Chemical engineering education ( Journal Site )

Material Information

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


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


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

Record Information

Source Institution:
University of Florida
Rights Management:
All applicable rights reserved by the source institution and holding location.
Resource Identifier:
oclc - 01151209
lccn - 70013732
issn - 0009-2479
sobekcm - AA00000383_00084
lcc - TP165 .C18
ddc - 660/.2/071
System ID:

Full Text

chemical engineering education



FALL 1984



APPLIED MATHEMATICS IN ChE . Lauffenburger, Dusan V., Ungar

Reddach aw ..



Bartholomew, Hecker
Converse, Grethlein

. Fair
. Edle

Gad a a


4wa0d .,mc *
Warren E. Stewart


achanawledesa wand tlhans....



Cddo.,s Il At

This is the 16th Graduate Issue to be published by CEE
and distributed to chemical engineering seniors interested
in and qualified for graduate school. As in our previous
issues, we include articles on graduate courses and re-
search at various universities and announcements of de-
partments on their graduate programs. In order for you to
obtain a broad idea of the nature of graduate work, we
encourage you to read not only the articles in this issue,
but also those in previous issues. A list of the papers from
recent years follows. If you would like a copy of a pre-
vious Fall issue, please write CEE.


Sawin, Reif




Wankat, Oreovicz



Weiland, Taylor
Baird, Wilkes

Butt, Kung

Chen, et al
Gubbins, Street

Guin, et al

Ray Fahien, Editor, CEE
University of Florida


Fall 1983

"Numerical Methods and Modeling"
"Plasma Processing in Integrated
Circuit Fabrication"
"Advanced Topics in Heat and Mass
"Chemical Reactor Design"
"Project Evaluation in the Chemical
Process Industries"
"Surface Phenomena"
"Research on Cleaning up in San
"Research on Combustion"
"Grad Student's Guide to Academic
Job Hunting"
"Book Writing and ChE Education"
"Grad Education Wins in Interstate
Fall 1982

"Oxidative Dehydrogenation Over
Ferrite Catalysts"
"Nucleate Boiling"
"Mass Transfer"
"Funds. of Petroleum Production"
"Air Pollution for Engineers"
"Polymer Education and Research"
"Research is Engineering"

Fall 1981

"Classical Thermodynamics"
"Catalysis & Catalytic Reaction
"Parametric Pumping"
"Molecular Thermodynamics and
Computer Simulation"
"Coal Liquefaction & Desulfurization"
"Oil Shale Char Reactions"
"Kinetics and Catalysis"
"ChE Analysis"
"Underground Processing"
"Separation Processes"
"Heterogeneous Catalysis"

Edgar, Schecter
Perkins, Pyle
Senkan, Vivian

Morari, Ray

Russel, et al.



Butt & Peterson




Carbonell &



Blanch, Russell

Bailey & Ollis

Fall 1980
"Polymer Fluid Dynamics"
"In Situ Processing"
"Wall Turbulence"
"Chemical Reactors"
"Systems Modelling & Control"

"Process Synthesis"
"Polymerization Reaction Engineering"
"Combustion Science & Technology"
"Plant Engineering at Loughborough"
"MIT School of ChE Practice"
Fall 1979
"Doctoral Level ChE Economics"
"Molecular Theory of Thermodynamics"
"Courses in Polymer Science"
"Integration of Real-Time Computing
Into Process Control Teaching"
"Functional Analysis for ChE"
"Colloidal Phenomena"
"Structure of the Chemical Processing
"Heterogeneous Catalysis"
"Mathematical Methods in ChE"
"Coal Liquefaction Processes"
Fall 1978
"Horses of Other Colors-Some Notes
on Seminars in a ChE Department"
"Chemical Reactor Engineering"
"Influential Papers in Chemical Re-
action Engineering"
"A Graduate Course in Polymer Pro-
"Reactor Design From a Stability
"The Dynamics of Hydrocolloidal
"Coal Science and Technology"
"Transport Phnomena in Multicom-
ponent, Multiphase, Reacting
Fall 1977
"Fundamental Concepts in Surface In-
"Electrochemical Engineering"
"Chemical Reaction Engineering
"Biochemical Engineering"
"Polymer Science and Engineering"

Fall 1976
"Electrochemical Engineering"
"Biochemical Engr. Fundamentals"
"Food Engineering"
"Distillation Dynamics & Control"
"Fusion Reactor Technology"
"Environmental Courses"
"Ad Bubble Separation Methods"
"Intro. Polymer Science & Tech."
"The Engineer as Entrepeneur"
"Energy, Mass and Momentum

FALL 1984

.2 'iv

Growth Through



If you're the kind of person who can take the
initiative and aggressively reach for increasing
. responsibility, consider a careerwith Rohm and
:- ; Haas. We are a highly diversified major chemi-
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their development and growth. When you join
S Rohm and Haas, you'll receive a position with

; : substantial initial responsibility and plenty of
.room for growth. And we'll provide the oppor-
tunities to acquire the necessary technical and
- 'managerial skills to insure your personal and
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STechnical Sales and Finance. For more infor-
;_mation, visit your College Placement Office,
or write: Rohm and Haas Company, Recruit-
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hato a


An Equal Opportunity Employer

1 9 .

~7~' ,a~t~
r *~
.1 `--i -- 'i.r


, LV


Department of Chemical Engineering
University of Florida
Gainesville, Florida 32611

Editor: Ray Fahien (904) 392-0857
Consulting Editor: Mack Tyner
Managing Editor:
Carole C. Yocum (904) 392-0861
Publications Board and Regional
Advertising Representatives:
Lee C. Eagleton
Pennsylvania State University

Past Chairman:
Klaus D. Timmerhaus
University of Colorado

Homer F. Johnson
University of Tennessee
Jack R. Hopper
Lamar University
James Fair
University of Texas
Gary Poehlesn
Georgia Tech
Robert F. Anderson
UOP Process Division
Lowell B. Koppel
Purdue University
William B. Krantz
University of Colorado
C. Judson King
University of California Berkeley
Frederick H. Shair
California Institute of Technology
Angelo J. Perna
New Jersey Institute of Technology
Stuart W. Churchill
University of Pennsylvania
Raymond Baddour
A. W. Westerberg
Carnegie-Mellon University

Charles Sleicher
University of Washington
Leslie W. Shemilt
McMaster University
Thomas W. Weber
State University of New York

Chemical Engineering Education

Views and Opinions
156 Common Misconceptions Concerning Graduate
School, J. L. Duda

Courses in
160 Applied Mathematics in Chemical Engineering,
Douglas Lauffenburger, Elizabeth Dusan V.,
Lyle Ungar

164 Chemical Engineering Practice: Graduate Plant
Design, Paul Marnell

166 Colloid and Surface Science, John F. Scamehorn
170 Transport Phenomena, D. B. Shah
174 Heterogeneous Catalysis Involving Video-Based
Seminars, Mark G. White

176 Linear Algebra for Chemical Engineers,
Kyriacos Zygourakis

Research on
180 Catalysis, Calvin H. Bartholomew, William C.

186 Bio-Chemical Conversion of Biomass,
Alvin O. Converse, Hans E. Grethlein

A Program in
190 Separations Research, James R. Fair
196 Graduate Residency at Clemson: A Real World
MS Degree, Dan D. Edie

200 Semiconductor Processing, Carol McConica

Award Lecture
204 Simulation and Estimation by Orthogonal
Collocation, Warren E. Stewart

153 Editorial
159 Division Activities
159, 185, 199,203 Book Reviews
195 Books Received

CHEMICAL ENGINEERING EDUCATION is published quarterly by Chemical
Engineering Division, American Society for Engineering Education. The publication
is edited at the Chemical Engineering Department, University of Florida. Second-class
postage is paid at Gainesville, Florida, and at DeLeon Springs, Florida. Correspondence
regarding editorial matter, circulation and changes of address should be addressed
to the Editor at Gainesville, Florida 32611. Advertising rates and information are
available from the advertising representatives. Plates and other advertising material
may be sent directly to the printer: E. O. Painter Printing Co., P. O. Box 877,
DeLeon Springs, Florida 32028. Subscription rate U.S., Canada, and Mexico is $20 per
year, $15 per year mailed to members of AIChE and of the ChE Division of ASEE.
Bulk subscription rates to ChE faculty on request. Write for prices on individual
back copies. Copyright 1984 Chemical Engineering Division of American Society
for Engineering Education. The statements and opinions expressed in this periodical
are those of the writers and not necessarily those of the ChE Division of the ASEE
which body assumes no responsibility for them. Defective copies replaced if notified
within 120 days.
The International Organization for Standardization has assigned the code US ISSN
0009-2479 for the identification of this periodical. USPS 101900

FALL 1984


views and opinions I



Pennsylvania State University
University Park, PA 16802
* * * * * *
Twenty-five years ago, I started graduate school at the
University of Delaware. Looking back on that time, I can
see that I was a typical graduate student in that I was
both excited and terrified, confident and anxious, sure of
success one day and afraid of failure the next. I did,
however, harbor certain basic misconceptions about the
experiences which lay ahead of me. In talking to our
graduate students here at Penn State, I found that those
same misconceptions are still common, and this insight
prompted me to give the following introductory address
to our incoming graduate students.

SIKE YOU TODAY, I was also entering graduate
-school twenty-five years ago. My mind was
also filled with questions and concerns. It was also
cluttered with certain misconceptions, which are
still popular today. I would like to look back on
that time with you and try to tell you how my
views on graduate school have changed.

The first misconception I had was that gradu-
ate school would be a continuation of my experience
as an undergraduate.

This was probably my greatest misconception.
First of all, graduate courses and undergraduate
courses are, in general, somewhat different. You
are an elite group since we only accept one out of
every fifteen applicants to our graduate program.
Consequently, there is no doubt in our minds that
you can perform well in graduate courses since
your ability in chemical engineering courses has
been demonstrated by your undergraduate record.
Therefore, graduate courses tend to be more re-
laxed, with less emphasis on evaluation and
certainly no hint of being a weeding-out process.
We feel that you are in these courses because you

Copyright ChE Division. ASEE. 1984

The key to graduate research is problem
solving, not the acquisition of specific information.
You will learn to solve problems by actually
performing this task under the
direction of an expert...

want to learn, and therefore our main emphasis
is on enhancing your technical expertise. You are
now engineers, not just high school graduates.
The main difference between undergraduate
and graduate education is related to the research
aspect of graduate studies. Very few of our gradu-
ate students fail to receive their graduate degree
because of their performance in courses. The main
hurdle is the ability to do independent research.
Up to now, in my opinion, your educational ex-
periences have been somewhat artificial. You have
studied in order to pass exams which cover very
specific and limited areas. In the past, you worked
certain problems on examinations. You knew
there was an answer. You also knew you had
enough data to reach that answer. Conducting
research in graduate school, on the other hand,
does not involve an artificial environment. You
will be working on problems where no one
knows the answer, and the problem itself might
not even be clear. Graduate research is similar to
an apprenticeship. You will be working directly
with an expert and will learn by doing and ob-
serving how this expert approaches problems.
The key to graduate research is problem solving,
not the acquisition of specific information. You
will learn how to solve problems by actually per-
forming this task under the direction of an expert,
not by studying the philosophy or idealized ap-
proach to problem solving.
What happened to me may also happen to some
of you. I slowly began to realize that research
was unlike anything that I had been exposed to
previously. There is a natural tendency to exagger-
ate the difference and come to the counter-mis-
conception that research has nothing to do with
your undergraduate work. This is not true either.


J. L. Duda is Professor and Head of the Department of Chemical
Engineering at The Pennsylvania State University. He received his BS
in chemical engineering at Case Institute of Technology and his MS and
PhD at the University of Delaware. He joined the staff at Penn State
in 1971 after eight years in research with The Dow Chemical Company.

Research is a natural extension of your learning
career to date, but it is also more than that. You
have been learning and obtaining information
from teachers, textbooks, and independent study
in libraries. But what do you do when the knowl-
edge you desire is not available in any book or
article, or when no individual exists who knows the
answer? Research in the physical sciences and
engineering is the process of learning by asking
nature questions. In a sense, nature becomes your
ultimate teacher. When you design experiments,
you are really formulating your questions for
nature. Unlike your previous teachers, nature does
not anticipate your question. You will get a direct
and honest answer to your question as it was
formulated. If you are misled or have difficulties,
it will not be because nature failed to answer your
question. It will be due to your failure in formulat-
ing the question or in interpreting the results. The
best researchers are the ones who ask what appear
to be very simple questions and receive earth-
shaking replies.
At this point, one might ask how theory fits
into all this if the basis of research is asking nature
questions through experimentation. As J. Willard
Gibbs said, "The purpose of theory is to find that
viewpoint from which experimental observa-
tions appear to fit the simplest pattern." You
want to determine this pattern so that you can
generalize your experimental observations and
minimize the number of experiments that have to
be conducted.

My second misconception concerning graduate
school was that the choice of a research topic was
one of the most important decisions of my life

since it would determine what area I would work
in for the rest of my career.
New graduate students continually forget that
the main purpose of research at the graduate level
is to learn how to do research and to solve prob-
lems. The acquisition of knowledge in a particular
area is of secondary importance. If you have
learned how to do research in area A, it is a rela-
tively minor step to acquire the facts and back-
ground needed to conduct research in area B.
Consequently, when choosing a research topic,
your main concern should not be whether you like
the research area, but whether this particular re-
search project and the director of this research
have the best chance of teaching you how to con-
duct research.
My third misconception was that my research
work would follow the idealized method of scientific
inquiry which involves a literature search, develop-
ment of a theory, design of the experiments, and
interpretation of results that tested the theory.
One quickly learns that research is often more
like a random walk than an idealized textbook ap-

... when choosing a research
topic, your main concern should not be
whether you like the research area, but whether
this particular research project and the director of
this research have the best chance of teaching
you how to conduct research.

proach. The young researcher is often quite upset
when discovering this fact. At first it is difficult
to accept this basic truth. It is much easier to
arrive at one of the following conclusions:
My thesis advisor is incompetent.
My research topic is a real lemon; I don't know how
anyone talked me into doing this.
My research has nothing to do with what I have
learned in the classroom.
No one else has problems like me; my project is
unique in its difficulty.
What the young researcher fails to realize is
that the way research results are presented in a
paper or a seminar has nothing to do with the
process that was followed in obtaining those re-
sults. Research cannot be planned like many other
human endeavors. It is, in fact, a form of art. If
you knew beforehand what your results were
going to be and the path you would have to take
to obtain them, it simply would not be research.

FALL 1984

No matter how badly things
are going, or how tortuous your route,
you should always maintain a clear
idea of your objective.

One frustration which all faculty members face
is that many funding organizations also do not
realize this. As a graduate student, you must be
careful not to confuse the formal presentation of
results in papers or seminars with the actual pro-
cess. A related misconception is that the results
you obtain in research should be in proportion to
the time and effort you have spent. The most
difficult aspect of research is that you do not
usually see a steady progression of results. Instead,
results come in bursts or surges. It takes tre-
mendous tenacity to hang in there and keep
plugging away when you are not aware of any
Many young researchers also feel that their
problem is so complex that it really cannot be ex-
plained to anyone else in a reasonable period of
time. No matter how badly things are going, or
how tortuous your route, you should always main-
tain a clear idea of your objective. If you cannot
give a clear overview of your research project in
a few short sentences, you have a good indication
that part of your problem is your inability to keep
things clearly defined in your own mind.
My fourth misconception was that the study of
chemical engineering had nothing to do with
human values, ethics, morals, etc.
When I started my graduate studies, I con-
sidered science to be ethically or morally neutral.
However, as Bronowski has pointed out, this is
confusing the results or findings of science with
the activity of conducting science. There is no
question that the results of your research will be
ethically neutral; however, at the center of scien-
tific inquiry is the standard that facts or truth, not
dogma, must dominate your research. By conduct-
ing research, you will be training yourself to avoid
and resist every form of persuasion but the facts.
The most difficult part will be to avoid deceiving
yourself. In everyone's career, there comes a time
when experimental observations are inconsistent
with a pet theory. It will be a true test of your ma-
turity as a researcher to unbiasedly look at the
facts and to determine if the experimental observa-
tions are consistent or inconsistent with the
theory, independent of your personal feelings. As

T. H. Huxley said, "The great tragedy of science
is the slaying of a beautiful theory by an ugly
fact." There is a natural tendency to formulate
vague theories which cannot be proven wrong, but
all good theories will eventually lead to their own
demise since they will finally predict something
which is inconsistent with experimental observa-
Science does not have a Hippocratic oath or any
other professionally induced ethical rule. How-
ever, you can be untruthful and still be a success-
ful doctor or lawyer. This is not a viable possibility
for the scientific researcher. As you develop into
a good researcher, you will develop the capability
of making judgments based solely on the facts. I
feel this training can have a very significant posi-
tive influence on the moral and ethical aspect of
your life since it tends to minimize self-deception
and rationalization.

My fifth and final misconception was that
graduate study was all hard work and the rewards
would come later when I had an interesting job
and was making a lot of money.
After I received my advanced degrees, I
realized that some of the best years of my life
were those I spent in graduate school. I found that
the pleasure and sense of accomplishment that
came with learning and creating far outweighed
the other pleasures in life. As graduate students,
you are among the fortunate few who will not
have to spend all of your time for the next few
years working to meet the material needs of your
life. Until this century, the great majority of
people had to spend 100% of their time just to feed
their bodies. A few privileged individuals, such as
the Brahmins, Mandarins, aristocrats, etc. had the
opportunity to simultaneously feed their bodies
and their minds. We have made great advances,
but today most people still spend a major part of
their lives working to fill their material needs. No
matter how difficult you find the days ahead, I am
confident that you will look back on these years
and be grateful that you had this opportunity to
devote all of your effort to learning and creating.
If you are very lucky, you might, after much
hard work, devotion, and frustration, be fortunate
enough to be the first person to see one of those
patterns to which Gibbs referred. That will be the
most rewarding time of your graduate studies,
not the moment you receive a piece of paper which
declares that you have now earned a specific de-
gree or that first pay check. E




The 1984 ASEE Chemical Engineering Di-
vision Lecturer was T. W. Fraser Russell of the
University of Delaware. The purpose of this
award lecture is to recognize and encourage out-
standing achievement in an important field of
fundamental chemical engineering theory of
practice. The 3M Company provides the financial
support for this annual lecture award.
Bestowed annually upon a distinguished engi-
neering educator who delivers the Annual Lecture
of the Chemical Engineering Division, the award
consists of $1,000 and an engraved certificate.
These were presented to this year's Lecturer at
the Annual Chemical Engineering Division Ban-
quet, held at the University of Utah on June 26,
The award is made on an annual basis with
nominations being received through February 1,

1985. The full details for the award preparation
are contained in the Awards Brochure published
by ASEE. Your nominations for the 1985 lecture-
ship are invited. They should be sent to Professor
E. Dendy Sloan, Colorado School of Mines, Golden,
CO 80401.

The newly elected ChE Division officers are:
Deran Hanesian, Chairman; D. Barker, Past
Chairman; Dendy Sloan, Chairman Elect; Bill
Beckwith, Secretary-Treasurer; and Lamont
Tyler, Director.

Four chemical engineering professors have
recently been recognized for their outstanding
achievements. Phillip C. Wankat received the
George Westinghouse Award for early achieve-
ment as a teacher and a scholar; James E. Stice
was presented with the Chester F. Carlson Award
for improving instructional techniques; Peter R.
Rony was the recipient of the Delos Award for
excellence in laboratory instruction; and Chung
King Law received the Curtis W. McGraw Re-
search Award for outstanding early achievement
in research.

book reviews


By G. V. Reklaitis, A. Ravindran,
K. M. Ragsdell: John Wiley and Sons,
NY (1983) 14 Chapters, 648 pages,
Reviewed by
A. W. Westerberg
Carnegie-Mellon University

This is an excellent text from which to teach
optimization techniques to engineering students.
It can be used at either the senior or graduate
level. All of the most important methods are pre-
sented that have appeared in the literature. The
level of detail given on each method should allow
one to see how and where to apply it to small up

to moderate-sized practical problems.
The book concentrates on methods for solving
well behaved, continuous variable optimization
problems. The methods included are unconstrain-
ed single and multivariable optimization, linear
programming, and a host of methods for equality
and inequality constrained nonlinear problems.
Not considered are methods directly applicable
for models containing ordinary and partial differ-
ential equations, nor is there very much on solving
problems where some or most of the variables can
take on only discrete values. Also the book does
not consider decomposition techniques, sparse
matrix techniques and the like, concepts usually
needed to allow the techniques covered to be ap-
plied to really large problems. The book is already
lengthy so it is completely reasonable that it
limits its coverage to the topics that it does.
The style of presentation is generally excel-
lent. The authors have concentrated on appealing
Continued on page 185,

FALL 1984

4 o4ae iet


University of Pennsylvania
Philadelphia, PA 19104

increasingly important in chemical engineer-
ing research over the past three decades, it is still
eyed with great trepidation by the typical first-
year graduate student. The nature of mathematics
is viewed as something alien to real engineering,
having little or no substance nor, curiously, logic.
A prevailing opinion among first-year students
is that mathematics is more closely related to
magic than it is to science. It has been presented
to them during their undergraduate years mainly
as a mere assortment of techniques, a "bag of
tricks," from which the right method for the spe-
cific problem at hand must be plucked. Because the
"why" of mathematics has not been learned,
students lack confidence in the "how" as well.
At Penn we believe that this situation must be
corrected if our graduate students are to be able
to productively use applied mathematics in their
research careers. Therefore, our set of six core
graduate courses includes a two-semester sequence
("Applied Mathematics in Chemical Engineer-
ing") which is required of every first-year student.
In addition, we now offer a strongly recommended
elective course as a third semester in that se-
quence. However, it is not only the formal empha-
sis on mathematics, but also the content and es-
pecially the approach of the courses that convey
our message to the students.
In order to gain confidence in using mathe-
matics in research, a student needs to know not
only how to apply some technique to solve a prob-
lem, but also when that technique is guaranteed to
work and why, what other alternatives exist, and
what methods are certain to be futile. Thus, our
courses are taught with what might be termed a
rather fundamental approach. That is, we empha-
size the internal logic and structure of mathe-

Copyright ChE Division, ASEE, 1984

In order to gain confidence in
using mathematics in research, a student
needs to know not only how to apply some technique
to solve a problem, but also when that technique
is guaranteed to work and why, what other
alternatives exist, and what methods
are certain to be futile.

matics, showing that equations can possess in-
trinsic, inviolable properties in themselves, by
providing rigorous definitions and stating and pro-
viding relevant theorems. It is these theorems
which guarantee that certain techniques will pro-
vide solutions for particular problems and that
others will not. Further, we show how the in-
trinsic properties of equations correspond inti-
mately with the natural behavior of the physical,
chemical, or biological system being modeled
mathematically by the equations. Once these
properties are understood, it becomes a straight-
forward matter to derive a large number of solu-
tion techniques, both familiar and new, to the
students' satisfaction. It is at this point that the
students finally appreciate the power of the ab-
stract approach, for they now have learned why
the tricks in their bag sometimes worked and
sometimes did not. And they realize that they are
now capable of reading applied mathematics re-
search literature to learn new techniques, since
they have a grasp of the necessary underlying
theoretical foundations. This is, of course, the
ultimate aim of a graduate course in any subject-
not to pretend to teach the entirety of knowledge
in the area but to enable the students to learn
whatever is of interest to them.
So, what at first may appear to be a rather im-
practical approach to engineering applied mathe-
matics turns out, in fact, to be of great utility. We
make the analogy to mastery of a musical instru-
ment; it might seem much more practical to
memorize a few songs that can readily be played
at parties instead of learning to read music and
practicing scales and arpeggios, but which ap-
proach will allow a new concerto to be faced with



The basis of our approach consists of teaching
as much as possible from a linear operator point
of view. The first semester course concentrates on
establishing the formal structure of linear, or
vector, spaces, with an emphasis on spaces of
finite dimension. This allows development of
solution procedures for systems of linear algebraic
equations and systems of linear ordinary differ-
ential equations. We also establish the formal
structure of nonlinear metric spaces, which leads
to techniques for approximate solution of non-
linear equations of both algebraic and ordinary
differential types. The second semester course
then focuses on linear spaces of infinite dimension.
Understanding of these spaces permits develop-
ment of solution procedures for partial differential
equations. Finally, the third (elective) semester
deals exclusively with nonlinear systems of
ordinary and partial differential equations, utiliz-
ing perturbation methods and bifurcation theory.
The underlying theme running throughout all
three semesters is one of considering problems
from within an operator framework. We stress
linear theory because, simply, only linear problems
can really be solved (excepting special cases).
Even approximate solution techniques for non-
linear problems, whether analytical or numerical,
can be shown to be based on transforming the non-
linear problem into a system of linear sub-
problems. (It might be noted that this point helps
to disabuse the notion that the computer has made

the understanding of mathematics less important
to the engineer.) Thus, if a student has a firm
grasp of the theory of linear problems, he or she
will be able to understand how nonlinear problems
may be approached. When this lesson is taken to
heart, the student acquires confidence from the
fact that he or she possesses sufficient mathe-
matical skill to attack theoretical or computa-
tional research problems without anxiety.
In the next few paragraphs we will attempt
to provide a brief summary of the course content.
The first lecture is devoted to defining linear
spaces rigorously, with a vector being simply an
element in such a space. It is pointed out that
these spaces are of importance essentially because
the desired solutions to systems of equations will,
in fact, be vectors in appropriately defined spaces.
We then show how spaces may be comprised of
linear subspaces, yielding the possibility of ob-
taining solution vectors as a combination of
vectors from different subspaces, using the con-
cept of direct sums. Convenient ways of develop-
ing such combinations are allowed by introducing
the idea of linear independence of vectors. The
number of terms needed for such a combination
is specified, using the notion of the dimension of
a space, leading to the crucial definition of a basis
for a linear space with finite dimension. Linear
transformations are then defined, and it is shown
that all systems of linear equations, no matter
what type, can be cast as a linear transformation
of a vector in one space to a vector in another.

Douglas Lauffenburger is
currently associate professor of
chemical engineering, having
arrived at Penn in 1979 after
receiving his BS degree at II- '
linois and his PhD at Minne-
sota. He spent the summer of
1980 as a Visiting Scientist at
the Institute for Applied Mathe-
matics at Heidelberg. His re-

havior. (L)
Elizabeth Dussan V. is presently on leave as a Guggenheim Fellow
at Cambridge University, holding the position of associate professor
at Penn. She received her BS degree at SUNY Stony Brook and her
PhD at Johns Hopkins, coming to Penn in 1973 following a post-
doctoral position at Minnesota. Among her areas of investigation
are included fluid mechanics and interfacial phenomena. (C)
are included fluid mechanics and interfacial phenomena. (C)

Lyle Ungar joined the faculty at Penn in 1984 as assistant professor,
having received his BS degree at Stanford and his PhD at MIT. His
research interests include application of perturbation methods, bi-
furcation theory, and finite element analysis to kinetic and transport
problems in continuum physics. Topics of current focus include crystal
growth and rapid solidification materials processing. (R)

FALL 1984

The first lecture is devoted to defining linear spaces rigorously with a
vector being simply an element in such a space. It is pointed out that these spaces are
of importance essentially because the desired solutions to systems of equations
will, in fact, be vectors in appropriately defined spaces.

Thus, the solution to any linear problem can be
understood in terms of solution of the general
linear transformation equation
Lx = y
where y is the "data" vector in the range space,
x is the "solution" vector in the domain space, and
L is the linear transformation. Regardless of
whether the problem is of algebraic, differential,
or integral type, the vectors and the transforma-
tion can be written in component form in terms
of basis vectors for the range and domain spaces,
so that all problems involving finite-dimensional
spaces are equivalent to matrix equations. In-
verse transformations are now defined, fore-
shadowing a number of solution techniques for
specific problems. This permits the uniqueness of
solutions, if they exist, to be determined.
Norms and inner products are introduced
next in order to add geometric structure to the
already present algebraic structure of linear
spaces. This allows formulation of orthogonal
basis vectors, which will be useful for generating
the most convenient solution combinations. Ad-
joints can now also be discussed, leading to the
Fredholm Alternative Theorem and the determina-
tion of existence of solutions. Finally, the concept
of eigenvalues and eigenvectors is presented, and
a Spectral Theorem is proved to demonstrate how
orthogonal basis solution expansions can be ob-
tained using the eigenvectors of a self-adjoint
operator. At this point, it is helpful to pull back
from abstract theory and apply the principles
learned so far to the solution of matrix equations.
As mentioned earlier, it is stressed that such
equations are actually involved in all finite-
dimensional problems. Given the theoretical back-
ground, a large number of alternative solution
techniques can be derived very quickly and easily,
and the student now understands the justification
for, as well as the limits of, these techniques.
We then step back into the realm of theory
and, in fact, temporarily remove all the algebraic
structure we have learned about linear spaces.
This leaves us with only geometric structure; that
is, the notions of size and distance generated by
the presence of norms in linear spaces. In non-

linear spaces, the function that measures the size
of an element, or the distance of it from another, is
called a metric. Thus, we present an introduction
to metric spaces, of which solutions to nonlinear
problems may be elements. We can rigorously de-
termine whether a sequence of elements converges
to a distinct element, a property crucial to the de-
velopment of approximate solution techniques (as
well as analytical solution methods for infinite-
dimensional space problems). It takes relatively
little time to move to the surprisingly powerful
Fixed Point Theorem. This can be used to delineate
circumstances under which an iterative approach
will converge to a solution, leading to development
of numerical methods for systems of nonlinear as
well as linear algebraic equations. It also can be
used to find regions of uniqueness and multi-
plicity of solutions to nonlinear equations. Finally,
we can use it as a bridge to ordinary differential
equations, since it is required in a simple and
direct proof of Picard's Theorem for existence
and uniqueness of solutions to initial-value prob-
lems. Iterative schemes for obtaining approxi-
mate solutions to nonlinear ordinary differential
equations can also be developed from the Fixed
Point Theorem at this time.
With the reintroduction of linear spaces, the
theory of linear ordinary differential equations
follows directly, because all the necessary back-
ground is in place. The general solution to a system
of such equations can quickly be developed in
terms of the fundamental matrix for the differ-
ential transformation. Students are pleased to see
the apparently disparate variety of solution
techniques they might have encountered previous-
ly fall out very easily from the general solution
expression and development. Methods for de-
termining the form of the fundamental matrix
are discussed next, primarily utilizing eigenvector
basis expansions for constant-coefficient problems
(thus explaining the "sum of exponentials" type
solutions commonly seen) and for variable-co-
efficient problems as well. The mystery is thus
taken out of the use of special functions (Bessel
functions, Legendre functions, etc.) for the latter
types of equations, as their forms are seen to be
derived in a consistent and rigorous way. The last


few days of the first semester are used to intro-
duce the ideas of asymptotic expansions and per-
turbation theory as means to solve nonlinear
problems by turning them into a sequence of
linear ones. Linearized stability theory and a quick
preview of bifurcation theory are also accessible
at this point.
The second semester begins with linear ordin-
ary differential equations of boundary-value type.
The solution procedure for these follows directly
from the fundamental matrix approach previously
developed for initial value problems. The fact that
solution properties are not completely specified at
one value of the independent variable (providing
"initial" conditions) but rather some are specified
at another value (yielding "boundary" conditions)
causes no breakdown of the approach. Unspecified
initial conditions can be assumed to be constants
as yet unknown, and the fundamental matrix pro-
cedure can be followed. The unknown constants
can then be determined by requiring the remain-
ing boundary conditions to be satisfied. At this
point it is useful to show how common solution
techniques are related to this approach. Of prime
interest is a presentation of Green's function
techniques, with the Green's function for a linear
differential operator demonstrated to be analogous
to the fundamental matrix.
We then move on to an extension of linear
operator theory to linear spaces of infinite dimen-
sion. The most significant change is in the defini-
tion of a basis for an infinite-dimensional space.
An infinite number of vectors is now required for
expansion of a solution vector, and the determina-
tion of the coefficients is greatly complicated. It
is here that the property of self-adjointness of a
linear operator becomes crucially important. For
such operators the expansion coefficients can be
determined individually in a straightforward
manner. Thus, it is worth taking some time at this
point to show how problems of unusual form can
sometimes be cast as self-adjoint problems by ap-
propriate definition of the inner product.
Linear partial differential equations can now
be approached as linear operator equations on in-
finite dimensional spaces. Thus, solutions to these
can be obtained as series expansions in terms of
the infinite set of basis vectors, which will be
orthogonal if the differential operator is self-ad-
joint. For non-self adjoint operators the eigen-
vectors will form a biorthogonal set with the
eigenvectors of the adjoint operators, although in
this case the eigenvalues will be more difficult to

find because they can be complex. The well-known
Sturm-Liouville problem is seen to be a special
case of a linear self-adjoint differential eigenvalue
equation, which allows eigenfunction expansion
Now that a foundation for series expansion
techniques for solution of linear partial differential
equations has been laid, we can go on to examine
a series of problems of increasing complexity and
subtlety. Examples include the Laplace and
Poisson equations, and the diffusion and wave
equations, in rectangular Cartesian, cylindrical,
and spherical coordinate systems on finite and
semi-infinite domains, with a variety of boundary
conditions. Problems involving non-self-adjoint
operators are also investigated, since the essential
concepts have previously been established.

