Chemical engineering education

Material Information

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


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


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

Record Information

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

UFDC Membership

Chemical Engineering Documents


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ceia education

Chemical Engineering Education
Department of Chemical Engineering
University of Florida
Gainesville, FL 32611

EDITOR: Ray W. Fahien (904) 392-0857
ASSOCIATE EDITOR: T Anderson (904) 392-2591
MANAGING EDITOR: Carole Yocum (904) 392-0861


E. Dendy Sloan, Jr.
Colorado School of Mines

Gary Poehlein
Georgia Institute of Technology

Klaus Timmerhaus
University of Colorado

Richard M. Felder
North Carolina State University

JackR. Hopper
Lamar University

Donald R. Paul
University of Texas

James Fair
University of Texas

I. S. Dranoff
Northwestern University

Frederick H. Shair
California Institute of Technology

Alexis T. Bell
University of California, Berkeley

Angelo J. Perna
New Jersey Institute of Technology

Stuart W. Churchill
University of Pennsylvania

Raymond Baddour
Massachusetts Institute of Technology

Charles Sleicher
University of Washington

Leslie W. Shemilt
McMaster University

Library Representative
Thomas W. Weber
State University of New York

Spring 1991

Chemical Engineering Education

Volume XXV Number 2 Spring 1991

62 Angelo J. Perna, of the New Jersey Institute of Technology,
Deran Hanesian

64 UCLA, D.T. Allen, S.M. Senkan

68 Developing a Course in Chemical Engineering Ethics: One Class'
Experiences, James C. Watters, Dominic A. Zoeller

74 An Introduction to Equilibrium Thermodynamics: A Rational
Approach to Its Teaching; Part 1, Notation and Mathematics,
Donald F. Williams, David Glasser

82 A Course in Immobilized Enzyme and Cell Technology,
William E. Lee, III

88 A Second-Year Undergraduate Course in Applied Differential
Equations, Thomas Z. Fahidy

106 Principles of Stagewise Separation Process Calculations: A
Simple Algebraic Approach Using Solvent Extraction,
Barry D. Crittenden

112 Computation of Multiple Reaction Equilibria, Alan L. Myers

80 We Hold These Truths to be Self-Evident, Richard M. Felder

92 Removal of Chlorine From the Chlorine-Nitrogen Mixture in a
Film of Liquid Water, Sarwan S. Sandhu

96 Undergraduate Education: Where Do We Go From Here?
Richard G. Griskey

98 Purdue-Industry Computer Simulation Modules: The Amoco
Resid Hydrotreater Process, R.G. Squires, G.V. Reklaitis,
N.C. Yeh, J.F. Mosey, LA. Karimi, P.K. Andersen

102 Crystallization: An Interesting Experience in the ChE Laboratory,
Te6filo A. Graber S., Maria E. Taboada M.

79 Call for Papers
79,97 Book Review
110 Books Received

CHEMICAL ENGINEERING EDUCATION (ISSN 0009-2479) is published quarterly by the
Chemical Engineering Division, American Society for Engineering Education and is edited at the
University of Florida. Correspondence regarding editorial matter, circulation, and changes of
address should be sent to CEE, Chemical Engineering Department, University of Florida, Gainesville,
FL 32611. Advertising material may be sent directly to E.O. Painter Printing Co., PO Box 877,
DeLeon Springs, FL 32130. Copyright 1991 by the Chemical Engineering Division, American
Society for Engineering Education. The statements and opinions expressed in this periodical are
those of the writers and not necessarily those of the ChE Division, ASEE, which body assumes no
responsibility for them. Defective copies replaced if notified within 120 days of publication. Write
for information on subscription costs and for back copy costs and availability. POSTMASTER:
Send address changes to CEE, Chem. Engineering Dept., University of Florida, Gainesville, FL

educator )


of the c

New Jersey

Institute of


T First... the student (1950) and then... the teacher (1991) -f k

New Jersey Institute of Technology
Newark, NJ 07102

A ngelo J. Perna (or Angie, as he is more familiarly
known to friends and colleagues) was born in
Brooklyn, New York, in 1931, to Vito and Marie
Perna, who had immigrated to the United States
from Italy. He was the fourth child in a family of
eight children.
Although Angie's early years paralleled the great
depression in the United States, the Perna family
was never unduly affected since Vito was self-em-
ployed and was able to continuously provide for his
family. Education was always highly stressed in the
Perna household, and the children were encouraged
to help one another to excel in academics.
Angie enjoyed, and was accomplished in, both
academics and sandlot sports as he was growing up.
He participated in baseball and football activities
and was on several championship teams in each
sport. He says that he always knew he would even-
tually go to college and become a teacher, but during
his early years he was undecided whether to pursue
engineering or history as a career-although he en-
joyed chemistry and mathematics, it was in history
that he received early academic recognition.
When Angie was a junior in high school his fa-
ther passed away after a long bout with cancer. The

lengthy siege of illness had created such a serious fi-
nancial drain on the family resources that when
Angie graduated from high school the following year,
he had to postpone his plans for college and join the
workforce instead. He worked first for the Motion
Picture Association of America and later in the gar-
ment industry before being drafted into the United
States Army in January of 1952.
Angie was sent to Camp Breckenridge, Kentucky,
for basic training before being sent to Korea in June
of 1952, where he served with Company K of the 279
RCT attached to the 45th Division until August of
1953. While in Korea he rose to the rank of staff
sergeant and earned several battle stars and the
Combat Infantryman's Badge.
Angie was honorably discharged in November of
1953 and through the GI assistance program he was
finally able to begin his postponed college education.
It is interesting to hear how he made the decision to
attend Clemson and take up chemical engineering:
When Igot out of the service Ifelt I could not go
to a school in the immediate area and live at
home. I really wanted to go to Brooklyn Poly,
but since all of my friends were now working, I
knew I would be socializing with them, and I
could never have undertaken a course of study
while continuing to intermingle with my friends;
therefore, the school I attended had to be one
which was far enough away so that I had to live

Copyright ChE Division, ASEE 1991
Chemical Engineering Education


*~ ~-

there instead of at home. In addition, it had to
be inexpensive enough so that my savings and
my GI support could see me through the studies.
Insofar as to why I chose chemical engineering-
this was simple. I happened to read an article
in the New York Times which gave a salary
survey for all engineers, and chemical engineers
were paid the most. This fact appealed to me,
and since I had done fairly well in chemistry,
my field of study was now fixed. As for Clemson,
a cousin of mine had gone there prior to the
second world war and a high school classmate
of mine was currently attending-and both of
them were enthusiastic about the place. So I
thought, 'Why not?" In addition, I remembered
they had a pretty good football team (even in
those days). I saw in the college catalog that
they offered chemical engineering and that it
was fairly inexpensive, so I applied for
admission, and I was accepted. I entered the
school in January of 1954. These decisions were
the most fortuitous ones I have ever made, and I
have been thankful to the fates ever since. I
found a school I respect, a profession I love,
and I met not only a great group of classmates,
but also Dr. Charles E. Littlejohn.

Dr. Littlejohn was a dedicated teacher who in-
stilled a sense of pride and professionalism in his
students, and he had a marked effect on Angie's life.
Even in the face of all of Angie's eventual technical
accomplishments in teaching and research, it is the
area of service to his colleagues and his profession in
which he places the greatest value. He credits Char-
ley Littlejohn with instilling in him a sense of re-
sponsibility toward both his chosen field of endeavor
and its related professional organizations.

After graduation from Clemson, Angie joined Un-
ion Carbide where he worked at the Y-12 plant in
Oak Ridge, Tennessee. While there he worked as a
production engineer, as a research-development en-
gineer, and finally as a production scheduler. He
found himself working on innovative powdered met-
allurgy techniques and isostatic pressing-interest-
ing work, but classified since it dealt with thermo-
nuclear weapons.
After more than three years at Union Carbide he
decided to return to school to work on his Master's
degree and to continue with his plan to enter the
teaching profession, so in September of 1960 he re-
turned to Clemson and became a member of the ini-
tial graduate class in chemical engineering.

