Homework assignments involving energy calculations (10%)
(4) Midterm exam (20%) (take-home)
(5) Final exam (20%) (take-home)

oral and written communication skills are emphasized, but
also provides students an opportunity to integrate knowledge
they have acquired in other engineering courses. Students
should know how to perform economics calculations as well
as do efficiency analysis using energy balances and thermo-
dynamics. I find that most of today's students do not retain
much information from their previous courses, so revisiting
key concepts in an energy context is useful.
While chemical engineering students are exposed to various
energy topics, such as distillation, in previous courses, they
do not understand how these topics relate to macroscopic
energy issues in the United States or the world. Rarely are
students conversant with order of magnitude information
like how many Btu's are in one standard cubic foot of natural
gas [answer = 1000] or how many Btu's can be liberated by

condensing one pound of steam [answer = 1000]. I place a
high value on being able to perform approximate calcula-
tions quickly because it is valuable for discussions with your
supervisor or the plant manager later in your career.
A take-home exam format, which allowed students to
research certain types of information (most use Google and
Wikipedia), was used exclusively and worked well. Each
take-home exam required about 10 hours of work, so it had
the advantage of considerable depth compared to the typical
one-hour exam. See Table 4 for the take-home mid-term exam
used in fall 2005.


typical homework assignment is given in Table 5. As
st energy solutions depend on economics, it is important
reinforce student background in this aspect. All energy
conservation applications involve spending capital
funds in order to achieve energy savings. As example,
I recently upgraded my air conditioning system to a 14
SEER unit, which can be justified based on reduced
cooling costs and various tax and rebate incentives (see
problem 2 in Table 5).
The final exam included somewhat similar problems
to the midterm, but I also included a question that was
intended to assess how much views on energy might
have been influenced by the class (see Table 6). It was
interesting to see how many students developed more
passionate views on energy conservation, the problems

Chemical Engineering Education

Take-Home Exam-Energy Course
1. It is 2025, and coal is now being gasified around the U.S.A. to produce synthetic methane, which is replacing dwindling supplies of natural gas.
A company has access to a large coal reserve in Wyoming, 1100 miles from an industrial site in Texas that needs the gas. The President of the
company must decide on the least cost strategy to transport the energy between Wyoming and Texas, using the following two scenarios:
(a) make pipeline quality gas from the coal in Wyoming, then transport the gas by pipeline to Texas. Assume the coal has a heating value of
10,000 Btu/lb.
(b) Ship the coal by rail to Texas, and then gasify the coal at the industrial site in Texas.
You have been hired as a consultant to help the President decide. What will be the cheaper transportation option between (a) and (b)? Provide
supporting calculations.
2. If a hydrogen economy develops in the future, there will be a need for increased transport of hydrogen by pipeline.
(a) In comparison to natural gas, it appears that hydrogen (with a heating value of one-third of CH4) would cost three times as much per 106
Btu to transport. However, the physical properties of H2 may be such that pressure losses are quite low, thus reducing costs. Explain.
(b) What are the added safety issues that must be addressed in H2 pipelines? Note that H2 pipelines exist and operate in Texas today.
3. It has been suggested in news sources that the production of ethanol from corn in the Midwest U.S. is a net energy loss, in that more energy may
be required to produce one gallon of ethanol than is available in the ethanol itself. Research this topic and determine if this statement is correct
or not. You may take into account energy requirements to grow the corn.
4. Building and home lighting directly affects our economy. As a nation, we spend approximately one-quarter of our electricity budget on lighting
- or more than $37 billion annually. An incandescent light bulb is highly inefficient because it converts only a small amount of the electrical
energy into light; the rest is converted to heat. In spite of this inefficient conversion of energy, the relatively inexpensive purchase price of incan-
descent bulbs when compared to fluorescent lighting accounts for their popularity among consumers.
A 75W (1220 lumens) bulb that is assumed to have the shape of a sphere has a diameter of 6 cm and a surface temperature of 250�C (when the
light is turned on). The surrounding room air temperature is 25�C. Heat transfer calculations indicate that the incandescent bulb has a heat loss
of 65W compared to 20W for the fluorescent bulb. The 75W incandescent bulb has a 750 hour life, while the 17W (1200 lumens) fluorescent
bulb averages 10,000 hours before failing. Find out the cost of both bulbs from a local supplier and calculate the rate of return for replacing the
equivalent of 20 75W lights (typical house), which are turned on an average of 4 hours/day.
For extra credit (5 pts) verify the heat loss of 65W mentioned above for an incandescent bulb using appropriate heat transfer calculations.

Homework--Energy Economics
1. A synthetic methane plant from coal is to be constructed at a cost of $4 bil-
lion dollars. It requires 14,000 tons/day of coal (10,000 Btu/lb) and will produce
130 MMSCF/day of synthetic methane. What is the thermal efficiency? What
is the cost of coal in the produced methane ($/MMBtu)? What is the equivalent
fixed cost of the plant capital cost in $/MMBtu? Assume that the plant operates
320 days per year.
2. New air-conditioning units have an EER of about 13. If a new AC unit
costs $3,000 after a City of Austin rebate, what is the payback on replacing an
AC unit with an EER of 9? Assume existing cooling costs of $1,200 per year
(May-September) with the current unit.

TABLE 6 Earlier I commented on how today's students do not
Final Exam Question normally make it a habit to read a daily newspaper. I
felt that students needed to read on a regular basis to
You have been appointed the U.S. energy czar. Discuss your personal view
of what changes (or not) should be made in the U.S.A. energy mix in 2025 see how energy issues are discussed in public forums,
(when you are over 40!). Assume that the amount of oil and gas available for by politicians, or by other thought leaders. Hence, one
energy use would be the same or less than in 2005. Rank relative increases on a of the other requirements in the class was for students
percentage basis; recognize that some technologies may take longer to develop. to collect one article per week of general relevance
Use 2005 usage levels as your baseline. You can choose to reduce oil imports in
the scenario developed. to energy from a newspaper or national magazine,
(a) solar either print-based or on the Internet. At the end of the
(a) solar
semester the students submitted a list of articles plus
a short overview of each one. While many students
(c) fuels from biomass voluntarily will read energy articles, there are always
(d) energy conservation some students who need to be coerced.
(e) coal
(g) oil shale Student presentations were a cornerstone of the
(h) hydrogen course. I wanted students to make individual choices
(i) other on which energy issues they would study in-depth.
Table 7 gives a list of the projects selected in fall
Comments: Write one page summarizing your ratings. 2005 after discussions with the instructor. Students
were required to give two talks, one on technology
of using coal, etc. This question was graded on how well the w r t g t , e o
. (about halfway through the semester) and the other a policy
students substantiated their views (i.e., many possible correct
One of the important points students need to understand TABLE 7
is the growing size of the energy demand, largely due to the Student Energy Project Areas
economic development of China and India. Even a 2% annual conservation of crude oil (fuels vs. chemical feedstock)
global growth rate can, over 30 years, dwarf what appear to heavy oil gasification
be measurable increases in energy supplies due to improved oil shale utilization
technology. One case in point is the Arctic National Wildlife
Refuge (ANWR) debate in the United States. The net addition wmd power
of this resource to oil supplies in the United States will only hydrogen technology
amount to one year's increase in the global energy demand. LNG (liquefied natural gas)
An interesting video on the Web by Chemistry Professor Na- oil importation effects on economy
than Lewis of Caltech ("Scientific Challenges in Sustainable energy conservation in wastewater purification
Energy Technology," ) environmental impact of auto mobile technology
lays out a compelling picture of the energy options in 2050
. . . fuel cells and hydrogen technology
after available oil and gas supplies decline. Lewis opines that
in 50 years massive efforts in solar energy will be required to personal auto use and conservation
prevent greenhouse gas buildup and to keep the U.S. standard photovoltaic technology for solar energy
of living the same. Students in today's classes will still be nontraditional hydrocarbon sources (hydrates)
around in 2050 to see what happens; professors like me will energy efficiency and conservation (green building)
not be here then, but our children and grandchildren will. effects of lifestyle choices on energy use
Students also need to understand that the U.S. public does
developing a positive image of nuclear energy
not have a rational view of their responsibility to share the a s
burden of energy consumption. The American transportation energy usage in developing countries
dependence (addiction?) on imported oil is perhaps the most sources of hydrogen
significant problem faced in the near term. Other notable ex- wind energy and power generation
samples include opposition to wind energy in Massachusetts nuclear fusion technology
and general resistance to new nuclear power plants almost electric vehicles
everywhere. The philosophy of many citizens has moved
from NIMBY ("not in my backyard") to BANANA ("build ethanol production
absolutely nothing anywhere near anything"). This attitude biodiesel production
will obviously need to change in the near future. carbon dioxide reduction
Vol. 41, No.3, Summer 2007 199

The students also held an "American energy idol" contest

to select the best talks.

presentation, which was given toward the end of the semester.
Both presentations were accompanied by a written report.
The policy assignment required them to review existing
government policies (mostly U.S. focused) and then propose
modifications to these policies. The topics in Table 7 were

Guidelines for 10-Minute Talks
1. Why is this issue or technology important to the energy situa-
2. What is the technical background? What are the technological
3. What is the economic feasibility?
4. What are the government policy issues?
5. Use 10 slides or less.

fairly general, and in the fall of 2006 most projects were more
specific (usually negotiated between faculty and student based
on his/her interest).

One problem created by so many presentations is how to
schedule them without taking away a large amount of time
from the lecture activities. A few extra class sessions were
scheduled for the technology presentations so that there was
a reasonable fit with the topics scheduled. This aspect of
the course turned out to be a pleasant surprise, namely that
students were able to teach each other. The quality of the pre-
sentations was quite good, so I found I did not need to cover
the same material. For example, two student presentations on
wind energy seemed sufficient, so I did not cover this topic.
The students also held an "American energy idol" contest to
select the best talks. I then posted the student presentations

Selected Lecture Notes and Presentations on the Course Web Site

1. U.S. Energy Supplies/Origin and Occurrence
a. Energy prices, supply, and demand
b. Geology of oil and gas
c. Energy true-false quiz
d. Global energy situation
e. Global energy overview to 2050
f. Oil importation effects on U.S. economy
g. China energy consumption
h. Energy economics

2. Oil Exploration and Production
a. The oil business
b. Crude oil trading
c. Heavy oil issues
d. LNG transporting and storage
e. Methane hydrates
f. CO, sequestration

3. Coal Combustion, Gasification, Liquefaction
a. Coal reserves and properties - Chapter 2[4
b. Coal extraction - Chapter 3[4]
c. Coal transportation - Chapter 41[4
d. Coal preparation and cleaning
e. Coal carbonization
f. Coal gasification - Chapter 7[4]
g. Coal liquefaction - Chapter 8V4
h. Coal combustion - Chapter 9[4]
i. Environmental impact

4. Recovery of Oil Shale/Tar Sands
a. Shale oil
b. Shale and tar sands

5. Fuel Cells, Hydrogen Economy, Sustainability
a. Hydrogen as a fuel (Shell Hydrogen)
b. Hydrogen storage technology

c. Sources of hydrogen and hydrogen economy
d. Fuel cell technology
e. Sustainability in the chemical and energy industries
f. Membrane separation of hydrogen

6. Energy and Transportation
a. Electrical vehicles
b. Auto engine efficiency improvements
c. Plug-in hybrids

7. Nuclear Power
a. Nuclear power
b. Fusion power

8. Solar Energy, Wind Power
a. Solar energy
b. Photovoltaic - solar cell
c. Wind energy

9. Biomass Production and Conversion
a. Ethanol
b. Bio-diesel

10. Energy Conservation
a. Effects of lifestyle choices on energy use
b. Energy conservation measures
c. Developing countries
d. Green buildings

11. Climate Change and Energy Utilization
a. CO, emission reduction technology
b. Carbon cycle
c. What causes climate change?