... it is useful to show how
common solution techniques are related to
this approach. Of prime interest is a presentation
of Green's function techniques ...

Examples of these include combined convection-
diffusion equations and the biharmonic equation.
Again, we stress the development of the solution
procedures from the linear operator theory frame-
work, emphasizing the unifying logic present
despite the apparent variety of problems found.
The second semester is, in a sense, more of a
"techniques" oriented course than the first semest-
er in that there is a great emphasis on how to
solve problems from a general linear operator
point of view rather than primarily proving
theorems. For example, proof of theorems relevant
to infinite dimensional vector spaces such as the
Spectral Theorem are neglected in favor of a de-
tailed discussion of the subtle differences between
finite and infinite dimensional spaces. We revisit
many of the topics developed during the first se-
mester with an almost exclusive focus on differ-
ential operators. We look at adjoint operators
and examine how their form intimately depends
on the choice of the inner product. We apply
Fredholm's Alternative to examine the conditions
under which solutions exist to Lx = y, where L
is a Fredholm operator. The students are sur-
prised to see that the existence of a solution to a
particular problem is very sensitive to the form
of the boundary conditions, and that the initial-
value problem can be thought of as a specific
type of boundary-value problem. The students
Continued on page 214.

FALL 1984

4 oa4e" ia



Manhattan College
Riverdale, NY 10471

T HE OBJECTIVE OF this year long graduate plant
design course [1, 2] is to provide the students
A fundamental appreciation of the profit motive that
drives business activity, and the role of the chemical
engineer in achieving this fundamental goal
Historical and contemporary perspectives on chemical
engineering practice
Confidence to tackle the wide variety of problems that
confront the chemical engineer
The emphasis throughout the course is on why
things are done the way they are. The "how to"
aspects of design are implemented only after their
needs have been established by a critical evalua-
tion of the various problems in process invention,
process development, and ultimately, detailed pro-
cess design. The spectrum of design tools, i.e., ball
park estimates, preliminary design techniques, and
detailed design procedures, is integrated with the
various phases in a process plant project.
The rapidly changing technological and social
climates demand that we produce generalists who
have been schooled in the basic aspects of the de-
sign methodologies and who can learn fast and
quickly bring themselves up to speed for a
particular application. Obviously, it is not possible
to teach all of the design and economic methods
that practicing chemical engineers use, so a
collection of procedures that will suffice for many
situations is emphasized. The students are also
trained to critically study the literature, including

The recent recession and its
disastrous effect on employment clearly
illustrated the fact, which is often missed by
students, that engineers provide services
to companies to help them achieve the
primary goal of an adequate profit.

Copyright ChE Division, ASEE, 1984

E t
Paul Marnell is an associate professor in the Manhattan College
chemical engineering department. He initiated and helped direct
the coal-water fuel technology research at Brookhaven National
Laboratory from 1980-83. Prior to joining Manhattan in 1976, he was
Director of Environmental Projects for the U.S. operations of the
Lurgi Company and also held engineering positions with the Stone
and Webster and Foster Wheeler Corporations. He obtained his BChE
from City College, his MS (nuclear engineering) from Union College,
and an EngScD (mechanical engineering) from Columbia University
in 1972.

patents, so that they may uncover or develop new
procedures and analogies which they can use with
confidence in situations that are new to them.
The rationale for and some of the methods used
to attain the course goals are discussed in the

"The Chemical plant is a dollar factory."
-William C. Reid [3]
The recent recession and its disastrous effect
on employment clearly illustrated the fact, which
is often missed by students, that engineers pro-
vide services to companies to help them achieve
the primary goal of an adequate profit. Thus,
technical expertise combined with engineering
economic analysis is the bedrock upon which engi-
neering judgments are made.
Engineers create devices by applying the laws
of nature and mathematics and using empiricism
and intuition where needed. Analysis to provide


basic knowledge is the province of the scientist
or mathematician. Analysis to provide insight on
the performance of a device is a valuable part of
the design process and one which can reduce the
cost of empiricism. However, often empiricism
must be used to create things within a reasonable
period of time. Thus, piping systems are designed
on the basis of the empirical friction factor cor-
relations for turbulent flow, and it will probably
be many years before a truly fundamental re-
lationship for turbulent pressure drop in pipelines
will be achieved. Similar considerations hold for
mass and heat transfer correlations and reaction
rate expressions. Nevertheless, chemical plants
have been built and will continue to be built by the
judicious blending of analysis, intuition, and em-
This brief essay is not the place to expand on
the various aspects of engineering economic
analysis that are considered in the course. How-
ever, two elements of critical importance are:
1. Multiple alternatives are generally available to
achieve a goal, and the engineer is constantly screen-
ing alternatives of increasing detail with tools of
increasing accuracy. The observation is valid at all
levels of decision making, from the selection of a
project to fund to the choice of a vendor for, say,
concrete reinforcing bars. Thus, several years ago
the Mobil Oil Corporation felt that buying Mont-
gomery Ward was an attractive venture to help
maximize profits, and currently the United States
Steel Corporation is shutting down more of its steel
plants while increasing its real estate holdings.*
Similarly, examples within the chemical process
industry form a hierarchy which ranges from the
general to the very specific. Which product should
be made to achieve a desired result, and which re-
action path should be used to produce it? Given the
reaction path, which separation technologies would
be best, and given that distillation might be desire-
able, should it be done in a plate or packed tower?
What type of plate tower should be used, and who
should the vendor be? Alternatives abound, from
broad strategic questions to very specific hardware
items, and usually one is more attractive than its
2. As with engineering analysis, the tools for economic
analysis range from crude to sophisticated, and the
choice represents a compromise between expediency
and accuracy that yields a result which is acceptable
for the circumstances.
"Nevertheless, it would be a mistake to
suppose that the present generation can

*While they are only noted here, the social and economic
implications of these transactions, especially the latter,
are explored in the course.

The first car built did not look like today's
Ferrari. Similarly, many current chemical plants are
much more complicated than their predecessors.

afford to ignore the labours of its predeces-
-Lord Rayleigh [4]
The first car built did not look like today's
Ferrari. Similarly, many current chemical plants
are much more complicated than their predeces-
sors. Modern ethylene, ammonia, and sulfuric
acid plants represent the evolution and refinement
of their underlying processes. All too often, study
of these highly integrated technologies can intimi-
date a student. It is essential to stress the fact
that they represent thousands of man-years of
engineering effort and decades of operating ex-
perience, and in no way, shape, or form were con-
ceived, developed, and built this way on the first
try. Engineers should recognize that technological
progress usually represents an evolution of pain-
staking improvements built upon a singular
revolutionary concept.
Engineers, like other creative people, design,
analyze, redesign, build, and refine their artifacts.
Hence, it is important to inculcate the philosophy
of not reinventing the wheel. Learn from what
has gone before. Minimize mistakes by learning
from those of others. Understand the logic of the
past to help guide the developments of the present
and the future.

". . the authors .... not include in their
books anything they themselves do not
-Linus Pauling [5]
The vast majority of what a chemical engineer
does is included in the categories of process de-
velopment, process design, and process improve-
ment. In these activities, analysis is the hand-
maiden of synthesis. How does the item that has
been created perform? Can it be improved?
During the sixties and seventies the "hand-
book" engineer was criticized [6]. He is a person
who presumably does not understand the basis of
his system, and who can use solutions in books but
cannot generate new ones for new situations.
In the eighties, the handbook engineer is being
replaced by the "black box" engineer, i.e., one who
is adept at filling out computer input forms, but
who has little understanding of the underlying
Continued on page 215,

FALL 1984

4CD AD SE in


University of Oklahoma
Norman, OK 73019

nomena in chemical engineering are becoming
increasingly abundant. In the search for new
technologies to solve pressing problems, such
techniques as enhanced oil recovery by surfactant
flooding, micellar catalysis, and surfactant-based
separation techniques have emerged. Traditional
technologies using surface and colloid science
have aroused new research interest: examples
are adsorption, detergency, and flotation.
The course discussed here was designed to
cover a wide range of some of the more important
topics in colloid and surface science (see Table 1).
Obviously, in covering this many topics, a great
deal of depth could not be attained, but when the
students finish the course they have a working
familiarity with a wide range of phenomena and a
quantitative knowledge of the more important
mathematical relationships in the field. Since tra-
ditional chemical engineering courses essentially
ignore surface and colloid phenomena, the in-
structor has to assume he is starting from ground-
level in almost all of these topics.
This course was designed for chemical engi-
neers, chemists, and petroleum engineers. A typi-
cal breakdown of enrollment by the three cate-
gories is 70%, 20%, and 10%, respectively. The
only prerequisite is chemical thermodynamics
(either physical chemistry or chemical engineer-
ing thermodynamics). The mixture of students
from different disciplines brings breadth to class-
room discussions and forces the instructor to
search for examples of applications which are out-
side of his immediate interests.

Unfortunately, there is no single textbook
which covers both surface and colloid science

Copyright ChE Division, ASEE, 1984

sufficiently well to be a basis for this course.
Therefore, required texts for the course are
Physical Chemistry of Surfaces, by Adamson [1],
for surface science, and Surfactants and Inter-
facial Phenomena, by Rosen [2], for colloid science.
Numerous handouts and references are also used.

As seen in Table 1, the first four major topics
are related to surface phenomena. Adamson [1]
is used in this part of the course, more as a refer-
ence than as a textbook.
First, considerable effort is expended in ex-
plaining the physical causes of surface tension,
since this is critical to future topics. One useful
example is to consider the creation of a vapor-
liquid interface as the reduction of the number of
nearest neighbors to a surface molecule in the
liquid from six to five. The surface tension per

John F. Scamehorn received his BSChE in 1973 and his MS in
chemical engineering in 1974, both from the University of Nebraska,
and worked for the Chemical Research Division of Conoco Inc. for
three years before returning to graduate school. He received his PhD
in chemical engineering from the University of Texas in 1980. He
then spent a year and a half in Corporate Research with Shell De-
velopment Co. before joining the chemical engineering and ma-
terials science department at the University of Oklahoma in 1981.
His research interests focus on applications of surface and colloid
science and of membrane science. He is specifically interested in
enhanced oil recovery, ultrafiltration, adsorption, electrodialysis, and
interactions between dissimilar surfactants in various phenomena.


unit area is then approximated as one-sixth of
the heat of vaporization of the surface molecules
occupying a unit area. Viewing the creation of
a surface as "fractional vaporization" provides
physical insight to the reason surface tensions
exist, and the crude calculation actually gives
values for surface tension within a factor of two
of the correct value. Demonstration of the actual
measurement of surface tension in the instructor's
lab also reinforces the concept that it takes work
or energy to create a surface. Using a Du-Noiiy
ring tensiometer, the students can see the surface
stretch under stress before breaking.
One of the greatest weaknesses of Adamson
[1] is the treatment of surface thermodynamics.
The derivations are generally not rigorous and
are often obscure. Therefore, the instructor
basically needs to derive fundamental thermo-
dynamic relationships (like the Kelvin equation
and the Gibbs equation) from scratch. The power
of the Gibbs equation and the importance of the
definition of the dividing surface can be illustrated
by a calculation of monolayer coverage of a sur-
factant from dilute solution from surface tension

... when the students finish the
course they have a working familiarity
with a wide range of phenomena and a quantitative
knowledge of the more important mathematical
relationships in the field.

When covering the third major topic, adsorp-
tion, the basic difference between localized and
mobile adsorption must be emphasized. Inter-
converting 2-D equations of state and mobile ad-
sorption isotherms using the Gibbs equation il-
lustrates this point. Hiemenz [3] is a useful refer-
ence concerning the electrical double layer.
At this point in the course (about half-way
through), the student has seen mostly theory and
is wondering about the usefulness of the material.
Even though applications are in a separate section
at the end of the course, to complete the ad-
sorption topic, adsorber design is discussed. First,
practical guidelines for selection of industrial ad-
sorbents for various applications are given. Then
some complications of adsorber design are touched

Course Outline

Definition and Reason for the Existence of Surface
Laplace Equation
Capillary Rise Phenomena
Measurement of Surface Tension
Surface Thermodynamic Properties
Kelvin Equation
Criterion of Equilibrium in Systems with Interfaces
Dividing Surface
Definition of Adsorption or Surface Excess
Gibbs Equation
Monolayer Coverage at the Air-Water Interface
Localized vs. Mobile Adsorption
Langmuir Adsorption Isotherm
BET Adsorption Isotherm
2-D Equations of State
Potential Theory
Adsorption from Solution
Electrical Diffuse Double Layer
Debye-Hiickel Theory and Debye Length
Stern Layer
Practical Applications and Adsorber Design
Young Equation
Measurement of Contact Angle

Classes of Surfactants
Micelle Structure
CMC Determination
Mass-Action Model
Pseudo-Phase Separation Model
Shinoda Equation
Locations of Solubilizate in Micelles
Driving Forces for Solubilization
Measurement of Solubilization
Mechanisms of Stabilization
Bancroft Rule
HLB Number
Breaking Emulsions

Gibbs Triangle
Mechanisms of Film Elasticity
Mechanisms of Foam Drainage
Foam Breaking and Inhibiting

Enhanced Oil Recovery by Surfactant Flooding
Marangoni Effects
Novel Separation Techniques Using Surfactants

FALL 1984

on: the mass-transfer zone, bed heat-up due to
heat of adsorption, and bed regeneration.
Examples of applications using activated carbon,
silica gel, and ion-exchange resin are given.
Handouts and suggested reading material supple-
ment lectures on design of adsorbers [4-7].
In covering the topic of contact angles, the
reasons that advancing and receding contact
angles may differ are explored. The physical mean-
ing of the Young equation in terms of the surface
tensions involved is emphasized.
Topics 5-7 are in the area of colloid science.
Rosen [2] is used as the text. It is easy to read and
is well organized, and the text is followed much
more closely in this section of the course than in
the surface science section.
In the consideration of micelle formation, the
variety of surfactants available is discussed, and
the value of McCutcheons' [8] in finding suppliers
of a certain type of detergent is stressed. The
various methods of CMC determination help il-
lustrate the properties of solutions containing
micelles and lead naturally into a discussion of
the mass-action and pseudo-phase separation
models of micelle formation. The fact that these
models coincide for large enough micellar aggre-
gation numbers is stressed. The iceberg structure
of water around hydrocarbon chains in solution
causing the micelle formation to be entropy-
driven and the subsequent concept of hydrophobic
bonds is then considered in the context of micellar
thermodynamics. The effect of electrolyte con-
centration and hydrocarbon chain length on the
CMC is shown to be described by the Shinoda
equation [9]. The value of Mukerjee and Mysels
[10] as the standard reference for literature CMC
values is useful to point out. Krafft temperature,
cloud point, and liquid crystals are briefly dis-
cussed to show that there are limits to conditions
resulting in the isotropic regions where micelles
form in surfactant solutions.
Under the topic of solubilization, the wide-
spread use of Henry's law to extrapolate solubiliza-
tions measured at unit activity using the maxi-
mum additivity method is discussed. This is
followed by consideration of deviations from
Henry's law and methods of measurement of
solubilization (vapor pressure, osmometry, vapor
phase UV, vapor phase GC, ultrafiltration) over
the entire concentration range. The importance of
solubilization in such applications as detergency
is worth mentioning.
In discussions of emulsions, the origins of

barriers to emulsion breaking are described. The
guidelines for the selection of surfactant by HLB
Number and tabulations of this value in Mc-
Cutcheons' [8] for commercial surfactants are em-
phasized. The importance of emulsions to chemical
and petroleum engineering operations is illustrated
by examples such as the severe problem of separat-
ing oils recovered by tertiary methods from pro-
duced water in the field because of emulsion for-
mation. The existence of emulsions in everyday
life in products such as milk and paint helps the
student feel more comfortable with the phe-
nomena. The fact that emulsions are not thermo-
dynamically stable is heavily emphasized. How-
ever, it must be mentioned that the so-called
"microemulsions" used in surfactant flooding can
be considered as a thermodynamic phase.
The fact that foams are not thermodynamically
stable is also stressed: that foams are sometimes
desirable (detergents) and sometimes undesirable
(causing entrainment in distillation columns) is
important to note. New applications of foams,
such as in enhanced oil recovery for mobility
control or foam fractionation, point out their im-
The applications portion of the course is de-
signed to show how important the phenomena
discussed are and to illustrate that many of them
can be occurring at the same time and have com-
plex interactions. The various methods of EOR
are first outlined (aided by a handout from
Exxon [11]), and the mechanisms by which they
function are discussed. Then surfactant flooding
is focused on. Theories to explain the ultralow
interfacial tensions present in these systems pro-
vide an opportunity to explore some subtleties of
interfacial tension, surface thermodynamics,
solubilization, and emulsion stability. Adsorption
of surfactants on minerals and precipitation
neatly show the tie between surface science and
colloid science. A discussion of the state-of-the-art
and the major remaining problems to be solved
in this technology are complimented by an outline
of the instructor's approach to solving these prob-
lems. A tour of the instructor's research lab where
the students can observe such things as middle
phases, surfactant precipitate, and cloud points
brings home the applications of the course to
Detergency also involves both surface science
(surfactant adsorption on fabrics) and colloid
science (solubilization). In addition, the rollback
mechanism of oil removal from fabrics provides


a practical example of contact angles and wetting.
Until this point in the course, equilibrium phe-
nomena have been almost exclusively considered.
A discussion of Marangoni effects demonstrates
non-equilibrium surface tension effects. A non-
mathematical article on tears which form on the
inside of a glass of wine [12] is supplemented by
passing around a wine glass containing vodka so
the student can see the tears form. The reduction
in liquid level in the glass after being passed
around the class can not always be accounted for
solely by evaporation. This practical demonstra-
tion of Marangoni effects is always popular.
The course is completed by discussion of a
favorite research topic of the lecturer: separation
techniques using surfactants. Among those dis-
cussed are foam fractionation and micellar en-
hanced ultrafiltration. Since the majority of the
class is composed of chemical engineers, these
novel applications of colloid science to replace
classical separation techniques illustrate the value
of colloid science.
In general, the students liked the relatively
high fraction of course content dedicated to
practical applications. They also liked the constant
emphasis on the physical significance of the ma-
terial. They appreciated the fact that the mathe-
matical content of the course was kept to a level
such that physical reality was not obscured.
The students had two main complaints: they
did not like Adamson as a text, and they found sur-
face thermodynamics to be less interesting than
the rest of the course. However, most of them
recognized the future value of Adamson as a
reference book and also realized the necessity of
a firm grounding in surface thermodynamics for
the later topics covered.
Teaching both surface and colloid science in
a single course is a challenging task. Some de-
partments choose to cover surface science in detail
with a more mathematical orientation and a
mention of colloidal phenomena in passing. In
order to learn surfactant science, another course
is needed. The dedication of two courses to this
area is not always possible or desirable (par-
ticularly for the MS student). This course was
developed as an attempt to integrate the basics
from both surface science and colloid science into
one course. Response from former students in in-
dustry concerning the value of the material learned

indicates that the course fulfills a need. O
1. Adamson, A. W., Physical Chemistry of Surfaces,
Fourth Edition, Wiley, New York (1982).
2. Rosen, M. J., Surfactants and Interfacial Phenomena,
Wiley, New York (1978).
3. Hiemenz, P. C., Principles of Colloid and Surface
Chemistry, Ch. 9, Marcel Dekker, New York (1977).
4. Kovach, J. L., in Handbook of Separation Techniques
for Chemical Engineers, Ch. 3.1, P.A. Schweitzer,
Ed., McGraw-Hill, New York (1979).
5. Calgon Corporation, Pamphlet on "Basic Concepts of
Adsorption on Activated Carbon," Calgon, Pitts-
6. Scamehorn, J. F., Ind. Eng. Chem. Process Des. Dev.,
18, 210 (1979).
7. Vatavuk, W. M., and Neveril, R. B., Chem. Eng., 90,
131 (Jan. 24, 1983).
8. McCutcheons' Emulsifiers & Detergents, North
American Division, McCutcheon, Glen Rock, N.J.
9. Shinoda, K., in Colloidal Surfactants, Ch. 1, K.
Shinoda, T. Nakagawa, B. Tamamushi, and T. Ise-
mura, Eds., Academic Press, New York (1963).
10. Mukerjee, P., and Mysels, K. J., Critical Micelle Con-
centrations of Aqueous Surfactant Systems, National
Bureau of Standards, Washington (1971).
11. "Improved Oil Recovery," a pamphlet by Exxon
Corporation, Exxon, New York, 1982.
12. Walker, J., Scientific American, 248, 163 (May, 1983).

FALL 1984






APPLE II can be made to function as
a data acquisition and control system
for under $3000.


Dr. P. Deshpande
Professor of Chemical Engineering
University of Louisville
Louisville, KY 40292

A CQe44eM irz


Cleveland State University
Cleveland, OH 44115

T HE PRIMARY OBJECTIVE in a course on transport
phenomena is to analyze physical problems in
heat, mass, and momentum transfer. The steps
involved in this process are understanding the
physical aspects of the problem, making appropri-
ate assumptions, deriving the necessary differ-
ential equations, and developing analytical solu-
tions. In this endeavor applied mathematics plays
a secondary, but a very powerful, role. Of course,
many problems of interest and practical im-
portance are quite complex, and it is not possible
to obtain analytical solutions for these cases. This
does not diminish the importance of finding exact
or approximate analytical solutions to the develop-
ed differential equations. Sometimes it is neces-
sary to obtain a closed form of the solution
in limiting cases. Such solutions under asymptotic
conditions are needed to validate the numerical
solution of the differential equations. A gradu-

Dhananjai B. Shah has a BChE from the Department of Chemical
Technology, University of Bombay, and MS and PhD (1975) from
Michigan State University, both in chemical engineering. He spent
two years at the University of New Brunswick, one year at McMaster
University, and three years at the Indiana Institute of Technology.
Since 1982, he has been an assistant professor of chemical engineering
at Cleveland State University. His research interests include simulation
and modelling of unsteady processes, adsorption and diffusion in
zeolites and catalysis.

ate course in transport phenomena, therefore,
should place considerable emphasis on common
methods of solution of differential equations, how
they are applied, and why they work.

Every fall, we offer a graduate course in
transport phenomena. The course meets four hours
a week for ten weeks, and it is one of the three
required of every master's student. It is the only
course a terminal master's degree candidate will
have that integrates the three transport processes.
Most students take this course in the first quarter
of their graduate program.
We have a relatively large percentage of part-
time graduate students. Some have come back to
school after a lapse of few years, and some have
had their baccalaureate degree in chemistry. They
need considerable help in solving the differential
equations. However, because of their practical ex-
perience, they have a good feel for physical situ-
ations and are good at making approximations
and engineering judgments. The full time students
are only slightly better prepared in solving the
differential equations. Many of them have not
had any undergraduate course in partial differ-
ential equations, and they tend to be overwhelmed
by the equations they come across in transport
phenomena. The course strives to achieve a bal-
ance between exposing the students to 1) ad-
vanced topics in transport phenomena, pointing
out similarities and differences between the three
transfer processes, and 2) common methods of
solving differential equations. The best way to
accomplish these objectives is to solve a large
number of problems. Daily homework assignments
are made throughout the duration of the course.
Textbooks by Bird, Stewart and Lightfoot
(BSL) and by Slattery (S) are used repeatedly.
Both the books abound with challenging problems
which are used extensively for classroom discus-
sion and for homework assignments. All of the
students coming into the course are expected to
Copyright ChE Division, ASEE. 1984


have been exposed to the first three chapters in
each of the three sections in BSL. At the end of
the course, it is hoped that the students will be
able to comprehend almost all the material in
BSL. In addition, a number of other books and
journal articles are consulted (listed in the refer-
ences to this paper).

The problems in transport phenomena are
formulated and analyzed in a series of steps as
outlined below.

Problem Visualization
The co-ordinate system based on the geometry
of the problem is chosen first. In most cases the
choice is obvious, but in some cases it is not easy.
For example, in considering diffusion from a point
source in a moving stream (17 K, BSL), it is not
easy to decide whether to use cylindrical or
spherical co-ordinates. After the co-ordinate
system is chosen, the physical aspects of the
problem are discussed. Any intuitive feeling about
the behavior of the system under some limiting
conditions is brought out. Directions of velocity,

The course strives to achieve
a balance between exposing the students
to 1) advanced topics in transport phenomena,
pointing out similarities and differences between the
three transfer processes, and 2) common methods
of solving differential equations.

temperature, and concentration gradients are de-
termined. Appropriate physical assumptions are
made to simplify the resulting set of equations.
One such assumption is to neglect end effects in
many momentum transfer problems. Another
example is the absorption of a component in falling
film where convective flux is neglected in the X-
direction and diffusive flux is neglected in the Z-
direction (17-5, BSL).

Differential Equations
The general equations of continuity, motion,
and energy are now applied to the problem under
consideration. With the help of information ob-
tained in the above section, the terms not applic-
able to the problem at hand are equated to zero.
The solution of the resulting set of differential

Classification of Problems According to
Method of Solution of Differential Equations


1) Flow near a wall suddenly set 1) Velocity distribution in plate and 1) Two large blocks brought in
in motion (4.1-1, BSL) cone viscometer (3T, BSL) contact (6.2.2.-2.5)
2) Heating semi-infinite slab 2) Unsteady laminar flow in a 2) Cooling of sphere in contact with
(11.1-1, BSL) circular tube (4.1-2, BSL) or in well stirred fluid (11.1-3, BSL)
an annulus (4L, BSL)
3) Unsteady evaporation 3) Unsteady tangential flow 3) Gas absorption in a falling film with
(19.1-1, BSL) (4Lb, BSL) chemical reaction (17L, BSL)
4) Gas absorption with rapid 4) Heating finite slab (11.1-2, BSL) 4) Packed adsorption column
chemical reaction or semi-infinite slab with con- modelling (22L, BSL)
(19.1-3, BSL) vective boundary condition
(6.2.3, S)
5) Boundary Layer Theory 5) Mass transfer within a solid 5) Unsteady diffusion with a first
Exact Solution for a) Momentum sphere (9.2.1-1, 9.2.1-2, S) order homogenous reaction
Transfer (3.5.1, 3.5.2, S) (9.2.2, S)
b) Momentum and Heat Transfer
(6.7.1, 6.7.2, S)
c) Heat, mass and momentum
transfer (19.3, BSL)
6) Unsteady interphase diffusion
(19K, BSL)

FALL 1984

equations subject to the appropriate initial and
boundary conditions is attempted by using one of
the following three techniques.
Similarity solution by combination of variables.
The differential equations which can be solved by
this method are characterized by boundary con-
ditions where the dependent variable has the same
value at different values of two independent vari-
ables. For example in fluid flow near a wall sudden-
ly set in motion (4.1-1, BSL), the boundary con-
ditions are V = 0 at t = 0 for all Z and at Z = co
at all t > 0. Such boundary conditions are quite
common in problems involving a semi-infinite
region. A new combined variable -q = Z/a t" is
defined which allows the above two boundary
conditions to merge, i.e. V = 0 at q = oo. The
value of n is chosen such that when Y] is substi-
tuted into the partial differential equation, on
simplification, an ordinary differential equation
is obtained. The choice of a is more arbitrary but is
generally taken as a reciprocal of n. When the
ordinary differential equation is solved, one ends
up with error functions and gamma functions.

The method also gives an opportunity to introduce
the concept of penetration thickness which is ex-
ploited later in the boundary layer approximation
discussion. The method is applied repeatedly to
many of the problems listed in Table 1. The empha-
sis is on why the method works, when it is ap-
plicable, and how it works.
Similarity Solution by Separation of Variables.
The boundary conditions in this case are such
that a combined variable cannot be formulated
that combines the two boundary conditions into
one. The boundary condition at Z = oo is either
replaced by a similar one at Z = L or is character-
ized by heat or mass transfer resistance. Such
problems are solved by the method of separation
of variables. The dependent variable is assumed
to be product of separable functions, each one of
which is in turn a function of one independent
variable only. The method requires that the
students be exposed to Sturm-Louiville theorem,
orthogonal functions, weighting functions, and the
limits of integration. Again, why the method
works for these boundary conditions is empha-

Simplification of Differential Equations


1) Cone and plate Viscometer 1) Graetz-Nusselt Problem 1) Squeeze film (12.4, Denn)
(3.5-3, BSL) a) Large distances (9.8, BSL)
b) Short distances (11.2-2, BSL)
2) Creeping flow between con- 2) Short contact times 2) Unsteady evaporation from a tube
centric spheres (3Q, BSL) a) (9.P, 9.R, BSL)
followed by separation of b) Heat transfer from wall to
variables falling film (10R, BSL)
c) Diffusion into falling liquid
film (17.5, BSL)
d) Solid dissolution into falling
film (17J, BSL)
3) Periodic heating of earth's 3) Navier-Stokes Equations 3) Unsteady evaporation of a drop
crust (11L, BSL) a) Re->0, Creeping flow
(chapter 12, Denn)
b) Re -> oo, potential flow
Inviscid flow (3.4.1, S)
c) Re-> o, Boundary
layer approximation (chapter 15,
4) Flow near an oscillating 4) Shrinking unreacted core model in
wall (3.2.4-4, S) gas-solid non-catalytic reaction
5) Flow between rotating discs 5) Efflux times for tank (7M, 7P, BSL)
(12.2, Denn)


sized by comparing the similar profiles, and how
it works is illustrated by solving a number of
problems, some of which are listed in Table 1.
In some cases, not only are the functions
separable, but one of the functions is easily formu-
lated from the boundary conditions. For example,
in describing a velocity field for flow near an
oscillating wall, the boundary conditions are at
Y = 0, V = Vo sin (wt e) and at Y = oo, V = 0.
The boundary conditions allow us to formulate
the solution as V = exp[i(wt e)]f(y). There
are many such cases, and some are listed in Table
Use of Laplace Transforms. Many of the
problems solved by combination of variables or
separation of variables can also be solved by using
the Laplace transform. However, it is preferably
applied where there are more than one partial
differential equations and variable of interest can
not be determined without solving for some other
variables first. An excellent example of this is the
cooling of a sphere in contact with well-stirred
fluid (11.2-1; BSL). By using Laplace transforms,
it is possible to evaluate the variation of solid
temperature with radius and time without having
to solve for the temperature history of the fluid.
A number of problems where the Laplace trans-
form method is applied and illustrated are listed
in Table 1.

Simplification of Differential Equations
Many times the differential equations derived
are quite complicated and none of the three
methods outlined above is applicable. Under these
conditions, one may wish to consider a limited
case where one or more terms in the differential
equations are neglected. However, it is very im-
portant to indicate how these approximations are
made and how a simplified set of differential equa-
tions is derived. This is illustrated with the classic
problem in fluid mechanics. The Navier-Stokes
equations are written in dimensionless form using
characteristic quantities. This introduces the
Reynolds number into the Navier-Stokes equations.
The behavior of these equations in the following
three cases is then investigated.
Creeping flow in the limit as Re 0
Potential flow in the limit as Re oo. This corres-
ponds to inviscid fluid flow far from the boundary
Boundary layer approximation in the limit as
Re -> oo for fluid flow in the immediate neighbor-
hood of a boundary
Excellent discussion of these topics is provided

Many times the differential
equations derived are quite complicated
and none of the three methods
outlined ... is applicable.

List of Additional Topics Covered in the Course
A) Potential flow and stream function
Creeping flow around sphere
(2.6, 4.2-1, BSL; 3.3.3, S)
B) Non-Newtonian fluid flow
Introduction to tensor algebra
Cone and plate viscometer (3.4-3, 3T, BSL;
3.3.2, S)
Flow in simple geometry (3.2.2-3.2.4, S)
C) Turbulent flow (Chapter 5, BSL)
Time averaged Navier-Stokes equations
Approximations to Reynolds Stresses
Velocity profiles in simple geometry
(5E, 5F, 5D, 5H, BSL)
D) Exact solution of Navier-Stokes equations
Converging flow in a channel
Other examples (Chapter 5, Schlichting)
E) Nusselt and Sherwood numbers in laminar and
turbulent flow (Ref. 2, 3)
F) Steady State multicomponent diffusion with homo-
geneous and heterogeneous reactions (18Q, 18S, BSL;
9.2.3, 9.2.7, S)
G) Diffusion from a point source in a moving stream
(10.2, S)
H) Macroscopic Balances
Pressure distribution in a manifold (7Q, BSL)
Heat exchangers (15J, BSL)
Heating of a liquid in an agitated tank (15M,
15.5-1, BSL)
Packed bed absorber and adsorber (22.5-1,
22.6-2, BSL)

by Slattery and Denn.
It is also pointed out to students that the
number of asymptotic cases considered for large
distances or short contact times treated in BSL
and Slattery represent another way of simplifying
the differential equations. Many cases of short
contact times let us assume that the depth of pene-
tration is much smaller than the length of region
of interest. This allows one to shift the boundary
condition at, say, Z = L to Z = oo. The students
immediately see the benefit of doing this as the
problem becomes solvable by the combination of
variables as outlined earlier. Various problems
of this type are listed in Table 2.
Another common concept used to simplify the
differential equations is the concept of pseudo
steady state approximation. The problems listed
in Table 2 are used to illustrate the application of
Continued on page 213.