During this period of time Angie became inter-
ested in the environmental area through his inter-

Spring 1991

action with George Meenahan, a professor in chemi-
cal engineering, and Gene Rich, chairman of the
civil engineering department and author of Unit Op-
erations of Sanitary Engineering. Angie helped Dr.
Rich by reviewing his book and (together with a
classmate, Bill Huffman) by solving the text prob-
lems. This period of time had a great influence on
his strong belief that chemical engineers are ideally
suited by their training to be a force in solving the
challenges that the environment presents. It was

Even in the face of all of Angle's eventual
technical accomplishments in teaching and
research, it is the area of service to his colleagues
and his profession in which he places
the greatest value.

during this time that Angie also began his associa-
tion with the unit operations laboratory when, as a
graduate assistant, he was given the responsibility
for the lab.
After obtaining his Master's in 1962, he went to
VPI to teach metallurgy for a year before going on to
the University of Connecticut for his PhD degree.
His classmates at UConn were an unusual group
since, like Angie himself, all of them had been out of
college for a period of time prior to returning to
college to pursue advanced degrees, and all of them
eventually went into teaching. The group consisted
of Herb Klei and Mike Howard of UConn, George
Knepple of William Patterson, and Pat Marino.
While at UConn, Angie was an instructor in
chemical engineering and taught the unit operations
laboratory. He did his research under Dr. L.F.
Stutzman in the area of distillation dynamics and
After receiving his PhD, Angie joined the Depart-
ment of Chemical Engineering and Chemistry at
Newark College of Engineering in Newark, New
Jersey, and he and I began what was to be a long co-
operative effort. In the late 1960s we worked to-
gether on a five-story unit operations lab and a sepa-
rate process dynamics and control lab, and in addi-
tion to designing about thirty experiments, we suc-
cessfully wrote proposals and received funding from
NSF, the State of New Jersey, and the industrial
sector, amounting to approximately one-half million
dollars. We developed a new teaching format that
included a six-hour once-a-week lab with three dif-
ferent types of lab reports and oral student presen-
Contined on page 86


ChE at U C

University of California
Los Angeles, CA 90024

The University of California at Los Angeles,
founded in 1929, is located in rolling green hills
just five miles from the ocean, in one of the most at-
tractive areas of Southern California. It is bordered
on the north by the residential community of Bel-Air
and the Santa Monica mountains. Its southern bound-
ary is Westwood Village, which serves as a shopping
and entertainment center for Los Angeles. The at-
tractive campus on 419 acres is the home of about
2000 faculty and 35,000 students.
The UCLA Department of Chemical Engineering
is part of the School of Engineering and Applied
Science, which was originally established as the Col-
lege of Engineering in 1944. The school has grown
steadily in stature and reputation and now ranks
among the top ten schools of engineering nationwide
and is among the top five schools of engineering at
public universities. Chemical engineering is a rela-
tively young department, officially established in
1983 and accredited by ABET shortly thereafter.
Prior to 1983 the department was part of a unified
undergraduate engineering program.
Since its establishment and accreditation in 1983,
the department has undergone steady growth in stat-
ure and reputation. At present the department of-
fers BS, MS, and PhD degrees in chemical engineer-
ing, and the current total enrollment is about 150
undergraduate and 50 full-time graduate students.
The department offices and most of the research
laboratories are housed in Boelter Hall, which is
currently undergoing a major renovation that will
double the available floor space.

At present the department offers BS, MS,
and PhD degrees in chemical engineering,
and the current total enrollment is about 150
undergraduate and 50full-time graduate
students. ... the annual research
budget is over 2 million dollars

Hoyce Hall, one of the four buildings that made up
the original UCLA campus in Westwood

The number of faculty has also increased stead-
ily, to a current level of twelve. This has led to a
spectacular increase in graduate research activity;
at present the annual research budget of the depart-
ment is over 2 million dollars, placing it in the top
fifteen in the nation in federal research funding.
These funds support our fifty graduate students,
numerous undergraduate research assistants, and
post-doctoral research associates. The department
typically admits about fifteen new graduate students
each year, including both domestic and international

The design of clean, environmentally compatible
technologies is a key challenge facing modern indus-
try and the profession. The UCLA chemical engi-
neering department is playing a leading interna-
tional role in developing the research and design
fundamentals needed for a rational approach. The
department presently houses two highly-visible na-

Copyright ChE Division, ASEE 1991
Chemical Engineering Education


tional research centers: the National Center for In-
termedia Transport (sponsored by the US Environ-
mental Protection Agency since 1981), directed by
Yoram Cohen, and the National Science Foundation
Engineering Research Center for Hazardous Sub-
stances Control (established in 1987), directed by
Sheldon Friedlander. Although many of our faculty
members participate in the activities of these cen-
ters, the research conducted in the department is
diverse, as can be seen in the following paragraphs
and in the Table 1 summary.
Reaction Engineering
Reaction engineering and kinetics is one of the major
research areas in the department. The research programs
undertaken by Professors Allen, Hicks, and Senkan seek a
better understanding of the mechanisms of homogeneous
and heterogeneous reactions at the molecular level. David
Allen's research emphasizes the application reaction en-
gineering principles to energy and environmental issues.
His current interests include the molecular modeling of
petroleum processing (particularly catalytic cracking) as
well as gas-to-particle reaction pathways in urban atmos-
pheres, and development of catalytic hydrodechlorination
processes. In his research, Robert Hicks studies the cata-
lytic oxidation of hydrocarbons using Pt and Pd as cata-
lysts, with the objective of developing more efficient auto-
mobile catalytic converters that will lead to reduced pol-
lutant emissions at cold-start conditions. Selim Senkan's
research in reaction engineering is directed toward the de-
velopment of detailed chemical kinetic mechanisms
(DCKM) describing high-temperature processes such as
hydrocarbon pyrolysis, oxidation, and combustion. DCKMs
developed by Professor Senkan involve the participation
of hundreds of species in thousands of elementary reac-


tions, and rely on the use of large-scale computing. The
data needed in the development of DCKMs are derived
from experiments conducted jointly with physical chem-
ists and theoretically via the use of computational qiuan-
tum mechanics.
Materials Processing
The research of Yoram Cohen involves the develop-
ment of novel materials and resins using polymer adsorp-
tion, polymer grafting, and surface silyation processes.
Traugott Frederking's research in thermodynamics and
transport phenomena at low temperatures (i.e., cryogen-
ics) is paving the way for the development and better
utilization of superconductors. Sheldon Friedlander
is investigating the development of new technologies
involving ultrafine particles, including the design of aero-
sol reactors and the engineering of submicron agglo-
merate structures composed of multicomponent aero-
sols. The deposition of semiconductor and metal thin
films for microelectronic devices using organometallic
chemical vapor deposition is an expanding area of re-
search of Robert Hicks.
At present, combustion and combustion-related activi-
ties are underway in the departments of chemical engi-
neering, mechanical engineering, and chemistry. Eldon
Knuth developed one of the first Molecular Beam Mass
Spectrometer systems in the world to study flame struc-
ture. He is currently exploring relaxation processes in
molecular beams and cluster formation in low-tempera-
ture freejets. Selim Senkan is investigating the effects of
halogens in hydrocarbon combustion, and in particular
their role in the formation of toxic combustion by-prod-
ucts. His research has important applications to hazard-
ous waste incineration. In addition, his research empha-


Students can enjoy swimming, skiing, and mountain climbing...
on the same day!

Spring 1991

sizes the use of combustion as a manufacturing process to
synthesize useful chemicals from abundant natural
resources by partial oxidation. Owen Smith's research
in combustion emphasizes the development of non-
intrusive optical diagnostics, such as particle image veloci-
metry and laser induced fluorescence. He recently de-
veloped a two-dimensional resonantly-stabilized dump
combustor which promises to be particularly useful in
waste incineration.

Transport Phenomena
Yoram Cohen and Sheldon Friedlander study the
transport of pollutants in air, water, soil, and other envi-
ronmental media, particularly through the National Cen-
ter for Intermedia Transport. These studies are not con-
fined merely to dispersion within single environmental
media; rather, they focus on processes occurring at inter-
faces (particularly air-soil and air-water interfaces) and
the incorporation of these intermedia transport processes
into multimedia studies of pollutant impact on the envi-
ronment. The application of transport phenomena at cryo-
genic temperatures is the specialty ofTraugott Freder-

king. He is currently working on screen and perforated-
plate compact cryocooler systems at liquid-helium tem-
peratures, with the objective of developing a basic under-
standing of thermal boundary layer conditions at super-
conductor-liquid interfaces.