12. Energy Policy and Technology

Chemical Engineering Education

Video Content for An Energy Course
"An Inconvenient Truth"-Paramount
"Who Killed the Electric Car?"-Sony
"Renewable Energy"-Modern Marvels (History Channel)
"Mega Oil Complex (Tar Sands)"-History Channel
"Coal Cowboy"-60 minutes (CBS)
"The Power of the Sun"-UCSB, Department of Physics

on the course Web site, which had the advantage of making
the Web site a substantial resource. The guidelines for the
presentations were fairly minimal (see Table 8).
The course Web site contains a significant amount of content
and is not password-protected. In addition to student presenta-
tions, it includes the instructor's lectures (many on coal) and
book chapters, guest lectures, exams, and the homework.
Table 9 gives the URL and an outline of the lectures on the
existing Web site; the coverage has become quite extensive
over two semesters. Several other presentations totally apart
from the course are also posted there. There are also a number
of excellent videos on energy that are reasonably technical
(see Table 10).
The notion that students can help develop content for a
course is not a traditional view (vs. instructor-developed
content or a textbook). Recently BoettcherE8' discussed this
phenomenon, relating the idea to the "active learning" move-
ment. In the acquisition of knowledge by the student, giving
a lecture on a given topic promotes learning by the student at
a higher level than lectures that involve interaction between
professor and students or multimedia software. Learners can
effectively learn content when they build their own knowledge
in an interactive environment. Boettcher suggests that today's
generation of students want to be doers, and active dialog with
other students in a class is a very desirable activity. Posting
student content on the Internet gives a higher level of value
to the student contributions, which certainly resonated with
the students in the class, and it also gives them a stronger self-
identity. I also used student solutions to the homework and
exam problems and posted them on the course Web site. In
some cases, if several alternative approaches to an open-ended
problem were submitted, it was beneficial for the students to
see multiple solutions. Boettcher[91 proposes that as much as
one-third of the content of many graduate courses could be
student-generated. The questions then arise as to how much
of this content will be stored for the indefinite future. There
is a limit to the number of student presentations that can be
posted when the class grows to more than 30 students, but I

have not reached any conclusions yet.
It is clear that students today feel the world energy dilemma
is much more palpable to them. In informal polls of students
in the class, the belief that global warming is occurring and
is caused partially by human activities has increased from
about 50% to 90% between 2005 and 2006. Students also are
recognizing that their individual actions have an impact on
both energy usage and the environment. Two sample com-
ments at the end of the class are shown below.
S "This class will affect what articles I read, how I vote,
what kind of home I will look for, and probably what
kind of car I will own for the rest of my life."
* "I bought a Prius because I don't think I could get a
car that wasn't as fuel efficient as possible after taking
your class. I picked my sister up from her high school
and there were three Hummers in the parking lot!"

These kinds of comments, which transcend the techni-
cal content in the course, make teaching this course very

Clearly the emerging energy situation in the United States
puts chemical engineering at the forefront of the large research
and education effort that will need to be undertaken during
the next 20 years. Chemical engineering undergraduates and
graduate students should be literate on energy alternatives and
the interconnection of technology, economics, environment,
and government policy. The course I am teaching and the
associated Web site will hopefully influence the knowledge
base of chemical engineering students, and I encourage other
departments to consider adding similar courses either as
regular courses, seminars, or campuswide offerings (where
students outside engineering are enrolled).

1. Roberts, P, The End of Oil, Houghton Mifflin Co., New York (2004)
2. Goodstein, D.L., Out of Gas: The End of the Age of Oil, Norton, New
York (2004)
3. Deffeyes, K.S., Beyond Oil: The Views from Hubbert's Peak, Hill and
Wang, New York (2005)
4. Edgar, T.E, Coal Processing and Pollution Control, Gulf Publishing
Co., Houston (1983)
5. Smil, V., Energy at the Crossroads, MIT Press, Cambridge, MA
6. Tester, J.P, E.M. Drake, M.J. Driscoll, M.W. Golay, and W.M. Peters,
Sustainable Energy - ( I" ..... Among Options, MIT Press, Cam-
bridge, MA (2005)
7. Olah, G.A., A. Goeppert, and G.K. Surya Prakash, The Methanol
Economy, Wiley, New York (2006)
8. Boettcher, J.V., "The Rise of Student Performance Content," Campus
Technology, 20 (2006) 1

Vol. 41, No.3, Summer 2007

M T= curriculum
-- U s__________________



Peer-to-Peer Interactions In a Research Group

University of South Carolina * Columbia, SC 29208
E educators have previously established the benefits of in-
troducing active learning into the passive environment Chrisl
4 chemi
of a traditional lecture setting.[1-4] But what, exactly, South
are the characteristics of this learning model? Silberman[2] cess c
provides an illustrative model description by saying: Rese~
When learning is active, students do most of the work. They
use their brains . .. studying ideas, solving problems, and
applying what they learn. Active learning is fast-paced, fun,
supportive, and personally engaging ... To learn .**. , i,
well, it helps to hear it, see it, ask questions about it, and Michael A. Matthews is a pro
Michael A. Matthews is a profess
discuss it with others. Above all, students need to "do it"- chair of the Department of C
figure .hi,,, out by themselves, come up with examples, try Engineering at the University o
out skills, and do assignments that depend on the knowledge Carolina. He is also principal inv
of the Research Communication
they already have or must acquire. proiect.

This description applies both in and out of the classroom.
Although some would argue active learning could take
place individually, a key component of many active learning
environments is interaction among participants. While most
investigations of active learning have dealt with traditional
classroom/lecture situations, undergraduate research and in-
dependent study are becoming increasingly more important
in the undergraduate experience. Undergraduates may now
do research at their own institutions during a typical semester,
and summer research experiences (the Research Experience

of So

topher E. Long received his Ph.D. in
cal engineering from the University of
Carolina in 2006, in the field of pro-
:ontrol. He served as a mentor in the
rch Communications Studio for two
He is presently employed by GE.

ssor and
f South
s Studio

y S. Thompson is retired from the
rtment of English at the University
uth Carolina. She is a founder of the
g Studio in the english department
s a co-principal investigator of the Re-
:h Communications Studio project.

� Copyright ChE Division of ASEE 2007
Chemical Engineering Education

for Undergraduates or REU) are becoming well-recognized.
Independent study, in connection with a research group, would
seem an ideal opportunity for fostering active learning. Little
attention, however, has been given in engineering education
to fostering active learning or measuring the outcomes.
The objective of this paper is to quantify the level of active
learning exchange in a research group composed of under-
graduate and graduate students, using analysis of the number
and types of verbal exchanges taking place. With funding
from the National Science Foundation, we have developed a
model called the Research Communications Studio (RCS),
which has served as the testbed for research on learning. While
data have been collected in the RCS environment, the means
of promoting active learning and the lessons learned should
be within reach of faculty and their own research groups. A
number of practices that make the studio approach a success-
ful model for facilitating active learning are recommended
to educators.
This paper details a number of principles that can be used by
engineering educators to facilitate active participation among
undergraduates in a research-learning environment. The RCS,
which is a refinement of the typical research group containing
undergraduate and graduate students, is presented as a test-
bed for the approach. A quantitative study of activity levels
is pursued and the subsequent analysis is presented.

While classroom teaching is usually governed by well-
organized textbooks and syllabi, the research group is typi-
cally more of an apprenticeship situation in which aspiring
researchers learn by doing. In our experience, a typical
research group may or may not employ structured learning
approaches, depending on the faculty director's preferences.
Research group leaders, whether faculty or senior gradu-
ate students, may improve the intensity of learning in their
undergraduates by explicit consideration of some guiding
principles, as well as educational theory. We recommend
the following four guiding principles be incorporated into a
research learning situation, and these should be made explicit
to student researchers:
- Instill personal ownership of the project
- Focus on communications products (papers, poster,
etc.), with appropriate instruction
- Promote awareness of distributed .., * '.i. *
- Facilitate peer-level interaction
These principles are further described below.
Instilling Project Ownership
When undergraduate students are in a position of ownership
of their projects, they are more likely to exhibit a genuine
interest in their own creative work and learning processes.
It becomes even more clearly the students' responsibility to

make progress in research and to take the initiative to learn.
We have found that a strong sense of personal ownership
drives undergraduates to stimulate conversation on their
project. In a research setting, students perform original work
(as opposed to well-defined homework or laboratory exercises
with predetermined solutions and presentation formats). This
is, in fact, inherent in the nature of all research groups. The
research group leader must put forth effort in order to promote
student ownership of their projects. As soon as is feasible,
students should clearly articulate their own objectives and
Focusing Students Toward Communications
"The job isn't over until the paperwork is done." Experi-
enced research mentors know that "paperwork" today may
mean journal article, contribution to a technical report, poster
presentation, oral/electronic presentation, research notebook,
or other form of research communication. It is essential to
orient the student early on to communication skills. By "fo-
cusing," we mean that the research group leader explains the
importance of communication in research, and specifically
identifies one or more forms of "paperwork" that are the
required research product. Typically, the end of an academic
or summer term is a good time to require final communica-
tion products, as setting deadlines also defines rigorous due
dates for papers, posters, and presentations. Students should
be required to regularly update their communication products
and submit them for review and comment by the advisor
and senior research associates. This requirement provides a
common ground for undergraduates in initiating discussions
with more experienced members of the research group. With
this orientation, students focus on how to best explain their
work to their peers as well as begin to perceive how their
communication products come across to others. Interactive
peer critiques of research deliverables aid the student on the
given product but also provide others with experiential learn-
ing from the activity.
Promoting Awareness of Distributed Cognition
Distributed cognition, simply defined, is the process of
learning through the combined knowledge and experiences
of diverse individuals. There are certainly times when the
researcher must forge ahead with individual effort, but much
research today is conducted in an interdisciplinary team
environment. Thus, undergraduate students should be taught
to actualize John Donne's words: "No man is an island,
entire of itself; every man is a piece of the continent, a part
of the main." Undergraduate researchers should be taught
the concept of distributed cognition and encouraged to use
it.P51 The learning that occurs through the group's distributed
cognition doubles back into new learning for the individual
students.P5 Practice helps them become more confident and
aware of their role in an active learning environment. Students
who are aware of how they learn will look for opportunities
both to give information out to and receive it back from their

Vol. 41, No.3, Summer 2007

Figure 1. A typical RCS session in which the undergradu-
ate researchers, mentors, and faculty meet to discuss all
aspects of research.