FALL 1984

4 Cowsce on



Georgia Institute of Technology
Atlanta, GA 30332-0100 .&

WE HAVE OFFERED, for the past three years, a
specialized seminar course entitled "Seminars
in Heterogeneous Catalysis" to students in our
research groups on alternating quarters, usually
fall and spring. The original purpose of these
seminars was to bring about a feeling of unity
to our program of heterogeneous catalysis and to
help educate our students on the nature of catalysis
outside the formal graduate lecture course we offer
once a year under the same name: Catalysis. After
the initial start-up of this seminar course we ex-
plored the benefits of such a communications-based
course which included the transfer of information
between graduate students working on similar
problems and the improvement upon communica-
tion skills. The next logical extension of the
course was to formalize the feedback mechanism
by which students could learn of their strengths
and weaknesses. Our first attempt at this feed-
back was rating sheets on which the audience
would mark the performance of the presenter as
"good" to "poor" for various aspects of the
seminar presentation, such as clarity of ideas,
organization, and the mechanics of the presenta-
tion (including quality of visual aids, nervous
mannerisms, etc.). As a result of this rating sys-
tem, we noticed a significant improvement in the
quality of the presentations, in both the content
and the style of presentation. An integral part of
the seminar program was a question-and-answer
period that followed the formal talk. As with all
novice speakers, the reaction to such interrogation

The setting of the video
seminar was a classroom equipped
with cameras in discrete locations and with
classroom-type tables having small
monitors located on them.

( Copyright ChE Division, ASEE. 1984

Mark G. White received his BSChE degree from the University of
Texas at Austin, his MSChE degree from Purdue University, and was
graduated with a PhD degree from Rice University. For the last six
years he has been teaching at the Georgia Institute of Technology.
His industrial experience includes a position as a summer engineer
with the Amoco Oil Company (Texas Division) and as a research
engineer with the Amoco Oil Research in Whiting, Indiana. His re-
search interests include heterogeneous catalysis and reaction kinetics.

ranged from fright to morbid fear. However, the
more experienced students began to see the value
of such questioning which forced the speaker to
defend his research and resulted in a better under-
standing of the work. In time, a fraction of the
students began to look forward to such question-
and-answer periods, except when they were the
presenters. As a result of the success of the feed-
back rating procedure and through a desire to
have further improvements in the seminar pre-
sentations, we chose the video-based format to
affect such improvements.

The video-taping of a formal presentation
shows both similarities to and differences from the
familiar seminar format. Among the similarities,
the speaker must convey thoughts through words
and illustrations which must be organized into a
cohesive unit. In one sense, the video-based format
demands better organization of the talk because
of the time limit imposed by rental of the on-
campus taping studio. The setting of the video
seminar was a classroom equipped with cameras


Sin discrete locations and with classroom-type
tables having small monitors located on them. An
audience was present for all the tapings, and the
lighting was only slightly brighter than normal
room conditions. These "familiar" conditions help
put the presenter at ease.
However, the differences associated with video-
taping are significant. Usually there were one or
two operators present in a control booth behind
the classroom to focus the remote-controlled
cameras and to record the talk. The students be-
came aware of the importance of communication
between the operators and themselves to ensure
the proper camera position when illustrations
were used in a presentation. In essence, the student
became both the star and the director in taping
the talk. Finally, fear of the unknown, coupled
with the excitement created by the medium of
television, made this experience something quite
We tried to meet some of these differences
with some preproduction planning and prepara-
tion. During the quarter immediately before the
taping, the students were given an article entitled
"The Video Performer," by Norm Herman (Edu-
cational and Industrial Television), which is aimed
at helping the first-time TV star to avoid some
common mistakes. Additionally, the students
were asked to submit titles and one-page abstracts
of their talks before the quarter began, to facili-
tate early planning of the seminar content. Dave
Edwards, Assistant Director of the Department
of Continuing Education at Georgia Tech, suggest-
ed we have two class sessions of planning and
preparation before the actual seminars were
taped. The first session would involve Dave giving
a short lecture on the dos and don't of video-
taped presentations, followed by a short presenta-
tion by this author demonstrating some of the
ideas. The students seemed to appreciate my feeble
attempt to make them feel at ease by blundering
my way through the presentation. The second
session was a three-minute taping of each student
giving his seminar topic and abstract; this taping
was followed by a review of all the presentations.
This preliminary taping session was a good way
of demonstrating how difficult it is to produce an
error-free talk with only one shooting.
Additional pre-production preparation in-
volved a series of meetings between the student
and this author to determine the scope of the 20-
minute presentation, to write a sketchy outline
(followed by a detailed outline), and finally to re-

view the illustrations for content and quality. We
have found that these pre-production meetings are
essential to producing a quality seminar for
taping. Finally, each student met with the camera
operators to review the illustrations on camera
and to discuss the camera angles, etc.
The studio was equipped with three cameras
operated by remote control from the booth. Two
of these cameras afforded shots of the commenta-
tor while the third, an overhead camera, was used
exclusively for the illustrations. The side camera
could be used to give angle shots of the speaker,
whereas the main camera gave head-on shots.
When appropriate, the side camera was used to
give better definition of three dimensional models.
Titles and names could be superimposed under the
speaker and split-screens could be used for extend-
ed discussions of illustrations. Although not used
in these seminars, split-screens and chrome-key
facilities are available in our campus studio;
needless to say, these exotic techniques require
more pre-production planning and direction on the
part of the student. Our experience shows that
the most successful talks, in terms of clarity and

An integral part of the
seminar program was a question-and-answer
period that followed the formal talk.

freedom of errors, were those which used a mini-
mum of visuals and few exotic techniques; as the
speakers mature, these other techniques will
certainly enhance the professional nature of their
The review of these seminars commenced im-
mediately following the talk. The objective of this
review was to show the student the success/failure
of his attempt to communicate a technical subject
in a formal setting. Success could be evaluated in
terms of how clearly the student told his story.
Did he connect the major points of the topic with
good transition sentences? Was the logic sound?
Did the illustrations convey the essence of the
thought with a minimum of information? In short,
did the student give a talk which was enjoyed by
his peers? During the review process I would
comment on the positive and negative aspects of
only the more subtle points; there was no need to
comment on the obvious blunders. Also, the
students became aware of distractive mannerisms
such as throat-clearing, nervous hand-waving,
Continued on page 189.

FALL 1984



Rice University
Houston, TX 77251

A FIRST-YEAR GRADUATE course (or sequence of
courses) in applied mathematics has become
an integral part of the curriculum in a large
number of chemical engineering departments.
Among the diverse subjects taught in these
courses, linear algebra usually enjoys a prominent
position. The reason for this popularity perhaps
lies in the fact that linear algebra is as central a
subject and as applicable as calculus. The pioneer-
ing work of Neal Amundson, and of his students
and disciples as well as other prominent scholars,
has established beyond any doubt that many sig-
nificant and complex chemical engineering prob-
lems may be solved by advanced linear algebra
techniques [1].
Linear algebra can also serve as an ideal
stepping stone for introducing the first-year
graduate student to the formal mathematical
language of functional analysis. The basic con-
cepts of matrix algebra, already familiar to the
student, can be formulated using the abstract
framework of linear vector spaces. The same
abstraction can also be used to unify apparently
diverse problems in finite dimensional spaces
under this common framework. Thus, the ground-
work is laid out for the introduction of functional
analysis in infinite dimensional spaces, which is
necessary for the study of differential and integral
operator problems [2].
Our linear algebra course strives to combine
both elements of mathematics-abstraction and
application. Many of the fundamental theorems
of linear algebra are rigorously derived in class.

Student responses to the course
evaluation questionnaire indicate that
they particularly enjoy the computational part
of the course since it points out some of the
real problems to which linear algebra
theory can be applied.

c Copyright ChE Division, ASEE. 1984

Course Materials
Strang, G., Linear Algebra and Its Applications, 2nd
Edition, Academic Press, (1980).
1. Amundson, N. R., Mathematical Methods in Chemical
Engineering: Matrices and Their Application, Pren-
tice Hall, (1966).
2. Braun, M., Differential Equations and Their Applica-
tions, 2nd Edition, Springer-Verlag (1975).
3. Dahlquist, G., A. Bjorck and N. Anderson, Numerical
Methods, Prentice Hall (1974).
4. Friedman, B., Principles and Techniques of Applied
Mathematics, John Wiley (1956).
5. Hirsch, M. W. and S. Smale, Differential Equations,
Dynamical Systems and Linear Algebra, Academic
Press (1974).
6. Noble, B. and J. W. Daniel, Applied Linear Algebra,
2nd Edition, Prentice Hall (1977).
7. Steinberg, D. T., Computational Matrix Algebra, Mc-
Graw-Hill (1974).

The theory, however, is motivated and reinforced
by examples derived from a wide range of chemi-
cal engineering problems. Particular emphasis is
placed upon the important aspects of computa-
tional linear algebra. In our opinion, it is impera-
tive to expose the students to some fundamental
computational methods and to study their efficiency
as well as their convergence problems. Student
responses to the course evaluation questionnaire
indicate that they particularly enjoy the compu-
tational part of the course since it points out some
of the real problems to which linear algebra theory
can be applied.

Eleven weeks (out of a total of fifteen) of
the fall semester course, "Applied Mathematics
for Chemical Engineers I," are devoted to the
study of linear algebra and its applications. The
remaining time is devoted to a brief review of
complex analysis and complex integration, which
is the final preparation step for the second course
in applied mathematics taught at Rice. This


Kyriacos Zygourakis received his diploma in chemical engineering
from the National Technical University of Greece in 1975 and his PhD
from the University of Minnesota in 1980. He is presently an assistant
professor in the Department of Chemical Engineering at Rice Uni-
versity. His main research interests are in the areas of reaction
engineering, applied mathematics and numerical methods.

second course covers the theory of differential and
integral operators, again using the functional
analysis approach.
The course meets twice a week for two hours
and runs largely as a lecture, although active
student participation is encouraged by frequent
questions from the instructor. The lectures are
accompanied by tutoring sessions which are de-

signed to help the students with their computer
projects as well as for the discussion of home-
work assignments in an informal way.
The students are urged to keep a complete
set of notes, which are regularly supplemented by
handouts providing lengthy theorem proofs or
summarizing the results established up to that
The assigned textbook is Linear Algebra and
its Applications (2nd Edition), by Gilbert Strang.
Although it is an extremely well-written book, it
is not followed closely (especially in the first part
of the course). The students are strongly en-
couraged to consult additional references (see
Table 1).
Homework problems are assigned almost
every week. In addition, the students are required
to complete one or two computational projects.
They also have to take a mid-semester and a final
exam, which consist of both open- and closed-book


The linear algebra part of the course (see
Table 2) consists of four parts:
Vector spaces and linear transformations
The solution of systems of linear equations

Topical Outline of the Linear Algebra Course

Overview of the problem of solving systems of
linear equations. Which applications give rise
to such systems? Which are the theoretical
porblems that must be answered?
Vector spaces and subspaces.
Linear dependence, basis and dimension.
Linear transformations between finite-dimension-
al spaces and their matrix representation.
Rank and nullity of linear transformations.
Elementary matrices and the computation of the
rank of a matrix.
The theory of simultaneous linear equations.
Homogeneous and nonhomogeneous systems.
The Fredholm alternative.
Gaussian elimination. LU--decomposition, pivot-
ing, operation count.
Error analysis. Ill-conditioned matrices.
Band matrices and how they arise in practice.
Finite differences solution of partial differ-
ential equations.

Overview of iterative methods for solving linear
Comparison of the various numerical algorithms.

Inner products, norms, orthogonality.
Eigenvalues and eigenvectors of matrices.
Diagonalization and similarity transformations.
Systems of difference equations.
Functions of matrices.
Solution of systems of ordinary differential
equations. Stability.
Unitary transformations. Normal matrices.
Spectral decomposition of operators.

Positive definite quadratic forms.
Minimization problems. Least squares.
Rayleigh quotient. Maximum and minimax
Numerical computation of eigenvalues and
Overview of the finite elements method.

FALL 1984

The students are thus presented with our objectives for the first part of the course. A brief review
of the algebra of matrices follows, reminding the student of the familiar concepts of multiplying a matrix
by a scalar to obtain another matrix and of summing two matrices to obtain a third one.

Th Elgnvale prble

The Eigenvalue problem
Quadratic forms and variational principles
The Linear Equation Problem A x = b
The course starts with an introduction to the
problem of solving systems of linear equations of
the form A x = b. Several applications that give
rise to such large systems are discussed and the
three fundamental questions are introduced:
Do these problems have a solution?
If they do, is the solution unique?
How can the solution be computed?
The students are thus presented with our ob-
jectives for the first part of the course. A brief
review of the algebra of matrices follows, remind-
ing the student of the familiar concepts of multi-
plying a matrix by a scalar to obtain another
matrix and of summing two matrices to obtain a
third one. It is also pointed out that these opera-
tions satisfy certain properties such as associativi-
ty, commutativity, distributivity, etc. This dis-
cussion serves as the motivation to introduce the
notion of abstract linear vector spaces. Several
examples of vector spaces are then presented,
covering sets of functions, polynomials, solutions
of differential or integral equations, etc. The
students come to realize that seemingly different
mathematical systems may be considered as
vector spaces and that this abstract framework
can unify these diverse phenomena into a single
The basic concepts of linear combinations, basis
sets, and dimension are then discussed. Thus, the
abstract quantities called vectors can be repre-
sented now in terms of their coefficients of ex-
pansion with respect to a particular basis set.
The first milestone is reached with the intro-
duction of linear transformations between finite-
dimensional spaces and their matrix representa-
tion. Most of the important theorems here are
rigorously derived in class and the concepts of
rank and nullity of transformations are formally
introduced. Armed with the conclusion that all
the results established for linear transformations
can be used for matrices (and conversely), we can
then establish the conditions for existence and
uniqueness of solutions of the first fundamental

problem of linear algebra A x = b. This is ac-
complished in one lecture using the previously
derived theorems.
Throughout this part of the course, emphasis
is placed on the generality of this approach, and
the students have the opportunity to see how the
results apply to linear differential and integral
operators, as well as to chemical engineering
problems. Such examples include first-order re-
action systems and the determination of the
number of independent chemical reactions in a
closed system using experimental measurements.
The practical problem of efficiently computing
the solution of systems of linear equations can now
be considered. The Gauss elimination procedure
and the LU decomposition are introduced, which
lead naturally to the idea of the operation count
as a measure of the computational effort required.
An important application which gives rise to large
systems of linear equations is then studied by
introducing the finite-difference method for solv-
ing ordinary and partial differential equations
subject to specified boundary conditions. The
students learn how to take advantage of the
matrix structure (band or positive-definite
matrices) in order to speed up the computational
process and how to use the LU-decomposition for
the efficient solution of iterative problems that
arise in the solution of nonlinear differential equa-
tions. The problem of ill-conditioned matrices is
outlined in sketchy form, along with a rudimentary
introduction to error analysis. Iterative methods
for the solution of linear systems of equations are
also briefly covered.
At this point a computer project is assigned.
The students are asked to solve a two-dimensional
partial differential equation using finite differ-
ences. They must use different grid sizes and
compare the numerical results to the true solutions
in each case.
The students must demonstrate that they can
correctly formulate the system of linear equations.
Following that, they use the library programs
available at our computer center to obtain the
results. The library programs LINPACK and
ITPACK (for the direct and iterative solution of
linear systems) have proven to be invaluable aids.


Thus, the emphasis is shifted from the drudg-
ery of computer programming to the analysis of
the results. The numerical simulations permit the
students to evaluate the relative efficiency of
numerical schemes (i.e. execution speeds, memory
requirements) and to determine which ones must
be used for the various structures and sizes of the
resulting matrices. Thus, the theoretical results
derived in class are reinforced and justified.
The second part of the computer assignment
exposes the students to the pitfalls which may be-
fall the unwary and uninstructed user of computer
software packages. The students are asked to
solve a system of equations for which the matrix
of the coefficients of the unknowns is badly ill-
conditioned (the notorious Hilbert matrix has
served as the perfect example in this respect). The
students are asked to compute the known solution
of a system of equations using single and double
precision computer arithmetic. They are then
asked to explain why the solution deteriorates as
the order of the system increases by monitoring
the magnitude of the pivoting elements, the con-
dition number of the matrix, and using the theory
presented in class.

The Eigenvalue Problem A x = Xx
The second part of the course starts with a
brief review of the theory of determinants. Their
properties are presented along with the basic
formulas for their computation. The operation
count for solving systems of linear equations using
Cramer's rate is derived and most of the students
are surprised to find out that even the most power-
ful computer would need about 10145 years to solve
a 100 x 100 system using this method. They are
reminded, however, that determinants give a very
useful invertibility test for square matrices, whose
main application will be used later on in the
course for the development of the theory of eigen-
values. The concepts of inner products of vectors
and of the norm of a vector are then presented
as abstract mappings of vectors into the field of
real (or complex) numbers and are related to the
familiar notions of angle between vectors and of
magnitude respectively.
A discussion of the solution of a simple 2 x 2
system of linear ordinary differential equations
motivates the introduction of the eigenvalues of a
matrix A. The main emphasis here is on the de-
velopment of the theoretical results needed for
the solution of systems of difference and ordinary

differential equations. The cases of operators with
distinct and non-distinct eigenvalues are treated
in detail, although the case of defective matrices
and the Jordan canonical form are only briefly
Throughout this part of the course it is con-
tinuously emphasized that the eigenvalues are
the most important feature of any dynamical
system. The students have the opportunity to
solve a large variety of chemical engineering
problems. They study:
The difference equations describing a cascade of
The differential equations describing isothermal and
nonisothermal CSTR's and their stability.
The problem of N first-order chemical reactions
taking place in a catalyst pellet.
The difference equations resulting when a con-
tinuous system is subject to piecewise constant inputs,
which provides them with an introduction to sampled-
data system theory.
The problem of N first-order reactions taking place
in a batch reactor. This is a long assignment, which

Throughout this part of the
course it is continuously emphasized
that the eigenvalues are the most important
feature of any dynamical system.

leads the students in a step-by-step fashion to derive
the theoretical results necessary to determine all the
rate constants, through a set of carefully designed
experiments [3]. This problem encompasses almost
everything the students have learned so far in the
course. As such, it has come to be known as the
"Everything you always wanted to know about first-
order reactions in batch (. . and more!)" assign-
The final part of the course introduces the
students to the concept of formulating the two
main problems of linear algebra, namely A x = b
and A x = Xx, as minimization problems. The
emphasis now shifts to pointing out the ad-
vantages of this approach for numerical computa-
tions. The problem of minimization of a multi-
variable function serves as the starting point for
an introduction of the concepts of quadratic forms
and positive definite matrices. The least squares
method is then developed formally, and its practi-
cal implications are considered. The course closes
with the formulation of the eigenvalue problem
as a minimization one. The Rayleigh and the mini-
max principles are presented, followed by a brief
Continued on page 213.

FALL 1984

ReAeatcWk oa


Brigham Young University
Provo, UT 84602

CATALYSIS IS A developing science which plays
a critically important role in the gas, petroleum,
chemical, and emerging energy industries. It com-
bines principles from the diverse disciplines of
kinetics, chemistry, materials science, surface
science, and chemical engineering. Catalysis re-
search at universities is typically pursued in de-
partments of chemical engineering and chemistry,
although some of the most successful centers of
catalysis research employ surface scientists, ma-
terial scientists, and physicists as well.
Catalysis research at Brigham Young Uni-
versity (BYU) had its beginning about eleven
years ago when Professor Bartholomew joined the
chemical engineering faculty and has since evolved
into an interdisciplinary program referred to as
the BYU Catalysis Laboratory. The Catalysis
Laboratory currently involves three faculty, two
postdoctoral fellows, two visiting scholars, and
fifteen students in basic investigations of hetero-
geneous catalysts.


The long term objectives of the laboratory are
Pursue basic research in the following catalysis-
related areas: adsorption, supported metal catalysis,
catalyst preparation, catalyst characterization, and
catalyst deactivation.
Obtain a basic understanding of catalyst functions
in energy- and air pollution-related processes such
as methanation, Fischer-Tropsch synthesis and
nitric oxide reduction which can be used by industry

Our guiding philosophies are that a
basic understanding of these relationships will
lead to the development of better catalyst technology
and that university laboratories are best suited
to carry out fundamental investigations ...

Copyright ChE Division. ASEE, 1984

to develop new and better catalyst technology.
Develop new and improve existing methods and tools
for catalyst study, e.g. adsorption techniques, calori-
metry, infrared and Moessbauer spectroscopies.
Train and educate 10-15 students on a continuous
basis in the science and art of catalysis research.
The emphasis in our laboratory is on basic
research relating the physical and chemical
properties of catalysts to their activity and se-
lectivity properties. Our guiding philosophies are
(i) that a basic understanding of these relation-
ships will lead to the development of better
catalyst technology, and (ii) that university
laboratories are best suited to carry out funda-
mental investigations of catalysts and catalytic
reactions while industry is better equipped to
undertake catalyst screening and development ac-
tivities. We subscribe to the "multitool approach";
namely, utilizing as many scientific techniques as
can be usefully applied to the study of a particular
catalyst or catalytic reaction.

Work over the past five years has focused on
preparation, characterization, activity/selectivity,
deactivation, and kinetic studies of cobalt, nickel,
and iron catalysts in methanation and Fischer-
Tropsch synthesis. Publications of the Catalysis

Current Laboratory Research Projects
1. Investigation of Boron Promoted Cobalt and Iron
Catalysts in Fischer-Tropsch Synthesis: Sponsors,
DOE Fossil Energy, Pittsburgh Energy Technology
2. Effects of Support on Adsorption, Activity/Selectivity
and Electronic Properties of Cobalt: Sponsor, DOE
Basic Energy Sciences, Division of Chemical Sciences
3. Investigation of Carbonyl-Derived Fischer-Tropsch
Catalysts: Sponsor, Atlantic Richfield Co.
4. Carbon Deposition on Fluidized Bed Methanation
Catalysts: Sponsor, BCR
5. Mathematical Modeling of Methanation on Monolithic
Nickel Catalysts: Sponsor, BYU
6. Infrared and Reaction Studies of Rhodium and Rhod-
ium-Molybdenum Nitric Oxide Reduction Catalysts:
Sponsor, BYU


Calvin H. Bartholomew received his BS degree from Brigham Young
University and his MS and PhD degrees in chemical engineering from
Stanford University. He spent a year at Corning Glass Works as a
Senior Chemical Engineer in Surface Chemistry Research and a summer
at Union Oil as a visiting consultant. In 1973 he joined the chemical
engineering department at Brigham Young University and was recently
promoted to professor. He has authored over 60 scientific papers and
3 major reviews in the fields of heterogeneous catalysis and catalyst
deactivation. Active in both teaching and research, he has also con-
sulted with 12 different companies and is currently President of the
California Catalysis Society. His major research and teaching interests
are heterogeneous catalysis (adsorption, kinetics, and catalyst character-
ization), Moessbauer spectroscopy, and air pollution chemistry. (L)
William C. Hecker received his BS and MS degrees from Brigham
Young University and his PhD degree from the University of California,
Berkeley (1982). He has considerable industrial experience, having
worked for Chevron Research, Occidental Research, Dow Chemical,
Exxon, and Columbia Gas Systems. His research and teaching interests
include heterogeneous catalysis, chemical kinetics, heat transfer,
and infrared spectroscopy. (R)

Laboratory since 1982 are listed in the References
section to this paper. A complete list of publica-
tions and areas of current investigation may be
had by contacting the authors. Recent investiga-
tions have considered metal boride catalyst prepa-
ration chemistry; adsorption of CO, H, and H2S
on nickel, cobalt, and iron and of 02 on reduced
and sulfided molybdenum catalysts; activities and
selectivities of cobalt, iron and nickel in CO and
CO, hydrogenation reactions; kinetics of CO and
CO2 methanation on nickel; interactions of co-
balt, iron, and nickel with various supports; ac-
tivities of monolithic nickel catalysts; and de-
activation of nickel catalysts by sulfur poisoning,
carbon deposition or sintering. Current research
projects (Table 1) are directed toward the under-
standing of activity and selectivity properties of
boron-promoted and carbonyl-derived cobalt and
iron catalysts in Fischer-Tropsch synthesis,;
effects of support and dispersion on the adsorp-
tion, activity, and selectivity properties of cobalt;
mathematical modeling of CO hydrogenation on

cobalt, iron, and nickel catalysts; and infrared/
reaction studies of NO reduction on Rh and Rh-Mo
From the above brief description it is ap-
parent that BYU's efforts in catalysis are diverse
in terms of the reactions and catalyst types
studied (i.e., methanation, Fischer-Tropsch, NO
reduction; metals, oxides, and sulfides). Never-
theless, the experimental approach in most of these
studies has a common feature, namely an empha-
sis on the characterization of these systems using
adsorption techniques and spectroscopy combined
with laboratory reactor studies to determine spe-
cific activity/selectivity properties. The breadth
of research interests in the Catalysis Laboratory
is further illustrated by the previous work with
nickel methanation catalysts which included
studies of CO and H2 adsorption stoichiometry,
activity/selectivity properties for CO2 and CO
methanation, CO and CO, methanation kinetics,
metal-support interactions, TPD of H2 desorption
for nickel on different supports, sulfur poisoning,
carbon deposition, sintering of nickel on different
supports and modeling of monolithic Ni reactors.
The following brief description of four recent
or ongoing studies illustrates the nature of cataly-
sis research at BYU. The first example concerns
a study of Oa adsorption on unsupported MoS2,
carried out by Bernardo Concha (M.S. candidate)
under the direction of Professor Bartholomew.
Oxygen adsorption uptakes and methanation ac-
tivities were determined for a series of MoS2
catalysts having a range of surface areas. The ex-
cellent linear correlation of the data (Fig. 1) indi-

0 400 "C

0 s -o

0 40
0C 60 C
0 0
Z, *

20 o
0 5 10 15 20 25
02 UPTAKE (pmnole/g)

FIGURE 1. Oxygen uptake of MoS2 catalysts after re-
action for 15-20 h versus steady-state methane pro-
duction (sulfiding temperatures are designated for each
catalyst). (Paper Ref. 10)

FALL 1984

to the number of oxygen adsorption sites. These
results have important application in the develop-
ment of techniques for characterizing sulfide
hydrotreating catalysts used to remove sulfur
from sour petroleum and synthetic crude feed-
The second example is the result of a joint
effort by Professors Bartholomew, Brewster, and
Philip J. Smith in cooperation with PhD candi-
dates Edward Sughrue and Philip R. Smith to
model both pellet and monolithic, fixed bed
methanators. This state-of-the-art model includes
complete kinetic rate expressions for CO and CO2
methanation reactions, for the water-gas-shift re-
action, and for inhibition by steam. It also in-
corporates the appropriate reaction rate terms
to account for pore diffusion, heat transfer, and
external mass transfer. Using this model it is
possible to predict reactor temperature profiles
and conversion-temperature profiles in good
agreement with experimental data for pellet or
monolithic packed bed methanators (see Fig. 2).
The third example, an ongoing study con-
ducted by Bruce Breneman (MS candidate) and
Huo-Yen Hsieh (PhD candidate) under the di-
rection of Professor Hecker, involves the use of
infrared spectroscopy to investigate NO reduction
catalysts. (NO reduction is an important function
of auto emissions catalysts.) A series of support-
ed rhodium catalysts have been prepared using
various preparation techniques and various
amounts of molybdenum in an effort to improve
their activity and selectivity. Activity/selectivity
measurements and two types of IR measurements
are made on each catalyst. In the first type, the
quantity and stoichiometry of various adsorbate
molecules (e.g. CO) adsorbed on the catalyst sur-
face at room temperature are determined. This

500 550 600 650
Temperature (K)
FIGURE 2. Comparison of experimental conversion-
temperature profile for 3% Ni/Al04/monolith with
model calculations. (E. L. Sughrue, Ph.D. Dissertation,
Brigham Young Univ., 1983)

cates that hydrogenation activity is proportional
information is used to determine useful correla-
tions with activity and selectivity. In the second
type, IR spectra are obtained under reaction con-
ditions and reveal important information regard-
ing the state of the catalyst surface and the nature
of the reaction intermediates. This information
is important in determining reaction mechanisms.
The fourth study, carried out by Robert Reuel
(MS graduate) under the direction of Professor
Bartholomew, involved the measurement of spe-
cific activities and product selectivities of cobalt
on different supports. These catalysts were found
to have a range of cobalt dispersions (fractions
of cobalt atoms exposed to the surface) which
varied over 2 orders of magnitude. While prepara-
tion, support, and cobalt loading influenced the
activity and selectivity properties, these data were
best correlated with dispersion (see Figs. 3 and

-8 -7 -6 -5 -4 -3 -2 -1
Ln (Nco)

FIGURE 3. Percentage dispersion (percentage of atoms
exposed to the surface) versus CO turnover frequency
(rate of CO conversion per site per second) at 2250C
for supported cobalt catalysts. (Paper Ref. 20)

4). These results indicate that the specific activity
of cobalt and its selectivity to high molecular
weight products both decrease with increasing
One important dimension of scientific work is
the careful technical communication of the results.
It is, in our opinion, the necessary finishing touch
to any project. The laboratory has been reasonably
productive in this regard. For example, during a
two-year period from 1981 to 1983, the personnel
of the laboratory participated in 8 different pro-
jects, published 42 papers and reports, completed
7 theses and dissertations, and presented 26 papers
and seminars.



0 13
13 A 0

uJ co/s102
5 C0 c.o

Average Carbon Number (wt. basis)
FIGURE 4. Average carbon number of hydrocarbons pro-
duced at 2250C and 1 atmosphere for 3 and 10 wt.%

supported cobalt catalysts as a function of dispersion.
(Paper Ref. 20)

The most important objective of our research
is to educate and train students in the science
and art of catalysis research. Th sis accomplished
at BYU in a number of ways: through participa-
tion in research projects and special courses, by
participation in the biweekly catalysis seminars,
and by attendance at regional and national meet-
ings. In addition to our basic graduate course on
kinetics and catalysis (see Chem. Eng. Ed., Fall,
1981), advanced graduate courses are offered bi-
yearly on special topics related to catalysis, e.g.,
catalyst deactivation, industrial catalysis, and re-
actor design. The laboratory is host to roughly
10-12 visitors each year of whom about 5-6 pre-
sent seminars. Graduate students are also pro-
vided with opportunities to attend and present
papers at regional and national catalysis meetings.
The Catalysis Laboratory is located in the
Clyde Building, which houses the engineering
disciplines. It presently includes 6 laboratories
(3,000 ft2) and the basic equipment listed in Table
2 to carry out adsorption, reaction, infrared, and
Moessbauer spectroscopy studies. Our facilities
for studying adsorption processes (two vacuum
systems, one flow system, a TGA system, and two
TPD systems) are scarcely equalled even by in-
dustrial laboratories. The temperature-program-
med-desorption (TPD) systems have proven to be
particularly valuable in determining the states and
energetic of H2 and CO adsorptions on cobalt,
iron, and nickel catalysts. The Moessbauer spectro-
meter has been extremely useful in determining

phase composition and oxidation states of iron in
Fischer-Tropsch catalysts while our new FTIR
infrared spectrometer is proving its worth in the
study of NO adsorption and reactions on Rh
catalysts. Having this variety of adsorption, re-
action and spectroscopic techniques at our dis-
posal makes it possible for us to pursue the multi-
tool approach.


The Catalysis Laboratory has weathered the
recent turbulent times of increased competition
and declining federal support through diversifica-
tiol of funding from both industry and govern-
ment agencies (see Table 2 and acknowledg-
ments). We presently receive about $200,000-
$250,000 in yearly support from sources outside
the university. A new fund raising effort, the
Industrial Affiliates program, was initiated about
two years ago. The objectives of this program
are to establish closer ties with our industrial col-


Facilities and Equipment of the
BYU Catalysis Laboratory

Six laboratories-3,000 ft2 with catalyst preparation
areas and preparation equipment
Three lab reactors including a Berty Autoclave
Two vacuum adsorption systems
One flow adsorption system
Five chromatographs-including HP-5830 and Sigma
I systems
TGS-2 thermogravimetric balance
Two TPD/TPR systems with mass spectrometer and
TC detection
Moessbauer spectrometer system
Nicholet 5-MX FTIR infrared spectrometer system
Sage II, 68000 computer system; 2 Macintosh and
one Lisa II-5 computers
Vacuum Atmospheres HE-43-2 Dri-Lab glove boxb

Six large computers (several VAX 750 and 780
systems, IBM-4341)
Transmission electron microscopes (Botany):
Phillips EM-400 (with EDAX) and Hitachi HU-11E.
(Both microscopes have been used for catalyst work;
TEM sample preparations have been developed.)
Calorimeters (The Thermochemical Institute)
GC-MS (Chemistry)
X-ray fluorescence spectroscopy (Chemistry)

aThree new laboratories added in 1982-83.
bEquipment added in 1983.
cEquipment added in 1984.