Fundamental and applied electrochemistry is the ma-
jor research thrust of Ken Nobe. Typical industrial appli-
cations that are addressed in his laboratory include reduc-
tion of corrosion rates in marine environments, reduction
of hydrogen embrittlement of high-strength steels, and
improvement of the efficiency of electrochemical manufac-
turing operations like the electrodeposition of specialized
metals like Invar. Along with the late Manuel Baizer, Pro-
fessor Nobe and his group have also pioneered paired
electroorganic syntheses in flow reactors. In a collabora-
tive activity, Vincent Vilker and Nobe are exploring elec-
troenzymology as a method for the synthesis of fine chemi-
cals and for the development of biosensors.

Chemical Engineering Faculty and Research Interests at UCLA

Environmental Reaction Engineering
Atmospheric Aerosol Chemistry Processing of Heavy Fuels
and Hazardous Waste Molecular Models of Catalytic
Cracking Chemistry

Polymer Science and Transport Phenomena
Polymerization Reaction Engineering Brownian Dynamics
ofMacromolecules Polymer Grafting and Adsorption *
Non-Newtonian Fluid Mechanics Water Purification *
Multimedia Transport of Toxic Chemicals and Exposure

Low Temperature Transport in Porous Media, Phase Separ-
ation, Thermo-mechanical Devices Heat Transfer Cryo-
cooler Components, Super-conductingDevices and Related
Transport Phenomena

Aerosol Technology and Air Pollution
Formation and Behavior of Submicron Particles Source
Allocation and Receptor Modeling Air Pollution Control *
Mass Transfer and Diffusion Particle/Surface Interactions

Surface and Interface Engineering
Catalysis Reaction Engineering of Organometallic Vapor

Molecular Dynamics in Gas Flow
Vibrational, Rotational, Translational Relaxations Conden-
sation and Evaporation Chemical Relaxations

Process Design, Dynamics and Control
Linear and Nonlinear Control Systems Design Integration
of Design and Control Process and Control Systems Design
for Microelectronic Material Manufacturing Waste Minimi-
zation Through Chemical Process Synthesis Separation
Network Synthesis

Biochemical Engineering
Biomimetic Membrane Systems Culture of Microbes that
Thrive at Extremes of Temperature, pH, and Salt Concen-
tration Biosystems for Heavy Metal Recovery Immobil-
ized-Cell Fermentations

Catalysis Battery and Fuel Cells Corrosion and Electro-
deposition of Metals and Semiconductors Bioelectro-
High-Temperature Chemical Kinetics and Reaction Eng.
Combustion, Gas Kinetics, Flame Chemistry Incineration
of Hazardous Materials Computational Quantum Mechan-
ics Synthesis of Useful Chemicals by Combustion
High-Temperature Chemical Kinetics Reaction Mechan-
isms in Combustion, Incineration and Chemical Vapor
Deposition Optical Methods for Combustion Diagnostics
Biochemical Engineering
Colloid and Interfacial Phenomena Proteins, Virus, and
Bacteria Bioelectrochemical Catalysis

6 Chemical Engineering Education

Biochemical Engineering
Professors Monbouquette and Vilker form the chemi-
cal engineering component of a strong collaborative re-
search program in biochemical engineering. Collaborating
with faculty in pharmacology, biological chemistry, mo-
lecular biology, microbiology, public health, and civil engi-
neering, they are working on problems related to the
cleanup of groundwater contamination, chemical synthe-
sis, and chemical sensors via the use of modern biochemi-
cal methods. Vincent Vilker's research is focused on bio-
catalysis of bacterial redox enzymes. He is developing
processes to detoxify trace contaminants in water, to syn-
thesize oxygenated hydrocarbons and fuel additives and is
undertaking research to optimize the production of en-
zyme system proteins in natural or cloned host bacteria.
Harold Monbouquette is pioneering the use of
archaebacteria (i.e., bacteria that thrive under extreme
conditions, such as temperatures in excess of 100 C and
pH levels below 1 and above 10) to synthesize highly
stable enzymes for use in the treatment of toxic wastes
and for the synthesis of new biomaterials.
Process Design and Control
The design and control of chemical processes for mini-
mal environmental impact is an underlying theme in much
of Vasilios Manousiouthakis' work. He has developed
the concept of mass-exchange networks, which is extremely
important in chemical process industries. He has also
developed approaches for estimating the waste minimiza-
tion potential of chemical processes. His research in proc-
ess control involves studies on the dynamic behavior and
control of generalized linear and non-linear systems using
algebra, topology, functional analysis, differential geome-
try, and optimization.
The overall goal of the separations program, guided by
Yoram Cohen and Harold Monbouquette, is the de-
velopment of novel separations processes, including
highly selective membranes and sorbent media, through
chemical tailoring of the phase interface. Current
projects include the construction and study of new
polymer-silica resins for selective sorption of organic
and heavy metals and biomimetic membranes for metal
recovery. They have recently initiated a collaborative proj-
ect involving the creation and testing of novel ceramic-
supported polymer membranes for applications in perva-
poration and hyperfiltration.
As is evident from the foregoing discussion, re-
search activities undertaken by chemical engineer-
ing faculty at UCLA span studies from the molecu-
lar level (characterized by length scales on the order
of Angstroms) to the design and control of large-
scale systems (characterized by length scales on the
order of meters to kilometers). As indicated, many of
the studies deal with environmental issues. An im-
portant outgrowth of these coupled activities is that
the students not only receive training in the funda-
Spring 1991

mental and applications of science and technology,
but they are also sensitized to the needs of society at
a time when crucial questions are being asked on
how to grow and innovate in an era of economic,
environmental, and energy constraints.
The environmental theme in the department's
research has also had a significant impact on under-
graduate education. Specialized courses in pollution
control technology, mass transfer of pollutants in
the ambient environment, and combustion, energy,
and the environment have been developed or are in
the planning stages. An undergraduate course on
toxic substances control (designed for non-engineers)
has also been created.
In addition to the development of specialized
courses, the department has focused on incorporat-
ing environmental issues into all parts of the cur-
riculum. Examples include design of a waste-to-
energy incinerator in the capstone design course and
the development of chemical reactors with minimal
by-product formation in the chemical reaction engi-
neering course.
The department also offers a variety of addi-
tional specialty courses, reflecting the breadth of the
research activities of the faculty. These courses are
complemented by hundreds of science and engineer-
ing courses offered in other departments. Exposure
to world-class researchers in chemistry, molecular
biology, atmospheric sciences, and other disciplines
provides exciting opportunities for the intellectual
growth of our students.


The faculty and students of UCLA enjoy a wealth
of cultural and recreational opportunities, both on
campus and in greater Los Angeles. Mountain climb-
ing and skiing, as well as surfing and sailing cen-
ters, are all easily accessible from campus and are
available virtually at any time of the year. World
renowned artists in dance, music, and the arts regu-
larly perform both on campus and at the nearby Los
Angeles Music Center. And of course, there is Holly-
wood, Universal Studios, Disneyland...
As LA has become one of the leading metropoli-
tan areas on the Pacific Rim, the city has become a
melting pot of many cultures. Los Angeles has a
Chinatown, a Little Tokyo, a Koreatown and many
other ethnic communities, together with an outstand-
ing selection of restaurants. These communities of-
fer students a window on the world which is avail-
able in few other cities. O




One Class' Experiences

University ofLouisville
Louisville, KY 40292

The 1988-89 ABET accreditation guidelines'"I for
engineering programs in the United States state,
"An understanding of the ethical, social, economic,
and safety considerations in engineering practice is
essential for a successful engineering career." This
tenet obliges engineering programs to incorporate a
minimum amount of coursework on engineering eth-
ics into what is already a tightly-packed curriculum.
The manner in which ethics are introduced into
the curricula allows for a number of choices. One
choice is to incorporate a discussion of ethics into the
context of an existing course or courses; another
choice is to develop a separate course that deals ex-
clusively with ethical and other closely-related is-
sues. Then the decision must be made as to what
level in the curriculum to place the course. Finally, a
curriculum must be developed which meets not only
the requirements of ABET but also the needs of the
students and the instructor.

The pros and cons of integrating "new" material
into existing courses versus devising a stand-alone
course to present the material, have long been de-
bated. In recent years, with the emphasis on incor-
porating developing technologies into our curricula,
there have been many champions of the integration
approach. Integration has the obvious advantage of
not adding any extra credits or courses to an already
demanding courseload. However, we believe that for

A stand-alone course in ethics has
advantages an instructor... can be given
free rein to develop the curriculum without being
confined by the boundaries of a traditional
theory or practice course.