Figure 2. A participant presenting or explaining her
research to the RCS group during a meeting.

peers. They look for others to contribute knowledge to solving
their particular problem and reciprocate by sharing what they
know to help others.
Facilitating Peer-Level Interactions
Undergraduate researchers may expect that the senior
investigator will tell them LI i dmlini., and they may have
no appreciation for the importance of active communication
among group participants at all levels. An integral piece of
the aforementioned distributed cognition, however, is the
interaction at peer level. An obvious way to facilitate peer-
level participant interaction is to train a graduate student or
post-doctoral scientist to moderate (not dominate) the research
group environment and actively elicit the participation of the
undergraduates. The research group leader (principal investi-
gator; senior faculty member) can then focus on stimulating
scholarly discussion, analyzing results, and creating openings
or opportunities for others to contribute.

The RCS is an innovative structure, funded by NSF, de-
signed to conduct cognitive research using the guidelines
and pedagogical theory described above.13 14] The RCS is an
ongoing effort to improve undergraduate education by creat-
ing an environment, similar to the typical research group, in
which students are actively learning to better perform their
own research using a communications-based approach. Studio
leaders actively elicit participant interaction. At our university,
the RCS activities are formally scheduled through a one-
credit-hour independent study course (for three semesters)
for which students receive academic credit in their majors.
This academic structure was purposely chosen, as independent
study courses are fairly common in undergraduate engineering
curricula. Small interdisciplinary groups of undergraduate
researchers with authentic projects meet weekly under the
mentorship of a senior (Ph.D.-level) engineering student.
The senior engineering graduate student is chosen based on
experience in the conduct of research, including publishing
and participating in confer-
ences. The experiences of
This senior student become
Engineering Faculty part of the knowledge base
(1 per Undergraduate of the distributed cognition
Researcher) system.

Figure 3. The studio is an
environment of distributed
_ cognition, in which think-
ing and learning processes
are distributed across the
network of participants.

Chemical Engineering Education

In the weekly studio meetings, students discuss, write about,
reflect upon, and present their research as it progresses, and in
doing so, they learn how to communicate more clearly (Fig-
ures 1 and 2). Through this approach, principles of research
and communication are made explicit. RCS activities enhance
learning outcomes through intensive practice of communica-
tion skills. Figure 3 shows the interactive relationship among
the interdisciplinary staff and undergraduates, along with
the connection of all participants to the engineering faculty
members. The RCS is a student-centered approach in which
all activities and the associated communications products
are driven by students and their advisors. While each studio
group has its own dynamics, the sessions have some elements
in common. The staff, which includes an engineering and a
communications graduate student, as well as a communica-
tions faculty member, encourages students to take control of
the discussion as much as possible. Staff comments are most
common in situations when the student seems to be unsure
of what to do next or has questions about best practices, such
as effective information arrangement and design for posters,
slide show presentations, and technical papers.
Further details of the RCS research initiative as well as a
detailed studio description can be found on the Web ( www.che. sc.edu/centers/rcs/rcsmain.htm>) and in the profes-
sional literature.[1317]

As communication is an integral part of active learning,
particularly in a group setting, we have investigated commu-
nication activity to verify the level of active participation. We
undertook an analysis of the linguistic interaction in studio
sessions, using theoretical constructs and techniques from
conversation discourse analysis. Among the most important
constructs are those of the linguistic event ("turn") and the
"floor." Here, a linguistic turn is considered an instance or
period of participation in which one is expressing a thought
or idea. This turn is the elemental building block of a con-
versation. Furthermore, the individuals) communicating at
a given point in time is said to have the floor.
Active participation can be confirmed through an investiga-
tion into the dynamics of the interactions taking place within
a given environment. To date, most studies on the processes
of learning and communication have been predominantly
qualitative in nature, as these processes are notoriously dif-
ficult to quantify. A few quantitative attempts have been made,
however. Among these is the development of an observation
system intended to capture the effects of differences in in-
structional approaches in engineering classrooms, especially
with regard to interaction levels and levels of student engage-
ment.[8] Interactions between educators and students, and
the resulting impact on education, have been quantified and
characterized using coding systems.[9 10] Clarke, et al. present

a review of techniques for analyzing classroom discourse as
well as a complex technique that overcomes the limitations of
many previous methods.[11 These works, however, focus their
attention solely on the classroom setting. This present study
employs a new coding methodology, similar to that of Power[91
and Stiles, et al.,[101 to analyze the interpersonal dynamics in
a learning environment other than the classroom. The activ-
ity levels in the RCS are verified by quantifying interaction
frequencies and conversation alignments.
To analyze how engineering students contribute to and
benefit from a distributed cognition environment, both au-
dio and video records of sessions were kept. These records
are the basis for this quantitative analysis to confirm active
participation levels.
A coding approach is used to review a number of repre-
sentative sessions and to create a chronological map of how
information is exchanged between studio members during a
session. The direction and duration of communication flow
between participants on an event-by-event basis is tabulated.
This includes noting the time at which a turn begins, who is
controlling the floor, as well as whom they are addressing
or communicating with. Note the analysis also captures key
aspects of communication such as gesture, body language, or
other nonverbal means of communication such as drawing,
and writing. To make the coding process manageable, how-
ever, hard-to-identify events such as head nods, hand waves,
and minimal verbal responses that do not significantly impact
the flow of conversation are ignored. More easily identifi-
able nonverbal events such as reading and writing silently
are recorded. Pauses in communication are also recorded as
events when no communication occurs between members for
a significant period of time.
A typical event (turn) has one active speaker, a set of re-
cipients (the audience) being addressed by the speaker, and
a set of bystanders who are not directly involved in the com-
munication exchange. In fact, the principle that one speaker
talks at a time (i.e., in a one-speaker floor) has formed the
basis for much linguistic research. Edelsky,20] however, shows
that this is not always the case. In many communicative situa-
tions, a distinction can be made between interaction in which
one identifiable speaker has the floor at any given time and
interactions in which the floor is shared, as in a collaborative
floor or during schisming (when one conversation among all
participants present splits into two or more distinct conver-
sations). In the present analysis, speakers frequently share a
collaborative floor and have schisming conversations.
The present study focuses on the analysis of representative
RCS sessions taken from each of three consecutive semesters.
The dates of the sessions were March 3 and Sept. 22, 2003, and
Feb. 2, 2004. It should be noted that the groups do not neces-
sarily involve the same undergraduates, mentors, and faculty,
as the groupings change on a semester-to-semester basis,
though all sessions do follow the typical RCS approach.

Vol. 41, No.3, Summer 2007

From the coding scheme, a wide variety of quantitative
information can be obtained that describes the dynamics of
the interactions in the distributed cognition environment.
The lowest level of information obtained is a simple average
frequency of turns in a given session. It was found that the
average turn frequency in the sessions considered ranged
from 5.7 to 7.3 turns per minute (Table 1). That is to say, the
floor changed hands roughly every 10 seconds throughout
the meeting. This is significantly more frequently than the
change of floor in the more passive learning model of the
traditional lecture environment. This, in itself, is an indicator
of active participation.
By noting the speaker in the coding process, the role of the
individual controlling the floor can be analyzed. It was found
that at any given time, a single person almost exclusively
controls the floor, i.e., through the "one-speaker floor." Only
in rare instances of a collaborative floor or schisming is the
floor shared. In general, the undergraduates control the floor
the majority of the time (32.6% to 46 %), followed by the
mentors (32.7% to 33.4 %), and then the faculty (20.7% to

20.9 %). This is to be expected, as the groups consist of more
undergraduates than mentors, and more mentors than faculty.
On a per person basis, however, the faculty member actually
takes the most turns, at roughly 20% (Table 1). This is still
a significantly reduced role as compared to the classroom
environment, in which the faculty member is expected to
dominate the floor. In another study on the RCS, Donath, et
al. found that the faculty member's contributions are mainly
elicitationn of critique" and "negotiation."'141 This reduced
role of a faculty member exemplifies the RCS distributed
cognition strategy in which the participants drive the discus-
sions and learn from each other, in addition to learning from
the mentors and the faculty.

The speaker and audience (or intended recipient) can be
further analyzed to indicate the difference that role (e.g., stu-
dent, linguistics mentor, etc.) makes in the verbal interactions.
In this way, we have examined the prevalence and specific
instances of peer-level interactions. It was found that the ses-
sions were dominated by multilevel interactions in which a
single person is addressing the whole group. In these cases,
interactions of all levels are taking place. That is to say, the

Summary of Quantitative Data of Studio Group Dynamics.
(*Multilevel interaction types account for interactions that include everyone and thus every interaction level.)
Session 1 (March 3, 2003) Session 2 (Sept. 22, 2003) Session 3 (Feb. 2, 2004)
Group Make-up ---- ---
Number of Participants 3 4 4
Number of Mentors 2 2 2
Number of Faculty 1 1 1

Group Activity --- ---- ---
Total No. of Turns 542 411 455
Session Duration (min) 74.1 61.6 80
Turn Frequency (turn/min) 7.3 6.7 5.7

Who has the floor? % Turns % Time % Turns % Time % Turns % Time
Undergraduates 33.9 32.6 48.1 43.8 38.5 46
Mentors 32.8 32.7 28.2 33.4 30.3 32.7
Faculty 20.3 20.7 21.4 20.9 30.1 20.7
Shared 12.9 14 2.4 1.8 1.1 0.6

Group Interactions % Turns % Time % Turns % Time % Turns % Time
Peer 4.6 3.5 12.9 8.8 2 1
Undergraduate-Mentor 25.1 33.2 19.2 16.7 26.4 25.4
Faculty-Undergraduate 21.4 18.2 22.1 14.6 35.4 27.7
Mentor-Mentor 5.2 3.5 3.2 3.6 0.7 0.2
Mentor-Faculty 3.9 2.9 2.4 1.9 3.5 1.6
Multi-level* 39.9 38.7 40.3 54.4 32.1 44.1

'06 Chemical Engineering Education

interactions include communication on the peer level, as well
as those between undergraduates and mentors, and between
undergraduates and faculty. This is expected, as the groups
are small and one could address everyone with relative ease.
These multilevel interactions accounted for 32.1% to 40.3%
of the total interactions on a turn basis (38.7% to 54.4% of
the interactions on a time basis). The pure peer-level interac-
tions accounted for 2% to 12.9% of the interactions on a turn
basis, and 1% to 8.8% of the interactions on a per-time basis
(Table 1). Again, this peer-level interaction is one indication
of active participation not necessarily encouraged in the
lecture setting. It is, however, a kind of interaction that the
studio staff strives toward.
Studies on the group as a whole provide useful informa-
tion with regard to how the studio provides a forum for
undergraduates to work with each other in the distributed
cognition environment. Although beyond the scope of this
paper, it is conceivable that exhaustive analysis of data on a
single participant, paired with long-term assessment, could
prove useful in showing the effect of active participation on
the individual's progress in the transition from novice to more
mature researcher. Nevertheless, the analysis of the three ses-
sions clearly indicates the consistency in the sustained activity
levels stimulated by the distributed cognition environment.