FALL 1984

leagues and obtain fellowship support for gradu-
ate students through annual subscriptions of
$5,000-$15,000. Affiliates of our program receive
advance copies of our publications and a special
annual study on some aspect of catalysis. Thus far,
three companies (Atlantic Richfield Co., Phillips
Petroleum Co., and Union Oil Co. of California)
have joined our program.


Catalysis at BYU is a growing cooperative
effort of faculty and students engaged in diverse
areas of basic research in heterogeneous catalysis.
While the Catalysis Lab is unusually productive
in terms of publications, its most important pro-
ducts are students well trained in the multitool,
multidisciplinary approach to catalysis research.
Looking ahead, members of the laboratory are
hoping to expand into other areas of catalysis re-
search including homogeneous catalysis and sur-
face science with the addition of a senior scientist
in each of these areas. O


The authors gratefully acknowledge financial
support from the AMAX Foundation; DOE,
Fossil Energy; DOE, Office of Basic Energy
Sciences; NSF; Atlantic Richfield Co.; Phillips
Petroleum Co.; Union Oil Foundation; and Brig-
ham Young University.

REFERENCES: Laboratory Publications since 1982
A. Contributions to Books
1. C. H. Bartholomew and J. R. Katzer, "Sulfur Poison-
ing of Nickel in CO Hydrogenation," in Catalyst De-
activation ed. B. Delmon and G. F. Froment, Elsevier
Sci. Pub. Co., Amsterdam, 1980.
2. C. H. Bartholomew, P. K. Agrawal, and J. R. Katzer,
"Sulfur Poisoning of Metals," Advances in Catalysis,
31, 136 (1982).
B. Journal Publications
1. C. H. Bartholomew, "Carbon Deposition in Steam Re-
forming and Methanation," Catalysis Reviews-Sci.
Eng., 24(1), 67 (1982).
2. C. H. Bartholomew and R. B. Pannell, "Sulfur Poison-
ing of H2 and CO Adsorption on Nickel," Appl. Catal.,
2, 39 (1982).
3. E. L. Sughrue and C. H. Bartholomew, "Kinetics of
CO Methanation on Nickel Monolithic Catalysts,"
Appl. Catal., 2, 239 (1982).
4. A. D. Moeller and C. H. Bartholomew, "Deactivation
by Carbon of Nickel, Nickel-Ruthenium, and Nickel-
Molybdenum Methanation Catalysts," I & EC Prod.
Res. & Develop., 21, 390 (1982).
5. C. H. Bartholomew and A. H. Uken, "Metal Boride

Catalysts in Methanation of Carbon Monoxide, III.
Sulfur Resistance of Nickel Boride Catalysts Com-
pared to Nickel and Raney Nickel Catalysts," Appl.
Catal., 4, 19 (1982).
6. G. D. Weatherbee and C. H. Bartholomew, "Hydro-
genation of CO2 on Group VIII Metals, II. Kinetics
and Mechanism of CO2 Hydrogenation on Nickel,"
J. Catal., 77, 460 (1982).
7. C. H. Bartholomew, "Response to Comments on Nickel-
Support Interactions: Their Effects on Particle
Morphology, Adsorption, and Activity Selectivity
Properties," I & EC Prod. Res. Develop., 21(3), 523
8. T. A. Bodrero, C. H. Bartholomew, and K. C. Pratt,
"Characterization of Unsupported Ni-Mo Hydrode-
sulphurization Catalysts by Oxygen Chemisorption,"
J. Catal., 78, 253 (1982).
9. C. H. Bartholomew, R. B. Pannell, and R. W. Fowler,
"Sintering of Alumina-Supported Nickel and Nickel
Bimetallic Catalysts in H2/H20 Atmospheres," J.
Catal., 79 34 (1983).
10. B. E. Concha and C. H. Bartholomew, "Correlation
of O, Uptake with CO Hydrogenation Activity of
Unsupported MoS2 Catalysts," J. Catal., 79, 327
11. E. J. Erekson and C. H. Bartholomew, "Sulfur
Poisoning of Nickel Methanation Catalysts, II. Effects
of H,S Concentration, CO and H20 Partial Pressures
and Temperature on Deactivation Rates," Appl.
Catal., 5, 323 (1983).
12. C. H. Bartholomew and W. L. Sorensen, "Sintering
Kinetics of Silica and Alumina-Supported Nickel in
Hydrogen Atmosphere," J. Catal., 81, 131 (1983).
13. J. M. Zowtiak, G. D. Weatherbee, and C. H. Bartholo-
mew, "Activated Adsorption of H2 on Cobalt and
Effects of Support Thereon," J. Catal., 82, 230 (1983).
14. J. M. Zowtiak and C. H. Bartholomew, "The Kinetics
of H, Adsorption on and Desorption from Cobalt and
the Effects of Support Thereon," J. Catal., 83, 107
15. C. K. Vance and C. H. Bartholomew, "Hydrogenation
of Carbon Dioxide on Group VII Metals, III. Effects
of Support on Activity/Selectivity and Adsorption
Properties of Nickel," Appl. Catal., 7, 169 (1983).
16. R. M. Bowman and C. H. Bartholomew, "Deactiva-
tion by Carbon of Ru/A1203 During CO Hydro-
genation," Appl. Catal., 7, 179 (1983).
17. T. A. Bodrero and C. H. Bartholomew, "Oxygen
Chemisorption on MoS2 and Commercial Hydrotreat-
ing Catalysts," J. Catal., 84, 145 (1983).
18. C. H. Bartholomew, "Finding Keys to Selectivity in
Fischer-Tropsch Synthesis," Industrial Chemical
News, 4(10), 1 (1983).
19. R. C. Reuel and C. H. Bartholomew, "The Stoichio-
metries of H2 and CO Adsorptions on Cobalt: Effects
of Support and Preparation," J. Catal., 85, 63 (1984).
20. R. C. Reuel and C. H. Bartholomew, "Effects of Sup-
port and Dispersion on the CO Hydrogenation Ac-
tivity/Selectivity Properties of Cobalt," J. Catal.,
85, 78 (1984).
21. G. D. Weatherbee and C. H. Bartholomew, "Effects
of Support on Hydrogen Adsorption/Desorption
Kinetics of Nickel," J. Catal. 87(1), 55 (1984).


REVIEW: Engineering Optimization
Continued from page 159.
to common sense to understand each of the op-
timization methods considered. Also, every method
is followed with an example to illustrate it. This
format is exactly right as the focus is on how to
use the methods. As the jacket flyer states, ". .
proofs and derivations are included only if they
serve to explain key steps and properties of
algorithms." The authors also offer their opinions
as to the strengths and weaknesses of the various
methods, and I found myself agreeing with them
in virtually all cases.
The book occasionally stops rather abruptly
on a topic, perhaps most noticeably with the
chapter on linear programming. The theory be-
hind sensitivity analysis for linear programming
is not that difficult to present, yet the text simply
presents some of the 'how to' aspects of this useful
subject. Also it does not develop generalized
duality theory, which can actually be done rather
agreeably at a level consistent with the rest of
the book. This theory is useful when attempting
to understand a number of concepts, such as the
saddlepoint conditions and dual bounding.
The variety of methods covered in the first 11
chapters is impressive. The authors have ob-
viously scoured the engineering literature for the
methods that have found their way into practical
use for engineering problems. Included are direct
and gradient based methods for unconstrained op-
timization problems; a simple presentation of the
simplex algorithm for linear programming; the
important theorems for constrained optimality;
both ordinary and generalized penalty function
methods; successive linearization methods; the
very effective generalized reduced gradient me-
thod; gradient projection methods; and very im-
portantly the ideas behind successive quadratic
programming methods, perhaps the best of the
methods developed so far for nonlinear constrain-
ed optimization. The final chapter on methods,
Chapter 11, covers briefly mixed integer linear pro-
gramming, quadratic programming and geometric
The last three chapters of the book, Chapters
12 to 14, are a chapter on studies which have been
performed to compare many of the methods pre-
sented, a very readable and important chapter of
the issues one must worry about when embarking
on an optimization study, and finally a chapter de-
scribing three larger case studies, obviously one

per author. The first of these chapters emphasizes
what the authors feel must be included in a com,-
parison study for methods if the study is to be
The homework problems are plentiful and
seem appropriate for the topics covered. Students
using this book will be much better off if they have
had a course on linear algebra.
The material could be taught in one semester,
if one is careful about not overdoing the detail
on some of the methods. O

by O. A. Williams
Marcel Dekker, Inc., 1983, 319 pages.

Reviewed by T. D. Wheelock
Iowa State University

This volume is the 13th in a special series of
reference books and textbooks relating to the
chemical industries. It treats pneumatic and
hydraulic conveying as separate and independent
subjects with seven chapters devoted to the former
and ten chapters to the latter. An additional
chapter is devoted to solid waste disposal areas,
landfills, and sluice ponds. The volume is based
largely on the author's considerable experience as a
designer and user of conveying systems. In line
with the author's statement that "the design of a
pneumatic conveying system is almost as much of
an art as it is in engineering function," the treat-
ment is largely descriptive and highly empirical.
Various types of conveying systems and their
operating characteristics are described. Also dis-
cussed are important features of system com-
ponents such as bins, feeders, exhausters, blowers,
pumps, piping, gates, and control units. In ad-
dition two chapters are devoted to detailed design
calculations for a number of different systems.
Since the volume provides a broad and rather
detailed introduction to the layout, design, and
operation of pneumatic and hydraulic conveying
systems, it will be of particular value to engineers
responsible for the design and/or operation of such
systems. It may also serve as a useful reference
for college-level process design courses. In ad-
dition, because it illustrates the highly empirical
nature of solids conveying technology, it may
stimulate further research and development in
this important field. D

FALL 1984

R6eceacih o#4


Dartmouth College
Hanover, NH 03755

T HE OBJECTIVE OF OUR WORK is to contribute to
the development of new practical processes for
the conversion of the cellulose found in biomass to
fuels, chemicals, and foods. Industrial scale plants
for the dilute acid catalyzed hydrolysis of the
cellulose in wood are currently operated in USSR,
and in the past both concentrated HC1 and dilute
HSO, processes have been developed in Europe
and the USA. However, these processes have not
been commercially viable in competition with
petrochemicals and soybean protein.

Our work in this area began in 1967 when
Andrew Porteous, then a student in the DE pro-
gram, recommended in the solution to his qualify-
ing examination (a design problem on which the


A. O. Converse is Associate Dean and professor of engineering at
the Thayer School of Engineering, Dartmouth College. He holds a BS
degree in chemical engineering from Lehigh University and the MS
and PhD degrees from the University of Delaware. Currently he is
involved in research associated with the conversion of biomass to
fuels and chemicals. (L)
H. E. Grethlein is professor of engineering at the Thayer School
of Engineering, Dartmouth College, where he specializes in biomass
hydrolysis with acid or enzymes, water treatment with membranes and
micro-organisms, and process development in biotechnology. He has
his BSChE degree from Drexel University and his PhD degree from
Princeton University. (R)

Obviously the costs and
corrosion problems associated with higher
temperatures limit the practical temperature, and
mixing and heating requirements established
a lower limit on the residence time.

student has 30 days to work) that a continuous
plug flow reactor be used to carry out dilute acid
hydrolysis of the cellulosic material found in
municipal wastes. Compared to the percolation re-
actor that had been developed for woody materials
by the Forest Products Laboratory at Madison,
Wisconsin [10], Porteous reasoned that the plug
flow reactor would be able to handle materials,
such as waste paper, that would not be porous
enough for percolation, and furthermore the pro-
cess would be fully continuous [9]. The kinetics for
Douglas fir [10] indicated that the yield of glucose
would increase as the temperature is increased
and the residence time is reduced. This is of par-
ticular importance because the yields obtainable
in a percolation reactor are inherently greater than
in a plug flow reactor.
With support from EPA, Fagen [2], for his
ME thesis, conducted batch hydrolysis experi-
ments and measured the kinetics constants for
paper, the principal cellulosic component of
municipal wastes. He found that they were similar
to those for Douglas fir and hence a plug flow re-
actor should be operated at high temperature and
a short residence time. Subsequent studies on many
biomass substrates have shown this conclusion to
hold true in general.
Obviously the costs and corrosion problems as-
sociated with higher temperatures limit the practi-
cal temperature, and mixing and heating require-
ments established a lower limit on the residence
time. Hence, we set out to develop a flow reactor
to determine the yields that could in fact be ob-
tained. From a more scientific point of view, the
flow reactor has another attraction: it allows one
to study the kinetics of hydrolysis under more
severe conditions than can accurately be studied

Copyright ChE Division, ASEE, 1984


in a batch reactor because short residence times
can be obtained without the heat up transients in-
volved in a batch reactor.
Lay [6], Thompson [11], and McParland [8]
(supported first by NSF and later by DOE), in
their respective ME theses, developed the present
flow reactor, shown in Fig. 1, and studied the
kinetics of several substrates. Currently the acidi-
fied slurry is pumped into the reactor along with
high pressure steam which condenses, mixes with,
and heats the mixture to reaction temperature in,
we estimate, about 0.7 sec. The minimum resi-
dence time used thus far is 7 sec. and the maxi-
mum temperature, 260 C. Under these conditions
the glucose yield is 55-60%. Current modifications
should permit operation at 280 C where a 70%
yield is expected.
Several other approaches are being taken in
an effort to increase the yield from acid hydroly-
sis. The glucose yields are reduced by the fact that
glucose decomposes under the same conditions as it
forms. Ward is currently studying whether the
presence of acetone, through the formation of glu-
cose-acetone complexes, can be used to reduce the
glucose decomposition. Holland is currently de-
signing a reactor which is to have a shorter resi-
dence time for the liquid, and hence less glucose
decomposition, than for the solids. Vick Roy [12]
has recently explored the use of SO2 catalyzed
hydrolysis under supercritical conditions.
Because of the difficulty in pumping slurries
containing a high concentration of wood, and the
practice of injecting live steam into the flow re-
actor, the sugar concentrations in the reactor
effluent are low. By using a nonaqueous immiscible
carrier fluid in place of water, we have found it
possible to increase the concentration of sugar in
the aqueous phase. This also permits another
means for separating the products. Woods have
small amounts of rosins and oils, and they would
be expected to concentrate in the nonaqueous
phase. Of course, these advantages must justify
the cost of any carrier fluid which is not recovered
as well as additional processing steps. Further
study is needed to allow such evaluation.

As an alternative to acid catalyzed hydrolysis,
enzymes can be used to catalyze the reaction. In
this case, the glucose yields, with proper pretreat-
ment of the substrate, are in the range of 95-
100%, considerably higher than is obtained with
acid hydrolysis. The reaction, however, is much

slower; 24-48 hrs. rather than 7 sec. Grethlein
[3] compared these two methods, using data from
Berkeley [13], and concluded that at that time
acid hydrolysis appeared more attractive. This
process evaluation is currently being updated
through a set of process studies sponsored by
In her DE thesis, Knappert [4] (with support
from NSF and International Harvester Corp.),
showed that by operating the flow reactor under
somewhat milder conditions (1% HSO, 7-10 sec.,
200 C) an effective pretreatment could be ob-
tained. Upon enzymatic hydrolysis of these pre-
treated solids, the glucose yield was >90% in 24
hrs. compared to 35% in 48 hrs. from unpretreated
solids. Knappert showed that this pretreatment

FIGURE 1. Flow reactor equipment.
increases the fraction of pores that are larger than
the enzyme molecule. Subsequent studies by Allen
[1] and others have shown that the crystallinity of
the cellulose remains unchanged and that the
lignin is not removed. The pores are increased by
the removal of a fraction of the hemicellulose, and
contrary to the prevailing view, we now believe
this to be the essential feature of an effective pre-
treatment. Grous is currently extending this
study to include other methods of pretreatment.
Although glucose is the principal sugar (maxi-
mum yield = 42% of dry hardwood), a significant
amount of xylose can be produced (maximum yield
= 18% of dry hardwood). Whereas glucose is
easily fermented to ethanol, xylose is not. Natural-
ly, efforts are underway at a number of labora-
tories to develop yeasts than can effectively carry
out such a fermentation. However, xylose can be
used to produce single-cell protein. Furthermore,
its decomposition product, furfural, has a con-

FALL 1984

These theses include both
process design and development,
and basic research in applied science, in keeping
with our two sets of graduate degrees...

siderable value, albeit to a small market. In his
PhD thesis, Kwarteng [5] (supported by Dow
Chemical Co. and DOE/SERI), reformulated
Root's kinetic model for the formation and de-
composition of furfural from xylose, and redeter-
mined the constants from experiments in the flow
reactor. He also extended the model to include the
formation of xylose from the xylan in the biomass.
In contrast to xylose and glucose decomposition,
furfural decomposition is second order. Hence,
the furfural yield is increased by using a more
dilute feed. This is countered by acid costs, product
concentration, and heating costs, all of which favor
a more concentrated feed. Process optimization
studies are underway to evaluate the optimum feed
concentration of biomass. Even at half the current
market price furfural is two to three times more
valuable than the sugars produced; hence its pro-
duction could have an important impact on the
profitability of the overall process.
Lignin is another byproduct that we plan to
study in the future. Some of it is solubilized in
the flow reactor, and the solubility of the residue
in solvents is increased. Furthermore, the short
residence time followed by flash quenching em-
ployed in the flow reactor is expected to give it
unique properties.

The overall process has three main parts:
hydrolysis of the biomass to produce sugars and
furfural, fermentation of the sugars to ethanol or
possibly other chemicals, and separation of the
ethanol to an anhydrous product if the ethanol is
to be added to gasoline. Even though it requires a
considerable amount of energy, distillation still
appears to be the preferred means of separation.
In his ME thesis, Lynd [7] proposed a new means
of combining heat pumps with distillation that sig-
nificantly reduces the energy requirement, par-
ticularly for dilute feeds which are usually en-
countered when fermentation is used to generate
the feed.
The azeotrope formed between ethanol and
water makes their separation more difficult, and
even if a salt such as potassium acetate (KAc) is
added to break the azeotrope, with normal distilla-

tion the reflux (and hence energy) must remain
high if the feed is dilute, e.g. 1-10 wt. %. Lynd's
innovation helps to overcome this requirement.
Hence, the use of KAc looks much more attractive.
Work is getting underway to test out the critical
aspects of this process experimentally.

Tricoderma reesei is a fungus which produces
the extracellular enzymes used in our enzyme
hydrolysis work described above. It must be grown
on a cellulosic substrate in order to produce these
cellulase enzymes, but unfortunately can not be
present during the main hydrolysis step since it
would consume the glucose product. Hence, the
enzymes must be produced in a separate step. Since
the pretreatment is effective in the hydrolysis step,
we are now testing its effectiveness in the kinetics
of the enzyme production step.
Some thermophylic bacteria have the ability
to ferment cellulose directly to ethanol. As the
name implies, they live at relatively high tempera-
tures and hence the likelihood of contamination
of this fermentation by other organisms is low.
However, they also have some limitations: they
ferment natural biomass, which contains lignin as
well as cellulose, very slowly; they have a low
tolerance compared to yeast for the ethanol that
they produce and hence produce dilute beers, and
they produce other products that compete for the
substrate. We think that it may be possible to
overcome these limitations through the use of
mild acid hydrolysis in the flow reactor as a pre-
treatment, combined with simultaneous fermenta-
tion and product removal using Lynd's distillation
scheme to remove the ethanol from the dilute beer
as it is formed thus altering the product distribu-
tion in the favor of ethanol. Lynd will undertake
a study of this in his DE thesis.
In order to emphasize the role of the students
in this work, the references cited are primarily
student theses rather than papers in the litera-
ture. These theses include both process design and
development, and basic research in applied science,
in keeping with our two sets of graduate degrees
-ME and DE for those interested primarily in
design and MS and PhD for those interested pri-
marily in research. The distinction is one of de-
gree since many theses involve both elements.
The undergraduate programs of the students in-
volved in this work have included biology, chemis-
try, engineering science, and civil engineering as
well as chemical engineering, in keeping with non-


departmental organization of the Thayer
School. O

1. Allen, D. C., "Enzymatic Hydrolysis of Acid Pre-
treated Cellulosic Substrate: Substrate Hydrolysis,
Process Development & Process Economics," ME
thesis, Thayer School of Engineering, Dartmouth
College, Hanover, NH 03755, 1983.
2. Fagan, R. D., "The Acid Hydrolysis of Refuse," ME
thesis, Thayer School of Engineering, Dartmouth
College, Hanover, NH 03755, 1969.
3. Grethlein, H. E., "Comparison of the Economics of
Acid and Enzymatic Hydrolysis of Newsprint," Bio-
tech Bioeng, Vol. XX, 503, 1978.
4. Knappert, D. R., "Partial Acid Hydrolysis Pretreat-
ment for Enzymatic Hydrolysis of Cellulose: A Pro-
cess Development Study for Ethanol Production,"
DE thesis, Thayer School of Engineering, Dart-
mouth College, Hanover, NH 03755, 1981.
5. Kwarteng, I. K., "Kinetics of Dilute Acid Hydrolysis
of Hardwood in Continuous Plug Flow Reactor,"
PhD thesis, Thayer School of Engineering Dartmouth
College, Hanover, NH 03755, 1984.
6. Lay, J. R., "The Acid Hydrolysis of High Solid
Content Cellulose Slurries," ME thesis, Thayer School
of Engineering, Dartmouth College, Hanover, NH
03755, 1978.
7. Lynd, L. R., "Energy Efficient Distillation with In-
novative Use of Heat Pumps," MS thesis, Thayer
School of Engineering, Dartmouth College, Hanover,
NH 03755, 1984.
8. McParland, J. J., "The Acid Hydrolysis of Cellulosic
Biomass: A Bench Scale System and Preliminary
Plant Design," ME thesis, Thayer School of Engi-
neering, Dartmouth College, Hanover, NH 03755,
9. Porteous, A., "Improved Manufacture of Polyure-
thane Foam," DE thesis, Thayer School of Engineer-
ing, Dartmouth College, Hanover, NH 03755, 1967.
10. Saeman, J. F., "Kinetics of Wood Saccharification,"
Industrial and Engineering Chemistry, 37, 32, 1945.
11. Thompson, D. R., "The Acid Hydrolysis as a Means
of Converting Municipal Refuse to Ethanol: Process
Kinetics and Preliminary Plant Design," ME thesis,
Thayer School of Engineering, Dartmouth College,
Hanover, NH 03755, 1978.
12. Vick Roy, J. R., "Biomass Hydrolysis with Sulfur
Dioxide," ME thesis Thayer School of Engineering,
Dartmouth College, Hanover, NH 03755, 1984.
13. Wilke, C. R., R. D. Yang and U. Von Stockar, Bio-
tech. Bioeng. Symp., 6, 155, 1976.

Continued from page 175.
and use of non-communicative words such as "uh",
etc. Sometimes the review sessions were absolutely
devastating for the presenter since these manner-
isms are greatly "amplified" by the video camera

and, of course, preserved for posterity. However,
I was pleasantly surprised by the light-hearted
attitude with which all students received the re-
view process. There was much good-natured
kidding about the errors, and no one seemed to be
embarrassed or hurt by the review.
The two best presentations (i.e. free from
errors) were edited, together with my brief com-
ments, into one tape which we shall use as a means
of external communication to industry and to
other academic institutions. For example, I plan
to send this tape to some industry contacts to intro-
duce our research group and to precede my visit
to a group I have yet to meet. Secondly, this tape
may be used as a subtle recruiting aid at academic
institutions which I may visit. Students seem to
listen intently to their peers regarding graduate
research experiences.
The student reactions to this new format were
varied. Some met the video-based seminar course
with enthusiasm, some with fear, and some with
indifference. A few were cynical about the value
of a seminar course which did not allow a tough
question-and-answer session. Many felt that furth-
er refinement of their seminar mechanics was un-
necessary. The professors showed the opposite
feelings, perhaps as a result of years of teaching
and giving technical presentations-seminars.
However, after the taping all were of the same
accord. Moreover, the students became more aware
of the original intent of this experiment: to pro-
vide a new format which would allow instant feed-
back on a seminar presentation. The video-based
format best satisfies that need for instant feed-
In conclusion, this brief experiment with
video-based seminars was successful with regard
to the original intent of improving visual com-
munication skills in a formal seminar setting. This
format is suitable for use as an occasional tool,
preferably with students who have had some ex-
perience in seminar presentation. We may not
repeat this experience until at least six to eight
quarters have elapsed. O
We acknowledge the generous help offered by
David Edwards and the crew in our Media Center
and the monetary support offered by Rohm and
Haas Company to cover the taping and studio costs.

FALL 1984

4 PSEPAS Ria in R


The University of Texas
Austin, TX 78712

A LL CHEMICAL ENGINEERS understand the im-
portance of separation processes in the manu-
facture of chemical products. Raw materials must
be purified, catalyst poisons eliminated, unreacted
materials separated for recycle, and end-products
refined to meet specifications. Further, waste
streams must undergo separations before they can
be discharged into the environment. Separation
processes pervade not only the classical chemical/
petroleum process industries but other ones as
well, such as electronics, food and biological,
metals, and so on. Investment in separation equip-
ment represents a large fraction of the industry
total, and the processes consume very large
amounts of energy. It is not surprising that there
is much interest in developing improved methods
for separating mixtures, not just for improved
economics but also for simply enabling isolation
of a material that is tightly bound in some parent
mixture. It is surprising, however, that there is
not more easily-identifiable research of a generic
type that can support the needs of an industry so
dependent on separations.
In fact, there is a great deal of research in pro-
gress that supports the development of improved
industrial separation processes. In academia, such
research covers areas of thermodynamics, trans-
port processes in various media, and reaction se-
lectivity. In industry, the research is often directed
toward specific problems that occur in the develop-
ment of new processes or products. In many re-
spects, there has been too little collaboration be-
tween the academicians and the industrialists who

The research areas targeted were:
distillation, adsorption, liquid-liquid extraction,
supercritical fluid extraction, membrane processes
for separating both gaseous and liquid mixtures,
chromatographic separations, electrochemical
separation methods, and separations
employing chemical reactions.

Copyright ChE Division, ASEE 1984

James R. Fair joined the chemical engineering faculty at The Uni-
versity of Texas in 1979, after many years with Monsanto Company.
At Texas he holds the Ernest & Virginia Cockrell Chair and also is
Head of the Separations Research Program. He has received numerous
awards from the AIChE and was honored as an Eminent Chemical
Engineer at the Diamond Jubilee meeting in November 1983. He is a
Fellow of AIChE and a member of National Academy of Engineer-
ing. He holds BS, MS and PhD degrees from Georgia Institute of
Technology and the Universities of Michigan and Texas, as well as
an honorary ScD degree from Washington University.

share common interests in separations ranging
from the fundamental to the applied. This paper
describes one attempt to foster greater industry-
university collaboration in the separations tech-
nology area, the attempt being identified as our
Separations Research Program at The University
of Texas at Austin.

A number of UT faculty had been conducting
separations-related research for several years
when in 1983 they were invited to participate in
an industry-funded consortium sponsored by the
Center for Energy Studies at UT. The center had
a line-item budget from the State of Texas and
had as one of its purposes the development of new
programs that could impact the efficiency of energy
usage by industry. Since the chemical and petrole-
um industries represent two of the three largest
energy-consuming segments of the total industry,
and since within them separations are the largest
energy-users, it was logical for the center to be
interested in industrial separation processes. This


led to a seed money grant that enabled the hiring
of a full-time program manager, Dr. J. L. Humph-
rey, to pursue the planning and organization of
the consortium. At the same time, a large (145,000
square feet) new research facility was approved
by the UT administration, and arrangements were
made for the separations work to utilize a signifi-
cant amount of the space.
The research areas targeted were: distillation,
adsorption, liquid-liquid extraction, supercritical
fluid extraction, membrane processes for separat-
ing both gaseous and liquid mixtures, chromato-
graphic separations, electrochemical separation
methods, and separations employing chemical re-
actions. All of these areas had some coverage by
faculty in the chemical engineering and chemistry
departments. The industries targeted were: chemi-
cal, petroleum refining, gas processing, biologi-
cal, pharmaceutical, food, and textile. Informal
talks were held with UT faculty members, uni-

Participants-Separations Research Program*

ABCOR, Inc./Koch Engineering
Air Products and Chemicals, Inc.
Albany International Corp.
Aluminum Company of America
Amoco Oil Company
ARCO Petroleum Products Company
The BOC Group, Inc.
Celanese Chemical Company
Combustion Engineering, Inc.
Dow Chemical Company
Dow Corning Corporation
E. I. duPont de Nemours & Co.
Ethyl Corporation
Exxon Research & Engineering Co.
Glitsch, Inc.
B. F. Goodrich Company
Hoffman-La Roche, Inc.
M. W. Kellogg Company
Koppers Company, Inc.
Monsanto Company
Neste Oy
Norton Company
Nutter Engineering/Chem-Pro Corporation
Osmonics, Inc.
Perry Gas Companies, Inc./Separex Corporation
Phillips Petroleum Company
Rohm & Haas Company
Shell Development Company
A. E. Staley Manufacturing Co.
Standard Oil of Ohio
Texaco, Inc.
Union Carbide Corporation

*As of June 1984

Since the chemical and petroleum industries
represent two of the three largest energy-consuming
segments of the total industry, and since within them
separations are the largest energy-users, it
was logical for the center to be interested
in industrial separation processes.

versity administration, and representatives of a
number of companies. A charter was written, and
the plan was further developed and published as
an 89-page prospectus. This document was mailed
widely to industry, and during the developmental
period twenty-two companies visited the UT
campus to learn more about the proposed pro-
gram. In May 1983 an informational meeting was
held, and 101 representatives from sixty com-
panies attended. A research participation agree-
ment was drawn up and mailed to companies with
an invitation to join the program. Formal opera-
tion was to begin in January 1984. It should be
mentioned that the cost of the prospectus, the in-
formational meeting, and the preparation of state-
of-the-art reports on the several separations areas
was underwritten by the Electric Power Research
Institute through a grant.
At this writing, thirty-two companies have
signed two-year participation agreements. They
are listed in Table 1.
The plan was for the research to be supervised
largely by regular UT faculty members. Thus, it
was necessary for the research area coverage to be
compatible with the interests of these people. It
was recognized that additional areas could be
covered by faculty yet to be hired, or by full-time
research scientists and engineers, but these were
deferred until a later time when resources and in-
dustry interests could justify the expansion. In
the following sections brief sketches will describe
the current work in progress.
Membrane Separations. This work is divided
into the separation of gaseous and liquid mix-
tures. For gases, direction is under D. R. Paul and
W. J. Koros. Both of these people have had active
programs in membrane separations for several
years, Dr. Paul at UT and Dr. Koros at North
Carolina State University. Arrangements were
made for Koros to move to UT as a full-time re-
searcher initially, followed by a faculty appoint-
ment. It is clear that the use of membranes for gas
separation is an industrial reality, with the
promise of a large expansion of the areas of

FALL 1984

application. It is equally clear that many im-
portant questions regarding application cannot be
answered with today's knowledge, and thus there
is the opportunity for more rapid expansion of
membrane technology through the support of
generic research. The current program has thrusts
in the following directions: pure gas sorption and
transport, mixed gas sorption and transport, mem-
brane durability, separation of vapors, asymmetric

SRP researcher William J. Koros measures the weight
gained by a tiny membrane sample as it sorbs, or takes
in, gas. A weight gain of 500 millionths of a gram
indicates a highly sorbent material.

membrane formation and characterization, and
module simulation/performance. As might be ex-
pected, emphases such as the foregoing can shift
as more knowledge is gained.
The liquid-mixture membrane program is
under the direction of D. R. Lloyd, who began his
research in this area at Virginia Polytechnic
Institute and State University before moving to
UT a few years ago. The program includes the
synthesis of polymers, the preparation of sheet-
and hollow-fiber membranes, transport studies,
and the investigation of possible applications in
the petrochemical, biochemical, pharmaceutical,
biomedical, and genetic industries. The unifying
theme of the research is the need to understand
the physicochemical factors that govern the sepa-
ration process.