James C. Watters is an associate professor of
chemical engineering at the University of Louisville,
and is currently the Acting Department Chair. He
received his BE in chemical engineering from the
National University of Ireland, University College
(Dublin, Ireland) and his MS and PhD degrees from Y <
the University of Maryland. His research interests
are in novel separation processes, membranes, poly-
mer synthesis, and methods of teaching and learn-
Dominic A. Zoeller (photo unavailable) received
the Master of Engineering degree in chemical engi-
neering from the University of Louisville in 1989. He
is currently a production engineer in the specialty
monomers plant of the Dow Chemical Company in
Midland, Michigan.

the integration approach to work, the topic must be
included in more than one existing course and thus
would probably be taught by more than one faculty
member. It has been our experience (in several engi-
neering disciplines) that many engineering faculty
members are uncomfortable with the area of ethics
as a subject to be included in their existing technical
courses. This discomfort may stem from their own
lack of knowledge or fear of ethical issues, or their
disdain for "diluting" the traditional courses with
"soft" topics. In any event, while the integration
approach may look like a good idea at first blush, we
contend that it is difficult to carry out in practice. As
a result of such delibertaions, at Louisville we insti-
tuted a two-credit course devoted to "Ethical Issues
in Chemical Engineering."
A stand-alone course in ethics has advantages.
From a teaching perspective, an instructor with
a genuine interest in the topic can be given free
rein to develop the curriculum without being con-
fined by the boundaries of a traditional theory or
practice course. Also, the student in such a course
can dwell on the course topics without worrying that
the "non-technical" issues are taking time from the
Copyright ChE Division, ASEE 1991
Chemical Engineering Education

seemingly "more important" technical topics of an
integrated course.
A disadvantage of the stand-alone course may be
the inability of students to integrate ethical issues
into technical coursework areas. Both students and
educators tend to neatly segment learning into sepa-
rate courses, with almost sacrosanct boundaries that
are not to be crossed. However, this problem can be
overcome by judicious placement of the course into
the curriculum.


Once we had decided to introduce a separate
course in ethics, the next hurdle was to decide where
it belonged in the curriculum. Should it be early (for
example in the sophomore year), before the student
has been exposed to many of the technical areas of
the profession and is still "fresh" or "naive"?
Or, should it be later (perhaps in the senior year)
when the more knowledgeable and, presumably,
more mature and "street-wise" student can better
synthesize his or her experiences in the profession to
The University of Louisville is unique among
chemical engineering programs in the United States
in that our accredited degree is the Master of Engi-
neering, a five-year program with mandatory coop-
erative internship training. We included the "Ethi-
cal Issues in Chemical Engineering" course in the
final semester of the fifth year, although it could
easily fit into the final semester of the fourth year in
a school with a more traditional program. We con-
sidered it most beneficial to approach ethical issues
from the more mature viewpoint of a fourth- or fifth-

year student. This was particularly helpful for our
students since they had all had co-op internships.
Many had already experienced or witnessed the grey
areas of real-world situations. In fact, many of them
identified with some of the classic case studies we
discussed and volunteered that they had experienced
similar quandries in their internships.
We elected to offer a two-credit course, meeting
once a week for one hour and forty-five minutes.
This framework ensured that students would take
the course seriously (since two credits were at stake),
and it allowed for the inclusion of class exercises and
films that would be difficult to use in a standard,
fifty-minute, time slot. The course was taught by one
of the authors (JCW), an Associate Professor in the
chemical engineering department who has an inter-
est in, and commitment to, teaching professional
responsibility. The pros and cons of using engineer-
ing faculty to teach ethics have been debated,'12,3 but
in our case, financial considerations dictated that it
be taught by one of our own faculty.


The course, first taught in the spring of 1988,
originally took a philosophical and historical per-
spective on ethics, an approach that the present
author was uncomfortable with. He elected instead
to use a case-study approach that was loosely based
on a now discontinued, cross-disciplinary course
called "Technology and Society" with which he had
been involved in the early 1980s.'4'
Table 1 lists the content of "Ethical Issues in
Chemical Engineering" as presented in the spring of
1989. Class format included lectures, discussions,

Course Outline: Ethics and Values in Engineering

The course will examine the foundations of our value sys-
tems and how these relate to our decisions as engineers. In
this context we will examine codes of ethics as proposed by
the various engineering societies, classic ethics case studies
from the literature, whistle-blowing and beyond, and our
rights and responsibilities as professionals. The format will
include lectures, videotapes, discussions, and presentations
by class members. Grading will be based on successfully
completing assigned homework and on participation in class


* Introduction
* Why engineers should be concerned with ethics
* Film: What You are Now is What You Were When

* Class discussion: Origin of our value systems
* Class exercise: Where do you draw the line?
* Codes of ethics: Advantages and drawbacks
* Ethics case studies: UTexas film and discussion
* Ethics case studies: Discussion of assigned problems
* Ethics-The Law: Professional societies
* Classic ethics cases: Student presentations
* Classic ethics cases: Student presentations
* Film: "Do Scientists Cheat?" (NOVA)
* Whistle-blowing: What, When, How
* Films: "Enemy of the People" (60 Minutes)
"Pomeroy File" (60 Minutes)
* Whistle-blowing: Support, discussion
* Responsibility: Film, Toxic Trials
Summary and Conclusions -

Spring 1991

Integration has the obvious advantage of not adding any extra credits or courses to an already
demanding courseload. However, we believe that for the integration approach to work,
the topic must be included in more than one existing course and thus would
probably be taught by more than one faculty member.

videotapes, and presentations by students. Class ma-
terials included texts, films, and experiential exer-
cises. Appendix A presents a brief annotated bibliog-
raphy of the materials used and referenced during
the semester. Topics addressed included the founda-
tion of our individual value systems, codes of ethics
and their limitations, whistle-blowing and its conse-
quences, and the whole concept of responsibility for
one's actions. Grades were based on weekly home-
work assignments, participation in classroom dis-
cussions, and presentations of assigned materials.
No examinations were given-the authors firmly
believe that a topic such as ethics is best taught and
best received by students in a non-threatening, semi-
informal format.
The first weeks of the course are devoted to an
examination of what each student believes on ethi-
cal and moral issues, where those beliefs came from,
and why such issues should be of concern. The film
What You are Now is What You Were When presents
a perspective that relates one's moral philosophy to
the major features of one's early upbringing. Stu-
dents are encouraged to apply this model to people
they know, such as parents, teachers, ministers, poli-
ticians, etc., and to discuss how applicable it is to
their own lives.

The next segment of the course deals with profes-
sionalism and the concept of ethics codes. Many codes,
such as those ofAIChE, IEEE, and NSPE, are exam-
ined for thoroughness, applicability, etc. Students
quickly learn that some codes (such as AIChE's) are
very vague, while others (such as NSPE's) are much
more detailed. Yet even the detailed ones do not
come close to addressing every situation and, in fact,
some of the tenets are potentially contradictory. The
student who is looking for a "quick fix" in the codes
soon realizes that absolution of personal decision-
making is rarely to be found.

The concept of taking responsibility for one's own
actions also starts to develop at this point in the
course. Students are asked to discuss the case stud-
ies presented by Kohn,'5' with particular reference
to the ethics codes, and they quickly realize that
even some of the seemingly simpler situations
involving ethical decision-making lack easy black-
and-white answers. When the student responses are

compared with those of employed engineers (tabu-
lated by Hughson and Kohn'61' the diverse opinions
are readily apparent. The comparison also allowed
us to see how opinions have changed over a period of
ten years.
The culmination of this segment of the course
was a discussion, based on Unger,[71 of the inter-
faces between ethics and the law, and between eth-
ics and professional societies. Students are struck by
the widely different levels of support afforded by the
various professional societies for engineers with
ethical dilemmas.
The last segment of the course deals with
whistle-blowing and its consequences. This topic ac-
tually weaves a thread through the whole course,
since many of the case studies evolved from someone
"blowing a whistle" or from someone having been the
victim of such action. The excellent NOVA film, "Do
Scientists Cheat?" demonstrates the consequences
of not blowing a whistle as well as what happens
when one does. The two 60 Minutes segments,
"Enemy of the People" and "The Pomeroy File,"
outline the histories of a whistle-blower and of
one who "dared" to speak out in public on a contro-
versial issue.
Each week students had to carry out a homework
assignment that consisted primarily of discussion
questions, many culled from Ethics in Engineering 8.
Around mid-semester, the students (working in pairs)
developed an in-depth study of a major ethics case.
Topics included Bhopal, the Challenger, BART, the
Corvair, the Pinto gas tank, Hooker Chemicals, etc.
In addition to a written report, the teams presented
their findings orally, either formally or in a role-
playing format.