Herbert Simon"181 points out that the basic principle of the
enterprise of cognitive studies is that "learning takes place
inside the learner and only inside the learner." Simon also
recognizes that "whether from books or people, at least
90% of what we have in our heads ... is acquired by social
processes, including watching others, listening to them, and
reading their writings."'18 The research group must take into
account this socially distributed nature of learning by building
an optimal environment for research learning to occur. The
RCS learners' knowledge construction process is aided by an
environment of distributed cognition in which participants at
all levels - experts, mentors, accomplished novices, and nov-
ices -learn from and teach each other. "] The explicit attention
to distributed cognition, accomplished in the RCS through a
focus on communication, addresses both the learners' cogni-
tive development and the development of communication
abilities within a system of distributed cognition.

Small groups provide an optimal environment for peers,
near-peer mentors, and communications faculty to interact
through various modes of communicating. The acts of speak-
ing, writing, drawing, gesturing, using computer programs,
etc., mediate individuals' construction of knowledge. At the
same time, these media represent knowledge externally for
others, who can both provide feedback and use it in their
own knowledge constructions. The process of constructing
knowledge is enhanced by expert guidance and feedback as
the learners work on increasingly challenging aspects of the
research projects they are involved in with their research
advisors. What learners can do initially with experienced

Vol. 41, No.3, Summer 2007

guidance they can do later by themselves. The distance
between what learners can do independently and their abili-
ties to solve problems with guidance was conceptualized by
\ i i ,k\' ' as the zone of proximal development. Research
groups comprising graduate students and undergraduate stu-
dents, as well as faculty and research staff, provide a zone
in which undergraduate engineering students from different
engineering disciplines, graduate student mentors also from
different engineering disciplines, graduate students from lin-
guistics and English, and communications faculty all interact
with and learn from one another. This interaction occurs in
a rich environment of advanced computer tools and all the
possibilities of intellectual stimulation provided by a college
of engineering.
From the discourse analysis of representative groups, it is
seen that the verbal and nonverbal communication activity
levels in the RCS (and, by extension, it is presumed in a
structured research group setting) can be elevated, particularly
in comparison to that expected in the traditional classroom.
The results are characteristic of the definition of an active
learning model.

The authors of this work would like to acknowledge for
the National Science Foundation for their support (NSF EEC

1. Johnson, D.W., R.T. Johnson, and K.A. Smith, Active learning: Coop-
eration in the College Classroom, Interaction Book Company, Edina,
MN (1991)
2. Silberman, M., Active Learning 101: Strategies to Teach Any Subject,
Allyn & Bacon, Boston (1996)
3. Niemi, H., "Active Learning-A Cultural Change Needed in Teacher
Education and Schools," Teaching and Teacher Education, 18, 763
4. Felder, R.M., and R. Brent., "Learning by Doing," Chem. Eng. Ed.,
37(4), 282 (2003)
5. Salomon, G., "No Distribution Without Individuals' Cognition: A
Dynamic, Interactional View," in G.Salomon (Ed.), Distributed
Cognitions: Psychological and Educational Considerations, 111-138,
Cambridge University Press, NY (1993)
6. Kirsh, D., "Distributed Cognition, Coordination, and Environment
Design," Proceedings of the European Cognitive Science Society
7. Bransford, J.D., A.L. Brown, and R.R. Cocking, How People Learn:
Brain, Mind, Experience, and School, National Academy Press, Wash-
ington, DC (2000)
8. Harris, A.H., and M.E Cox, "Developing an Observation System to
Capture Instructional Differences in Engineering Classrooms," J. of
Eng. Ed., pg. 329 (2003)
9. Power, C.N., "Effects of Student Characteristics and Level of Teacher-
Student Interaction on Achievement and Attitudes," Contemporary
Educational Psychology, 2(3), 265 (1977)
10. Stiles, W.B., C.S. Waszak, and L.R. Barton., "Professorial Presump-
tuousness in Verbal Interactions with University Students," J. of
Experimental Social Psychology, 15(2), 158 (1979)
11. Clarke, J.A., and B.W Carss, "A Procedure for Analyzing Classroom
Dialogue," Int. J. Educational Research, 12(4), 427 (1988)
12. Glasgow, N., Doing Science: Innovative Curriculum for the Life Sci-

ences, SAGE Publications (1996)
13. Thompson, N.S., E.M. Alford, R. Johnson, C. Liao, and M.A. Matthews,
"Integrating Undergraduate Research into Engineering: A Communica-
tions Approach to Holistic Education," J. ofEng. Ed. (2005)
14. Donath, L., R. Spray, N.S. Thompson, E.M. Alford, N. Craig, and
M.A. Matthews, "Characterizing Discourse Among Undergraduate
Researchers in an Inquiry- Based Community of Practice," J. ofEng.
Ed., 94(4), 403 (2005)
15. Donath, L., and R. Spray, "Linguistic Evidence of Cognitive Distri-
bution: Quantifying Learning Among Undergraduate Researchers in
Engineering," Proceedings of the American Society for Engineering
Education (ASEE) Annual Meeting and Exposition, Salt Lake City
16. Long, C., E.M. Alford, J. Brader, L. Donath, R. Johnson, C. Liao, T.
McGarry, M.A. Matthews, R. Spray, N.S. Thompson, and E. Vilar,
"The Research Communications Studio as a Tool for Developing
Undergraduate Researchers in Engineering," Proceedings of the

American Society for Engineering Education (ASEE) Annual Meeting
and Exposition, Salt Lake City
17. Alford, E.M., N.S. Thompson, J. Brader, B. Davidson, S. Hargrove-
Leak, and E. Vilar, "Introducing Engineering Graduate Students
to Learning Theory and Inquiry-Based Learning: A Collaborative,
Interdisciplinary Approach," Proceedings of the American Society
for Engineering Education (ASEE) Annual Meeting and Exposition,
18. Simon, H.A., "Learning to Research About Learning," in S. Carver
and D. Klahr (Eds.), Cognition and instruction: Twenty-five years of
progress, Erlbaum, Mahwah, NJ, 205-226 (2001)
19. Vygotsky, L.S., Mind in Society, Harvard University Press, Cambridge,
MA (1978)
20. Edelsky, C.. Who's Got the Floor?: Gender and Conversational Interac-
tion, Deborah Tannen, Ed., Oxford University Press, Oxford, 189-227
(1993) 1

Chemical Engineering Education




Application to Granulation Processes


n many chemical engineering degree programs world-
wide, particle and powder technology is not afforded the
same attention in the curricula as processes and technolo-
gies incorporating liquids and gases."1 Consequently, it is not
surprising that plants handling solids perform less optimally
than those processing only liquids and gases.[2] There is there-
fore need for new courses in particle science and technology
in the established chemical engineering curricula.
Chemical engineers are used to handle mass, energy, and
momentum balances in modeling and designing equipment
for the chemical industry. Often, however, they are not as
familiar with the population balance equation (PBE) to de-
scribe important attributes of particulate streams (e.g., particle
size distributions). While the PBE is generally agreed to be
difficult to solve, many students find even formulating it to
be very complicated.
An optional course for education in particle technology has
been introduced in the last year of the chemical engineering
program at the Universidad Nacional del Sur, Argentina.

During instruction of the PBE formulation, we found that
analogies with chemical reaction principles (well known
by the alumni) helped the students to understand this "new"
constitutive equation.
In this work we are particularly focused on the approach
to teaching PBE formulation in the context of granulation

Veronica Bucal is a professor of chemical engineering at Universidad
Nacional del Sur (Bahf Blanca, Argentina). She received her B.S. and
Ph.D. degrees in chemical engineering from the same university. She
held a postdoctoral research fellow position at Massachusetts Institute of
Technology, Cambridge, Mass. Her research interests are in the area of
chemical reaction engineering and simulation of solids processes.
Juliana Pina is an assistant researcher in the Chemical Engineering De-
partment at the Universidad Nacional del Sur (Bah f Blanca, Argentina).
She received her B.S. and Ph.D. degrees in chemical engineering from
the same university. She held a postdoctoral research fellow position at
University of Western Ontario, London, Canada. Her research interests
include modeling and simulation of catalytic chemical reactors and
granulation processes.

� Copyright ChE Division of ASEE 200;

Vol. 41, No. 3, Summer 2007

Figure 1 shows a schematic diagram of a granulation unit.
The seeds-i.e., particles whose diameters are smaller than
those of the granular product-may be fed to the system
either initially (batch processes) or continuously (continuous
granulators). Inside the granulation "box," these particles
undergo an effective growth. A liquid solution (e.g., a concen-
trated solution or melt) is sprayed into the granulation unit.
Depending on the type of granulator, air can be fed into the
unit to fluidize the bed. 31
Inside the granulator the particles are involved in many
mechanisms of size enlargement or reduction. Depending
on the process, they can occur alone or simultaneously. This
is the reason why the seeds' particle size distribution (PSD)
evolves to a different exit or final PSD (see Figure 1). The PBE
is the tool that allows, for example, predicting the granules'
size distribution.

The PBE formulation requires understanding of the phe-
nomena the particles are subjected to during the granulation
evolution. Figure 2 schematically shows the nucleation,
layering, coalescence, attrition, and breakage processes. All
these processes are well explained by, among others, Litster,
et al.,[3 and Rhodes.J41
Nucleation is the formation of new seeds from liquid or fine
powder feed. New granules can be formed when the liquid
drops (produced in the spray) solidify before they reach the
surface of the seeds. This mechanism is discrete. This adjec-
tive means that the new nuclei just appear, i.e., they are not
produced gradually. Layering increases the granule size by
coating the particle surface with drops produced in the spray
zone. The growth is differential, i.e., the particle size augments
progressively. Particles may also undergo coalescence, i.e.,
two particles agglomerate to give a bigger one, this being a
discrete phenomenon. By means of the attrition mechanism
the particles suffer surface wearing, a differential granule size
reduction. The granule breakage is also a discrete process, where

one particle can produce more than two fragments due to colli-
sions with other particles and/or with the granulator walls.[4 5]
The PBE has to capture all the granulation rate processes
to predict the granulometry of the final product. Before dis-

oo 5eeds


SGranular 0 0
Product O0

Seeds PSD Product PSD
Particle Particle
Property Property
Jj -.+ PBE [-- I

dp dp

Figure 1. A schematic diagram of a granulation unit and
its relationship with the PBE.

0� 00

O + + - OJ

oo- _o o.

O -r * J

Figure 2. Granulation rate processes.

Sieve Analysis of a Single Sample, Using Different Sets of Sieves
Fine Grid Coarse Grid 1 Coarse Grid 2
Size Range, mm Count, # n(dp), #/mm dPa,,, mm Size Range, mm Count, # n(dp), #/mm dPav, mm Size Range, mm Count, # n(dp), #/mm dPav, mm
0 00-021 0 0 00 011 0 00-0 297 0 0 00 015 000-021 0 000 011
021-0297 0 000 025 0297-059 30 10239 044 021-042 10 4762 032
0297-042 10 81 30 036 059-1 19 90 15000 089 042-084 50 11905 063
042-059 20 11765 051 1 19-200 160 19753 160 084-1 68 160 19048 126
059-084 30 12000 072 200-336 40 2941 268 1 68-238 90 12857 203
084-1 19 60 171 43 102 336-476 0 000 406 238-476 10 420 357
1 19-168 100 20408 144 476-566 0 000 521 476-566 0 000 521
1 68-200 60 18750 184 NT=320 NT=320
200-238 30 7895 219
238-336 10 1020 287
336-476 0 000 406
476-566 0 000 521
210 Chemical Engineering Education






secting the population balance equation, it is necessary to
understand how to represent particle populations properly. In
the next section different particle size distributions (PSDs)
will be discussed.