Distillation. This old friend, and its associates
absorption and stripping, is being studied under
the direction of J. R. Fair. As is well known, it is
the dominant separation method in the process
industries and for many good reasons is likely to
remain so. The work at UT is directed primarily
to the mass transfer efficiency of common types
of contacting devices for distillation columns. Of
the several segments of distillation technology
(phase equilibria, mass and energy balances,
efficiency, and equipment design), understanding
of the mass transfer process is in the lowest stage
of development. Two particular devices are being
studied: the crossflow sieve tray and high-efficien-
cy packing. The sieve tray is widely used and is
uniquely amenable to mechanistic modeling. The
high-efficiency packing types, only recently de-
veloped, are making possible large energy savings
in vacuum fractionations. The ultimate goal of
this work is to have the form of mechanistic
models that enable the reliable prediction of per-
formance for both new and retrofitted distillation
Supercritical Fluid Extraction. This work is
under the direction of K. P. Johnston. Supercriti-
cal fluid extraction (SFE) is a hybrid process that
uses benefits from both distillation and liquid ex-
traction. The process has the additional advantage
that slight changes in temperature and pressure
near the critical point cause extremely large
changes in the solvent density and thus its dis-
solving power. In comparison with conventional
separation processes, SFE offers considerable
flexibility for an extractive separation through
the control of pressure, temperature, choice of
solvent and co-solvent ("entrainer"). There are a
few SFE processes that have reached commercial-
ization, but in general the method still awaits
better understanding of phase behavior as well
as the transport processes that take place in SFE
equipment. The program at UT is directed toward
the acquisition of fundamental thermodynamic
data and the development of predictive models that
can guide solvent selection and processing con-
ditions. Of particular interest is the use of co-
solvents which in small amount can greatly en-
hance the separation factors.
Liquid-Liquid Extraction. This work is under
the direction of J. R. Fair and J. L. Humphrey.
Liquid-liquid extraction (LLE) is another old
friend, though not nearly as old as distillation. It
has gained increased attention recently as an
alternative to distillation that for some cases can


result in distinct energy savings. For temperature-
labile mixtures, LLE can also offer advantages if
the labile species do not undergo high tempera-
ture conditions in the solvent stripper. As for
distillation, little is known about the mass transfer
processes that take place in LLE equipment, and
this is partly due to the dominance of proprietary-
type extraction devices in commercial practice.
Under study at UT are sieve tray extractors and
high-efficiency packed columns, both of which are
non-proprietary and amenable to mechanistic
modeling. It is expected that with the new under-
standing gained there will be resulting develop-
ments in more energy-efficient extraction device
In a related area, work is underway to deter-
mine the mass transfer characteristics of a con-
tinuous-flow supercritical fluid extraction system
using a counterflow solvent/feed arrangement.
Adsorption. Drs. Fair and Humphrey are also
directing work in this area. Interest in the area
is high because of breakthroughs in the applica-
tion of pressure-swing adsorption to separating
gas mixtures such as air into their components
without excessive thermal gradients. There are
two areas of initial study at UT: mechanisms of
thermal and pressure regeneration steps for con-
ventional fixed bed gas adsorbers, and break-
through relationships for liquid-phase adsorption.
There is future interest in the study of moving
bed and fluid bed adsorption processes. Progress
in adsorption technology has been largely through
the development of improved adsorbents such as
zeolite and carbon molecular sieves. The work at
UT is centered on the kinetics of adsorption and
desorption on and from these adsorbents as well
as the more traditional adsorbents (where new
process applications may be envisioned).
Electric-Based Processes. This work comes
under the direction of A. J. Bard of the UT chemis-
try department. Two areas are currently being
studied: electrochemistry in critical aqueous solu-
tions and electrically controlled adsorption. Funda-
mental research on electrochemical processes in
critical aqueous solutions has not been performed
previously. Thermodynamic (PVT) and conduct-
ance studies have illustrated that the structure of
water solutions changes dramatically near the
critical point (375C and 220 atmospheres for
pure water). Since the dielectric constant of water
decreases to that of a "normal" fluid at high
temperatures and pressures, critical and super-
critical water becomes a good solvent for nonionic

At poster session representatives from companies listen
to program manager J. L. Humphrey describe the sepa-
rations test facilities to be installed in the new research

organic species. However, a wide range of super-
critical temperatures and pressures is accessible
for which water is still a good electrolytic solvent.
The electrochemical study of these systems there-
fore provides a unique opportunity to examine se-
lectively soluble, electroactive species in situ.
With respect to electrosorption, the extent of
adsorption of substances at the solid/liquid inter-
face depends upon the potential difference across
this interface. Thus, the adsorption of organic
species on conductive carbon particles can be con-
trolled by the potential applied. This type of sepa-
ration has not been exploited, mainly because the
fundamental data have not been obtained and be-
cause of construction problems associated with
large-scale adsorbers where a uniform applied po-
tential could be used.
Separations with Chemical Reactions. This pro-
gram represents an expansion of work started
several years ago at UT by G. T. Rochelle, the
director of the present work. His quite compre-
hensive program has dealt largely with the re-
moval of sulfur dioxide from stack gases, common-
ly called flue gas desulfurization (FGD). The
technology of FGD dominates commercial ap-
proaches to pollution abatement in fossil-fired

FALL 1984

Newer programs deal with
the more general area of acid gas
removal from gas mixtures and involves basic
absorption/reaction modeling studies.

power plants but is expensive, presents operating
problems, and produces by-products of limited in-
dustrial use. However, it is unlikely to be dis-
placed by other technologies and by its nature
suggests that there are many possible improve-
ments. The program at UT has involved enhance-
ment of SO, absorption by buffer additives to the
CaCOs slurry scrubbing medium, and has pro-
duced mechanistic models for the total diffusion/
reaction process. Studies have included the use of
dry CaO and "dry" Ca(OH), scrubbing media.
Simulation work is underway that encompasses
the entire process, including regeneration and re-
Newer programs deal with the more general
area of acid gas removal from gas mixtures and
involves basic absorption/reaction modeling
studies. Mass transfer in such separations is fre-
quently enhanced by fast chemical reactions and
at the very least is accompanied by nonlinear
equilibria associated with chemical reactions.
Thus, technical quantification of such separations
can require measurements of chemical kinetics,
equilibria, and mass transfer at representative
Chromatographic Separation Processes. The
use of high-pressure liquid chromatography
(HPLC) or gel-permeation chromatography
(GPC) for the separation of macromolecular solu-
tions is being studied under the direction of D. R.
Lloyd. Aqueous and organic solutions containing
synthetic polymers, natural polymers, proteins,
pharmaceuticals, and the like are under investiga-
tion. The objective here is to study the design con-
siderations that are required to scale up from
laboratory to pilot plant. It is clear that this work
will have an important bearing on developing bio-
technology-type processes.

The Separations Research Program is ad-
ministered by a program head, J. R. Fair, and a
program manager, J. L. Humphrey. One repre-
sentative from each participating company makes
up the SRP Industrial Advisory Committee, which
meets twice a year to review and advise the pro-
gram. Separate study groups meet twice yearly

to review individual programs in detail; for
example, in May 1984 there were separate study
group meetings for membranes, distillation, ex-
traction (conventional and supercritical), and
chemical reaction separations. The Industrial Ad-
visory Committee receives overviews of programs,
whereas the study groups interact closely with
faculty, graduate students and, very importantly,
with themselves. An effort is made to obtain in-
puts from the companies that can influence the
directions that some programs can take, even
though the principal investigators (faculty/staff)
retain final control over specific research studies.
An example response from the companies to a
questionnaire is shown in Table 2.
A question often asked both by academicians
and industry people, with regard to consortia of
this type, is "What advantage does a participant
have over a non-participant, since the research
results will eventually be placed in the public
domain through theses, dissertations and pub-
lished articles ?" The response to this question can
be quite positive, and follows these lines: (1) the
participant receives results early, in the way of
progress reports, discussions with the researchers,
theses and dissertations that can be delayed for
publication; (2) the participant receives a royalty-
free license to practice any patents resulting from
the program; (3) the participant has a mechanism

Research Topics-Participating Company Interest
(26 companies reporting)

Degree of Interest

Separation of gas
mixtures by membranes
Separation of liquid
mixtures by membranes
Supercritical fluid
Liquid/liquid extraction
Separation by chemical
Electrochemical separation

High Mod.
19 6



17 8 1 42

16 8 2 40

14 7 5 35

10 12 4 32
11 9 6 31
9 7 10 25

7 7 12 21

*Weighted rating: high = 2, moderate = 1, low = 0


Panel discussion at Industrial Advisory Committee meet-
ing, with members, from left, James R. Fair, program
head; Herbert H. Woodson, director, Center for Energy
Studies; Jimmy L. Humphrey, program manager; Donald
R. Paul, principal investigator and chairman, Depart-
ment of Chemical Engineering.

for keeping up to date in separations areas where
there is not justification for doing so in-house-
for example, in an area of only peripheral interest
presently but possibly more active in the future;
(4) the participant benefits from interaction of
its people with those in other organizations with
kindred interests. In some ways, the last-named
benefit can be the greatest of them all, if the par-
ticipant works it carefully.


We expect the separations field to continue in
the forefront of chemical processing technology,
along with the allied areas of reaction engineer-
ing and transport processes. Developing interest
in specialty chemicals, such as those in the bio-
technology and electronics industry segments,
carries with it the critical need for recovery and
purification, often under non-classical operating
conditions. Tonnage chemicals will remain under
continuous pressure to reduce costs and conserve
energy, and this means retrofitting a like separa-
tion technique, substituting a new separation tech-
nique, or adopting novel combinations of separat-
ing methods. Much of the time-honored technolo-
gy, for example in distillation, is still not well
understood and thus may be difficult to exploit
economically. In summary, chemical engineers
will continue to deal heavily with separation prob-
lems, and we expect to provide them with some
The future of the Separations Research Pro-

gram at The University of Texas also seems
bright. Along with the new research laboratory
space will come new equipment provided by the
university, some of it of a fairly large scale. A
number of companies have recently expressed
interest in becoming participants. Plans are de-
veloping for the use of visiting scholars and full-
time research personnel. We have outside grants
and contracts in the separations field that serve
to leverage the funding provided by the industrial
participants. Importantly, the entire program is
being staffed with excellent graduate students,
and the learning experience for them and the
principal investigators is, indeed, the raison
d'etre for the entire effort. D

books received

Gas Tables: International Version, Joseph H. Keenan, Jing
Chao, Joseph Kaye. John Wiley & Sons, Somerset, NJ
08873; 211 pages, $37.95 (1983)
)Vetering Pumps: Selection and Application, James P.
Poynton. Marcel Dekker, Inc., New York 10016; 216
pages, $29.75 (1983)
Chemical Grouting, Reuben H. Karol. Marcel Dekker, Inc.,
New York 10016; 344 pages, $45.00 (1983)
Basic Chemical Thermodynamics, Third Edition, E. Brian
Smith. Oxford University Press, New York 10016; 160
pages, $21.95 (1983)
Los Alamos Explosives Performance Data, Charles L.
Mader, James N. Johnson, Sharon L. Crane. University of
California Press, Berkeley, CA; 811 pages, $45.00 (1983)
Practical Quality Management in the Chemical Process
Industry, Morton E. Bader. Marcel Dekker, Inc., New
York 10016; 160 pages, $27.50 (1983)
Fourth Symposium on Biotechnology in Energy Pro-
duction and Conservation, Charles D. Scott, Editor; John
Wiley & Sons, Inc., Somerset, NJ 08873; 495 pages, $65.00
NMR and Chemistry: An Introduction to the Fourier
Transform-Multinuclear Era, Second Edition, J. W. Akitt.
Chapman & Hall, 733 Third Avenue, New York, NY 10017;
263 pages, $16.95 (paperback) (1983)
Waste Heat: Utilization and Management, S. Sengupta
and S. S. Lee; Hemisphere Publishing Co., New York
10036; 1010 pages $125.00 (1983)
Journal: Particulate Science and Technology, Vol. 1, No.
1, J. K. Beddow, Editor; Hemisphere Publishing Co., New
York, NY 10036; $27.50/year indiv. rate.
Prudent Practices for Disposal of Chemicals in Labora-
tories, Nat. Academy Press, 2101 Constitution Ave., Wash-
ington, DC 20418; 282 pages, $16.50 (1983)
The Chemistry and Technology of Coal, James G. Speight,
Marcel Dekker, New York 10016; 544 pages, $69.75 (1983)

FALL 1984

4 Pfaym /e,


"A Real World MS Degree"

Clemson University
Clemson, SC 29631

"I would like to get an MS degree but
I first want to see what industry is like."

W E HAD HEARD this statement (or some varia-
tion of it) over and over as we tried to con-
vince quality undergraduate students to seek ad-
vanced training after graduation. It was especially
hard for me to counter this statement since I felt
the same way when I completed my Bachelor of
Science degree. Of course, most undergraduates
cannot realize how truly difficult it is to leave in-
dustry and return to graduate school. Also, they
do not fully appreciate the problems that the
shortage of American graduate students is
causing as universities and industry attempt to fill
teaching and research positions.
This desire for industrial experience and the
decline in the number of American graduate
students was extensively discussed in the fall
1980 meeting of the Clemson Department of
Chemical Engineering faculty and the depart-
ment's Industrial Advisory Board. The discussions
led to a new approach to graduate funding and
training at Clemson called the Graduate Residency
Program. This program seems to be that rare in-
stance where the student, industry, and the uni-
versity all benefit through cooperation in gradu-
ate education. The Graduate Residency Program
offers an increased level of financial support for
the student and, at the same time, provides the

This is the third year of
the Industrial Residency program.
Thus far, eight students have completed their MS,
four are presently in their final work period
completing their MS thesis research, and
three are just beginning the program.

C Copyright ChE Division, ASEE. 1984


Dan Edie is professor of chemical engineering at Clemson Uni-
versity. He received his BS degree from Ohio University and his
PhD degree from the University of Virginia. Before joining Clemson
he was employed by NASA and the Celanese Corporation. At Clemson
he has served as Graduate Program Coordinator and his research
interests include rheology and polymer processing.

student with an opportunity to gain significant
industrial research experience.

First, companies submit proposed research
projects to the faculty, and these projects are re-
viewed for their suitability as thesis topics. The
approved topics are then given to the Graduate
Residency Program applicants who have pre-
viously applied to the graduate program and who
typically have a 3.5/4.0 or better undergraduate
grade point average. The applicants indicate their
preference of both the thesis topic and company.
Next, the applicants and company representatives
are invited to the Clemson campus for one day of
interviews during which the applicants can ask
further questions about both the companies and
the research topics. The companies can evaluate
the applicants at the same time. Finally, the com-
panies indicate their preference, and applicants
are informed of this selection. The applicant can
either accept or reject the residency research
position offered.


A student graduating with a BS degree in
chemical engineering in May would begin this
master's degree program immediately. The Gradu-
ate Residency Program begins with an initial
three-month summer work period with the spon-
soring company. The student normally spends this
first summer getting to know the company pro-
cedures as he or she begins to work on the research
project proposed by the company and agreed upon
by the student. The student meets biweekly with
the faculty advisor and company advisor. At the
end of this first summer the research project is

FIGURE 1. Bill Thornton of Milliken and Company (L)
and Kyle Veatch (R) discussing Graduate Residency

fairly well defined, and the student returns to the
Clemson campus for two consecutive semesters.
During these two semesters, the twenty-four se-
mester hours of formal lecture courses required
for the MS degree are completed. Also during this
period of full-time study, the student is able to
interact academically and socially with the full-
time graduate students in the university. Six
hours of research credits taken during the work
periods complete the 30 hours required for the
Upon completion of the formal course work,
the student returns to the sponsoring company and
resumes work on the project begun the previous
summer. The project is supervised by an industrial
and a faculty advisor through biweekly meetings
with the student. At the completion of this seven-
month work period, a formal thesis based on the
project is presented to an advisory committee
composed of the faculty advisor (committee chair-
man), the industrial advisor, and two faculty
members from the department of chemical engi-
neering. After committee approval of the thesis,

the student receives the Master of Science degree
in December, thus obtaining the degree nineteen
months after completion of the BS degree.
The sponsoring company provides financial
support for the student by providing Clemson
with a grant of approximately ten-months salary
for a BS-level chemical engineer (the time period
the student is actually working on the research
project). The university then awards this support
to the student in the form of a fellowship. Thus,
the student receives a stipend of approxi-
mately $1000 per month throughout the nineteen-
month master's degree program. This is signifi-
cantly higher than typical financial support for
graduate students and, coupled with the oppor-
tunity to obtain ten months of industrial ex-
perience, has allowed us to attract top-notch
undergraduates to our graduate program. The
program offers several advantages to the student,
the company, and the faculty.

Advantages to the Graduate Student
The student can obtain a master's degree in nineteen
months, with ten months spent working on a spe-
cific industrial problem while compensated by a
fellowship of $1000 per month.
Since the student begins work on the project during
the summer prior to the start of formal course work,
graduate courses may be selected and tailored to his

FIGURE 2. Craig Leite, holder of a Graduate Residency
Fellowship, preparing an emulsion in his research into
emulsion stability.

FALL 1984

FIGURE 3. Dr. John Beard (L) served as the faculty ad-
visor for Bill Rion (R) who just completed the residency
program. The thesis topic involved an energy balance
on a large polymer plant.

or her research needs, which increases motivation in
The student is exposed to an industrial environment,
including specific industrial problems, prior to decid-
ing the direction of his or her career.
The student has excellent day-to-day supervision, ex-
perimental facilities, and analytical equipment avail-
able to him or her at the company location (which
is normally an industrial, technical or research

Advantages to the Sponsoring Company
The participating company can evaluate the future
potential of the graduate student on a first-hand
The research results have more than compensated
for the support paid to the student.
The company is able to draw on the expertise of
top level BS chemical engineers as well as Clemson
University faculty to solve problems of specific
interest to the company.

Advantages to the Faculty
Faculty members are exposed to a wide variety of
industrially oriented problems in a number of
companies. This helps them stay current with in-

dustrial needs. This, in turn, increases their prob-
ability of developing more industrially-oriented on-
campus research projects.
The department has obtained a significant new source
of financial support for graduate education which
can supplement industrial, state, and federal grants.
The department of chemical engineering now has in-
dustrial research facilities and resources at its dis-
posal which it could not otherwise afford.
The department of chemical engineering at Clemson
has become a more vital and productive partner with
the rapidly growing chemical and polymer industries
in the state of South Carolina.
Even publication of results has posed no great
problem. Although a couple of MS theses have been
held two years before being placed in the uni-
versity library, most thesis topics have been based
on non-proprietary problems and the results have
been freely published.


Companies such as Tennessee Eastman, the
Allied Corporation, DuPont, Exxon Enterprises,
Celanese, and Milliken & Company are presently
supporting Industrial Residency students. These
students had obtained their BS degrees from
several universities. Thesis topics have been excit-
ing and challenging to both students and faculty
alike. They have covered topics such as

Control of emulsion polymerization
Effect of additives on theological characteristics of
resin system
Mathematical modeling of radial temperature effects
during melt spinning
Parametric studies of binary distillation columns
Rheology of dye systems
Solvent extraction using supercritical carbon dioxide

This is the third year of the Industrial Resi-
dency program. Thus far, eight students have
completed their MS, four are presently in their
final work period completing their MS thesis re-
search, and three are just beginning the program.
The program has had a significant impact on our
MS program, not only by adding more top-notch
students to our graduate program, but also by
providing over $250,000 to support quality gradu-
ate students during these three years. The faculty
and the sponsoring companies are enthusiastic
about this unique blend of a full-time Master of
Science program and "real world" research. But
the best measures of success is that the Industrial
Residency students themselves are delighted with
the program. O


book reviews


By David S. Azbel and Nicholas P. Cheremisinoff:
Butterworth Publishers,
Woburn, MA (1983) $49.95
Reviewed by
David B. Greenberg
University of Cincinnati

Fluid Mechanics and Unit Operations is de-
finitely not just another overworked theme on the
topic of momentum transport. It is, rather, a
serious attempt on the part of the authors to pres-
ent the subject uniquely in the language of the
practitioner and in a fashion that bridges the ob-
vious gap between theory and practice or, more
appropriately, between classroom and application.
It is relatively detailed in the subject matter treat-
ed and massive in size (over 1100 pages). The
book is, however, focused solely on those opera-
tions that are based primarily on momentum
transport. These include single and multiphase
fluid flow, fluid transport by pumps and compres-
sors, separation techniques such as filtration,
fluidization, sedimentation and centrifugation, and
the theory and application of mixing. Those
operations which require detailed knowledge of
the remaining transport science trilogy, namely
heat and mass transport coupled with fluid dy-
namics are not covered in this work but, as the
authors suggest, are best treated separately in
additional volumes. One might assume, therefore,
that the authors ambitiously intend to complete
the trilogy at some point in the future.
The text naturally partitions into several
sections. The first of these includes the funda-
mental development of the subject of fluid dy-
namics and covers introductory and descriptive
material on the thermodynamic and transport
properties of fluids, similitude, modelling and di-
mensional analysis, hydrostatics and a section
which the authors denote as internal problems
of hydrodynamics. This latter portion is actually
an elementary development of the associated con-
servation equations of fluid dynamics and their
application to flow in pipes and conduits. The
treatment here is far from complete but adequate
for an introductory sophomore or junior course,
or as a reference for the practicing engineer. The

text is easy to read, the diagrams are clear, and
the example problems are detailed in scope and
effectively presented. It is clear that this section,
which covers about one-third of the book, is
roughly equivalent to many of the elementary
texts available on the subject.
In the second section of the book the authors
apply the theoretical concepts developed earlier
to fluid transport in pumps and compressors.
Here, the reader is guided through a detailed de-
scription and classification of the various basic
pump designs, their associated operational details,
and where each of these designs is best used. There
is also a section on selection and special applica-
tions as well as a set of practical problems at the
end of each chapter. The practitioner should es-
pecially appreciate the fashion in which the ana-
lytical and descriptive material is synergistically
presented. Moreover, the student, whose knowl-
edge of the subject is more application limited,
will gain considerably, not only by the theory-
practice blend but also through the examples and
problems which are well couched in an industrial
The last two sections of the book deal with the
application of fluid flow to external problems of
hydrodynamics and heterogeneous systems. The
authors introduce the topic of physical separations
briefly and then develop the topics of sedementa-
tion, gravity settling, filtration, electrostatic pre-
cipitation, and centrifugal techniques from con-
sideration first of single-particle motion in liquid-
solid and gas-solid systems. Emphasis is placed on
the requisite theoretical concepts which lead the
student directly to the salient design considera-
tions of the topic. The theory is well supported by
useful practical examples and problems which
cover a range of contemporary unit operations.
The chapter on fluidization which is especially
descriptive will be quite useful to the engineer in
industry who is concerned with the design of such
equipment. Practical treatment of complicated
phenomena in multiphase systems is presented in
a clear, concise fashion with some needed detail
devoted to the effects of such parameters as hold-
up, classification, bubble size effects and entrain-
ment upon the design of these systems. Moreover,
the authors devote a final chapter to the hydro-
dynamics of gas-liquid flow. Much of this ma-
terial is quite new and relevant, and is probably
not available in earlier texts on fluid dynamics.
Because two-phase flow is still a most complex and
Continued on page 212.

FALL 1984



Colorado State University
Fort Collins, CO 80523

CHEMICAL ENGINEERING includes the science of
reactor design and optimization. As any pro-
duction environment becomes process limited, the
role of chemical engineering increases in im-
portance. Semiconductor manufacturing is an
ideal example of a maturing process ready for re-
actor optimization and design. As we break into
the technology of Very Large Scale Integration
(VLSI) and Ultra High Speed Integrated Circuits
(UHSIC), yields in the fabrication facility be-
come very important. High-throughput, high-yield
processes must be developed so that our industries
will be viable in a marketplace filled with over-
whelming foreign competition. Such processes can
only be developed after the fundamental physics
and chemistry of the chemical reactions are well
At Colorado State University (CSU), the de-
partments of chemical engineering, electrical
engineering, physics, and chemistry have respond-
ed to industry's need by creating a graduate pro-
gram in integrated circuit (IC) process engineer-

C. M. McConica received her PhD (1982) in chemical engineering
from Stanford University. She spent three years with Hewlett Packard
(1979-1982) developing state-of-the-art deposition/etching processes
for their 128Kb RAM and 640Kb ROM, all fabricated with 1 micron
NMOS double-layer metal technology. The chips utilizing this tech-
nology are now sold in the HP 9000.

National Average Monthly Salary Offers (BSChE)**

Total Offers
% of Offers
% of Offers
% of Offers

1984* 1983 1982 1981
827 2023 6952 11695

11.5 15.8 4.4 2.9
$2173 $2109 $2112 $1915

13.0 16.6 36.7 41.5
$2358 $2329 $2329 $2068

47 34.5
$2304 $2260

39 36
$2241 $2016

*1984 data through June only
**CPC Salary Survey, The College Placement Council

ing. A student trained in most classical BSEE
programs lacks the background in fluid mechanics,
heat transfer, reaction kinetics and chemistry
which is essential to integrated circuit manu-
facturing. While students with BSChE degrees
have the best education for processing integrated
circuits, they lack an understanding of circuit de-
sign, device physics, and EE language. The gradu-
ate programs in integrated circuit processing at
CSU give students an opportunity to broaden their
background while pursuing research on a state-
of-the-art level.

The electronics industries have recently begun
to recognize the value of hiring chemical engineers
to fulfill their processing needs. Table 1 lists cur-
rent salary offers and the percentage of the total
number of offers made by the electronics, petrol-
eum, and chemical industries to BSChE gradu-
ates. The statistics were compiled annually from
the College Placement Council (CPC) Salary
Survey between 1980 and 1984. The actual number
of offers made by both the electronics and
petroleum industries declined, but more so for
Copyright ChE Division, ASEE. 1984


While students with BSChE degrees have the best education for
processing integrated circuits, they lack an understanding of circuit design, device
physics, and EE language. The graduate programs in integrated circuit processing at CSU give students an
opportunity to broaden their background while pursuing research on a state-of-the-art level.



10 -

1980 1981 1982 1983 1984
FIGURE 1. Percent of BSChE offers from microelectronics
industries in the USA.

the latter. The table clearly shows the growing
importance of the electronics industry for chemi-
cal engineers. In 1981, only 3% of all offers to
BSChE graduates came from electronics, while
40% came from the petroleum industry. By 1983,
however, 13% of all offers were coming from
electronics firms and only 17% from petroleum
industries. The chemical industries have con-
sistently made 30% to 50% of all job offers to
graduating chemical engineers. Fig. 1 presents the
hiring trend by the electronics industry in bar-
graph form.
At CSU the hiring rate by electronics firms has
increased much more rapidly than the national
rate (Fig. 2). This is a reflection of the proximity
of microelectronics companies to CSU. Many
companies have western headquarters and locate
their research and fabrication facilities in appeal-
ing locations. While there is little petroleum re-
fining or chemical production in Colorado, micro-
electronics is pervasive and growing. This is also
true for Arizona, New Mexico, Idaho, Utah, Ore-
gon, Washington, Minnesota and, most obviously,
California. Other states with active microelec-
tronics industries also have active petrochemical
or traditional chemical industries. These industries
are still hiring the majority of chemical engineers
in those states.
The salaries offered to BSChE graduates by
electronics companies since 1981 are an average of

$196/month less than offers given by petroleum
companies, and $127/month less than those offered
by chemical companies. This is simply the result
of hiring into an EE-dominated discipline where
salaries have traditionally been lower. Many high
tech companies believe that their remote locations,
informal dress requirements, flexible work hours
and stock option-profit sharing plans compensate
for this salary differential. Female engineers in
microelectronics firms enjoy the support of a
relatively young professional work force and a
primarily female fabrication work force.
The employment statistics listed are for
BSChE graduates and clearly reflect the high de-
mand for chemical engineers in electronics. We
believe this demand would extend to the MS and
PhD level if graduate students could be given the
opportunity to pursue research relevant to micro-
electronics. The following sections describe the
coursework and the research topics and facilities
currently available to graduate students interested
in integrated circuit fabrication.


The presumed prerequisites for MSChE
candidates are given in Table 2. Students with-
out an engineering background may enter the pro-
gram and complete these undergraduate courses
at CSU. The MS program for a student with a BS



1980 1981

FIGURE 2. Percent of CSU chemical engineering gradu-
ates working in the field of microelectronics.

FALL 1984


Prerequisites for M.S. ChE
Organic Chemistry
Physical Chemistry
Fluid Mechanics
Unit Operations
Electrical Circuits
Reactor Design
Chemical Engineering Design

in chemical engineering normally contains 26
hours of coursework. An additional 4-6 credits are
earned for the thesis. Chemical engineers in the
IC processing program are required to take four
core chemical engineering courses, and then are
allowed to choose the remainder of their credits
from courses offered by EE and other depart-
ments. A typical two-year MS course schedule is
given in Table 3. The PhD program is an ex-
tension of the MS program, requiring more credits
of coursework and successful defense of a dis-
sertation based on original research. Many of the
electrical engineering courses emphasize material
properties, fabrication technologies, and solid state
physics. No special prerequisites are required of
the BSChE student. Chemical engineers do quite
well in these courses because of their solid back-
ground in thermodynamics and transport phe-
nomena. Students have the option to pursue
courses which emphasize device design and de-
vice physics. These are not required of chemical
engineers due to their more classical EE prerequi-


At Colorado State University there is an active
solid state research group in the departments of
chemical engineering, electrical engineering, and
physics. Work is sponsored by the Department of
Defense, the Department of Energy, the National
Science Foundation, and the Colorado Micro-
electronics Industry. The focal point of the re-
search work is a clean semiconductor fabrication
laboratory. Current research activities include
selective chemical vapor deposition of refractory
metals (C. M. McConica), oxides and interfaces
of silicon and compound semiconductors (C. W.
Wilmsen), photovoltaic devices (J. Sites), transi-
tion metal silicides (J. E. Mahan), and polycrystal-
line silicon devices (J. E. Mahan).
The major research facilities supporting the
research are

Solid state device fabrication facility (class 100
clean room, metallization, diffusion, oxidation, photo-
lithography, wet chemistry, plasma etching, ion
beam sputtering).
Electron microscopy (ISI Super-II, ISI 100B and
Hitachi HHS-2R scanning electron microscopes,
Hitachi HU-200F transmission electron micro-
X-ray diffraction (GE diffractometer, Laue camera).
Transport properties measurements (galvanomag-
netic effects, thermoelectric power, temperature-
controlled cryostat).
Surface analysis facility (Auger electron spectro-
scopy, ESCA, UPS, SIMS analysis).
The current semiconductor research effort in
chemical engineering emphasizes an understand-
ing of the kinetics of low pressure chemical vapor
deposition. Metallic films are deposited on single
wafers in a high vacuum system which can be
used as a differential flow reactor. Classical
methods of kinetics and catalysis are utilized to
determine the kinetic parameters which govern


M.S. ChE Course Schedule


Mathematical Modeling
Semiconductor Devices I
Thin Film Phenomena


Advanced Reactor Design
Solid-Gas Kinetics
Principles of Semiconductors

3 credits
3 credits
3 credits
1 credit
3 credits
13 credits

3 credits
3 credits
1 credit
3 credits
10 Credits

Remaining courses in second year (3-9 credits)
to be chosen from:
Introduction to Electron Microscopy
Organometallic Chemistry
Technique in Inorganic Chemistry
Surface Chemistry
Advanced Process Control
Advanced Mass Transfer
Semiconductor Devices II
VLSI Plasma Processing
Semiconductor Materials
Optical Materials and Devices
VLSI Processing
Topics in Plasma Dynamics
Solid State Physics I
Solid State Physics II
THESIS-4-6 credits


the deposition reactions. The deposited films are
then analyzed for electrical and physical proper-
ties. Through cooperation with local industries
the students fabricate devices using the latest thin
film technology. Other students are using CSU's
kinetic results to model the behavior of industrial
reactors. Again, local industries cooperate by al-
lowing the comparison between our models' pre-
dictions and their deposition results.
The Department of Chemistry actively partici-
pates along with the previously mentioned de-
partments in Colorado State University's Con-
densed Matter Sciences Laboratory. Current re-
search activities include the study of molecular
condensed phases (E. R. Bernstein), electrode
surface modification (C. M. Elliott), techniques of
elemental analysis and the chemical characteriza-

tion of surfaces (D. E. Leydon), and NMR studies
of solids (G. E. Maciel).