As a fifth-year student in engineering, I felt a
great deal of apprehension in attending my first
ethics class. It seemed strange that after spending
five years honing my skills in making cold, calculat-
ing, right-or-wrong decisions, the administration now
felt it necessary to train me in ethics. Unfortunately,
this attitude was shared by most of my classmates.
However, I found that several aspects of the course

Chemical Engineering Education

enabled me to take the concepts and theories beyond
the walls of the classroom.
The first tool was the textbook,r7 which was clear-
cut and easy to read. In some cases, the author ad-
mitted that there were no right answers, even with
the aid of hindsight. This was refreshing. By using
current and semi-current examples from the engi-
neering field, the author was able to keep the inter-
est of the reader. In many cases the incidents pre-
sented were already common knowledge, while other
events had taken place prior to our collective mem-
ory. It was interesting to compare class reactions to
these two different stimuli. In the first case, the
class usually had preconceived notions about the
case, but when the incident was unfamiliar they
were at the mercy of the materials presented for
making their conclusions. In most cases the class
easily formed a consensus on ethical issues.
The second tool for generating interest in the
class was the syllabus. Dr. Watters recognized that
it would be impossible to alter the psychological
constitution of the students and sought instead to
raise our level of consciousness in the area of ethical
questions. By working through several scenarios,
reading the text and several handouts, watching
some video presentations on ethical issues, and hold-
ing candid discussions, he hoped we might recognize
our position in the ethical loop.
The effect of this candid approach to what could
have been a boring do-the-right-thing course was
profound. We began to view the class as a lively
forum rather than a waste of time. As we prepared
for each class through the reading assignments and
our weekly reports, we were intrigued by the ques-
tions we could not answer. We explored the difficulty
of enforcing a uniform code of ethics in a predomi-
nantly free-will society. We discovered the moral
dilemma of self-preservation versus doing what is
right, and we discussed legislative efforts to man-
date morals. We discovered that being ostracized by
your peers and associates is often the penalty of
being ethical.
Dr. Watters realized that such a class does not
lend itself to the general form of the engineering
curriculum and that he could not simply spout
platitudes to the class. Instead he allowed us to
"discover" the ethical questions of which we were

There was also an investigative assignment for
the class to carry out. Transcripts of several ethical
incidents were distributed to the class and were to

be researched by teams of two. The students were
required to research their individual case and pres-
ent to the class the ethical issues involved, the mis-
takes that were made, where the blame lay, and, if
possible, where the players are now.
The selection of cases consisted of three major
types. First was the historical case. The incident
was usually common knowledge to all participants,
the data were available from simple research, and a

We explored the difficulty of enforcing a uniform
code of ethics in a predominantly free-will
society. We discovered the moral dilemma of self-
preservation versus doing what is right, and we
discussed legislative efforts to mandate morals.

conclusion had in most cases been made. For such a
case, the students were able to perform all of the
tasks of the investigation unless some of the infor-
mation had been lost in history.
The second form was a historical case which was
not common knowledge. Like the previous example,
there is a great deal of information available and a
conclusion has probably been made. However, their
lack of familiarity with the incident allows the stu-
dents to arrive at their own conclusions. Care must
be taken, however, that the students do not simply
write a book report, but rather that they seek out
sources for several viewpoints.
The third type of case was the current event, and
it was the most difficult to research. Since ethics,
or the lack thereof, is a popular subject in the
press, there are usually several general examples
from which to select. However, it may be difficult
to get enough information to make legitimate deci-
sions since in many cases the incidents are still
under investigation. When that is the case, the sce-
nario may better serve the class as a source of im-
promptu discussion.
From my perspective as a student, there are sev-
eral effective ways to spark interest:
Emphasize participation over a letter grade
Promote open-ended discussions
Moderate discussion in an unoffensive manner
Use reading and AV materials as a starting point for
dialogue, not as an end unto itself
Keep all of the students involved in the discussions
Use interactive exercises where possible
Allow time for dialogue
Instructors should be open-minded about students'
opinions and, if need be, avoid subjects on which they
have a strong personal bias

Some important concepts taken from the class

Spring 1991

include the following:
Personal convictions dictate the level of an individual's
IEEE is a model for a professional organization's support
of its members on ethical issues.
Persistent and tactful communication is the most
powerful weapon available to the subordinate engineer
for the prevention of serious ethical blunders.
In many cases ethical dilemmas are "lose-lose" situations:
to be a whistle-blower can result in firing and/or
blackballing, but allowing an unethical practice to persist
poses personal problems as well as leads to the possibility
of being fired, blackballed, or imprisoned.
The most common and most difficult dilemma is faced
when one must choose between survival and "doing the
right thing."


When I first volunteered to teach the ethics course
I experienced some feelings of trepidation. After all,
how was I going to have any impact on the ideas and
ideals of a group of young adults, in their early- to
mid-twenties, who had known me for several years
socially as well as in the classroom? However, this
uncertainty actually led me to the approach I took.
Because we knew each other, I felt we could be hon-
est with each other and refrain from juding each
other by each other's opinions. We could be critical of
those opinions and we could try to change or influ-
ence them, but we would not judge a classmate sim-
ply by his or her opinion on some topic. This ap-
proach led to some initial reticence, but everyone
soon became comfortable with talking in our group,
and some excellent discussions resulted.

A feature which aided the give-and-take of our
discussions was the removal of the pressures of an
examination. Class goals, objectives, and require-
ments were clearly spelled out from the beginning,
and the students knew what they had to do to "make
the grade." They came to look upon the ethics class
not only as a break from the normal routine of the-
ory and research, but also as something which would
be important in their future.

Just how topical and current an ethics course can
be was illustrated by an incident which happened
during the course of the semester-the vessel, Exxon
Valdez, hit a reef in Alaska. For several weeks the
class followed this developing story, and we dis-
cussed the ethics of supertankers, drunk-driving pi-
loting, complacency on safety issues, progress ver-
sus the environment, the rising price of gas at the
pumps, etc. It was invaluable as a learning experi-
ence, it reinforced theory, and it illustrated that a
well-designed ethics course should be flexible enough

to capitalize on current events.

Overall, the course was well received by the stu-
dents. The discussions were lively and the effort
they put into the assigned projects was excellent. To
involve all the students in the discussion, class size
should be small (preferably less than twenty stu-
dents). This type of course requires that students be
treated as adults, and students thus treated will
generally respond favorably. The result is a satisfy-
ing and fulfilling experience for all concerned.

1. Accreditation Board for Engineering and Technology, Inc.,
(ABET), Criteria for Accrediting Programs in Engineering in
the United States, New York, NY (1987)
2. Tucker, W.H., "Dilemmas in Teaching Engineering Ethics,"
CEP, p. 20 April (1983)
3. Wilcox, J.R., "The Teaching of Engineering Ethics," CEP,
p. 15, May (1983)
4. Lindauer, G.C., and D.J. Hagerty, "Ethics Simulation in the
Classroom," CEP, p 17, July (1983)
5. Kohn, P.M., "Perplexing Problems in Engineering Ethics,"
Chem. Eng.,, p. 96, May 5 (1980)
6. Hughson, R.V., and P.M. Kohn, "Ethics," Chem. Eng., p. 132,
September 22 (1980)
7. Unger, Controlling Technology: Ethics and the Responsible
Engineer, Holt, Rinehart, Winston, New York, NY (1982)
8. Martin, M.W., and R. Schinzinger, Ethics in Engineering,
McGraw-Hill, New York, NY (1989)

The following is a list of materials (books, films,
articles, etc.) used or usable in an ethics course. It is
by no means complete. The opinions expressed are
those of the senior author (JCW) and are intended to
aid an instructor formulating a new course in ethics.