The particle size distributions are presented in many books,
such as Litster, et al., 31, Rhodes,[41 and Randolph and Larson.[6]
The proper particle size distribution to compare populations
is the density function as suggested, for example, by Litster,
et al.[3 The students, however,-and even chemical engineers
working in industry--frequently use the plot of number of
particles (or mass fraction) as a function of mean diameters
to represent the size distribution of a given particle popula-
tion. In this section, the need for using the density function
is presented through an example. This didactic explanation
was found understandable by all the students that participate
in the classes. The working example was sufficiently clear to
prove the need for using the density function as a description
of the particle size distribution.
Table 1 shows different data size analyses performed to
the same particle sample. First, the population was analyzed

150- Fine Grid
0 75-

150- Coarse Grid 1
1 100-
6 75

150- Coarse Grid 2
50 -
0 1 2 3 4 5 6
dp, mm

Figure 3. Histogram of frequency (number)
vs. particle size.
Vol. 41, No. 3, Summer 2007

employing 11 sieves (fine grid). Secondly, some sieves were
extracted from the original set of sieves, and the same sample
was studied by using just 6 sieves (coarse grid 1). Finally, the
sample was analyzed by using 6 different sieves from those
of coarse grid 1 (coarse grid 2). From this information, the
histogram of frequency (count) vs. particle size can be built
for the three grids presented in Table 1. Figure 3 shows the
histograms that were thus obtained. Even though the same
population has been analyzed, the histograms are very differ-
ent. Therefore, the graphs of count vs. particle size cannot be
used to evaluate size population similarities. The number of
particles is often plotted as a function of the average diameter
of the size interval. As can be seen in Figure 4, an inspection of
the curves does not indicate that the distributions are similar,
in agreement with the histograms of frequency (Figure 3).
The density function (n) is a particle size distribution that
allows comparison of populations,[3] and it is defined in a
discrete form as:

n,(dp)= n(1)

where n, is the number of particles between two contigu-
ous sizes (dp and dp ,) and Adp is the interval width (dp,1
- d ). The continuous density function can be expressed as

n(dp) =--

where N is the number cumulative distribution and has the
units of number of particles (#). The density function n (#/L;
where L indicates a generic length unit) represents the number
of particles per unit of particle size. The continuous density
function verifies the following equation:

fn(dp)d(dp)= NT (3)

dp,, mm

Figure 4. Particle number as a function of the
average diameter.

Often the frequency or density distribution is expressed as
a normalized distribution:

n(d) (dp)= f f(dp)d(dp) = 1 (4)

where NT and f(dp) are the total number of particles (#) and
the normalized density function (L 1), respectively.
Eq. (3) indicates that the total area under the curve n(dp)
vs. dp has to be equal to the total number of particles. Figure
5 shows the histogram of the density function, calculated
according to Eq. (1), for the fine grid presented in Table 1.


200 -Fine Grid


o 100


0 1 2 3
dp, mm

4 5 6

Figure 5. Density function as a function of the
particle diameter.
--- Fine Grid
200 o Coarse Grid 1
o Coarse Grid 2
E 150


0 1 2 3 4 5 6
dpav, mm
Figure 6. Density function as a function of the average
diameter for the sample analyzed with
different sets of sieves.

o00 c0

V1 V2 V=V1 +V2

Figure 7. Preservation of volumes in the
coalescence process.

Since Eq. (3) has to be satisfied, from the discrete representa-
tion histogramm) it is possible to obtain a continuous density
function that preserves the area under the curve n(dp) vs. dp
(this is the continuous curve that appears in Figure 5). As
can be noticed, the original particle number attributed to a
size interval in the histogram representation can be assigned
approximately to the average diameter of the size interval for
the continuous curve. That is the reason why the continuous
density function is often plotted as a function of the arithmetic
mean of the size range.
Figure 6 shows the number density function for the fine and
coarse grids of Table 1. It is clear that the data of coarse grids
1 and 2 track well the density function calculated from the
fine grid. This fact indicates that independent of the number
of sieves employed in an experimental analysis or the grid
points selected in a numerical procedure, the density function
of a unique sample has to be equal. The density distribution is
independent of the interval widths used for experimentation
or numerical analysis. This point is very important, since the
density function is commonly used to formulate the popula-
tion balance equation.
When agglomeration takes place, particles of different
volume coalesce to give a bigger one. As seen in Figure 7,
the new particle has a volume equivalent to the sum of the
volumes of the individual ones. For this reason, the PBE
commonly uses the density function in terms of volume
rather than particle diameter.4, 7 8] When the volume is se-
lected as the representative size of the particles, the density
function becomes:


where AVp is the volume interval width. For Eq. (5), the
density function n has the units of #/L3.
At this point, the students should have in mind that the
density function is the proper distribution for characterizing
particulate systems and that the density function based on
particle volume is appropriate to represent coalescence pro-
cesses. Certainly, these items have been already treated in
the literature3 5s 6]; nevertheless students often have difficulty
understanding these two key points. The order of explanation
of the topics was found adequate in the performed teaching

The ideal granulation units are classified according to their
flow pattern into perfectly mixed and plug flow granulators.
These are exactly analogous to the Continuous Stirred Tank
Reactor (CSTR) and the Plug Flow Reactor (PFR) in chemi-
cal reactors, respectively.[3] The PBE for size enlargement
processes has been introduced in several books and publica-
tions, among others, Litster, et al.,[31 Rhodes,[4] Randolph and

Chemical Engineering Education

Larson,[61 and Heinrich, et al.[910] Even though the PBE derivation can be
found in the literature, the internal coordinates (particle properties) are
hard to visualize for many students. In the following sections, the flow of
particles in the internal coordinates is specifically discussed, focusing on
the clear definition of the control volume to derive the PBE. Moreover,
the granulation rate processes and flow of particles are compared with
the chemical reactions and flow patterns occurring in chemical reactors,
respectively. This didactic strategy, employed to some extent by Litster, et
al.,[3] was found very useful in teaching the subject to advanced chemical
engineering students.

Figure 8 shows what can be seen through a window in a perfectly mixed
granulator. Inside the unit, particles of different diameters are located
everywhere. The perfectly mixed condition implies that the particle size
distribution is identical throughout the granulator volume.
If the population of Figure 8, which is identical in any position of the
granulator, is classified in baskets of different sizes, the particles contained
in the granulator of Figure 8 can be schematized as shown in Figure 9.
For a granulator like the one presented in Figure 1, a seed particle dis-
tribution is fed continuously to the system. In the "baskets" representation
of the particle population inside the granulator (Figure 9), the addition
contributes particles of different sizes that have to be classified in the
size compartments. Similarly, a granular product extraction involves the
removal of particles from different size boxes. In a common granulation
process, the additions will specifically increase the number of particles
in the smaller-size boxes.
If two particles coalesce to give a bigger one, in a discrete manner,
both particles will abandon their respective size 'baskets" to increase
the number of particles of a compartment that stores bigger particles.
The effect of the binary breakage is opposite to the one caused by the
agglomeration or coalescence phenomenon. Coalescence and breakage
produce the birth of particles for some sizes and simultaneously the death
of particles for other sizes. Nucleation leads to the birth of particles of

small size. Even though it is not shown in Figure
9, the particle population generated by nucleation
has a density function distribution. Therefore,
the nuclei can enter several size compartments.
Layering and attrition cause the differential
particle enlargement and diminution. Therefore,
the particles gradually leave the size clusters to
the contiguous ones."11
A similar conceptualization of the flow of
particles shown in Figure 9 was introduced by
Heinrich, et al.[91 In this paper, however, a com-
plete description of all the feasible flows into and
out of the particles "baskets" is given, facilitating
the student's comprehension.
Once the influence of the granulation rate
processes on the movement of particles from one
size "basket" to others is understood, the PBE
formulation can be discussed.
For the PBE derivation, the frequency distri-
bution per unit of granulator volume (n+) is also

O Of 0 0O o


O O 0 0
0 0o

o OoO�
o 0o000oo o
00 �?0

A Figure 8. Conceptual-
ization of a perfectly
mixed granulator.

4 Figure 9. Classifica-
tion of the particles
according to the volume

Vol. 41, No. 3, Summer 2007


extractions ----- ------------
Breakage Attrition


commonly used. This distribution is related to the density
function n according to the following expression:

n (Vp) n(Vp) (6)

where V is the volume of the granulation unit. Therefore,
n (Vp) has #/L6 units.
The symbol i+ (Vp) is reserved for the frequency dis-
tribution per unit of volume and time (#/L6 t), and is used
to represent birth and death rates; fi(Vp) is completely
equivalent to the chemical reaction rate of a chemical reactor.
In order to understand these new properties better, Table 2
shows the analogy of the particle size distributions presented
in this work with the variables commonly used in the design
of chemical reactors.
Bearing in mind the concepts introduced in Figure 9, the
particle number balance for a generic "basket" of volume
AVp can be expressed as:

Number of particles Number of particles
in time t in time t+At
INumber of particles"in" [Number of particles "out"t
by layering/attrition I [by layering/attrition
INumber of particles "in" [Number of particles
by coales./break./nucleationj ["out" by coales./break.j
[Number of particles Number of particles
"in" by additions " out" by extractions

n+(Vp) AVp VLt n+(Vp) AVp Vltt
+(G-A)n+(Vp)V At I,

-(G -A)n+ (Vp)V At A Vp V

+lb (Vp) Vp VAt-tl (Vp) AVpV At

+Q,n n (Vp) AVp At
-Qout n+, (Vp) AVp At = 0

where G is the growth or layering rate (L3/t); A, the attrition
rate (L3/t); ibirth(Vp), the birth of particles of class Vp by
coalescence, breakage, and nucleation; nideah(Vp), the death
of particles of class Vp by coalescence and breakage; Qn and
Qout are the inlet and outlet particle volumetric flow rate (L3/t);
and n+ (Vp) and no, (Vp) are the density distributions of the
seeds and granular product streams (#/L6).
Dividing the entire resulting Eq. (6) by AVp and At and
taking the limit as AVp and At tend to zero, the differential

PBE for a perfectly mixed granulator is obtained:

& n (Vp)V] & (G- A)n (Vp)V
at Vp
+nbrth (Vp)V - death (Vp)V
+Q,nn+ (Vp)- Qoun+ (Vp)= 0 (9)

As mentioned above, nibth and neaih are terms analogous to
the chemical reaction terms in chemical reactors.[11 The birth
and death coalescence and the breakage rates all require the
use of theoretical or empirical models that depend on nW, as
the chemical reactions are functions of the concentration of
different species.
Since the granulation is supposed to be perfectly mixed,
the outlet density function of the population can be as-
sumed to be equal to the distribution inside the granulator,
n+t((Vp)= n+(Vp). Considering this relationship and Eq.
(6), Eq. (9) becomes:
On O[(G-A)n]
at &Vp
+nb,, h death

+ n - un =0 (10)

A similar derivation of the PBE can be found elsewhere.[3.4]
The sequential presentation of the process conceptualization,
shown in Figure 9 and the PBE derivation, were found helpful
while teaching, however. From our experience, this compre-
hensive view of the internal coordinates makes understanding
Eq. (10) easier.
Eq. (10) has the following two first derivative terms: the
accumulation term for unsteady state behavior, and the dif-
ferential term of layering and attrition. The second first deriva-
tive represents a convective term in the Vp direction because
there is a plug flow of particles in the volume particle axis.
Therefore, a granulator that is perfectly mixed with respect

Figure 10. Drum granulator scheme.