Chemical engineers are currently contributing
to the electronics industry in growing numbers.
Colorado State University has responded to in-
dustry demand for chemical engineers by offering
a graduate program emphasizing integrated cir-
cuit processing. The program utilizes courses from
several departments while allowing the student
to apply chemical engineering techniques to an
integrated circuit fabrication research topic.
Graduates are receiving multiple offers from top
quality semiconductor companies throughout the
United States. O

S book reviews

Edited by J. A. Essers
Hemisphere Publishing Corp., 1983; 360 pages,

Reviewed by G. K. Patterson
University of Arizona

This book consists of six contributions in the
general field of numerical simulation of turbulent
flows. Each article is a strong contribution on the
topic covered. Those topics are: "Numerical
Methods for Coordinate Generation Based on a
Mapping Technique," by R. T. Davis; "Intro-
duction to Multigrid Methods for the Numerical
Solution of Boundary Value Problems," by W.
Hackbusch; "Higher-Level Simulations of Turbu-
lent Flows," by J. H. Ferziger; "Numerical
Methods for Two- and Three-Dimensional Re-
circulating Flows," by R. I. Issa; "The Computa-
tion of Transonic Potential Flow," by T. J. Baker;
and "The Calculation of Steady Transonic Flow
by Euler Equations with Relaxation Methods,"
by E. Dick.
To the novice attempting to learn the basics
of numerical turbulence simulation, the organiza-
tion of the book is not optimum. Although it is
logical thematically to present grid generation,
multigrid solution methods, and higher-level
simulation in the first half of the book to lay a
theoretical basis for the more practical topics to

follow, the novice would feel more comfortable
reading first about general methods for Reynolds-
averaged modeling as presented for recirculating
flows and transonic flows in the fourth through
sixth chapters.
The book offers much to those who already have
some knowledge of numerical simulation of turbu-
lent flows. The treatment is not general and
comprehensive for the entire turbulent and
transonic flow modeling field. Each chapter pre-
sents a rather narrow topic from the author's par-
ticular viewpoint. Even though the collection
represents the notes for a course presented at the
von Karman Institute, no effort was made to link
the presentations. Indeed, only one chapter was
supplied with a nomenclature list, and each chapter
has a different set of symbols.
The book would be valuable to those with some
familiarity with numerical simulation of flow but
without expertise in numerical modeling of
turbulent, transonic flow. They should probably
read the chapters in the order: 4, 5, 6, 2, 1, 3. That
order corresponds to problem complexity and so is
easier for non-experts. The book probably does not
present much in each topic that an expert on that
topic does not already know, so it should not be
expected to provide much that is new if only that
chapter is read. Its value is in its possible intro-
duction of experts in one field, say coordinate
generation and mapping, to another field where
that expertise can be used, say external, transonic,
turbulent flows. Having known little about tran-
sonic flows but much about incompressible turbu-
lent flow modeling, I learned much from the last
two chapters. O

FALL 1984

hwad 2.ectue



The Chemical Engineer-
ing Division Lecturer for
1983 is Warren E. Stewart
of the University of Wis-
consin. The 3M Company
provides financial support
for this annual lectureship
A native of Wisconsin,
Warren Stewart began his
chemical engineering studies
at the University of Wiscon-
sin, attaining the BS degree in 1945 (as a Navy V-12
trainee) and the MS in 1947 after completion of his naval
service. He received his ScD in 1951 from the Massachusetts
Institute of Technology, where he worked with Harold
Mickley on interactions of heat, mass, and momentum
transfer in boundary layers.
He joined Sinclair Research Inc. in 1950, and worked
there for six years, participating in the development of
a catalytic reforming process and in early work on com-
puterized process simulation. His continuing interests in
chemical process modelling and numerical methods date
from this industrial research experience.
In 1956 he joined the chemical engineering faculty of
the University of Wisconsin where he was department
chairman from 1973 to 1978. He has held two visiting ap-
pointments at the Mathematics Research Center of the
university, and is now a regular member of the center.
In 1957, Professors R. Byron Bird, Warren E. Stewart,
and Edwin N. Lightfoot began work on a textbook for a
new course in chemical engineering. The resulting book,
Transport Phenomena, published in 1960, has had a wide
influence in engineering education.
Professor Stewart is a Fellow of AIChE, and received
their Alpha Chi Sigma Award for Chemical Engineering
Research in 1981. He also received the Benjamin Smith
Reynolds Teaching Award of the College of Engineering
at the University of Wisconsin in 1981. He is an associate
editor of the Journal of Computers and Chemical Engineer-
ing and an honorary advisor to the Latin American Journal
of Chemical Engineering and Applied Chemistry.
Stewart's research emphasizes new mathematical ap-
rpoaches to practical analysis of chemical process systems.
He has worked extensively in the areas of fluid mechanics,
transport properties, chemical reactor modelling, and
weighted residual methods.

University of Wisconsin-Madison
Madison, WI 53706

T IS A PLEASURE to talk and write on a favorite
theme to my fellow chemical engineers. My
theme for today is orthogonal collocation-its
origins, its relation to other approximate methods,
and some examples of its use in engineering.
Orthogonal collocation is a technique for solv-
ing transport problems efficiently by fitting a trial
solution at selected points. The points are chosen
by use of orthogonal functions to minimize the
approximation error over the given region. The
speed of the method has proved valuable in
modelling and controlling chemical reactors, and
shows similar promise for staged separation
Two kinds of approximations are important
in process modelling: approximations of the
problem and of the solution. Examples of each
kind are listed in Table 1. Orthogonal collocation
belongs in the second category, among the weighted
residual methods now to be described.

Consider a generalized problem statement,
typical in process modelling and in physical theory.
A vector y of unknown functions of coordinates x
is to be found by solving the equations
Lvy = fv(x,y) in V (1)
Lsy = fs(x,y) on S (2)
in which Lv and Ls are the local parts of a linear
operator L. Eq. (1) denotes the equations (differ-
ential or other) to be solved in the main region of
the problem, and Eq. (2) denotes any needed initial
and boundary conditions. The regions V and S may
be continuous (as in distributed models of re-
actors) or physically lumped (as in stagewise
models of plate columns). We assume that any
desired approximations of the original problem
have been done, so that Eqs. (1) and (2) are to be


Copyright ChE Division, ASEE, 1984

solved as given.

Weighted residual methods employ an approxi-
mating function for y in Eqs. (1) and (2). A
popular form is
y = yo(x) + 1 ai (x) (3)
with chosen functions yo(x), (o(x), ... ,n_ (x)
and adjustable coefficients a, .. a.-,. Often the ai
are treated as functions of one of the coordinates,
as in the method of Kantorovich [11] for reducing
two-dimensional problems to ordinary differential
form. If each basis function q (x) is non-zero only
within a corresponding subdomain, Eq. (3) is
called a spline or finite-element approximation.
Approximation of y by y in the problem gives
the residual functions

Lvy fv(x,y) = ev in V (4)

Lsy-fs(x,y) = Es onS (5)
which locally measure the errors incurred. For
given choices of the functions yo and 0i, the
residuals depend on x and on a, . an1.
If a general solution of Eq. (1) or (2) is known,
we can use it in (3) and thus eliminate ev or
es. Elimination of E, is often possible, and yields
an interior approximation (only Ev appears).
Elimination of Ev may be possible when fv = 0;
this yields a boundary approximation (only Es ap-
pears). Examples of the latter are the eigen-
function expansions used in problems of potential
theory, heat conduction, and Newtonian creeping
flow. If such general solutions are not available,
or are not used in y, both ev and Es will appear; the


Kinds of Approximation Methods
1. Approximation of the problem
A. Linearization
B. Asymptotic methods and perturbations
C. Physico-chemical assumptions and simplifications
2. Approximation of the solution
A. Weighted residual methods
Least squares
Orthogonality method
Variational methods of Rayleigh and Ritz
Galerkin method
Collocation methods
Finite element methods
B. Finite difference methods

The following poem was submitted by R. B. Bird to
commemorate Warren Stewart's birthday on July 3,
1984, and was accompanied by the observation that
"I don't quite understand how such a young chap
got to be so old so fast, do you?"

on his 60th birthday

A student came in to see Warren
And said in voice quite forlorn
"I can't find a path
Through this quagmire of math
These nablas to me are quite foreign."
So Warren, who's also called Earl,
Decided to help this young girl.
Without using a book
He unflinchingly took
The Laplacian of grad div curl curl.
-r. b. bird

result will then be a mixed approximation.
A weighted residual method (projection
method) is then used to determine the coefficients
ao, . an-1. Standard criteria [8, 11, 12, 16, 19, 24]
include least squares

S (E,) = 0

i = 0 ,.... n-1

the method of moments (here weight functions
g, (x) must be chosen)
(e,gi) = 0 i = 0,... n-1 (7)
the method of Galerkin [7] (which includes the
variational methods of Raleigh [4] and Ritz [6]
when the latter are applicable)
(e, i) = 0 i = 0... n-1 (8)
and the method of collocation or selected points.
e(xi= 0 i = 1,...n (9)

The inner product (e,g,) denotes the sum or inte-
gral of the product Egi over all points of V and S.
Egs. (6), (8) and (9) can be regarded as special
forms of Eq. (7), with the weights gi chosen as
aE/Zai, Oi(x), and 8(x-xi+1), respectively.

Eq. (9) is the most convenient criterion, but to
make it reliable one needs a way of choosing good
collocation points. A simple way is to approximate
Eq. (5), (6) or (7) by use of an optimal n-point

FALL 1984

quadrature of the inner product. This leads to Eq.
(9) directly, with the xi now chosen as the quadra-
ture abscissae. The points thus found are always
zeros of one or more orthogonal functions; this
prompted the name orthogonall collocation" given
to this method in [18]. This approach was initially
proposed by the writer to Lou Snyder in 1964
during his research on flow in packed beds [17],
and was implemented with John Villadsen [18]
beginning in 1965.
The theory of optimal quadratures, begun by
Gauss [1], has yielded good points and weights for
approximating many kinds of integrals in one
dimension [14, 15] and in several [15, 23]. One can

This leads to Eq. (9) directly, with the
xi now chosen as the quadrature abscissae. The
points thus found are always zeros of one or more
orthogonal functions; this prompted the name
orthogonall collocation"...

use these points directly for collocation with cor-
responding regions and approximating functions.
Quadratures over discrete point sets have ap-
parently not been studied, but good grid points can
be found, as in [55] and [57], by use of classical
polynomials orthogonal on such regions [5, 10].
A more analytical approach is to write inter-
polation functions Qnv(x,x1, . xn) and/or
Qns(x,x, .. Xn) for the collocated residuals. Then
the residual functions, or their effects, can be ap-
proximately minimized by doing the collocation at
those points which minimize a suitable measure
of Qnv and Qs. For example, replacement of E by
Qn in Eq. (6), (7) or (8) yields a grid-point
criterion for a correspondingly weighted orthog-
onal collocation scheme. This method makes clear
the restrictions implied by collocation at standard
quadrature points, and also yields collocation
points for other criteria or basis functions as de-
sired. Examples of this approach to collocation
may be found in Lanczos [13], DeBoor and Swartz
[27], Carey and Finlayson [34], and in several of
our papers [18, 26, 37, 48, 50, 55, 56, 57].
Lanczos [13] chose Q,v in one dimension as the
polynomial (x-xi) ... (x-x,) with least maximum
magnitude on the interval [-1, 1]. The resulting
polynomial is Tn(x) = cos(n cos-1 x), as found by
Tschebychef [2]. This choice of grid points, xi =
cos[i 1/2)rr/n], gives a minimal upper bound on
the residual in collocation [13], just as in ordinary
interpolation [9], provided that the residual and
its first n derivatives are continuous. Different grid

points should be used for collocation, as shown
in [50], if one wishes to minimize the maximum
deviation y yl.
Consider a system of symmetric second-order
differential equations in one space dimension
Lvy = f(x2,y) for 0 < x2 < 1 (10)
The region considered is the interior of a slab, long
cylinder, or sphere. The boundary conditions are

y = y(l) at x2 = 1
and (for a cylinder or sphere)

dy 0 at x = 0



The solution is symmetric [y = y(x2)], and is as-
sumed to be continuous. This kind of problem and
extensions of it are important in fluid mechanics
and reactor modeling.
A polynomial approximant y(x2) consistent
with Eqs. (11) and (12) is

S+ 1 .n
y = y(1) + (1-x) I ax"


Thus the boundary residuals are zero, and the de-
termination of ao,... a,-_ is an interior approxima-
tion problem.
The interior residual Ev is computable, for any
particular form of Eq. (10), by inserting y in place
of y. The result will depend on x2 and on the un-
known coefficient vectors ai. Thus, it will be tedious
to apply Eq. (6), (7) or (8) unless Eq. (10) is
Suppose we collocate y with Eq. (10) at some
set of points, x,2 < x22 < ... Xn2. Then the residual
vanishes at those points, and assuming continuity,
it can be approximated throughout the interval by

ev = (x2 x12) ... (x2 x2) [bo + blx2 + ...] (14)
according to Weierstrass' theorem [14]. Here bo,
b1, etc., are bounded constants. We can now choose
x2, . xn2 by requiring that the leading term of
Ev satisfy Eq. (7) for arbitrary bo. This gives the
orthogonality conditions

f gi(x) Q(x2) d(xa) =0

i = 1,...n (15)

for the polynomial Q (x2) whose zeros are x,2, ...


x,2. Here d(x") is a generalized volume element,
with a = 1 for a slab, 2 for a long cylinder, or 3
for a sphere. Eq. (15) determines the grid points
uniquely, provided, of course, that the functions
g, (x2), . g(x2) are linearly independent on the
interval of integration.
To get a Galerkin-like collocation method from
Eq. (15), as in [18], we choose g (x2) = (x2)
(1 x2)X2 and obtain

(1 (1- x2) x2 Qn(X2) d(xa) = 0 i=l n -1
f (Galerkin analog)
From this it follows that Q. is one of the Jacobi
polynomials, derived in [3] and given in [15], [18]
and [38]. For the slab geometry (a = 1), the points
xi, .. .. x+, at which (1 x2) Qn(x2) vanishes
are the abscissae of a (2n + 2)-point symmetric
Radau quadrature formula (or Lobatto formula).
The interior points xl, . x are used as collocation
points for Eq. (10), and the point xn+, = 1 is used
for the outer boundary condition.
To get a least-squares collocation method for
Eq. (10), we choose weights consistent with Eq.
(6) and the leading term of Eq. (14). Noting that
the collocation makes ao, ... a,_n implicit functions
of x2, ... Xn2, we obtain the relations

-- f [(x2-x2) .. (x2-X.)]2d(xa) = 0
i = ,... n (17)
which may be rearranged to give

Sx2i Qn(x2) d(xa) = 0 i = 0,...n-1
o (least squares analog) (18)
and yield another kind of Jacobi polynomial. Ex-
plicit formulas for the Q. of Eq. (18) are given in
[15] and [38]. For the slab geometry (a =1), Qn
is a Legendre polynomial and the interior grid
points x, ... Xn are the positive abscissae of a 2n-
point Gauss quadrature formula. The point Xn.+ =
1 must be added for collocation of the outer
boundary condition.
For numerical work it is convenient to rewrite
Eq. (13) as a Lagrange interpolant

y = S lj(x2)yj (19)
3 (x2) 0+ (X- Xk2)
k=j (Xj2 -Xk) (20)

... consider the steady-state
performance of a tubular isothermal
catalytic-wall reactor of radius R and catalytic
length L, fed with pure reactant A in developed
laminar flow with centerline velocity Vmax.

in which yj stands for y (xj). Derivatives and inte-
grals of y then follow readily; for example,

dx xi


S( dlj (x2)
j=1 dx xi

1 Aij

I 2 V'2x2) Yi=
ii> | i

Y BijYj

f f(x2)xa-dx =

n+1 n+1
I1 j f (x)x"-dx f(xj2) = 1
j=1 f=1


The final polynomial, 10.+(x2), in Eq. (19) is pro-
portional to Q,(x2). This gives a simplification of
Eq. (23) when (18) is used, since Q.(x2) is then
orthogonal to x0 and consequently W,,0 vanishes
exactly. Eq. (23) is exact for f(u) of degree 2n
(here u = x2) when Eq. (16) is used, and 2n 1
when Eq. (18) is used.
The constants xi, Aij, Bi, and Wi are tabulated
in [18] for the criterion in Eq. (16). Tables for
both criteria, (16) and (18), are given by
Finlayson [24]; subroutines are given by Villadsen
and Michelsen [38].

As a simple example, consider the steady-state
performance of a tubular isothermal catalytic-wall
reactor of radius R and catalytic length L, fed with
pure reactant A in developed laminar flow with
centerline velocity vmax. The catalytic wall, which
begins at z = 0, induces a first-order hetero-
geneous reaction A -> B with rate constant k,"
cm/s. The fluid is considered Newtonian with
constant density p, viscosity t, and binary
diffusivity DAB. Longitudinal diffusion is neglected.
An expression for the flow-mean fractional con-
version as a function of z is desired.
The continuity equation for species A under
these conditions can be written in dimensionless

FALL 1984

form as


[1-2] 2DY

1 D DY
x (x
x ax 'xax

0 x<1

in which y = ACAF/C, x = r/R, and Z = zDAB/R2Vmax.
The boundary conditions are
y=l for 0

Yi = 1 at Z = 0

-4y + 4y = -Ky, for 0 < Z < ZL (33)

-4y + 4y2 = 0 for Z > ZL (34)
Insertion of Eqs. (33) and (34) into Eq. (31)

DY =0 at x=0 for Z>0


ay- Ky at x=1 for 0 Dx

Y -=0 at x=l for Z>ZL (28)
Eq. (27) is a reactant mass balance on an element
of catalytic surface. It contains two dimensionless
parameters: K = kl"R/DAB and ZL = LDAB/
R vmax. Finally, let

(1-x2) [1- y(x,Z)] xdx


(1-x2) xdx

denote the flow-mean reactant conversion at Z.
For a quick, approximate answer we will use
collocation with n = 1. For this two-dimensional
problem, we extend Eq. (19) as follows
n+l ,-
y = (x) yj (Z) (30)
thus immediately satisfying Eq. (26) and the
symmetry of the problem. Since y is not known at
x = 1, we will choose the points according to Eq.
(18). The collocation constants then become, with
a = 2 and n = 1:

[xi] = [V\112 [Ai] = -2V2 2V2

[Bjl] = -8 [W,] = 1/2
-8 8 L 0

Collocation of Eq. (24) at the interior locus x =
x, gives the ordinary differential equation

1 dy = -8y' + 8y2
2 dZ (31)

Collocation of Eqs. (25), (27) and (28) gives

_ 16Ky, for 0 4 + K

dy, =0 for Z > ZL
The solution for the grid-point states is

4 = 4 exp
yJ 4 + K

for 0 < Z < ZL

YL = 1 ( 16K
Y1 exp 4+
Y2 L -4



4 + K}

S)for Z> Z

and values at other radii can be interpolated with
Eq. (30). The flow mean conversion, computed
from Eqs. (23) and (29), is

X= 1 yfor all Z> 0


since the quadrature weight W2 is zero for the
grid points used here.
The inlet profile in Eq. (25) is approximated
only roughly here since y(x,0) is a parabola
satisfying Eq. (27). Eq. (32) causes the parabola
to give the correct flow-mean inlet composition.
The inlet condition would be better approximated
if a larger n were used; however, a much better fit
could be obtained by use of a properly singular
function y,, as in (56).
This problem can also be worked via Eq. (13),
with y(1,Z) and a,(Z) as the unknown coefficients.
Several examples of this approach are given in
[18] and [21]. We prefer the method based on
ordinates yi, because it is less affected by round-
ing errors at large n [49] and also handles initial
conditions more directly.
The collocation method also gives quick solu-
tions with axial diffusion included, or with other
forms of kinetics. Nonlinear kinetics will usually
call for numerical treatment of Eq. (31) and of


the wall boundary condition; several pocket com-
puters now have this capability.
An interesting correspondence exists between
traditional reactor models and collocation approxi-
mations to Eq. (24). Collocation with n = 1
yields Eq. (31), which has the same form as a
plug-flow reactor model. The collocation solution
also gives expressions for the radial profile and
wall transfer coefficient, which the plug flow
model does not provide [22, 38].
Collocation solutions with n > 2 reveal dis-
persion effects [51, 52] through the presence of
unequal velocities v. (xi) at the interior grid points.
In developed laminar flow no artificial term is
needed to describe the dispersion, and no feed-
back of material is predicted other than longi-
tudinal molecular diffusion.
Orthogonal collocation has been used extensive-
ly in chemical reactor simulation and design. A
survey of early work is given in [31]. Applications
have ranged from one-point radial collocation of
catalyst particle models [20] and tubular reactor
models [22] to detailed simulations of multidimen-
sional reactors [25, 26, 49]. Electrochemical re-
actors have also been treated [35], with major re-
ductions in computing time.
Fig. 1 shows temperature profiles from a simu-
lated startup of an o-xylene oxidation reactor
[26, 49]. Orthogonal collocation was used, with
piecewise polynomials in the axial direction and
global polynomials in the radial coordinates of the
particles and tube. Improvements in the algorithms
since the original work [26] have reduced the
computation time from 240 s to 40 s on a Univac
1100 for the first 600 s of reactor operation [49].
Various approximations for reactor engineer-
ing have been developed, and existing models test-
ed. One-point collocation of intraparticle transport
problems [20] has given useful insight regarding
particle shape effects, ignition and extinction phe-
nomena, as well as proper particle sizes for.
measurements of intrinsic kinetics. One-point col-
location of the radial derivatives in two-dimension-
al models of tubular reactors [22, 38] yields equa-
tions formally similar to the plug-flow model, but
provides also the radial profiles and wall transfer
coefficients, as in the example of the preceding
section. Multipoint simulations of catalyst par-
ticles [28] show that the ignition and extinction
limits are somewhat sensitive to the particle
shape, and are often well approximated by one-


390 500
T 400
(C) 300
380 200

370 --=--------r100s

.5 I. I.5m
FIGURE 1. Bulk temperature profiles during startup
of an o-xylene oxidation reactor [26, 49]. The first
0.8 m of the bed is diluted to 50% catalyst; the re-
mainder is 100% catalyst.

point collocation. Collocation analyses of packed
bed reactors have been made by Young and Finlay-
son [30] to determine when axial dispersion may
be neglected. Collocation studies of multiple re-
actions in porous particles [48] have shown sig-
nificant effects of catalyst pore size distribution.
Collocation has also proved effective in solving
multicomponent reactor problems with dispersion
[52], and has made it clear that the dispersion co-
efficients are rather complicated functions of the
chemical kinetics.
Orthogonal collocation has proved useful in
nonlinear estimation problems where extensive
parameter spaces need to be explored. A useful
short-cut, given in [36], is the direct computation
of parametric sensitivities by a simple extension
of the Newton solution algorithm. Bayesian esti-
mation algorithms are demonstrated in [36] and
[46] for multiresponse reactor data. Computer aids
to formulation and testing of reaction models are
described in [41] and [45]. Pulse-response experi-
ments and collocation analysis are used in [39] to
determine the thermal conductivity and heat ca-
pacity of an extruded catalyst.
Transport problems in various geometries have
been analyzed. Paper [29] analyzes the sensitivity
of Clusius-Dickel column performance to imperfect
centering of the heated rod or wire. Papers [32]
and [33] deal with the Graetz problem for tubes and
for packed beds, with longitudinal conduction in-
cluded; a fuller analysis for tubes is given in
[38]. Paper [56] tests a model of viscoelastic fluids
by comparing predicted and observed flow fields in
a cavity with a rotating lid.
Fast reactions and boundary layers give rise
to steep solutions, which are hard to fit with global
polynomials. Basis functions derived by lineariza-
tion have proved effective in several such cases

FALL 1984

[37, 44, 48, 49] when used in orthogonal collocation
schemes. For example, Table 2 shows multicom-
ponent profiles for catalytic reforming in a spheri-
cal particle, computed by orthogonal collocation
with hyperbolic functions [48]. These functions are
tailor-made for the given problem, thus permitting
good accuracy with a small set of collocation points.
Piecewise polynomials (finite elements) are
widely used in computing steep solutions. They are
commonly fitted by orthogonal collocation on each
element [27, 34, 40, 43, 51, 54]. Integral methods
such as least squares, however, are applicable to
polynomial elements of lower order, and have been
used in [47] to derive a robust algorithm with
moving finite elements. Finite-element schemes
are attractive for systems with localized action,
whereas global schemes are still the most efficient
for computing smooth solutions.
Orthogonal collocation has been applied re-
cently to large plate columns [42, 53, 55, 57] to
obtain reasonable simulations in shorter comput-
ing times. The states in each module of the column
are interpolated by polynomials of low order n,
and these are fitted by applying the column model
at n collocation points. The preferred points [55, 57]
are obtained by a least-squares principle in which
the sum of squares (Qn,Q,) over the stages is mini-
mized with respect to the grid-point locations
x1, ... x, (which can have non-integer values).
The resulting orthogonal polynomial was dis-
covered by Tschebychef [5] in a different context,
and rediscovered by Hahn [10], for whom it is

" C3 t 2.0 hr




8. 0- li
S 5 1t 15 2e 25 38 35
FIGURE 2. Transient response of the liquid states in a
binary 32-stage still to a step change in boilup rate
[55, 57]. Solid curves: interpolated full 32-stage solu-
tion. Points and dashed curves: nodal states and inter-
polated profiles found by 8-point orthogonal collocation.

named. Fig. 2 shows the nice results achieved by
this method when eight nodes are used to describe
the transient response of a 32-stage column to a
step change in boil-up rate. The collocation method
closely approximates the full solution, and takes
about 1/12 as long. This method should be useful
in the design and control of distillation systems,
and it has interesting possibilities for particulate
modelling of reactors.
There are many excellent applications in the
literature. Only a sample is reported here. I ask


Profiles for Catalytic Reforming in a
Spherical Particle of Radius R = 0.9 mm*
Concentrations, mole cm-3.106

n-Heptane Iso-heptanes Naphthenes


Toluene Cracked

1.0000 15.84 0. 15.84 237.6 15.84 0. 769.24
0.9904 15.50 0.69 13.00 238.2 17.88 0.07 768.80
0.9488 14.13 2.79 5.70 239.6 23.17 0.38 767.64
0.8718 11.99 4.88 1.47 240.5 26.35 0.89 766.92
0.7578 9.62 6.52 0.44 240.7 27.34 1.52 766.70
0.6074 7.56 7.69 0.33 240.8 27.67 2.17 766.63
0.4250 6.10 8.40 0.32 240.8 27.88 2.73 766.59
0.2188 5.28 8.72 0.32 240.8 28.01 3.11 766.56

*Computed by orthogonal collocation with the grid points shown, and a bimodal pore size distribution [48].




the understanding of the reader for the sparse
selection that has been made.


Orthogonal collocation is an approach designed
to minimize problem size and computation time.
It is adaptable to basis functions of global or piece-
wise form, and to various weighted residual cri-
teria; thus the user's insights can be built in. The
grid-point strategy can be summarized simply as
follows: do to the interpolant Qn (x,x, . x,) as
you would to the residual e, if you had unlimited
time. OE


Thanks are due to the 3M Company for spon-
soring this lecture, and to my chemical engineer-
ing friends at Washington University, Virginia
Tech, Carnegie-Mellon and Ohio State University
for their hospitality. Above all, I thank my
students and John Villadsen for their collaboration
in this and other areas of research.


1. Gauss, C. F., "Methodus Nova Integralium Valores
per Approximationem Inveniendi," Comm. Soc. Reg.
Sci. Gottingen, III, 165 (1816) ; Werke, 3, 163.
2. Tschebychef, P. L., "Sur les Questions de Minima,
qui se Rattachant a la Representation Approximative
des Fonctions," Mim. Acad. sc. Petersb., Ser. 6, Vol.
7, 199 (1859); Oeuvres, 1, 271.
3. Jacobi, C. G. J., "Untersuchungen fiber die Differ-
entialgleichung der hypergeometrischen Reihe," J.
reine angew. Math., 56, 149 (1859); Werke, 6, 184.
4. Rayleigh, Lord J. W. S., "Some General Theorems Re-
lating to Vibrations," Proc. London Math. Soc., IV,
357 (1873).
5. Tschebychef, P. L., "Sur l'Interpolation des Valeurs
Equidistantes," Zapiski Imperatorski Akademii Nauk,
25 (1875); Oeuvres, 2, 217.
6. Ritz, W., "tTber eine neue Methode zur LUsung ge-
wisser Variationsprobleme der mathematischen
Physik," J. reine angew. Math., 135, 1 (1908).
7. Galerkin, B. G., "Rods and Plates. Series Occurring
in Various Problems of Elastic Equilibrium of Rods
and Plates," Vestnik Inzhenerov i Tekhnikov, 19, 897
(1915). Translation 63-18924, Clearinghouse, Fed. Sci.
Tech. Info., Springfield, VA.
8. Frazer, R. A., W. P. Jones and S. W. Skan, "Approxi-
mations to Functions and to the Solutions of Differen-
tion Equations," Gt. Brit. Air Ministry Aero. Res.
Comm. Tech. Rept. 1, 517 (1937).
9. Lanczos, C., "Trigonometric Interpolation of Em-
pirical and Analytic Functions," J. Math. Phys., 17,
123 (1938).
10. Hahn, W., "tUber Orthogonalpolynome, die q-Differen-

zengleichungen genfigen," Math. Nachrichten, 2, 4
11. Kantorovich, L. V., and V. I. Krylov, Approximate
Methods in Higher Analysis, Gostekhizdat (1949).
English translation, Interscience, New York (1958).
12. Crandall, S. H., Engineering Analysis, McGraw-Hill,
New York (1956).
13. Lanczos, C., Applied Analysis, p. 504, Prentice-Hall,
Englewood Cliffs, NJ (1956).
14. Kopal, Z., Numerical Analysis, Second Edition. Chap-
man & Hall, London (1961).
15. Abramowitz, M., and I. Stegun, Handbook of Mathe-
matical Functions, National Bureau of Standards
Applied Mathematics Series 55, Washington, DC
16. Finlayson, B. A., and L. E. Scriven, "The Method of
Weighted Residuals-A Review," Appl. Mech. Rev.,
19, 735 (1966).
17. Snyder, L. J., and W. E. Stewart, "Velocity and Pres-
sure Profiles for Newtonian Creeping Flow in Regu-
lar Packed Beds of Spheres," AIChE J., 12, 167, 620
18. Villadsen, J. V., and W. E. Stewart, "Solution of
Boundary Value Problems by Orthogonal Colloca-
tion," Chem. Eng. Sci., 22, 1483 (1967); 23, 1515
19. Krasnosel'skii, M. A., G. M. Vainikko, P. P. Zabreiko,
Ya.B. Rutitskii, and V.Ya. Stetsenko, Approximate
Solution of Nonlinear Operator Equations, Russian
Edition, Moscow (1969). English translation by D.
Louvish, Wolters-Noordhoff, Groningen, The Nether-
lands (1972).
20. Stewart, W. E., and J. V. Villadsen, "Graphical Calcu-
lation of Multiple Steady States and Effectiveness
Factors for Porous Catalysts," AIChE J., 15, 28, 961
21. Stewart, W. E., "Solution of Transport Problems by
Collocation Methods," Chapter 4 in Lectures in Trans-
port Phenomena, by R. B. Bird, E. N. Lightfoot, T. W.
Chapman and W. E. Stewart, AIChE Continuing
Education Series No. 4 (1969).
22. Finlayson, B. A., "Packed Bed Reactor Analysis by
Orthogonal Collocation," Chem. Eng. Sci., 26, 1081
23. Stroud, A. H., Approximate Calculation of Multiple
Integrals, Prentice-Hall, Englewood Cliffs, NJ (1971).
24. Finlayson, B. A., The Method of Weighted Residuals
and Variational Principles, Academic Press, New
York (1972).
25. Kjaer, J., Computer Methods in Catalytic Reactor
Calculations, Haldor Tops6e, Vedvaek, Denmark
26. Stewart, W. E., and J. P. Serensen, "Transient Re-
actor Analysis by Orthogonal Collocation," Fifth
European Symposium on Chemical Reaction Engineer-
ing, pp. B8-75, C2-8, C2-9, Elsevier, Amsterdam
27. De Boor, C., and B. Swartz, "Collocation at Gaussian
Points," SIAM J. Numer. Anal., 10, 582 (1973).
28. Sorensen, J. P., E. W. Guertin, and W. E. Stewart,
"Computational Models for Cylindrical Catalyst
Particles," AIChE J., 19, 969, 1286 (1973); 21, 206

FALL 1984

29. Serensen, J. P., M. S. Willis, and W. E. Stewart,
"Effects of Column Asymmetry on Thermal Diffusion
Separations," J. Chem. Phys., 59, 2676 (1973).
30. Young, L. C., and B. A. Finlayson, "Axial Dispersion
in Nonisothermal Packed Bed Chemical Reactors,"
Ind. Eng. Chem. Fund., 12, 412 (1973).
31. Finlayson, B. A., "Orthogonal Collocation in Chemi-
cal Reaction Engineering," Catal. Rev., 10, 69 (1974).
32. Sorensen, J. P., and W. E. Stewart, "Computation
of Forced Convection in Slow Flow through Ducts and
Packed Beds-I. Extensions of the Graetz Problem,"
Chem. Eng. Sci., 29, 811 (1974).
33. Serenson, J. P., and W. E. Stewart, "Computation of
Forced Convection in Slow Flow through Ducts and
Packed Beds--III. Heat and Mass Transfer in a
Cubic Array of Spheres," Chem. Eng. Sci., 29, 827
34. Carey, C. F., and B. A. Finlayson, "Orthogonal Col-
location on Finite Elements," Chem. Eng. Sci., 30, 587
35. Caban, R., and T. W. Chapman, "Rapid Computation
of Current Distribution by Orthogonal Collocation,"
J. Electrochem. Soc., 123, 1036 (1976).
36. Stewart, W. E., and J. P. Serensen, "Sensitivity and
Regression of Multicomponent Reactor Models,"
Fourth International Symposium on Chemical Re-
action Engineering, DECHEMA, Frankfurt, 1-12
37. Guertin, E. W., J. P. Sorensen, and W. E. Stewart,
"Exponential Collocation of Stiff Reactor Models,"
Comp. Chem. Engng., 1, 197 (1977).
38. Villadsen, J. V., and M. L. Michelsen, Solution of
Diferential Equation Models by Polynomial Approxi-
mation, Prentice-Hall, Englewood Cliffs, NJ (1978).
39. Stewart, W. E., J. P. Sorensen, and B. C. Teeter,
"Pulse-Response Measurement of Thermal Properties
of Small Catalyst Pellets," Ind. Eng. Chem. Fundam.,
17, 221 (1978); 18, 438 (1979).
40. Finlayson, B. A., Nonlinear Analysis in Chemical
Engineering, McGraw-Hill, New York (1980).
41. Serensen, J. P., and W. E. Stewart, "Structural
Analysis of Multicomponent Reactor Models: Part I.
Systematic Editing of Kinetic and Thermodynamic
Values," AIChE J., 26, 98 (1980).
42. Wong, K. T., and R. Luus, "Model Reduction of High-
Order Multistage Systems by the Method of
Orthogonal Collocation," Can. J. Chem. Eng., 58, 382
43. Ascher, U., J. Christiansen, and R. D. Russell, "Col-
location Software for Boundary Value ODEs," ACM
Trans. on Math. Software, 7, 209 (1981).
44. Caban, R., and T. W. Chapman, "Solution of Bound-
ary-Layer Transport Problems by Orthogonal Col-
location," Chem. Eng. Sci., 36, 849 (1981).
45. Stewart, W. E., and J. P. Serensen, "Computer-Aided
Modelling of Reaction Networks," in Foundations of
Computer-Aided Process Design, R. S. H. Mah and
W. D. Seider, Eds., Engineering Foundation, New
York, II, 335 (1981).
46. Stewart, W. E., and J. P. Serensen, "Bayesian
Estimation of Common Parameters from Irregular
Multi-Response Data," Technometrics, 23, 131 (1981);

24, 91 (1982).
47. Miller, K., and R. N. Miller, "Moving Finite Elements.
I, II.," SIAM J. Numer. Anal., 18, 1019, 1033 (1981).
48. Serensen, J. P., and W. E. Stewart, "Collocation
Analysis of Multicomponent Diffusion and Reaction
in Porous Catalysts," Chem. Eng. Sci., 37, 1103
49. Sorensen, J. P. Simulation, Regression, and Control
of Chemical Reactors by Collocation Techniques. Dr.
Techn. Thesis, Technical University of Denmark,
Lyngby (1982).
50. Co, A., and W. E. Stewart, "Viscoelastic Flow from
a Tube into a Radial Slit," AIChE J., 28, 644 (1982).
51. Wang, J. C., and W. E. Stewart, "New Descriptions
of Dispersion in Flow through Tubes: Convolution
and Collocation Methods," AIChE J., 29, 493 (1983).
52. Wang, J. C., and W. E. Stewart, Coupled Reactions
and Dispersion in Pulse-Fed Tubular Reactors, Paper
57e, AIChE National Meeting, Los Angeles (1982).
53. Cho, Y. S., and B. Joseph, "Reduced-Order Steady-
State and Dynamic Models for Separation Processes,"
AIChE J., 29, 261, 270 (1983).
54. Davis, M. E., Numerical Methods and Modelling for
Chemical Engineers, Wiley, New York (1984).
55. Stewart, W. E., K. L. Levien, and M. Morari, "Col-
location Methods in Distillation," in Proceedings of
the Second International Conference on Foundations
of Computer-Aided Process Design, A. W. Wester-
berg and H. H. Chien, Eds., CACHE Corporation,
New York (1984), page 535.
56. Nirschl, J. P., and W. E. Stewart, "Computation of
Viscoelastic Flow in a Cylindrical Tank with a Rotat-
ing Lid," J. Non-Newtonian Fluid Mech. (in press).
57. Stewart, W. E., K. L. Levien, and M. Morari, "Simu-
lation of Fractionation by Orthogonal Collocation,"
Chem. Eng. Sci. (in press).