* Books
Unger, Stephen H., Controlling Technology: Ethics and
the Responsible Engineer, Holt, Rinehart, and Winston,
New York (1982)
A concise survey of many aspects of the ethics question,
including the codes of ethics, the role of engineering societies,
ethics and the law, and how to avoid conflict. The author
takes a down-to-earth approach to his topic and the text is
liberally laced with case studies which illustrate the theory.
The book is biased towards electrical engineering (reflecting
the background of the author), so there is heavy emphasis on
the IEEE code and EE case studies. The book was generally
well received by the students in my class, though the value for
money was questioned ($20* for a 190-page paperback).

Martin, M.W., and R. Schinzinger, Ethics in Engineering,
McGraw-Hill, New York, NY (1983, 1989)
This book is subdivided into four sections: The Scope of

Chemical Engineering Education

Engineering Ethics; The Experimental Nature of Engineering;
Engineers, Management and Organizations; and Career Choice
and Future Issues. The approach is more philosophical in
nature than Unger's, especially in the first section. However,
the text is generally readable and has a broader scope than
Unger's. It contains excellent discussion problems for
homework or in-class analysis. There are some problems in
the first edition which are omitted from the second, and the
second edition includes some recent case studies such as
Bhopal and Challenger, along with some new problems.

Flores, A., Ethical Problems in Engineering, Vol. One:
Readings, Rensselaer Polytechnic Institute, Troy, NY
This volume consists of a series of essays by several authors
on the general topics of professionalism, codes of ethics,
competitive practice, employed professionals, and social
responsibility. As with any series of papers, this one lacks the
continuity of a monograph and the entries sometimes overlap.
The resulting text tends to drag and makes very dry reading.
However, a short, judiciously-chosen selection could enhance
a lecture course.

Baum, R.J., Ethical Problems in Engineering, 2nd ed., Vol.
Two: Case Studies, Rensselaer Polytechnic Institute, Troy,
NY (1980)
This is the companion volume to the book by Flores. It presents
analyses of, and essays on, many of the classic ethical cases
from about 1960 to 1980. Included are the BART case, the
Pinto gas tank, the Corvair, Hooker Chemicals, and many
others, some of which are not so well known. They serve as
excellent starting points for student research and classroom
discussion. Some of the studies are quite brief, while others
extend to twenty or more pages.


"What You are Now is What You Were When"
This film, about ninety minutes long, is a monologue by Dr. R.
Massey, formerly of the University of Colorado-Boulder, which
examines the origins of our value systems by looking at
influences in our past lives, such as family, church, schools,
peers, media, etc. His model is then applied to different
generations to see how events in their teens and twenties
influence their outlook and actions today. Massey is a dynamic
presenter who talks "a mile a minute" with a strong Texas
twang. Students either love him and find him hilarious, or
loathe him and find him nauseous. My version of the film is
somewhat dated (1976), but I understand there is a more
recent edition available. The film contains some mild profanity,
but nothing the students haven't heard in the movies, or
indeed in the AIChE room!

"Do Scientists Cheat?" NOVA (1989)
This excellent film examines if and how practitioners of science
cheat in presenting research results. The pressures put on
young scientists to publish and win grants are cited as major
causes for this errant behavior. Some classic and recent cases
are examined in detail. The consequences for one scientist
who "blew the whistle" on another's falsified data are
discussed, leading to the seeming conclusion that neither of
them escaped from the situation unscathed. The film makes a
good jumping-off point for classroom discussion of whistle-
blowing, ethics in academe, falsifying of data, etc. (lasts about
one hour).

"Enemy of the People," 60 Minutes
An examination of the case of an employee of Lockheed
Georgia who made an issue of cost overruns in government
contracts. He was ostracized byhis community (a one-company
town), his church, and his employer. When he was fi.,ally
reinstated in the company, it was in a "paper-pushing"
position. The issue of whistle blowing as a lose-lose situation
is very evident in this film (lasts about twenty minutes).

"The Pomeroy File," 60 Minutes
This film examines the case of a pilot for Continental Airlines
who spoke up at a town meeting against a proposed nuclear
power plant and later found out that a national security file
had been compiled on him, citing him as a subversive. The
issues of freedom of speech, national security files on
individuals, "subversives," and the use of such files as leverage
with an individual's employer, are discussed.

Ethics Case Studies, Chemical Engineering Department,
University of Texas. Contact: D.M. Himmelblau
This film features role-playing of five of the cases presented
by Kohn (1980), including analysis by a panel of "experts."
While the acting leaves something to be desired and the
dialogue and roles are highly sexist, it is helpful to see these
case studies portrayed as "real life" situations (lasts about
thirty minutes, about five to seven minutes per case).

The concept of responsibility within the chemical
industries is highlighted in many recent NOVA and
Frontline films. Some examples are "Toxic Trials"
(concerning chemicals in the groundwater being
linked to above-normal incidences of leukemia in
Woburn, Massachusetts), "Who's Killing Calvert
City?" (about pollution problems and local politics in
Calvert City, Kentucky), and "Nuclear Legacy" (about
the nuclear-waste disposal problem). Each film lasts
about one hour.

* Simulations / Games

Where Do You Draw the Line? An Ethics Game (Simile II,
Del Mar, CA 1977)
Five (or less) groups of participants make ethical judgments
about the behavior of people described in a variety of situations.
Each group makes decisions about different sets of situations
and as the results are tabulated some interesting discussions
occur. Once it is made apparent that each group was
considering different situations, discussion can be directed
towards discovering the assumptions which the groups used
to make their judgments and the implications of those
assumptions. The issues raised are stealing, income tax
evasion, and withholding of information (takes about ninety
minutes, including discussion time).

Whistle-blowing Case (Lindauer and Hagerty, 1983)
A young engineer is presented with an ethical dilemma and is
forced to make a decision on blowing the while on his
employer. A cast of ten to twelve characters, representing
various interests in the case, provide him/her with support or
harassment (takes about one hour to complete, with up to
another hour for discussion). O

Spring 1991




A Rational Approach to Its Teaching

PART 1: Notation and Mathematics'

University of the Witwatersrand
Johannesburg, South Africa

traditionally, undergraduate students of thermo-
dynamics have difficulty understanding the sub-
ject and its material. While we do not deny that
there are conceptual difficulties to overcome, it seems
to us that there are two factors in the usual ap-
proach that make a student's introduction to ther-
modynamics more difficult than is necessary.
First, there is the underlying mathematics of the
state functions and the notation associated with it.
This often seems to suggest that the "state func-
tions" and their mathematics are different from the
functions which the student has already met in his
previous mathematical education. Second, the way
in which the state functions (internal energy,
entropy, and temperature) are introduced is not
easily related to the students' previous background
in physics.
In order to address these two problems, we devel-
oped an approach which has now been taught to
third-year chemical engineering undergraduates for
the last six to seven years. It has been our experi-
ence that the students have been able to relate the
material to their previous work in mathematics and
physics with relative ease, and that they have been
able to assimilate the subject without undue diffi-
culty. As a result, the general level of understand-
ing-of both the students and the teachers-has been
significantly improved.
Since the approach tackles the two factors men-
tioned above, which have applicability in quite dif-
' Part 2 of this paper, "Internal Energy, Entropy, and Tempera-
ture," will appear in the next issue of CEE.

Donald Williams has taught at the University of the
Witwatersrand since 1967. He has a special interest
in teaching chemical engineering to students at the
junior end of the curriculum and has recently devised
a new course to be taught to first-year students. His

m- n itl irl et llJpruvniy itha tahinsiy ui a trimuodynamics
was first aroused while being taught by David Glas-
ser in one of his earliest efforts.