Chemical Engineering Education



to the real flow pattern exhibits a convective term in a new
coordinate. The particle size is recognized as an internal co-
ordinate; while the spatial coordinates of the equipment are
commonly called external coordinates.J6 12]
In short, a perfectly mixed granulator behaves as a plug
flow for the chosen particle property the population balance
is focused on. This analogy was found effective in teach-
ing the process to advanced chemical engineering students,
who are familiar with chemical reaction engineering. In
the example described, the number variation was evaluated
for changes in the particle volume. Other particles proper-
ties, however,-such as porosity and density-can also be
considered. The size classification given in Figure 9 can be
adapted to other particle properties for processes with several
internal coordinates.

The drum granulators are basically inclined cylinders that
are rotated to facilitate the movement of particles toward one
end of the unit (see Figure 10). As a rough approximation, it
can be assumed that the granules flow through the drum in
plug flow.[31 In this section, the PBE is derived for this type
of ideal granulator.
As is the case for chemical reactors, the flow of particles in
plug flow granulators can be associated with a series of perfectly
mixed units, as shown in Figure 11. For a Az length element,
the particles can also be classified according to their sizes, as
schematized in Figure 12 (see page 216). The real flow of
particles only occurs in the axial direction, though a flow of
particles in the Vp direction is also needed in order to capture

all the rate processes that can occur during granulation.
For a volume element AVp A Az, where A is the granulator
cross section (L2), a number balance turns into:
Number of particles _Number of particles
in time t J in time t+At
[Number of particles"in" Number of particles "out"
by layering/attrition by layering attrition
[Number of particles "in" iNumber of particles
Sby coales./break./nucleationj ["out" by coales./break.

"in" by convective flow ["out" by convective flow

n+(Vp) AVp A Az - n+ (Vp)AVp AAz, zt
+(G-A)n+ (Vp)A AzAt-

(G- A) n (Vp) AAz At I p

nbirh ,(Vp) AVp A Az At
-ndeath(Vp)AVpA AzAt
+v A n+(Vp)AVp Atlz
-v, A n+(Vp)AVp AtAt = 0

where vz is the velocity of the particles (L/t).
Dividing the entire resulting Eq. (12) by A, AVp, Az and
- At and taking the limit as AVp,
' Az and At tend to zero, the dif-
o Seeds ferential PBE for a plug flow
0o 4 granulator becomes:

o On+ 0 (G - A)n
.0 at OVp

Figure 11. Conceptualization of a plug flow of particles.

Analogy Between the Properties of Granulators and Chemical Reactors

Granulators Reactors

Symbol Description Units Symbol Description Units

n Frequency distribution #/L3 NA Moles of the A specie mol
n+ Frequency distribution per #L6 CA Concentration mol/L3
unit of volume
+ Frequency distribution per #L6 t rA Reaction rate mol/L t
unit of volume and time
Vol. 41, No. 3, Summer 2007


- nbrth

-1i = 0

Eq. (13) shows the fol-
lowing three first derivative
terms: the accumulation
term, and two convective
terms in the Vp (internal) and
z (external) coordinates.
It is important to stress
that the control volume to


Figure 12. Change of particle size in internal and external coordinates.

derive the PBE for this system is not clearly presented in the
literature. The conceptualization of the control volume given
in Figure 12 lets the students understand in a rapid and easy
way the PBE for plug flow granulators.

The PBE given by Eq. (13) can be generalized to a system
where convective flow may occur in all the granulator real
coordinates, considering that many particle properties may
change during the granulation. Following the same line of
reasoning as the one for plug flow granulator, the generalized
PBE equation can be obtained[6]:

On+ [v n [Ov n O vzn+
Ot Ox ay Oz
Sv, n+ .+
- Ox +bnrth death =


where v , Vy, and vz are the velocities of the particles in the
external coordinates x, y and z of the granulation unit; v cor-
responds to the rates of the selected particle properties that
change in a differential manner; x are the internal coordinates,
while m symbolizes the number of internal coordinates chosen
to represent particle properties. The units of v , vy, and vz are
L/t, while v has the units of the internal coordinates x per
unit of time.

As mentioned, the described material was used to teach
the formulation of the population balance equation applied to
granulation processes in the framework of an optional course
given for advanced students of chemical engineering. The
course is an elective in the last year of the chemical engineer-
ing career at the Universidad Nacional del Sur, Bahia Blanca,
Argentina. The course entitled "Solids Processing" covers
the following main topics: particle size analysis, particles in
fluids, fluidization, solids conveying, gas solid and solid sepa-
ration, solids storage, solids caking, solids mixing, particle

Chemical Engineering Education

size comminution and enlargement. The population balance
equation is introduced when the last two chapters are covered.
The approach described in this contribution is particularly
useful for the last chapter (size enlargement). The emphasis
on granulation processes is motivated by the presence of an
industry that produces about 1 million tons of granulated
urea/year in our city. It is important to note that the material
presented in this work was also successfully employed to teach
the "meaning and potential uses" of the PBE for granulation
processes to engineers working at fertilizer plants.
The textbooks used in the course are, among others,
the ones written by Rodhes,[4] Litster, et al.,[3] Seville, et
al.,[13] and Kunii and Levenspiel.[14] The homework and
exams assigned to the students include the development
of the population balance equation for various granulation
equipment and different particle properties. Regarding
the solution of PBEs, only the simple cases for which
analytical solutions can be found are covered in the un-
dergraduate course.

The method presented in this paper for introducing the
derivation of population balance equations was used to
teach the subject both to chemical engineers that work in
a granulation plant and to chemical engineering students.
The conceptualization of the internal coordinates was clear
and comprehensible for all of them. Our approach can be
considered valuable as a teaching strategy to explain the
PBE in the context of granulation processes. In particular,
the analogy with chemical reactors is useful because this is
a subject well known by the advanced chemical engineer-
ing students. Probably the PBE is not as extensively used
as it could be, due to early difficulties understanding its
derivation and then solving the final equation. The pres-
ent contribution may help students/teachers that want to
start learning/teaching population balances for model size
enlargement processes.

This work has been supported by the Consejo de Investiga-
ciones Cientificas y Tecnicas (CONICET), Agencia Nacional
de Promoci6n Cientifica y Tecnol6gica (ANPCyT, Grant:
PICT 25541) and Universidad Nacional del Sur, Argentina.

1. Fitzpatrick, J.J., N. Zumaeta, and E.P Byrne, "Teaching Particle and
Powder Technology in Chemical Engineering at University College
Cork," Fifth World Congress on Particle Technology, Orlando, FL,
April 2006
2. Bell, T.A., "Challenges in the Scale-Up of Particulate Processes-An
Industrial Perspective," Powder Technology, 150, 60-71 (2005)
3. Litster, J., B. Ennis, and L. Liu, The Science and Engineering of Granu-
lation Processes, Particle Technology Series, 15, Kluwer Academic
Publishers, London (2004)
4. Rhodes, M., Introduction to Particle Technology, John Wiley & Sons,
West Sussex, England (2003)
5. Iveson, S.M., J.J. Litster, K. Hapgood, and B.J. Ennis, "Nucleation,
Growth, and Breakage Phenomena in Agitated Wet Granulation Pro-
cesses: A Review," Powder Technology, 117, 3-39 (2001)
6. Randolph, A.D., and M.A. Larson, Theory of Particulate Processes,
Academic Press, New York (1971)
7. Ramkrishna, D., Population Balances. Theory and Applications to Par-
ticulate Systems in Engineering, Academic Press, San Diego (2000)
8. Scarlett, B., "Particle Populations-To Balance or Not To Balance,
That is the Question," Powder Technology, 125, 1-4 (2002)
9. Heinrich, S., M. Peglow, and L. Mbrl, i ,,.I, ..I and Steady State
Particle Size Distributions in Batch and Continuous Fluidized Bed
Granulation Systems," Chem. Eng. J., 86, 223-231 (2002)
10. Heinrich, S., M. Peglow, M. Ihlow, and L. Msrl, "Particle Population
Modeling in Fluidized Bed-Spray Granulation-Analysis of the Steady
State and Unsteady Behavior," Powder Technology, 130, 154-161
11. Cameron, I.T., EY. Wang, C.D. Immanuel, and E Stepenek, "Process
Systems Modeling and Applications in Granulation: A Review," Chem.
Eng. Sci., 60, 3723-3750 (2005)
12. Ramkrishna, D., and A.W Mahoney, "Population Balance Modeling:
Promise for the Future," Chem. Eng. Sci., 57, 595-606 (2002)
13. Seville, J.PK, U. Tuizin, and R. Clift, "Processing of Particulate Sol-
ids," Particle Technology Series, Blackie Academic and Professional,
London (1997)
14. Kunii, D., andO. Levenspiel, i I.,,I, ..... i .i.._... ..... "Butterworth-
Heinemann: Newton, MA (1991) [

Vol. 41, No. 3, Summer 2007

M]n1= class and home problems

The object of this column is to enhance our readers' collections of interesting and novel prob-
lems 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 dif-
ficult concepts. Manuscripts should not exceed 14 double-spaced pages and should be accompanied
by the originals of any figures or photographs. Please submit them to Professor James 0. Wilkes
(e-mail: wilkes@umich.edu), Chemical Engineering Department, University of Michigan, Ann
Arbor, MI 48109-2136.



An Exercise for Understanding the Nature of

False Solutions and How To Avoid Them


University of Alicante * Alicante, Spain 03080
One major objective of a thermodynamics course is to
introduce the modeling of vapor-liquid equilibrium
(VLE) and liquid-liquid equilibrium (LLE). The
analysis of flash methods used to obtain this equilibrium data
involves the simultaneous solution of a set of equilibrium
and mass balance equations. When these methods are used
for LLE, finding the equilibrium solution can be difficult, as
different problems can arise. For example, the solutions may
be very sensitive to the objective function, the initial-guess
values, and the algorithm used in the optimization method.
Many papers in the past have discussed different aspects and
strategies proposed to solve the LLE calculations. Information
published in scientific papers, however, covers different and
very specific aspects, and the topic is complex, making it very
difficult to extract general and clear conclusions about the best
procedure to evaluate LLE data. Nowadays, on the other hand,
the commercial process simulators - such as Aspen Plus, Hy-
sys (Aspen Tech), and ChemCAD (Chemstations) -include
phase equilibrium calculation strategies capable of overcom-
ing the above important difficulties, but they do not include
details about their internal calculations. Process simulators
are introduced to and used by students in different graduate

courses, but these computer tools are not useful for compre-
hension of the phase equilibrium problem.
This paper presents an exercise for chemical engineering
students in LLE data calculations, and shows limitations of

Antonio Marcilla is a professor of chemical engineering at Alicante
University. He has presented courses in Unit Operations, Phase Equilibria
and Unit Operations, and Chemical Reactor Laboratories. His research
interests are pyrolysis, liquid-liquid extraction, polymers, and rheology.
He is also currently involved with the study of polymer recycling via
catalytic cracking and the problem of simultaneous correlation of fluid
and condensed phase equilibria.
Maria del Mar Olaya completed her B.S. in chemistry in 1992 and Ph.D.
in chemical engineering in 1996. She teaches a wide range of courses
from freshman to senior level at the University of Alicante, Spain. Her
research interests include phase equilibria calculations and polymer
structure, properties, and processing.
Juan A. Reyes-Labarta received both his B.S. and Ph.D. in chemical
engineering in 1993 and 1998, respectively, at the University of Alicante
(Spain). After post doctoralstays at Carnegie Mellon University (USA) and
the Institute of Polymer Science and Tecnology-CSIC (Spain), he is now
a full-time lecturer in Separation Processes and Molding Design.
Isabel Ibarra and Maria Dolores Serrano are recent chemical engineer-
ing graduates of the University of Alicante. They are currently postgradu-
ate students, working on different aspects of phase equilibria.