REVIEW: Fluid Mechanics
Continued from page 199.
difficult phenomena to quantitate, this chapter pro-
vides a reasonable summary of the key features of
this topic. Again the emphasis is primarily on
the design aspects. It provides, in effect, a point-
of-departure for someone who wishes to gain an
initial insight into the area.
In summary, therefore, the authors have
written a comprehensive text that covers those
unit operations which have a unique basis in fluid,
dynamics. The book is generally well written and
liberally laced with pertinent detailed examples
drawn from industrial situations. Although the
material covered extends well beyond that normal-
ly found in a first course in fluid dynamics, it does
include the requisite essence and could easily be
used as a text in such a course. I suspect, however,
that it will find much more use as a handy refer-
ence for the practicing engineer. I do hope that
the authors complete the trilogy. O]


Continued from page 173.
this method. However, emphasis is placed on when
such an approximation can be invoked by develop-
ing ideas on multiple time scale analysis. The
method is illustrated by considering shrinking
unreacted core model in gas-solid reactions and
evaporation of a drop in a stagnant fluid.
Additional topics covered in the course are
listed in Table 3. These include non-Newtonian
fluid flow, turbulent flow, some cases of exact
solution of Navier-Stokes equations, evaluations
of Nussclt and Sherwood numbers in laminar and
turbulent flow, and some cases of mass transfer
where no analogs in heat transfer are available.
Finally, some examples of macroscopic balances
are also solved.
The course is essentially a survey in transport
processes. An attempt is made to give students a
thorough understanding of the topics covered, so
that they can formulate the necessary differential
equations. They are given sufficient insight into
some of the powerful tools available to analyze
and solve these equations. It is emphasized that
the answers obtained must be checked to see if
the assumptions made in deriving them are ful-
filled. It is also stressed that in most cases, knowing
the distribution of velocity, temperature, and con-
centration is not as important as knowing the
fluxes at the interface. These in turn are then'
related to friction factor, Nusselt, and Sherwood
numbers respectively. The course as described
here has been well received by the students. Good
students tend to feel they are ready to tackle more
difficult topics. Terminal master's students feel
they have a solid foundation in transport phe-
nomena on which they can continue to build their
practical experience. O
1. Bird, R. B., W. E. Stewart, E. N. Lightfoot, Transport
Phenomena, 7th printing, Wiley, New York, 1960.
2. Bird, R. B., W. E. Stewart, E. N. Lightfoot, and
T. W. Chapman, AIChE Continuing Education Series,
No. 4, 1969.
3. "Selected Topics in Transport Phenomena," Chem.
Eng. Symp. Ser., No. 58, 61, 1965.
4. Denn, M. M., Process Fluid Mechanics, Prentice-Hall,
Inc., Englewood Cliffs, N.J., 1980.
5. Schlichting, H., Boundary-Layer Theory, 7th Edition,
McGraw-Hill, New York, N.Y., 1979.
6. Slattery, J. C., Momentum, Energy and Mass Transfer
in Continue, Robert E. Kreiger Publishing Company,
2nd Edition, Huntington, N.Y., 1981.

Continued from page 179.
discussion of simple numerical methods for the
computation of eigenvalues. In order to further
establish the importance of the variational
methods, the finite element method is briefly out-
lined at the end of the course, using tools that
the students already possess.

Our course attempts to introduce the students
to the essentials of linear algebra and, at the
same time, to convey the fact that these elegant
results can be applied to a wide range of engineer-
ing problems. Significant emphasis is placed upon
the development of basic and efficient compu-
tational methods. There is hardly any need to
stress again the importance of exposing the chemi-
cal engineering graduate student to the basics of
numerical analysis. Our experience indicates that
the essentials of computational linear algebra can
be successfully integrated into an applied mathe-
matics course. A large number of students go on
to take a rigorous numerical analysis course given
by the Mathematical Sciences Department at Rice,
which covers methods for the solution of ordinary
and partial differential equations. They have dis-
covered that their background in computational
linear algebra was adequate.
We plan to introduce still another computer
project in future offerings of this course, in order
to familiarize the students with some of the most
useful methods for the numerical computation
of eigenvalues and eigenvectors of large matrices.
The emphasis will again be on the understanding
of the physical problem and the resulting mathe-
matical one, and on the study of the relative ad-
vantages of the various algorithms. E

The author wishes to acknowledge the in-
fluence of his mentors, Rutherford Aris, Neal
Amundson and D. Ramkrishna, who have shown
him that applied mathematics can also be enjoy-
able and who have shaped his ideas about teach-

1. Amundson, N. R., Chem. Eng. Edn., 3, 174 (1969).
2. Ramkrishna, D., Chem. Eng. Edn., 13, 172 (1979).
3. Wei, T. and C. D. Prater, Adv. Catalysis, 13, 204

FALL 1984

Continued from page 163.
also enjoy seeing the connection between the non-
existence of a solution determined by the applica-
tion of a mathematical theorem to a physically
generated problem to be equivalent to a violation
of a basic conservation principle such as mass,
energy, or momentum. This helps them develop a
further appreciation for the practical importance
and usefulness of mathematical theorems. When
we present partial differential equations, we begin
by emphasizing the characteristics of the "typical"
problem which can readily be solved by pointing
out the restrictions that must be placed on the
shape of the domain, the boundary conditions, and
the form of the operator. This brings together
many of the concepts developed over the first two
semesters. Then we proceed to analyze a number
of specific problems which violate in one form or
another these restrictions and show that the
manipulations that must be performed to make
these problems solvable, which might have ap-
peared as "tricks," can be rationalized and under-
stood based upon their in-depth knowledge of the
structure and properties of vector spaces. Thus,
the students have developed a deeper appreciation
for the key role played by mathematical theory in
being a creative applied mathematician.
The third semester covers the solution struc-
tures of nonlinear equations and the perturbation
methods used to analyze them. Three different
areas of perturbation analysis are studied: bound-
ary layer theory, bifurcation theory, and finite ele-
ment-based numerical methods. The semester
starts with a general introduction to perturba-
tion techniques. Following a rigorous definition
of order and asymptotic series, a variety of ex-
pansion techniques can be seen to be different
formalisms for singular perturbation.
The bulk of the course covers bifurcation
theory: a set of perturbation techniques for de-
termining the multiple solutions to nonlinear
algebraic, ordinary differential, and partial differ-
ential equations, their stability, and their de-
pendence on parameters. Theoretical concepts de-
veloped in the first two semesters, such as Fred-
holm's Alternative and the Implicit Mapping
Theorem, are central to bifurcation analysis. Spe-
cific examples from fluid mechanics and reactor
design show how the theory may be used to
analyze transitions between the multiple steady
states which frequently arise.
The course concludes by covering computer

implementation of perturbation techniques using
the Finite Element Method. Computer-aided
analysis relies heavily on the same local ex-
pansions covered earlier in the course. Any ana-
lytical technique can be implemented on a com-
puter, but the ability to trade off more steps and
unknowns for simpler calculations at each step en-
courages the use of lower order expansions and
local basis functions rather than, for example,
eigenfunction expansions. Using linear operator
notation highlights the similarities between com-
puter-based techniques for analyzing the ordinary
differential equations that arise upon discretizing
partial differential equations and analytical per-
turbation techniques for studying the original
partial differential equations.
Though it is difficult to find a text that presents
the necessary concepts in the manner we have just
described, it is important for the students to learn
to read applied mathematics literature. Therefore,
we do require a few texts and assign correspond-
ing sections from them. For the first semester
course, we have used either Mathematical Founda-
tions in Engineering and Science by Michel and
Herget or Linear Operator Theory in Engineering
and Science by Naylor and Sell as the major text.
We make up our own homework problems, how-
ever, which include extending theoretical concepts
and proving theorems as well as solving problems
arising from chemical engineering applications.
For the section on matrices, readings from Mathe-
matical Methods in Chemical Engineering, Vol. I:
Matrices and Their Application by Amundson and
Linear Algebra and its Application by Strang are
assigned. For the section on metric spaces, we find
helpful supplemental reading in Green's Functions
and Boundary Value Problems by Stakgold and
Introductory Functional Analysis with Applica-
tions by Kreysig. In the second semester, the
aforementioned book by Stakgold is the major
text. Other references include Principles and
Techniques of Applied Mathematics by Friedman,
and the text by Naylor and Sell mentioned pre-
viously. For the third semester, the principal
texts are Perturbation Methods in Applied Mathe-
matics by Cole and Elementary Stability and Bi-
furcation Theory by loos and Joseph.
We are convinced that our approach to teach-
ing applied mathematics for chemical engineer-
ing graduate students has been very successful.



Despite the rigorous and initially abstract per-
spective, student reaction has been overwhelming-
ly favorable. Probably the primary reason for this
is that we try very hard to stress the "why" of
applied mathematics, so that the "how" of solving
problems is seen to follow logically and naturally
from an understandable conceptual framework.
The major criticism of our approach might be that
fewer specific techniques can be included because
of the time devoted to the underlying theory. How-
ever, we strongly believe that this is no real short-
coming because the students are now equipped to
learn a wider assortment of new techniques on
their own because they have the background
necessary to comprehend the basis of unfamiliar
methods. And this, after all, is the objective of
graduate education. O

Continued from page 165.
theory and its limitations and those of the
numerical procedure utilized to reach a solution.
The proliferation of engineering software houses
is alarming. Are they becoming the de facto engi-
neering companies of the future?
It appears that in the headlong rush to utilize
the computer, the art of creating a reasonable and
useful model of physical reality may be declining.
The measure of the sophistication of a mathemati-
cal model is not what you include but, rather,
what you leave out. However, the capability of
computers to crunch complicated differential
equations and systems of equations encourages
overly complex models that can conceal the sig-
nificant variables and their relationship.
Often, simple models and simple procedures
are all that are required for the problem at hand.
With the bewildering array of software being
marketed and the significant use of computer
design in industry, it is extremely important that
the student appreciate the roles of the various
levels of analysis in his work. Using a sledge
hammer when a tack hammer would suffice is a
cardinal sin which demonstrates a serious lack of
judgment and/or knowledge. Students are en-
couraged to keep it as simple as possible, con-
sistent with the results desired.
Concerning analysis itself, all too often the
student is faced with papers and texts that pre-
sent skimpy discussions of the physical aspects of
the model, and pages and pages devoted to solving
the resulting equations. They are both important,

especially when the model is not correct.
A good example of a meager discussion about
the physical basis of a model is the no slip
boundary condition of fluid mechanics. Consult a
modern text on fluid mechanics and it is probable
that this boundary condition is stated with no dis-
cussion, as if it were a self-evident truth. Consider
the student who has seen mercury flow in a glass
thermometer; would he not question the validity
of this statement? If Coulomb, Poisson, Navier,
and Stokes and others of similar scientific stature
debated this point during the 19th century [7],
does it not deserve some textbook discussion so
that the student can appreciate the turmoil that
is often encountered in creating a good physical
In addition to the current information ex-
plosion problem, misinformation is also trouble-
some. For example, in one year, in just one journal,
at least three authors [8, 9, 10] discussed the mis-
application of Le Chatelier's Principle, while
Pauling [5] describes some recent textbook errors
he has detected.
To help the students develop confidence in
their understanding of the literature and their
creative and analytical abilities, they are required
to rigorously justify the rationales for their de-
signs, the bases for their design calculations, and
the expected accuracies of their results.
If our students achieve these three primary
goals, then I have no doubt that they will be able
to design the bioengineering and materials pro-
cesses of the future as well as the innovative petro-
chemical processes required to retain the vitality
of the chemical process industries. O
1. Kelleher, E. G. and N. Kafes, Chem. Eng. Ed., Fall,
1972: 178-180.
2. Kelleher, E. G., Chem. Eng. Prog. 68, No. 8: 35-36.
August, 1972.
3. Reid, W. C., Chemical Engineering, Dec. 14, 1970. 147-
4. Strutt, J. W. (Lord Rayleigh), Scientific Papers, Vol.
1, pp. 196-198. Cambridge, University Press. 1899.
5. Pauling, L., Chemtech. 14, No. 6: 326-327. June 1984.
6. Churchill, S. W., Chem. Eng. Prog. 66, No. 7: 86-90.
July 1970.
7. Goldstein, S. (ed.), Modern Developments in Fluid
Dynamics, Vol. 2, pp. 676-680. New York, Dover
Publications. 1965.
8. Treptow, R. S., J. Chem. Ed. 57, No. 6: 417-420. June
9. Mellon, E. K., J. Chem. Ed. 56, No. 6: 380-381. June
10. Bodner, G. M., J. Chem. Ed. 57, No. 2: 117-119. Febru-
ary 1980.

FALL 1984


I I k

1 -

I1 :1 1L'i





=! *-"1

Chemical Engineering at




I.G. DALLA LANA, Ph.D. (Minnesota): Kinetics, Heterogeneous

D.G. FISHER Ph.D. (Michigan): Process Dynamics and Control,
Real-Time Computer Applications.

M.R. GRAY Ph.D. (Cal. Tech.): Chemical Kinetics,
Characterization of Complex Organic Mixtures, Bioengineering,
Natural Gas Processing.

D.T. LYNCH, Ph.D. (Alberta): Catalysis, Kinetic Modelling,
Numerical Methods, Computer-Aided Design.

J. MARTIN-SANCHEZ, Ph.D. (Barcelona): Process Control,
Adaptive-Predictive Control, Systems Theory.

J.H. MASLIYAH Ph.D. (British Columbia): Transport Phenomena,
Numerical Analysis, Particle-Fluid Dynamics.

A.E. MATHER, Ph.D. (Michigan): Phase Equilibria, Fluid
Properties at High Pressures, Thermodynamics.

A.J. MORRIS, Ph.D. (Newcastle-Upon-Tyne): Process Control,
Real Time Use of Microcomputers, Process Simulation.

K. NANDAKUMAR, Ph.D. (Princeton): Transport Phenomena,
Process Simulation, Computational Fluid Dynamics.

W.K. NADER Dr. Phil. (Vienna) Heat Transfer, Transport
Phenomena in Porous Media, Applied Mathematics.

F.D. OTTO, (CHAIRMAN), Ph.D. (Michigan): Mass Transfer,
Gas-Liquid Reactions, Separation Processes, Heavy Oil Upgrading.

Modelling and Economics.

Thermal and Volumetric Properties of Fluids, Phase Equilibria,

J.T. RYAN Ph.D. (Missouri): Energy Economics and Supply,
Porous Media.

S.L. SHAH Ph.D. (Alberta): Linear Systems Theory, Adaptive
Control, Stability Theory, Stochastic Control.

S.E. WANKE Ph.D. (California-Davis): Catalysis, Kinetics.

R.K. WOOD Ph.D. (Northwestern): Process Dynamics and
Identification, Control of Distillation Columns, Computer-Aided

For further information contact:

Department of Chemical Engineering,
University of Alberta,
Edmonton, Canada T6G 2G6



The Chemical Engineering Department at the University of Arizona is young and dynamic with a fully accredited
undergraduate degree program and M.S. and Ph.D. graduate programs. Financial support is available through
government grants and contracts, teaching, and research assistantships, traineeships and industrial grants. The
faculty assures full opportunity to study in all major areas of chemical engineering. Graduate courses are offered
in most of the research areas listed below.


University of Florida, 1984
Liquid Solution Theory, Solution Thermodynamics
Polyelectrolyte Solutions

WILLIAM P. COSART, Assoc. Professor
Ph.D., Oregon State University, 1973
Heat Transfer in Biological Systems, Blood Processing

JOSEPH F. GROSS, Professor
Ph.D., Purdue University, 1956
Boundary Layer Theory, Pharmacokinetics, Fluid Mechanics and
Mass Transfer in The Microcirculation, Biorheology

SIMON P. HANSON, Asst. Professor
Sc.D., Massachusetts Inst. Technology, 1982
Coupled Transport Phenomena in Heterogeneous Systems, Com-
bustion and Fuel Technology, Pollutant Emissions, Separation
Processes, Applied Mathematics

GARY K. PATTERSON, Professor and Head
Ph.D., University of Missouri-Rolla, 1966
Rheology, Turbulent Mixing, Turbulent Transport, Numerical
Modelling of Transport

DON H. WHITE, Professor

THOMAS W. PETERSON, Assoc. Professor
Ph.D., California Institute of Technology, 1977
Atmospheric Modeling of Aerosol Pollutants, Long-Range Pollutant
Transport, Particulate Growth Kinetics, Combustion Aerosols

Ph.D., Iowa State University, 1962
Simulation and Design of Crystallization Processes, Nucleation
Phenomena, Particulate Processes, Explosives Initiation Mechanisms

THOMAS R. REHM, Professor
Ph.D., University of Washington, 1960
Mass Transfer, Process Instrumentation, Packed Column Distillation,
Computer Aided Design

FARHANG SHADMAN, Assoc. Professor
Ph.D., University of California-Berkeley, 1972
Reaction Engineering, Kinetics, Catalysis, Coal Conversion

JOST O. L. WENDT, Professor
Ph.D., Johns Hopkins University, 1968
Combustion Generated Air Pollution, Nitrogen and Sulfur Oxide
Abatement, Chemical Kinetics, Thermodynamics, Interfacial Phe-

Ph.D., Iowa State University, 1949
Polymers Fundamentals and Processes, Solar Energy, Microbial
and Enzymatic Processes

Tucson has an excellent climate and
many recreational opportunities. It
is a growing, modern city of
450,000 that retains much of Ihe
old Southwestern atmosphere.

For further information.
write to:
Dr. Farhang Shadma.n
Graduate Stady Con m ittee
Department of
Chem ical Engitine ring
ULniversity, of A rizona.
Tucson, A r:izona 85 ^21

The Uniers.i/ of Ar.zona .. an
equal opporlunily educal.onal
instftul;on'equal opporluntry employer



Graduate Programs
for M.S. and Ph.D. Degrees
in Chemical and Bio Engineering

Research Specializations Include:

Our excellent facilities for research and teaching are
complemented by a highly-respected faculty:
James R. Beckman, University of Arizona, 1976
Lynn Bellamy, Tulane University, 1966
Neil S. Berman, University of Texas, 1962
Llewellyn W. Bezanson, Clarkson College, 1983
Timothy S. Cale, University of Houston, 1980
William J. Crowe, University of Florida, 1969 (Adjunct)
William J. Dorson, Jr., University of Cincinnati, 1967
R. Leighton Fisk, MD, University of Alberta, Canada, 1972 (Adjunct)
K. Kumar Gidwani, New York University, 1978 (Adjunct)
Eric J. Guilbeau, Louisiana Tech University, 1971
Robert Kabel, Pennsylvania State University, (Visiting)
James T. Kuester, Texas A&M University, 1970
Gregory Raupp, University of Wisconsin, 1984
Castle O. Reiser, University of Wisconsin, 1945 (Emeritus)
Vernon E. Sater, Illinois Institute of Technology, 1963
Robert S. Torrest, University of Minnesota, 1967
Bruce C. Towe, Pennsylvania State University, 1978
Imre Zwiebel, Yale University, 1961
Fellowships and teaching and research assistantships are
available to qualified applicants.
ASU is in Tempe, a city of 120,000, part of the greater Phoenix
metropolitan area. More than 38,000 students are enrolled in
ASU's ten colleges; 10,000 of whom are in graduate study.
Arizona's year-round climate and scenic attractions add to ASU's
own cultural and recreational facilities.
Imre Zwiebel, Chairman,
Department of Chemical and Bio Engineering
Arizona State University, Tempe, AZ 85287





Auburn t r |
Engineering W* L.A



R. P. CHAMBERS (University of California, 1965) Biomedical/Biochemical Engineering Process Simulation
C. W. CURTIS (Florida State University, 1976) Biomass Conversion Reaction Engineering
J. A. GUIN (University of Texas, 1970) Coal Conversion Reaction Kinetics
L. J. HIRTH (University of Texas, 1958) Environmental Pollution Separations
A. C. T. HSU (University of Pennsylvania, 1953) Heterogeneous Catalysis Surface Science
Y. Y. LEE (Iowa State University, 1972) Oil Processing Transport Phenomena
R. D. NEUMAN (Inst. Paper Chemistry, 1973) Process Design and Control Thermodynamics
T. D. PLACEK (University of Kentucky, 1978) Interfacial Phenomena Pulp and Paper Engineering
C. W. ROOS (Washington University, 1951)
A. R. TARRER (Purdue University, 1973) THE PROGRAM
B. J. TATARCHUK (University of Wisconsin, 1981)
D. L. VIVES (Columbia University, 1949) The Department is one of the fastest growing in the Southeast and
D. C. WILLIAMS (Princeton University, 1980) offers degrees at the M.S. and Ph.D. levels. Research emphasizes
both experimental and theoretical work in areas of national
FOR INFORMATION AND APPLICATION, WRITE interest, with modern research equipment available for most all
Dr. R. P. Chambers Head types of studies. Generous financial assistance is available to
Chemical Engineering qualified students.
Auburn University, AL 36849
Auburn University is an Equal Opportunity Educational Institution


-- I~







Ph.D., M.S., & M.E. Degrees
ChE. Masters for Chemists Program
Research Programs

Biomedical Engineering
Coal Gasification
* Faculty

Electrochemical Engineering
Fluid Mechanics

Fossil Fuels Recovery
Thermochemistry &

D. H. Barker, (Ph.D., Utah, 1951)
C. H. Bartholomew, (Ph.D., Stanford, 1972)
M. W. Beckstead, (Ph.D., Utah, 1965)
D. N. Bennion, (Ph.D., Berkeley, 1964)
|B. S. Brewster, (Ph.D., Utah, 1979)
J. J. Christensen, (Ph.D., Carnegie Inst. Tech, 1958)
R. W. Hanks, (Ph.D., Utah, 1961)

W. C. Hecker, (Ph.D., U.C. Berkeley,
P. O. Hedman, (Ph.D., BYU, 1973)
J. L. Oscarson, (M.S., Michigan, 1972)
R. L. Rowley, (Ph.D., Michigan State,
P. J. Smith, (Ph.D., BYU, 1979)
L. D. Smoot, (Ph.D., Washington, 1960)
K. A. Solen, (Ph.D., Wisconsin, 1974)

Beautiful campus located in the rugged Rocky Mountains
Financial aid available
Address Inquiries to: Brigham Young University, Dr. Douglas N. Bennion,
Chemical Engineering Dept., 350 CB, Provo, Utah 84602
FALL 1984


,... ~ -.

*.-.-.- ~


The Department offers programs leading to the
M.Sc. and Ph.D. degrees (full-time) and the M.
Eng. degree (part-time) in the following areas:

Thermodynamics-Phase Equilibria
Heat Transfer and Cryogenics
Kinetics and Combustion
Multiphase Flows in Pipelines
Fluidization-Grid Region Transport Phenomena
Environmental Engineering
Ultra Pyrolysis of Heavy Oils
Enhanced Oil Recovery
In-Situ Recovery of Bitumen and Heavy Oils
Natural Gas Processing and Gas Hydrates
Antibiotic Production in Immobilized Cells
Biorheology and Biochemical Engineering
Computer Control and Optimization of
Engineering Processes

Fellowships and Research Assistantships are
available to qualified applicants.


The University is located in the City of Calgary,
the oil capital of Canada, the home of the world
famous Calgary Stampede and the 1988 Winter
Olympics. The city combines the traditions of the
Old West with the sophistication of a modern
urban centre. Beautiful Banff National Park is
110 km west of the City and the ski resorts of the
Banff, Lake Louise and Kananaskis areas are
readily accessible.

Dr. M. F. Mohtadi, Chairman
Graduate Studies Committee
Dept. of Chemical & Petroleum Eng.
The University of Calqary
Calgary, Alberta T2N 1N4 Canada


(Wash. U.)
(Birm. U.K.)
(W. Ont.)
(Penn. State)
(Imp. Coll. U.K.)
(Birm. U.K.)


I ~ I







... offers graduate programs leading to the Master
of Science and Doctor of Philosophy. Both pro-
grams involve joint faculty-student research as
well as courses and seminars within and outside
the department. Students have the opportunity
to take part in the many cultural offerings of
the San Francisco Bay Area, and the recreational
activities of California's northern coast and moun-

Alexis T. Bell (Chairman)
Harvey W. Blanch
Elton J. Cairns
Morton M. Denn
Alan S. Foss
Simon L. Goren
Edward A. Grens
Donald N. Hanson
Dennis W. Hess
C. Judson King
Scott Lynn
James N. Michaels
John S. Newman
Eugene E. Petersen
John M. Prausnitz
Clayton J. Radke
Jeffrey A. Reimer
David S. Soong
Charles W. Tobias
Charles R. Wilke
Michael C. Williams

Department of Chemical Engineering
Berkeley, California 94720



Course Areas
Applied Kinetics and Reactor Design
Applied Mathematics
Colloid and Interface Processes
Fluid Mechanics
Heat Transfer
Mass Transfer
Process Dynamics
Semiconductor Device Fabrication
Separation Processes
Transport Processes in Porous Media

UC Davis, with 19,000 students, is one of the major
campuses of the University of California system and
has developed great strength in many areas of the
biological and physical sciences. The Department of
Chemical Engineering emphasizes research and a pro-
gram of fundamental graduate courses in a wide variety
of fields of interest to chemical engineers. In addition,
the department can draw upon the expertise of faculty
in other areas in order to design individual programs
to meet the specific interests and needs of a student,
even at the M.S. level. This is done routinely in the areas
of environmental engineering, food engineering, bio-
chemical engineering and biomedical engineering.
Excellent laboratories, computation center and
electronic and mechanical shop facilities are available.
Fellowships, Teaching Assistantships and Research
Assistantships (all providing additional summer support
if desired) are available to qualified applicants.

Degrees Offered
Master of Science
Doctor of Philosophy

RICHARD L. BELL, University of Washington
Mass Transfer, Biomedical Applications
ROGER B. BOULTON, University of Melbourne
Enology, Fermentation, Filtration, Process Control
BRIAN G. HIGGINS, University of Minnesota
Fluid Mechanics, Coating Flows, Interfacial
Phenomena, Fiber Processes and Refining
ALAN P. JACKMAN, University of Minnesota
Environmental Engineering, Transport Phenomena
BEN J. McCOY, University of Minnesota
Separation and Transport Processes
AHMET N. PALAZOGLU, Rennsselaer Polytechnic
Process Synthesis and Control
ROBERT L. POWELL, The Johns Hopkins University
Rheology, Fluid Mechanics
DEWEY D. Y. RYU, Massachusetts Inst. of Technology
Biochemical Engineering, Fermentation
JOE M. SMITH, Massachusetts Institute of Technology
Applied Kinetics and Reactor Design
PIETER STROEVE, Massachusetts Institute of Technology
Mass Transfer, Colloids, Biotechnology
STEPHEN WHITAKER, University of Delaware
Fluid Mechanics, Interfacial Phenomena, Transport
Processes in Porous Media

Davis and Vicinity
The campus is a 20-minute drive from Sacramento
and just over an hour away from the San Francisco
Bay area. Outdoor sports enthusiasts can enjoy water
sports at nearby Lake Berryessa, skiing and other alpine
activities in the Sierra (2 hours from Davis). These rec-
reational opportunities combine with the friendly in-
formal spirit of the Davis campus to make it a pleasant
place in which to live and study.
Married student housing, at reasonable cost, is
located on campus. Both furnished and unfurnished
one- and two-bedroom apartments are available. The
town of Davis (population 36,000) is adjacent to the
campus, and within easy walking or cycling distance.

For further details on graduate study at Davis, please
write to:
Graduate Advisor
Chemical Engineering Department
University of California
Davis, California 95616
or call (916) 752-0400





UCLA's Chemical Engineering Depart-
ment maintains academic excellence in its
graduate programs by offering diversity in
both curriculum and research opportunities.
The department's continual growth is demon-
strated by the newly established Institute for
Medical Engineering and the National Center
for Intermedia Transport Research, adding to
the already wide spectrum of research

Fellowships are available for outstand-
ing applicants. A fellowship includes a waiver
of tuition and fees plus a stipend

Located five miles from the Pacific
Coast, UCLA's expansive 417 acre campus
extends from Bel Air to Westwood Village.
Students have access to the highly regarded
sciences programs and to a variety of expe-
riences in theatre, music, art and sports on

Admissions Officer
Chemical Engineering Department
NGELES 5405 Boelter Hall
Los Angeles CA 90024
Los Angeles, CA 90024

D.T. Allen
Yoram Cohen
S. Fathi-Afshar
T.H.K. Frederking
S.K. Friedlander
E.L. Knuth

Ken Nobe
L.B. Robinson
0.I. Smith
W. D. Van Vorst
V. L. Vilker
A.R. Wazzan
F.E. Yates

Thermodynamics and Cryogenics
Reverse Osmosis and Membrane Transport
Process Design and Systems Analysis
Polymer Processing and Rheology
Mass Transfer and Fluid Mechanics
Kinetics, Combustion and Catalysis
Electrochemistry and Corrosion
Biochemical and Biomedical Engineering
Aerosol and Environmental Engineering


*, ." .p *: ;- .tz '._ : T *, :.. ..2-":, .


Ph.D. (Waterloo)
Two Phase Flow, Reactor Safety,
Nuclear Fuel Cycle Analysis
and Wastes
Ph.D. (Purdue)
Biochemical Engineering, Fermentation
Nuclear Systems Design and Safety,
Nuclear Fuel Cycles, Two-Phase Flow,
Heat Transfer.
OWEN T. HANNA Ph.D. (Purdue)
Theoretical Methods, Chemical
Reactor Analysis, Transport
Ph.D. (Stanford)
Adsorption and Heterogeneous
Radiation Damage, Mechanics of
Ph.D. (Purdue)
Computer Control, Process
Dynamics, Real-Time Computing.