David Glasser is a professor of chemical engineering
at the University of the Witwatersrand. He holds de-
grees from the University of Cape Town and Imperial
College (London). His main areas of interest are reac-
tion engineering and mathematical modeling. He has
been interested in teaching thermodynamics eversince
he first became involved after being "made an offer"
as the most-junior member of the academic staff.

ferent areas, it is convenient to divide our presenta-
tion into two parts. Part 1 will consider notation and
the mathematical development, and Part 2 (which
will appear in the next issue of CEE) will be
concerned with the introduction of the state func-
tions. The notation which we introduce was
developed by Harris,11,21 and the axiomatic
approach adopted in Part 2 is based on Callen,131
who suggested this method as long ago as 1960.
We find it surprising that Callen's approach has
not found more favor with educators. It is the pur-
pose of this paper to show how these ideas can be
combined to form a logical and consistent introduc-
tion to thermodynamics.
Notation and Mathematical Development
Thermodynamics traditionally employs a deriva-
tive notation which is rarely used elsewhere and
which is not obviously consistent with the mathe-
matics which students learn and use in other courses.
Thus, the conceptual difficulties are compounded by
the need to learn a sort of thermodynamicc mathe-
Copyright ChE Division, ASEE 1991
Chemical Engineering Education

x ~z

matics" which has special kinds of partial deriva-
tives and non-exact differentials. The mere manipu-
lation of the notation becomes such an arcane proc-
ess that this ability is in itself regarded as "thermo,"
and purely mathematical results are confused with
the results of thermodynamics.
These non-standard forms arise for historical
reasons and from the problems which arise in using
the same symbol to denote a value as well as a
function. We will outline below an alternative method
of presenting the material which is entirely consis-
tent with the mathematics of functions to which
students are accustomed.
We start by emphasizing that the development
at this stage is purely algebraic, and no physical
significance is intended to be attached to any of the
variables we use. Everything could, in fact, be devel-
oped in terms of x, y, and z. However, we prefer to
adopt a set of symbols in which the equations we
develop will turn out (when at a later stage we do
give significance to some of the symbols) to be di-
rectly useful.
Consider a variable H which may be expressed
as a mathematical function (that is a rule for obtain-
ing a value for a dependent variable from given
values of a set of independent variables) of two other
variables T and P. For example, we might write that

H=T2 +2Tlog(P) (1)
Now suppose that another variable V may also
be expressed as a function of T and P; suppose, for
example, that V = T/P. Since we can solve this rela-
tionship to give P = T/, we can substitute in Eq. (1)
to express H as a function of T and V

H = T2 + 2T log(T / V) (2)
We thus have two possible functions for H. The
first gives us the rule for calculating a value of H
from given values of T and P. The second is the rule
for calculating a value of H from values of T and V.
We might be tempted to indicate these two possible
functions for H by some such notation as H(T,P) and
H(T,V). However, this is contrary to all the rules for
functions we have learned in mathematics, where if
H(T,P) is given by Eq. (1), then it follows that
H(T,V) = T2 + 2T log(V) (3)
which is not the same as Eq. (1) and will not give the
required value for H as Eq. (2) will when the state of
the system is given by corresponding values of the
variables P, V, and T. To keep to the mathematical
Spring 1991

We find it surprising that Callen's approach
has not found more favor with educators. It is the
purpose of this paper to show how these ideas can
be combined to form a logical and consistent
introduction to thermodynamics.

formulation to which we are accustomed, we need to
write something like

for Eq. (1), and

H = f(T,P)

H = g(T,V)
for Eq. (2), the corresponding relationship in terms
of T and V, where we use f and g to indicate that
different functions are involved. It is clear that we
need to avoid confusion between the value of H at
certain conditions and its functional form in terms of
the chosen independent variables.
The difficulty in thermodynamics arises from two
factors. First, the actual functional relationships are
rarely known explicitly, and we are usually forced to
work only with their derivatives and other proper-
ties. Second, given the large number of dependent
variables of interest (H) and the even larger possible
number of combinations of independent variables
(P,T,V, .), there are not really enough function
symbols (f,g, .) to go around. Even if there were
enough, it would be very tricky to remember which
function symbol represented which variable as a
function of which independent variables.
We solve this problem by adopting a notation
where f and g are replaced, respectively, by HTP and
HTV. We may then write equations such as
H = HTP(T,P) and H = H"(T,V), where the super-
scripts remind us both that we are dealing with in-
dependent functional forms and of the independent
variables with which we are concerned, while the
terms in brackets tell us the values of these vari-
ables at which to evaluate the function. For the
example above, we will now have the functions

HTP = T2 +2T log(P)


HV = T2 + 2T log(T / V) (4b)
Note also that values such as HTP(273,1) and
HT(273,22.4) are clear and unambiguous.
Of course, we usually find in thermodynamics
that we are concerned not so much with the func-
tions, that is f or g or HTP (which indeed often turn
out to be unknown), but with their derivatives. For

the function f of Eq. (1) there are two possible de-
f and f
aT aP
These derivatives are defined in the usual fashion.
For example
f li (f(T + AT, P)- f(T,P) (5)
aT m0 AT (5)T
Using our superscript function notation, we may
write the two derivatives of f as
TP and TP
aT aP
This notation is found to be considerably less
confusing for the student than the conventional one
in which the first of the above derivatives is written
as (
aT )p
where the P is usually read as "at constant P." Be-
side being somewhat clumsy, this (as we all know)
can lead the student into the confusion shown
by many classic 'howlers,' such as denying the
existence of this derivative at a point in a process
in which P is not constant. In fact, of course, as
the superscript notation emphasizes, P is not a con-
stant, but is an independent variable of both H"T and
aHTP/aT, of exactly the same status as T.
We stress the need to understand the usual nota-
tion, which the students will, of course, find in texts
and other sources which they consult, even if (in the
initial stages at least) this understanding is reached
by translating into our own notation in order to
clarify the functional dependencies. It is, in fact,
interesting to note that students may frequently be
observed using the superscript notation for this pur-
pose when working with the differential equations of
other courses, such as transport phenomena.
Consider now the equation y = f(x). We define dy
and dx to be any two variables which satisfy the
dy = dx (6)
and we call dy and dx differentials. (We need to
write the derivative with the symbol a to avoid con-
fusion with the differentials using the symbol d.)
Note that dy and dx are any quantities which satisfy
this equation; in particular, there are no implica-
tions about the "smallness" of these quantities. It is
clear that dx and dy define a line which is tangent to
the f(x) curve at the point (x,y).
Similarly, for our function H"P we define the dif-

ferentials dT, dH, and dP as quantities which satisfy
dH = H dT+ H p-dP (7)
aT aP
If we divide Eq. (7) by dT, we obtain
dH aH HTP dP (8)
dT- 3T P dT
where we emphasize that the first and last terms
are merely the ratios of two differentials, not deriva-
Notice that from Eq. (7), if dP is zero (which is
perfectly acceptable since we have not divided
through by dP at any stage), we obtain
dT dP T (9)
Just as the differentials of Eq. (6) define a tangent
line to the curve y = f(x), the differentials of Eq. (7)
represent movement on a plane which is the tangent
plane at the point (P,T) to the H = H"r(P,T) surface.
The important point to note is that the left-hand
side of Eq. (9) is an algebraic expression, not a limit
as in Eq. (5). This is a direct consequence of the
definition of Eq. (7) and the fact that the differen-
tials are not necessarily small quantities. The im-
portant result is that all future manipulations will
be algebraic; the limit process only occurs in the
definition of the derivative in Eq. (5).
We need to note, however, that when we place a
constraint such as dP = 0 on an expression such as
the quotient on the left of Eq. (9), the values of dH
and dT are no longer arbitrary, as we have con-
strained their variation.
Using these concepts (especially that of Eq. 9),
the student may develop all of the familiar relation-
ships using only simple and unambiguous algebra.
For example, consider the two differentials dH and
dT. It is clear that
d /d (10)
dHT dT
where we emphasize that the two terms are ratios of
differentials, not derivatives. Now, consider Eq. (10)
when dP = 0. From Eq. (9) we obtain
H 1 T )11
If we consider the following ratios of differentials:
dH dH dV (12)
dT dV dT12)
we may, from the situation when dP = 0, obtain the
well-known relation
dH dH dV (13q
T V 3T (13)
Chemical Engineering Education

Shorthand Notation for Derivatives
The notation which we have adopted for deriva-
tives, although clear, makes for slightly tedious writ-
ing and somewhat more tedious typing or typeset-
ting (although certainly no more so than the tradi-
tional notation). We may save some effort and space
by adopting a shorthand in which
aHTP is replaced by H
Although useful for simple statements and equa-
tions, this notation is somewhat more difficult for
the novice to use in performing algebra. It may be
preferable to use the expanded form, especially in
handwriting, to perform manipulations such as those
of Eqs. (10) to (13) above. This notation may easily
be extended to higher derivatives, as the functions of
thermodynamics are sufficiently "smooth" that the
order of differentiation is not important. (Alterna-
tively, if the order of differentiation is important, we
may use notation such as HT'P' and HP'T' to indicate
the difference.)