� Copyright ChE Division ofASEE 200,

Chemical Engineering Education

the isoactivity criterion as the unique search condition. This
criterion is combined with the common tangent line condition
to prevent false equilibrium solutions, in a way that is easy
for graduate students to program, for example, in EXCEL.
Also, an adaptation of the vector method proposed by Eubank,
et al.,11 has been used for LLE calculations, showing some
interesting aspects that can be discussed in postgraduate
courses on phase equilibria.

The two usual approaches for solving phase equilibrium
problems are the K-value method, where a set of material
balances and equilibrium equations are solved simultaneously,
and the Gibbs energy minimization (GEM) method.[2]
K-Value Method
At constant temperature (T) and pressure (p), a heteroge-
neous closed system, consisting of P phases and c components,
is in equilibrium when the following condition is satisfied:
t, = iC = ....= It, (1)

where tp is the chemical potential of the component i in
phase P.
For two liquid phases (I and II), Eq. (1) can be written as:
a=a a or ,x, =mx, (2)
where a, , P, x are the activity, activity coefficient, and mo-
lar fraction of the component i in phase P, respectively. Alter-
natively, Eq. (2) can also be written as K, = x" / x = I
where K is the phase equilibrium constant for the component i.
Consider the problem when calculating compositions of
conjugated liquid phases that are obtained from a hetero-
geneous ternary mixture, M. To solve the problem, mass
balances and equilibrium conditions [Eq. (2)] should be
Models such as NRTL or UNIQUAC, which can be used to
calculate the activity coefficient, need the
values of binary interaction parameters A
(six parameters for a ternary system). The o
DECHEMA Chemistry Data Series[3' col- GM/RT
lects such parameters for most published
phase equilibrium data.
Gibbs Energy Minimization Method
The two-liquid phases and the c-com-
ponent equilibrium problem can be inter-
preted geometrically in the dimensionless
Gibbs energy of mixing (GM/RT=gM) vs. 0 X
composition space. In this context, the so-
lution requires determination of the minor
common tangent line/plane/hyperplane
to the GM/RT curve/surface/hypersurface Figure 1. Differ
at two points (compositions)-without
intersections to such curve/surface/hy-
Vol. 41, No. 3, Summer 2007

persurface. The latter condition ensures a global minimum
solution to the LLE problem. Therefore, the phase equilibria
solution minimizes the total Gibbs energy of the system.
Three principal algorithms have been proposed to solve the
total GEM problem:
a. The tangent line/plane method by Michelsen"41 and
Iglesias-Silva, et al.l21
b. The maximum area method developed by Eubank, et
al.,1l' and Elhassan, et al.f5s
c. The equal area method of Eubank and Hall.'6

The usual engineering approach for solving phase equilib-
rium problems is to use the K-value procedure. This method,
however, often fails because of the computational procedure.
For example, if the initial guesses for the iterative procedure
are too far from the correct solution, the program converges
to a local minimum rather than to a global one. Therefore,
the K-value method can predict a wrong phase equilibrium.
Only one solution, however, minimizes the total Gibbs en-
ergy. For binary systems, K-values succeed even with poor
initial guesses, but for more complex systems, Gibbs energy
minimization is preferable.
The high nonlinearity of the equations in NRTL or UNI-
QUAC is one of the reasons for the high sensitivity of solu-
tions to initial-guess values and to the algorithm used in
the optimization method. There is another reason not often
mentioned, that can also cause problems in finding the LLE
solution. It is desirable that the dimensionless mixture Gibbs
energy function (GM/RT) give a very good definition of the
two equilibrium points, as is shown in Figure 1( side a) for a
binary system, where the points with the lower common tan-
gent line are clearly defined. We have, however, verified that

molar fraction)

0 x(molar fraction)

ent possibilities for dimensionless Gibbs energy of mixing (Gm/
RT) for a binary system: a) good definition, and
b) poor definition of the equilibrium points.


for many systems the GM/RT function obtained with NRTL or
UNIQUAC models is very linear between equilibrium points
[Figure 1 (side b)]. This poor definition of the equilibrium
solution can have dramatic consequences in the tie-line cal-
culations, but the dimension of the problem also depends on
the algorithm used to find the equilibrium solution.
The K-value method is affected by this problem. The conse-
quence on LLE calculations in ternary systems, for example,
is that many solutions corresponding to very low values of
the activity objective function
O.F.(a) = (a - a")2 (3)
i 1
can be obtained and, therefore, wrong tie-lines are calculated.
On the other hand, the probability of this problem arising
increases when equilibrium compositions are closer to each
An Example
The following example illustrates this problem: the metha-
nol (1) + diphenylamine (2) + cyclohexane (3) system at
25 �C. More precisely, the tie-line obtained from the global
mixture M (z, = 0.5365; z2 = 0.0230; z3 = 0.4405) will be
calculated. The NRTL model is used to calculate the activity
coefficients, with a=0.2 and the values for the binary interac-
tion parameters obtained from DECHEMA Chemistry Data
Series[3] (Table 1).
The Solver package of Microsoft Excel 2000, accessible
to all the students at Alicante and very easy to use, has been
used to solve the problem. In Figure 2, some of the solu-
tions obtained using different initial-guess values are shown
together with the experimental data. Obviously, only one of
the calculated solutions corresponds with the true tie-line. For
this system, there is not a good agreement between experi-
mental and calculated tie-lines. This fact is not relevant for
our discussion, but is only an example of the limitations of
the NRTL model. What we are concerned with is how wrong
tie-lines can be obtained that correspond with very low values
of the activity objective function (i.e. O.F(a)<1012). Even in

0,04 --false cal
--false cal
---false cal
0,03 --cal
0,02 -


0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1

Figure 2. Comparison between tie-lines: experimental
and calculated with NRTL. False calculated tie-lines
are included corresponding to O.F.(a)<10-12.

NRTL Binary interaction parameters (K) for methanol (1) +
diphenylamine (2) + cyclohexane (3) at 25 �C.
A12= 873.57 A21= -1245
A13= 379.39 A31= 578.07
A23= -987.32 A32= -856.11

this example, if the true calculated tie-line is considered with
five significant figures for the molar fractions, the value of the
objective function is O.F(a) = 8.75 10 10, higher and worse
than those obtained for false calculated tie-lines.
The previous example shows that sometimes the isoactivity
criterion is not sensitive enough to calculate equilibrium data
and, as a consequence, problems in finding the true solution
can arise depending on the method or algorithm used for the

The K-value method can be modified to avoid false solu-
tions and converge more efficiently to the equilibrium solu-
tion. A possible modification adds another contribution to the
objective function, which considers the deviation of the minor
tangent line to the GMRT curve common to two compositions,
obtained in the sectional plane that contains the two points
considered as potential equilibrium points in each iteration.
When the true tie-line is calculated, both of the following
conditions are satisfied:
1. The activities of the three components in the two liquid
phases are equal (isoactivity).

2. The two liquid phases have a common tangent line to
the gM curve.
Therefore, the difference between false and true tie-lines,
all with very low activity objective function values, is that
false tie-lines have no common tangent line. We have checked
this second contribution to the objective function, and found
it is much more sensitive to very small deviations of the tie-
line. The common tangent line contribution to the objective
function is:

0gM (Og"M
O.F.(t) = &x i TD 3 +
0[9 pT,D p ,T,D

dx3 P,T, TD

where D is the slope of the line through the points I and II,
calculated as

x" - x
D= 22
x3 - x3

xM - X1
M 3
x3 - x3

Chemical Engineering Education

This means the partial derivatives of the dimensionless Gibbs
energy of mixing (gM) are calculated in the direction given
by the line from I to II compositions, one that also contains
the overall mixture M.
The combined objective function
O.F.= O.F.(a)+ O.F.(t) (6)

is sharper than the activity objective function, improving the
convergence of the optimization and avoiding false solu-
tions. This will be illustrated using the example previously
presented. When the same calculation has been carried out,
but the activity objective function [O.E(a)] changed to the
combined objective function (O.F) that also considers the
common tangent line condition [O.F(t)], the true tie-line
is always calculated far from the solution-even with bad
initial guesses.
For a better understanding of the behavior of both objective
functions, we have calculated and represented the minimum
values of both functions [O.E(a) and O.F] around the solu-
tion (Figure 3) using a sheaf of straight lines (defined by the
a-angle) passing through the common point corresponding to
the composition of the ternary global mixture M, very similar
to the vector method explained in the next section.[1'
Figure 3 shows that for all the a-angles around the true
tie-line solution it is possible to find two conjugated points
that satisfy the mass balance and give a very low activity
objective function value: O.F(a)<1012. These results show
the magnitude of the problem, from which two very important
consequences can be derived:
1. When the isoactivity criterion is used as the equi-
librium condition, we should be very strict in the
requirementsfor activity qualities.

1 E-04









1 E-05

OE+00 -x-

3.14 3.15 3.16 3.17 3.18

Figure 3. Objective function values [O.F.(a), O.F., and
O.F.(a) using the vector method] vs. a-angle for the ter-
nary tie-line calculation example.

Vol. 41, No. 3, Summer 2007

2 2

:* . I I * * : .
1 a b 3 1\ -r 3
(a) (b)

Figure 4. (a) Graphical explanation of the vector method
proposed to calculate the tie-line obtained from the
initial mixture M. (b) Scheme showing the Gm/RT
curve in a line I between r and s, and the two
common tangent points I and II.

2. The addition of the common tangent line objec-
tiveifunction to the isoactivity condition improves
convergence of the optimization because a sharper
minimum is obtained (Figure 3).