Ph.D. (Michigan)
(Dean of Engineering)
Boiling Heat Transfer.

Ph.D. (M.I.T.)
Radiation Effects in Solids, Energy
Related Materials Development.

Ph.D. (M.I.T.)
Bionuclear Engineering, Fusion
Reactors, Radiation Transport

Ph.D. (Caltech)
Chemical Reactor Design, Catalysis,
Energy Conversion, Air Pollution.

Ph.D. (Berkeley)
Transport Phenomena, Separation

Ph.D. (Princeton)
Process Control, Computer Control,
Process Identification.

The Department offers M.S. and Ph.D. de-
gree programs. Financial aid, including
fellowships, teaching assistantships, and re-
search assistantships, is available. Some
awards provide limited moving expenses.

One of the world's few seashore campuses,
UCSB is located on the Pacific Coast 100
miles northwest of Los Angeles and 330
miles south of San Francisco. The student
enrollment is over 14,000. The metropoli-
tan Santa Barbara area has over 150,000
residents and is famous for its mild, even

For additional information and applications,
write to:

Professor Sanjoy Banerjee, Chairman
Department of Chemical & Nuclear
University of California,
Santa Barbara, CA 93106


PROGRAM OF STUDY Distinctive features of study in
chemical engineering at the California Institute of Tech-
nology are the creative research atmosphere and the strong
emphasis on basic chemical, physical, and mathematical
disciplines in the program of study. In this way a student
can properly prepare for a productive career of research,
development, or teaching in a rapidly changing and ex-
panding technological society.
A course of study is selected in consultation with one
or more of the faculty listed below. Required courses are
minimal. The Master of Science degree is normally com-
pleted in one calendar year and a thesis is not required.
A special M.S. option, involving either research or an inte-
grated design project, is a feature to the overall program
of graduate study. The Ph.D. degree requires a minimum
of three years subsequent to the B.S. degree, consisting of
thesis research and further advanced study.

JAMES E. BAILEY, Professor
Ph.D. (1969), Rice University
Biochemical engineering; chemical reaction

Ph.D. (1964), University of Minnesota
Applied kinetics and catalysis; process control
and optimization; coal gasification.

ERIC HERBOLZHEIMER, Assistant Professor
Ph.D. (1979), Stanford University
Fluid mechanics and transport phenomena

L. GARY LEAL, Professor
Ph.D. (1969), Stanford University
Theoretical and experimental fluid mechanics;
heat and mass transfer; suspension rheology;
mechanics of non-Newtonian fluids.

Ph.D. (1977), University of Minnesota
Process control; process design

FINANCIAL ASSISTANCE Graduate students are sup-
ported by fellowship, research assistantship, or teaching
assistantship appointments during both the academic
year and the summer months. A student may carry a
full load of graduate study and research in addition to
any assigned assistantship duties. The Institute gives
consideration for admission and financial assistance to
all qualified applicants regardless of race, religion, or sex.
APPLICATIONS Further information and an application
form may be obtained by writing
Professor G. N. Stephanopoulos
Chemical Engineering
California Institute of Technology
Pasadena, California 91125
It is advisable to submit applications before February
15, 1985.

C. DWIGHT PRATER, Visiting Associate
Ph.D. (1951), University of Pennsylvania
Catalysis; chemical reaction engineering;
process design and development.
JOHN H. SEINFELD, Louis E. Nohl Professor,
Executive Officer
Ph.D. (1967), Princeton University
Air pollution; control and estimation theory.
FRED H. SHAIR, Professor
Ph.D. (1963), University of California, Berkeley
Plasma chemistry and physics: tracer studies
of various environmental and safety related
fessor Ph.D. (1978), University of Minnesota
Biochemical engineering; chemical reaction
Ph.D. (1958), University of New South Wales
Mechanical properties of polymeric materials;
theory of viscoelastic behavior; structure-
property relations in polymers.

W. HENRY WEINBERG, Chevron Professor
Ph.D. (1970), University of California, Berkeley
Surface chemistry and catalysis.

Oan Stereo

A New Release from Pittsburgh's High Performance Group





Modeling and design of chemical reactors. Deactivating catalysts. Flow
equipment. Laser induced effects.


Chemical Engineering

M.S. and Ph.D. Degrees

Stanley Cosgrove
Robert Delcamp
Joel Fried
Rakesh Govind
David Greenberg
Daniel Hershey
Sun-Tak Hwang
Yuen-Koh Kao
Soon-Jai Khang
Robert Lemlich
William Licht
Joel Weisman

pattern and mixing in chemical

Computer-aided design. Modeling and simulation of coal gasifiers, activated carbon columns, process unit
operations. Prediction of reaction by-products.

Viscoelastic properties of concen-
trated polymer solutions.
Thermodynamics, thermal analysis
and morphology of polymer blends.
Modeling and design of gas clean-
ing devices and systems.
Boiling. Stability and transport
properties of foam.
Longevity, basal metabolic rate,
and Prigogine's and Shannon's
entropy formulae.

Chairman, Graduate Studies Committee
Chemical & Nuclear Engineering, #171
University of Cincinnati
Cincinnati, OH 45221

Membrane gas separation, continuous membrane reactor column, equilibrium shift, pervaporation, dy-
namic simulation of membrane separators, membrane preparation and characterization.

ar sonl

O M.S. and Ph.D. programs
O Friendly atmosphere
O Vigorous research programs supported by
government and industry
O Proximity to Montreal and Ottawa
O Skiing, canoeing, mountain climbing and other
recreation in the Adirondacks
O Variety of cultural activities with two liberal arts
colleges nearby
O Twenty-one faculty working on a broad spectrum
of chemical engineering research problems

Research Projects are available in:
o Colloidal and interfacial phenomena
O Computer aided design
O Crystallization
O Electrochemical engineering and corrosion
O Heat transfer
0 Holographic interferometry
O Mass transfer
O Materials processing in space
O Optimization
O Particle separations
O Phase transformations and equilibria
O Polymer processing
O Process control
O Reaction engineering
0 Turbulent flows
O And more...

Financial aid in the form of:
O instructorships
0 fellowships
O research assistantships
0 teaching assistantships
O industrial co-op positions

6r For more details, please write to:
Dean of the Graduate School
Clarkson University
Potsdam, New York 13676


001 010

Graduate Coorcdnator
^. Chemical Engitneering Dept.
Clemson., SC 29651

FALL 1984 231
li: i

FAL 198 231iirii





A. J. Kidnay, Professor and Head; D.Sc., Colorado School
of Mines. Thermodynamic properties of coal-derived
liquids, vapor-liquid equilibria in natural gas systems,
cryogenic engineering.
J. H. Gary, Professor; Ph.D., University of Florida. Up-
grading of shale oil and coal liquids, petroleum re-
finery processing operations, heavy oil processing.

E. D. Sloan, Jr., Professor; Ph.D., Clemson University.
Phase equilibrium thermodynamics measurements of
natural gas fluids and natural gas hydrates, thermal
conductivity measurements for coal derived fluids,
adsorption equilibria measurements, stagewise pro-
J *cesses, education methods research.

V. F. Yesavage, Professor; Ph.D., University of Michigan.
Thermodynamic properties of fluids, especially re-
lating to synthetic fuels. Oil shale and shale oil
processing; numerical methods.

R. M. Baldwin, Associate Professor, Ph.D., Colorado
School of Mines. Mechanisms of coal liquefaction,
kinetics of coal hydrogenation, relation of coal
geochemistry to liquefaction kinetics, upgrading of
coal-derived asphaltenes, supercritical gas extrac-
tion of oil shale and heavy oil.

M. S. Graboski, Associate Professor; Ph.D., Pennsylvania
State University. Coal and biomass gasification pro-
cesses, gasification kinetics, thermal conductivity of
coal liquids, kinetics of SNG upgrading.

M. C. Jones, Associate Professor; Ph.D., University of
California at Berkeley. Heat transfer and fluid me-
chanics in oil shale retorting, radiative heat transfer
in porous media, free convection in porous media.

M. S. Selim, Associate Professor; Ph.D., Iowa State
University. Flow of concentrated fine particulate
.. "suspensions in complex geometries; Sedimenta-
'- ; tion of multisized, mixed density particle suspensions.
A 1-' A. L. Bunge, Assistant Professor; Ph.D., University of
~ . _-. California at Berkeley. Chromatographic processes,
t enhanced oil recovery, minerals leaching, liquid
membrane separations, ion exchange equilibria.

For Applications and Further Information
On M.S., and Ph.D. Programs, Write
S5 -i Chemical and Petroleum Refining Engineering
Colorado School of Mines
_- t- ,ii Golden, CO 80401

Colorado State University

CSU is situated in Fort Collins, a pleasant community of 80,000
people located about 65 miles north of Denver. This site is
adjacent to the foothills of the Rocky Mountains in full view
of majestic Long's Peak. The climate is excellent with 300 sunny
days per year, mild temperatures and low humidity. Opportunities
for hiking, camping, boating, fishing and skiing abound in the
immediate and nearby areas. The campus is within easy walking
or biking distance of the town's shopping areas and its new
Center for the Performing Arts.

Degrees Offered:
M.S. and Ph.D. programs in
Chemical Engineering

Financial Aid Available:
Faculty: Teaching and Research Assistantships paying
F-c4 a monthly stipend plus tuition reimbursement.
Larry Belfiore, Ph. D., I.
University of Wisconsin
Bruce Dale, Ph.D.
Purdue University
Jud Harper, Ph.D.,
Iowa State University
Naz Karim, Ph.D.,
University of Manchester
Terry Lenz, Ph.D.,
Iowa State University
Jim Linden, Ph.D.,
Iowa State University
Carol McConica, Ph.D.
Stanford University
Vince Murphy, Ph.D.,
University of
Massachusetts Research Areas:
Alternate Energy Sources
Biochemical Engineering
Chemical Vapor Deposition
Computer Simulation and Control
7 Fermentation
Food Engineering
Polymeric Materials
Porous Media Phenomena
Semiconductor Processing
Solar Cooling Systems
Thermochemical Cycles
Wastewater Treatment

For Applications and Further Information, write:
Professor Vincent G. Murphy
Department of Agricultural and Chemical Engineering
Colorado State University
Fort Collins, CO 80523

FALL 1984

Chemical Engineering at



A place to grow...

with active research in

biochemical engineering
applied mathematics/computer simulation
energy technology
environmental engineering
kinetics and catalysis
surface science
heat and mass transfer
polymer science
fluid dynamics
rheology and biorheology
reactor design
molecular thermodynamics/statistical mechanics

with a diverse intellectual climate-graduate students arrange
individual programs with a core of chemical engineering
courses supplemented by work in other outstanding Cornell
departments including

biological sciences
computer science
food science
materials science
mechanical engineering
business administration
and others

with excellent recreational and cultural opportunities in one
of the most scenic regions of the United States.

Graduate programs lead to the degrees of Doctor of
Philosophy, Master of Science, and Master of Engineering
(the M.Eng. is a professional, design-oriented program).
Financial aid, including attractive fellowships, is available.

The faculty members are:
Douglas S. Clark, Joseph F. Cocchetto, Claude Cohen, Robert
K. Finn, Keith E. Gubbins, Peter Harriott, Robert P. Merrill,
William L. Olbricht, Ferdinand Rodriguez, George F. Scheele,
Michael L. Shuler, Julian C. Smith, Paul H. Steen, William B.
Street, Raymond G. Thorpe, Robert L. Von Berg, Herbert F.

Professor Claude Cohen
Cornell University
Olin Hall of Chemical Engineering
Ithaca, New York 14853



of Delaware

awards three


degrees for

studies and

practice in

the artand

science of



An M.Ch.E. degree based upon course work and a thesis problem.
An M.Ch.E. degree based upon course work and a period of in-
dustrial internship with an experienced senior engineer in the
Delaware Valley chemical process Industries.
A Ph.D. degree for original work presented in a dissertation.

G. Astarita (1/2 time)
M. A. Barteau
C. E. Birchenall
K. B. Bischoff
C. D. Denson
P. Dhurjati
B. C. Gates
M. T. Klein
A. M. Lenhoff
R. L. McCullough
A. B. Metzner
J. H. Olson
M. E. Paulaitis
R. L. Pigford
T. W. F. Russell
S. I. Sander (Chairman)
J. M. Schultz
A. B. Stiles (1/2 time)
R. S. Weber
A. L. Zydney

Thermodynamics and Separ-
ation Process
Rheology, Polymer Science
and Engineering
Materials Science and
Fluid Mechanics, Heat and
Mass Transfer
Economics and Management
in the Chemical Process Industries
Chemical Reaction Engi-
neering, Kinetics and
Catalytic Science and
Biomedical Engineering-
Pharmacokinetics and
Biochemical Engineering-
Fermentation and Computer Control

Department of Chemical Engineering
University of Delaware
Newark, Delaware 19716





Gainesville, Florida
Graduate study leading to

Tim Anderson Thermodynamics, Semiconductor
Processing/ Seymour S. Block Biotechnology
Ray W. Fahien Transport Phenomena, Reactor
Design/ Gar Hoflund Catalysis, Surface Science
Lew Johns Applied Mathematics/ Dale Kirmse
Process Control, Computer Aided Design,
Biotechnology/ Hong H. Lee Reactor Design,
Catalysis/ Gerasimos K. Lyberatos Optimization,
Biochemical Processes/ Frank May Separations
Ranga Narayanan Transport Phenomena/ John
O'Connell Statistical Mechanics, Thermodynamics
Dinesh O. Shah Enhanced Oil Recovery,
Biomedical Engineering/ Spyros Svoronos
Process Control/ Robert D. Walker Surface
Chemistry, Enhanced Oil Recovery/ Gerald
Westermann-Clark Electrochemistry, Transport

Graduate Admissions Coordinator
Department of Chemical Engineering
University of Florida
Gainesville, Florida 32611




Graduate Studies in Chemical Engineering ...


Center for Disease Control
Commercial Center of the South
High Museum of Art
All Professional Sports
Major Rock Concerts and
Recording Studios
Sailing on Lake Lanier
Snow Skiing within two hours
Stone Mountain State Park
Atlanta Symphony
Ten Professional Theaters
Rambling Raft Race
White Water Canoeing within
one hour

For more information write:
Dr. Gary W. Poehlein
School of Chemical Engineering
Georgia Institute of Technology
Atlanta, Georgia 30332

Chemical Engineering
Air Quality Technology
Biochemical Engineering
Catalysis and Surfaces
Electrochemical Engineering
Energy Research and Conservation
Fine Particle Technology
Interfacial Phenomena
Mining and Mineral Engineering
Polymer Science and Engineering
Process Synthesis and
Pulp and Paper Engineering
Reactor Design
Transport Phenomena

Graduate Programs in Chemical Engineering

University of Houston

The Department of Chemical Engineering at the University
of Houston has developed research strength in a broad
range of areas:
Chemical Reaction Engineering, Catalysis
Biochemical Engineering
Electrochemical Systems
Semiconductor Processing
Interfacial Phenomena, Rheology
Process Dynamics and Control
Two-phase Flow, Sedimentation
Solid-liquid Separation
Reliability Theory
Petroleum Reservoir Engineering
The department occupies over 75,000 square feet and has over $3
million worth of experimental apparatus.
Financial support is available to full-time graduate students through re-
search assistantships and special industrial fellowships.
The faculty:

For more information or application forms write to:
Director, Graduate Admissions
Department of Chemical Engineering
University of Houston
Houston, Texas 77004
(Phone 713/749-4407)

N. R. Amundson
O. A. Asbjornsen
V. Balakotaiah
H.-C. Chang
E. L. Claridge
J. R. Crump
H. A. Deans
A. E. Dukler
R. W. Flumerfelt
C. F. Goochee
E. J. Henley
D. Luss
R. Pollard
H. W. Prengle, Jr.
J. T. Richardson
F. M. Tiller
F. L. Worley, Jr.



The Department of
Chemical Engineering
Graduate Programs in
The Department of
Chemical Engineering
leading to the degrees of








Francisco J. Brana-Mulero
Ph.D., University of Wisconsin, 1980
Assistant Professor
T. S. Jiang
PhD., Northwestern University, 1981
Asssitant Professor
John H. Keifer
Ph.D., Cornell University, 1961
G. Ali Mansoori
Ph.D., University of Oklahoma, 1969
Sohail Murad
Ph.D., Cornell University, 1979
Assistant Professor
Satish C. Saxena
Ph.D., Calcutta University, 1956
Stephen Szepe
Ph.D., Illinois Institute of Technology, 1966
Associate Professor
Raffi M. Turian
Ph.D., University of Wisconsin, 1964

The MS program, with its optional
thesis, can be completed in one year.
Evening M.S. can be completed in three years.
The department invites applications for
admission and support from all qualified candidates.
Special fellowships are available for minority students.
To obtain application forms or to request further
information write:

Process synthesis, operations research, optimal
process control, optimization of large systems,
numerical analysis, theory of nonlinear equations.
Interfacial Phenomena, multiphase flows, flow through
porous media, suspension rheology

Kinetics of gas reactions, energy transfer processes,
laser diagnostics

Thermodynamics and statistical mechanics of fluids,
solids, and solutions, kinetics of liquid reactions,
solar energy
Thermodynamics and transport properties of
fluids, computer simulation and statistical mechanics
of liquids and liquid mixtures
Transport properties of fluids and solids, heat and
mass transfer, isotope separation, fixed and fluidized
bed combustion
Catalysis, chemical reaction engineering, energy
transmission, modeling and optimization

Slurry transport, suspension and complex fluid flow
and heat transfer, porous media processes,
mathematical analysis and approximation.

Professor S. C. Saxena
The Graduate Committee
Department of Chemical Engineering
University of Illinois at Chicago
Box 4348,
Chicago, Illinois 60680


The chemical engineering department
--- -offers graduate programs leading to the
M.S. and Ph.D. degrees

"-----'- 0 The combination of distinguished faculty,
outstanding facilities and a diversity of
E research interests results in exceptional
opportunities for graduate education.


50 629I
Faculty 579
Richard C. Alkire I I I I I
Harry G. Drickamer
Charles A. Eckert
Thomas J. Hanratty
Jonathan J. L. Higdon
Walter G. May
Richard I. Masel
Anthony J. McHugh
Mark A. Stadtherr
James W. Westwater
Charles F. Zukoski, IV


For Information and Application Forms Write

S.l' O Department of Chemical Engineering
University of Illinois
Box C-3 Roger Adams Lab
1209 W. California Street
Urbana, Illinois 61801

Graduate Studies in

Chemical Engineering

Illinois Institute of Technology
Chicago, Illinois

I --- i i - -
iFaculty- ...
R.L. Beissinger
A. Ci nar- -
D. Gidaspow
ID-T.' Hatziavrami-dis
iJ.R. Selman
S.M. Senkan I -..
iB.S.i Swanson I
D.T. Wasan
W.A. Weigand
C.V. Wittmar

Research Areas
'Biochemical and Biomedical -
Chemical Reaction Engineering
Combustion -. -
Computer-Aided Design
Electrochemical Engineering .
Fluid Mechanics --. ----
Interfacial and Colloidal
-Phenomena .... -. -
!Process Dynamics and C
Transport Phenomenai'
i _. ....... .. -.i..... .

" .....i .. "". '". .."' _ l . .
4----- \
r t r,
.......i .... I i l

, i !

-, -s

I~...._. I.. _

K \




A> I I
I -

- -I ~ -

&' For Mor Information Write to:
Chemical engineering Department -
Graduate admissions Committee
Illinois Ins tute of Technology j
I.I.T. Cen r
Chicago Illinois 60616 I I
U.S. S

_ . ~_II _

i------- I--



is an independent
graduate school. It has
an interdisciplinary
degree program
designed for B.S.
chemical engineering
graduates. Fellowships
and full tuition
scholarships are
available to qualified
U.S. and Canadian
Citizens. Our students
receive S9,000.00
fellowships each
calendar year.

Our research activities
span the papermaking
process including:

plant tissue culture
surface and colloid science
fluid mechanics
environmental engineering
polymer engineering
heat and mass transfer
process engineering
simulation and control
separations science and
reaction engineering

For f,.rrhe-r nformal'on contfOt:
D.recior of Admissions
The Insi.iule of Paper Chem;slr,
P Bo. 1039 Appleion WI 54912
Telephone 414 734J9251



la F

B i ll ll in lll

el l Graduate Program for
*M.S. and Ph. D. Degrees in
Chemical and Materials Engineering

__Research Areos
Bi _* Kinetics and Cotalysis
Biomass Conversion
Membrane Separations
Particle Morphological Analysis
Air Pollution
MassTransfer Operations
Numerical Modeling
Particle Technology
Atmospheric Transport
Bioseparations and Biotechnology
Process Design
-J Surface Science
I Transport In PorousMedia

For additional information and application write to:
Graduate Admissions
Chemical and Materials Engineering
The University of Iowa
Iowa City, Iowa 52242.
1 NI



_ _




William H. Abraham
Thermodynamics, heat and mass transport,
process modeling
Lawrence E. Burkhart
Fluid mechanics, separation process, process
George Burnet
Coal technology, separation processes
Charles E. Glatz
Biochemical engineering, processing of
biological materials
Kurt R. Hebert
Electrochemical engineering, corrosion
James C. Hill
Fluid mechanics, turbulence, convective transport,
air pollution control
Kenneth R. Jolls
Thermodynamics, simulation
Terry S. King
Catalysis, surface science, catalyst applications
Maurice A. Larson
Crystallization, process dynamics
Allen H. Pulsifer
Solid-gas reactions, coal technology
Peter J. Reilly
Biochemical engineering, enzyme and fermentation
Glenn L. Schrader
Catalysis, kinetics, solid state electronics
Richard C. Seagrave
Biological transport phenomena, biothermo-
dynamics, reactor analysis
Dean L. Ulrichson
Solid-gas reactions, process modeling
Thomas D. Wheelock
Chemical reactor design, coal technology,
Gordon R. Younquist
Crystallization, chemical reactor design,

For additional information, please write:
Graduate Officer
Department of Chemical Engineering
Iowa State University
Ames, Iowa 50011

*- "P-1. -Y. 'v, "-z

_ -- ..... S -t-,- _. y
-.- -- "- .

!!:: =4.p



Department of Chemical and Petroleum Engineering

Offers graduate study

leading to the

M.S. and Ph.D. degrees

For further information, write to
Professor George W. Swift, Graduate Advisor
Department of Chemical and Petroleum Engineering
4006 Learned Hall
The University of Kansas
Lawrence, Kansas 66045

Faculty and Areas of Specialization *

Kenneth A. Bishop, Professor (Ph.D., Oklahoma); reser-
voir simulation, interactive computer graphics,
John C. Davis, Professor and chief of geology research
section, Kansas Geological Survey (Ph.D., Wyoming);
probabilistic techniques for oil exploration, geologic
computer mapping
Kenneth J. Himmelstein, Adjunct Professor (Ph.D.,
Maryland); pharmacokinetics, mathematical model-
ing of biological processes, cell kinetics, diffusion
and mass transfer
Colin S. Howat, III, Assistant Professor (Ph.D., Kansas);
applied equilibrium thermodynamics, process de-
Don W. Green, Professor and Co-director Tertiary Oil
Recovery Project (Ph.D., Oklahoma); enhanced oil
recovery, hydrological modeling
James O. Maloney, Professor (Ph.D., Penn State);
technology and society
Russell B. Mesler, Professor (Ph.D., Michigan); nucleate
and film boiling, bubble and drop phenomena
Floyd W. Preston, Professor (Ph.D., Penn State); geo-
logic pore structure

Harold F. Rosson, Professor and Department Chairman
(Ph.D., Rice); production of alternate fuels from agri-
cultural materials
Bala Subramaniam, Assistant Professor (Ph.D., Notre
Dame); kinetics and catalysis, insitu characterization
of catalyst systems
George W. Swift, Professor (Ph.D., Kansas); thermo-
dynamics of petroleum and petro chemical systems,
natural gas reservoirs analysis, fractured well
analysis, petrochemical plant design
John E. Thiele, Assistant Professor (Sc.D., MIT); struc-
ture/property relationships of polymers, polymer
chemistry and physics, polymer viscoelasticity
Shapour Vossoughi, Associate Professor (Ph.D., U. of
Alberta); enhanced oil recovery, thermal analysis,
applied rheology and computer modeling
Stanley M. Walas, Professor Emeritus (Ph.D., Michigan);
combined chemical and phase equilibrium
G. Paul Willhite, Professor and Co-director Tertiary Oil
Recovery Project (Ph.D., Northwestern); enhanced
oil recovery, transport processes in porous media,
mathematical modeling

FALL 1984

Graduate Study in Chemical Engineering


DURLAND HALL-New Home of Chemical Engineering

M.S. and Ph.D. programs in Chemical
Engineering and Interdisciplinary
Areas of Systems Engineering, Food

Science, and Environmental

Financial Aid Available
Up to $12,000 Per Year
Professor B. G. Kyle
Durland Hall
Kansas State University
Manhattan, Kansas 66506





M.S. and Ph.D. Programs


J. Berman, Ph.D., Northwestern
Biomedical Engineering; Cardiovascular
Transport Phenomena; Blood Oxygenation
D. Bhattacharyya, Ph.D.
Illinois Institute of Technology
Novel Separation Processes; Membranes;
Water Pollution Control
G. F. Crewe, Ph.D., West Virginia
Catalytic Hydrocracking of
Polyaromatics; Coal Liquefaction
C. E. Hamrin, Ph.D., Northwestern
Coal Liquefaction; Catalysis; Nonisothermal Kinetics
R. I. Kermode, Ph.D., Northwestern
Process Control and Economics

E. D. Moorhead, Ph.D., Ohio State
Electrochemical Processes; Computer
Measurement Techniques and Modeling
L. K. Peters, Ph.D., Pittsburgh
Atmospheric Transport; Aerosol Phenomena
A. K. Ray, Ph.D., Clarkson
Heat and Mass Transfer in Knudsen
Regime; Transport Phenomena
J. T. Schrodt, Ph.D., Louisville
Simultaneous Heat and Mass Transfer;
Fuel Gas Desulfurization
T. T. Tsang, Ph.D., Texas-Austin
Aerosol Dynamics in Uniform and Non-Uniform Systems

Fellowships and Research Assistantships are Available to Qualified Applicants
For details write to:
E. D. Moorhead
Director for Graduate Studies
Chemical Engineering Department
University of Kentucky
Lexington, Kentucky 40506-0046

FALL 1984



ii r
"~ru~YYisslll$l~s~" ~l~lldl




Baton Rouge is the state capitol and home of the major
state institution for higher education-LSU. Situated in
the Acadian region, Baton Rouge blends the Old South
and Cajun Cultures. The Port of Baton Rouge is a main
chemical shipping point, and the city s economy rests
heavily on the chemical and agricultural industries. The
great outdoors provide excellent recreational activities
year round, additionally the proximity of New Orleans
provides for superb nightlife, especially during Mardi Gras.

M.S. and Ph.D. Programs
Approximately 70 Graduate Students
IBM 434 I with more than 50 color graphics terminals
Analytical Facilities including GC/MS, FTIR, FT-NMR,
LC's, GC's...
Vacuum to High Pressure Facilities for kinetics, catalysis,
thermodynamics, supercritical processing
Shock Tube and Combustion Laboratories
Laser Doppler Velocimeter Facility
Bench Scale Fermentation Facilities

Department of Chemical Engineering
Louisiana State University
Baton Rouge, LA 70803

Control, Simulation, Computer Aided Design
K. M. DOOLEY (Ph.D., Delaware)
Heterogeneous Catalysis, Reaction Engineering
M. F. FRENKLACH (Ph. D., Hebrew Univ.)
Combustion, Kinetics, Modeling
F. R. GROVES (Ph.D., Wisconsin)
Control, Modeling, Separation Processes
D. P. HARRISON (Ph.D., Texas)
Fluid- Solid Reactions, Hazardous Wastes
A. E. JOHNSON (Ph.D., Florida)
Distillation, Control, Modeling
M. HJORTSO (Ph.D., Univ. of Houston)
Biotechnology, Applied Mathematics
F. C. KNOPF (Ph.D., Univ. of Purdue)
Computer Aided Design, Supercritical Processing
E. McLAUGHLIN (D.Sc., Univ. of London)
Thermodynamics, High Pressures, Physical Properties
R. W. PIKE (Ph.D., Georgia Tech)
Fluid Dynamics, Reaction Engineering, Optimization
Sugar Technology, Separation Processes
G. L. PRICE (Ph.D., Rice Univ.)
Heterogeneous Catalysis, Surfaces
D. D. REIBLE (Ph.D., Caltech)
Transport Phenomena, Environmental Engineering
R. G. RICE (Ph.D., Pennsylvania)
Mass Transfer, Separation Processses
D. L. RISTROPH (Ph.D., Pennsylvania)
Biochemical Engineering
C. B. SMITH (Ph. D., Univ. of Houston)
Non-linear Dynamics, Control
A. M. STERLING (Ph.D., Univ. of Washington)
Biomedical Engineering, Transport Properties, Combustion
D. M. WETZEL (Ph.D., Delaware)
Physical Properties, Hazardous Wastes

Tax-free fellowships and assistantships with tuition
waivers available
Special industrial and alumni fellowships with higher
stipends for outstanding students
Some part-time teaching positions for graduate students
in high standing


0 University of Maine at Orono


* Sponsored projects val-
ued at$1 million peryear
are in progress.
* Faculty is supported by
extensive state-of-the-art
* Relevancy of the Depart-
ment's research is in-
sured by continuous liai-
son with engineers and
scientists from industry
who help guide the fac-
ulty concerning emerg-
ing needs and activities
of other laboratories.
* Research and teaching
assistantships are avail-
* Outstanding candidates
(GPA between 3.75 and
4.00) wishing to pursue
the Ph.D. are invited to
apply for President's Fel-
lowships which provide
$4000 per year in addi-
tion to regular stipend
and free tuition.


William H. Cockler
Sc.D., MIT, 1960
* Heat Transfer
* Pressing & Drying
* Energy from Low Btu
* Process Simulation

Albert Co
Ph.D., Wisconsin, 1979
* Transport phenomena
* Polymeric Fluid
* Rheology

Arthur L. Fricke
Ph.D., Wisconsin, 1962
* Properties of Polymeric
* Polymer Processing and
* Rheology of Polymeric

Joseph M. Genco
Ph.D., Ohio State, 1965
* Process Engineering
* Pulp & Paper
* Wood Delignification

Marqueta K. Hill
Ph.D., University of
California, 1966
* Black Liquor Chemistry
* Pulping Chemistry
* Ultrafiltration

John C. Hassler
Ph.D., Kansas State, 1966
* Process Analysis and
Numerical Methods
* Instrumentation and
Real-Time Computer

John J. Hwalek
Ph.D., University of
Illinois, 1982
* Heat Transfer
* Process Control Systems

Erdogan Kiran
Ph.D., Princeton, 1974
* Polymer Physics and
* Thermal Analysis and
* Supercritical Fluids

James D. Lisius
Ph.D., University of Illinois,
* Transport Phenomena
* Electrochemical
* Mass Transfer

Kenneth I. Mumm6
Ph.D., Maine, 1970
* Process Modeling and
* System Identification &

Hemant Pendse
Ph.D., Syracuse, 1980
* Colloidal Phenomena
* Particulate Systems
* Porous Media Modeling

Ivar H. Stockel
Sc.D., MIT, 1959
* Pulp & Paper
* Droplet Formation
* Fluidization

Edward V. Thompson
Ph.D., Polytechnic Institute
of Brooklyn, 1962
* Polymer Material Prop-
* Membrane Separation
* Pressing & Drying

Douglas L. Woerner
Ph.D., University of
Washington, 1983
* Concentration Polariza-
* Ultrafilter Operation
* Light Scattering

University of Maryland

Robert B. Beckmann
Theodore W. Cadman
Richard V. Calabrese
Kyu Y. Choi
Larry L. Gasner
James W. Gentry
Albert Gomezplata
Randolph T. Hatch
Juan Hong
Thomas J. McAvoy
Thomas M. Regan
Wilburn C. Schroeder
Theodore G. Smith

The University of Maryland is located approximately 10 miles from
the heart of the nation, Washington, D.C. Excellent public
transportation permits easy access to points of interest such as the
Smithsonian, National Gallery, Congress, White House, Arlington
Cemetery, and the Kennedy Center. A short drive west produces
some of the finest mountain scenery and recreational opportunities
on the east coast. An even shorter drive east brings one to the
historic Chesapeake Bay.

"3'^ "I^ ~Degrees Offered.
SM.S. and Ph.D. programs in
: '~l j Chemical Engineering.

Financial Aid Available:
Teaching and Research Assistantships
I. :. at $9,640/yr.
-- -" *-~. .:" ,' .

Research Areas:
Aerosol Mechanics
Air Pollution Control
Biochemical Engineering
Biomedical Engineering
Laser Anemometry
Mass Transfer
Polymer Processing
Process Control
Risk Assessment
Separation Processes

For Applications and Further Information, Write:
Professor Thomas J. McAvoy
Department of Chemical and Nuclear Engineering
University of Maryland
College Park, Md. 20742

Full Text