The vector method is not an alternative equilibrium condi-
tion, but a method for directing or controlling the search for
the unknown compositions to find the true tie-line. The vector
method needs an equilibrium condition such as the isoactiv-
ity criterion, the minimization of the global Gibbs energy of
mixing, or the common tangent plane.
In the previous calculations, the iterative procedure to
obtain the unknown compositions is directed by the optimi-
zation algorithms included in the Solver. Therefore, in those
calculations, the vector method has only been used as a tool
to study the values of different objective functions in the area
around the solution. In this section, a different procedure to
calculate the tie-line has been evaluated. In this procedure, an
adaptation of the vector method proposed by Eubank, et al.,[1]
is used as a guided LLE search. This method is schematically
represented in Figure 4.
Consider the ternary system 1-2-3, where the binary 1-3 is
partially miscible and the other two binaries, 1-2 and 2-3, are
completely miscible. The problem is to find the LLE tie-line
that connects the compositions generated from the hetero-
geneous global mixture M. The tie-line for the 1-3 binary
system must be previously known [i.e., a, b in Figure 4(a)].
If not, it will be calculated using, for example, the isoactiv-
ity criterion. With the binary tie-line and the initial mixture
M, the two lines, r and s, are obtained, which limit the zone
where the ternary tie-line (if it exists) will be confined (shaded
area in the Figure 4(a)). The a-angle is defined to character-
ize any lines from r to s with the common point M. This is a

x O.F. (a) <1012
- O.F.=O.F.(a)+C
Vector method

* I
O.F.(a) .

. j

* )
* I
* ;

modification of the procedure presented in the original paper,
where the a-angle (-90',+90�) was not limited. The benefit
is that the tie-line search is restricted to a more limited area,
where the solution is probably located, improving the con-
vergence of the calculation. In any of the lines (1) between r
to s, the dimensionless mixture Gibbs energy function (gM)
can be calculated using, for example, the NRTL equation for
excess contribution.
At this point, Eubank, et al.,E'1 proposed the area method.
For a constant value of the a-angle, this method consists of
locating the two points (I and II in Figure 4(b)) where the area
(A) confined between the tie-line and the gM is the largest in
absolute value. This condition is equivalent to locating the two
points with the lower common tangent to the gM function on
the fixed direction, 1. Next, the a-angle for the tie-line must
be found using an equilibrium condition. There are several
conditions that can be used as the LL equilibrium condition,
when common tangent points such as I and II are calculated
as a function of the a-angle value.
Representative conditions are:
1. The isoactivity condition.
2. The minimization of the overall Gibbs energy
of mixing.
3. The minor common tangent plane criterion.

In this respect, note that the global maximum of the areaA,
among all maxima obtained at different a-angles, is not an
equilibrium condition to find the tie-line a-angle, as discussed
by Elhassan, et. al.J51
Next, the results obtained from combining the vector meth-
od with two different equilibrium conditions-isoactivity,
and minimization of the overall Gibbs energy of mixing -are
presented for the example previously discussed.
The Isoactivity Condition
In Figure 3, the values of the activity objective function,
O.E(a) using the vector method calculated by comparing the
two points with a minor common tangent line for different
values of the a-angle, have been graphically represented as a
function of the a-angle for the methanol (1) + diphenylamine
(2) + cyclohexane (3) system at 25 �C, and the mixture
point of the previous example. The comparison in Figure
3 of the three different approaches used to find the ternary
tie-line shows that a sharper minimum, corresponding with
the "true" tie-line obtained from the global mixture con-
sidered, is obtained when the vector method is used. Using
this method, the true solution is obtained without multiple
or false solution problems.
On the other hand, it is very important to underline that
when the vector method is used both the isoactivity and com-
mon tangent line conditions are not simultaneous [as is the
case of Eq. (6)] but sequential:
1. The two compositions I and II in Figure 4, with the minor

common tangent line, are obtained for each a-angle.
2. The minimum of the activity objective function, cal-
culated comparing these two compositions [Eq. (3)],
as function of the a-angle, is located using, e.g., the
Newton-Raphson method.
Therefore, when the isoactivity condition is combined with
the common tangent line criterion, either simultaneously
[Eq. (6)] or sequentially (vector method), a more efficient
equilibrium calculation can be carried out, avoiding false
solutions with very low values of the activity objective
Minimization of Overall Gibbs Energy of Mixing
The vector method with the equilibrium condition based on
the minimization of the overall GEM has also been evaluated.
When the lower common tangent points to the (gM) function
are obtained in each line from r to s, the value of the dimen-
sionless GEM for the overall composition M can be calculated
(gTL in Figure 4(b) where TL denotes the tangent line). The
minimum of the gTL curve vs. a-angle corresponds with the
minimization of the global Gibbs energy and, therefore, with
the true tie-line obtained from the overall composition M.
The results obtained applying this procedure to the previous
example are shown in Figure 5. The procedure converges to
the solution without false tie-line problems. The false tie-lines
obtained for this system using only the isoactivity criterion
have also been included in Figure 5.

3.)5 3.10 3.15 3.20 3. 5
SX Tie-line
-0.412 - False tie-lines


C -0.415 -






Figure 5. Dimensionless global Gibbs energy of mixing
obtained from the common tangent line (gL) as
a function of the a-angle for the ternary
tie-line calculation example.
Chemical Engineering Education

The MATLAB (MathWorks, Inc.) tool for the three-dimen-
sional representations is used by the students to represent
the dimensionless GEM (gM) in all the composition space.
Figures obtained are discussed in the computer laboratory,
while looking for the best views to see the most important
topological aspects of this function. In Figure 6, one of these
representations is shown as an example that corresponds with
the system methanol (1) + diphenylamine (2) + cyclohexane
(3) at 25 C. The gM surface for this system is very flat, which
favors the false solution appearance. The three false tie-lines
for this system have been included and a magnification is
Furthermore, the sectional plane of these 3D figures passing
through the calculated tie-line can be represented to validate
the tangent line condition and show the form of the GM/RT
surface in the direction of the tie-line.

After one of the previous strategies for calculating one tie-
line is implemented in the computer, the construction of LLE
diagrams is carried out by the successive calculation of tie-
lines, until the homogeneous region is reached. For example,
the procedure sketched in Figure 7 can be used to obtain
the next tie-lines. After the first ternary tie-line is calculated
from the initial mixture M1, its middle point is obtained and
a new initial mixture point M2 is considered, maintaining
the same ratio of molar fractions in components 1 and 3, and
increasing component 2 by a constant amount (Ax2). The new
initial mixture, M,, will be the heterogeneous composition
for the calculation of the second ternary tie-line, and so on
for mixture points 1M, M4, M5, ... until the homogeneous
region is reached.
If the vector method is used for the LLE calculation, the

Mixture Gibbs Energy Surface

Figure 6. Representation of GM/RT surface for methanol(1) +
diphenylamine(2) + cyclohexane(3) at 25 C, using the NRTL
equation, and a magnification of the region where the
true and false tie- lines are located.
Vol. 41, No. 3, Summer 2007

Figure 7. Graphical explanation of a possible
method to set new initial mixtures to
construct the entire LLE diagram.

maximum and minimum values of a-angles that limit the
area where the solution is confined must be calculated using
the information of the previous tie-line calculated. As an
example, in Figure 7 this area is shown where the tie-line
passes through the initial mixture M,, where the limiting
lines, r2 and s2, are obtained connecting the point M2 with the
conjugated phases of the first tie-line through M (i.e., a , b ),
previously obtained.

This sequential procedure finishes when the overall mixture,
M, is in the single-phase region. To detect this situation, we
propose evaluating the sign of the second derivative of gM
to know whether two common tangent points exist. The
method we use is an extension for ternary systems of the
condition for the stability of a binary mixture.
For a homogeneous binary mixture at constant T and
p, the second derivative is always positive [Figure 8(a),
next page]:

--p- >0 (7)

On the contrary, for a global mixture that splits into two
liquid phases, the second derivative has negative values. To
be exact, the negative area in the representation of (2gM /
\ :)PT vs. x corresponds to compositions located between
the two inflections points, A and B, on the gM curve shown
in Figure 8(b).
This property of the second derivative can be extended
to the ternary systems and adapted to the vector method.



- .

o0 x3

For a constant value of the a-angle (or the slope D), the
system can be considered as pseudobinary and, therefore,
if the second derivative (,Q / T\:)p.T.D is always positive
in the sectional plane that corresponds with the a-angle
set, no two common tangent points to the g" will be found.
The situation will be similar to that represented in Figure
8(a) for a binary system, and the next a-angle value will
be considered for the tie-line search. When the mixture
point, M, is within the single-phase region, the sign of the
second derivative is always positive for all the values of
the a-angle, from the minimum to the maximum one, and
the tie-line calculation procedure has finished.
Also, we use the second derivative criterion with another
different purpose, to limit the composition values where the
two common tangent points must be located. For example,
if the situation shown in Figure 8(b) is considered, the
search will be confined to the compositions from x = 0 to
the point A, for one phase, and from the point B to x= 1 for
the conjugated phase. Therefore, the compositions located
between the two inflection points represented as A and B
are removed from the calculations, thus avoiding possible
trivial and false solutions and making the convergence of
the calculations easier.
Considering all the information previously presented, students
construct the LLE diagram of the methanol (1) + diphenylamine
(2) + cyclohexane (3) ternary system at 25 C, used to illustrate
all the different parts discussed here. The results obtained are
available on theWeb ()
as supplementary data to this paper, in Table 1S. Furthermore,
sectional planes passing through the calculated tie-lines in
Table 1S are represented in Figure 1S for the best view of
the gM function, and also to validate the results obtained from
the common tangent line criterion viewpoint. For all sectional
planes that contain the ten calculated tie-lines, the equilibrium
points have a common tangent line to the gM curve. This is a
necessary, but not sufficient condition, for ternary LLE and
can be helpful to reject false solutions.
Also, in the evolution of tie-lines 1 to 10, students can
observe how the cavity between the Gibbs energy curve and
the common tangent line is decreasing [lined area in Figure
l(a), showing how the LL region is disappearing, the limit
situation being similar to that represented in Figure l(b)].
The difficulties found in calculating tie-lines very close to
the plait-point are explained in this context.

An exercise to compute LLE data and to construct the phase
diagram for ternary systems is presented. The NRTL equa-
tion is used to model the activity coefficient, but any other
model can be used and the same conclusions would be made.
Some problems are illustrated that arise when the isoactivity
equilibrium condition is used in the LLE calculations. A much
more efficient condition is obtained when isoactivity is com-




g2 ,
0 x 10 x

Figure 8. Variation of g^, (gM /3x)PT and (2gM a/3x2)
with composition for a binary system: (a) completely
miscible binary, and (b) partially miscible.

bined with the common tangent line criterion, avoiding false
solutions that correspond with very low values of the activity
objective function. The Solver optimization tool included in
the Excel worksheet can be used by students to solve this
LLE exercise. The successive calculation of tie-lines allows
the students to obtain the ternary composition diagram. Also,
3D figures are represented to discuss the topological aspects
of the dimensionless Gibbs energy of mixture function (gM)
and to validate the results obtained from checking the common
tangent line criterion. Two ideas should be emphasized:
1. The isoactivity condition must be used very carefully
for LLE to avoid false solutions.
2. The topological concepts related with the equilibrium
condition formulated on the basis of the GM/RTfunc-
tion are very useful to validate the obtained solutions.

The authors wish to thank the Generalitat Valenciana and
the University of Alicante for financial support of projects
GV05 191 and GRE04-17, respectively.

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2. Iglesias-Silva, G.A., A. Bonilla-Petriciolet, PT. Eubank, J.C. Holste,
and K.R. Hall, Fluid Phase Equilibria, 210, 229-245 (2003)
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Franckfurt (1980)
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Chemical Engineering Education

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