We define an integral in the usual way as the
limit of a sum. That is, over some path V = V(S) from
S, to S2
S2 / N
fTSdS= lim Tsv S.V Si[5 ASi
I ASi o i=l x
1 N-+
where NASi = S, S2. (There is no ambiguity about
dS when used in conjunction with the integral sign.)
Canonical Variables
Consider a function USV. This function leads to
differentials given by

dU-= o dS+ dvdV (14)
or, expressed more concisely in the shorthand nota-
tion explained above
dU= Us dS+Usv dV (15)
If we define the functions
TsV = Us and PSV =-USV (16)
then obviously
dU = TdS PdV (17)
We may now regard this equation as being a
differential relationship between U and four vari-
ables (T, P, V, and S), only two of which are inde-
As many readers will know, we can show that
Spring 1991

there is a "special" relationship between U and the
pair of variables, S and V, which is not shared by the
other variables, T and P. The reasoning is outlined
as follows.

Consider the (known) relation

Assume that from the function TSV we may uniquely
solve for S; that is
S = S (19)
We may substituted S = S'v into U = Usv to get
=U SV(s Vv)= U (20)
By similar arguments, we may obtain UsP, U"",
UTs and all the other various combinations of inde-
pendent variables.
We now note, however, that the reverse processes
are not possible. If we have U"T we cannot uniquely
obtain Usv. This is because in the process of differen-
tiating Usv to obtain T or P we lose information.
Suppose, for example, that the functional form of
Usv is such that
Usv = K+As + Bv + Cs (21)
Then in the process of differentiating U with respect
to S in order to obtain Tsv as defined by Eq. (18), we
lose all information about K and the function Bv. It
is therefore not possible to reconstruct USV from U',
since the integration process which reverses the dif-
ferentiation involves the addition of arbitrary "con-
stants" (they may be functions of V) about which we
have no information from UTV.
This special nature of Usv is expressed by saying
that S and V are the canonical variables of U.
The question obviously arises: Is this behavior
peculiar to UsV, or are there other functions which
have different canonical variables? It turns out
that there are such functions. If we invent a new
function A = U TS, then A can be shown (by a
similar argument to the one above) to have canoni-
cal variables T and V. By a similar process, if we let
H = U + PV and G = U TS + PV, then H has as its
canonical variables S and P, while G has T and P.
These new functions HSP, GTP, and A" are the only
new ones we can define with these properties among
the four variables T, P, S, and V, and so they have a
special significance. (For students with suitable
mathematical backgrounds, one may of course ob-
tain H, G, and A directly by Legendre transforms;
for others, the argument above may suffice.)
Useful Relations
We may notice from the definition of H above


that the quantity T, which we defined by T = Us,
will also be equal to HS'P. We may thus obtain the
familiar relationships for T, P, S, and V, such as
T = U = Hs P (22)

Maxwell Relations
These relationships may be obtained as shown in
the following example, where we have set the de-
rivatives out in full for clarity. Since
Tsv = Us (23)
then, provided the functions are twice continuously
differentiable, it follows that
av av (24)

Ts a
I (1Usv j

ap sv



This result may be written more succinctly as
TSv' = ps'. By similar methods, we may obtain the
usual other results, known as Maxwell Relations, or
Cross-Differentiation Identities.
Path-Dependent Functions
Consider the difference AU between the values
U1 and U2 of the function USV at two points (S,,V,)
and (S2,V2). This is given by
AU = U2 U1 (27a)
U= Usv(Si,Vi) (27b)
U2 =USV(S2,V2) (27c)

We may also calculate AU from dU = TdS PdV
2 2 2 2 2
AU= dU= TdS-jPdV= UsvdS-jUsvdV (28)
1 1 1 1 1
We see that the term TdS is a function of S and
V, and will in general therefore have different val-
ues at different points on the (S,V) plane. The JTdS
term is a line integral whose value will depend upon
the path from (S1,V,) to (S2,V2) along which we evalu-
ate it. The same applies to the term JPdV.
The student might see this more clearly if it is
explained in the following fashion. At every point on
the (S,V) plane, there is a value of P, since we may
write P = Psv. We may therefore draw the path on

the (P,V) plane corresponding to the path on the
(S,V) plane along which we are integrating from
point 1 to point 2. On the (P,V) plane, the term JPdV
is simply the area under the curve, which obviously
depends upon the P-V path we are considering.
For future convenience we shall define these two
path-dependent integrals as





so that Eq. (28) becomes
AU=Q+W (31)
We note that while the value of AU depends only
on the initial and final states (S,,V,) and (S2,V2), the
values of Q and W depend on the path between those
two states along which we evaluate their defining
Functions of More Variables
All the functions which we have considered above
have been functions of two variables. The reasoning
may be extended in a straightforward fashion to
functions of a larger number of variables. Although
there is nothing radically new here, experience sug-
gests that in the classroom situation it is better to
start, as we have done above, with only two inde-
pendent variables. Once the concepts are grasped
for these functions, students have no trouble under-
standing the similar results for functions of more
Let us then consider n further independent
variables. We shall give these the symbols
N1, N2, ... N. Nn. The symbolism [N] represents
this whole set of variables. We shall aiso need the
set of n-1 variables [N ] that is N1, N2, ... N_1, Ni+ ,
Nn excluding N1.
We may then consider the function
U UsV[Nj (32)
from which we may write the differential
S V[N.] SV['N. SVN.IN. ji
dU=U Sv[dS +U dV+ U dNi (33)
We may then define
We may then define

SV [Nj]





Substituting these definitions into Eq. (33), we ob-

Chemical Engineering Education

dU=TdS-PdV + idNi (37)
The above definitions of T and P are no different
to those we have used previously. We may define the
functions A, H, and G as we have done before. Thus
and H and G are defined in an analogous fashion.
There are also many new functions we could de-
fine with canonical variables involving one or more
of our new variables [N]. For instance
B= U-g 1N1 = B 1 (38)
but these in general do not turn out to be useful
functions, so we shall not explore this avenue fur-
We may also obtain, as we did above, a set of
Maxwell relations. For example, from the second
derivatives of U, we may obtain
SV'[N S V[Nj]
T = -P (39)
while from A we may obtain
TV'[Nj] T'V[Nj
S =P (40)
Many other relationships are of course possible.
For example
TPNj [Njkj] TPN [Nk i] (41)

It perhaps needs to be stressed again at this
point that all the above development is purely mathe-
matical. All the relations we have developed follow
from the properties of functions and their deriva-
tives and from our (arbitrary) definition of the sym-
bols P and T in terms of the derivatives of Usv. We
have not yet done any "thermodynamics"!
The development that may be referred to as
"thermo" (including the identification of our symbols
T and P with their usual meaning) will form the sub-
ject of Part 2 of this paper.
We may also note that in this approach the mathe-
matics we use is entirely consistent with that which
a student has learned in the standard mathematics
course. In particular, we have no need for any spe-
cial kinds of derivatives. We have found in our teach-
ing that students readily assimilate this material

and do not appear to have the same problems of
understanding that the authors did when they were

1. Harris, W.F., ChemSA, 7(12), 259 (1981)
2. Harris, W.F., ChemSA, 8(7), 82 (1982)
3. Callen, H.B., Thermodynamics, John Wiley & Sons, New
York, NY (1960) 0

book review

by Gael D. Ulrich
John Wiley & Sons; 472 pages, $33.95 (1984)

Reviewed by
Andrew N. Hrymak
McMaster University
This book is intended as a reference text for a
course using case studies such as those from the
AIChE design competition. Topics covered in the
book fall into three main categories: process design,
economics, and technical report writing. Extensive
references to well-known chemical engineering texts
and handbooks are found throughout the book.
The first section is entitled "Process Design." The
chapters within this half of the book cover the design
process, process conception, flowsheets, and the speci-
fication and design of individual pieces of equip-
ment. In Chapter 2, the reader is introduced to the
importance of understanding the process and ob-
taining typical flowsheets from the literature and
Chapter 3 summarizes flowsheet preparation and
common symbols.
Chapter 4 is a lengthy chapter devoted to the
specification and design of individual pieces of proc-
ess equipment. Separate sections cover different
classes of units (such as heat exchangers, pumps,
reactors, etc.). Each section gives a brief overview of
Continued on page 95.

Spring 1991

Each year Chemical Engineering Education publishes a special fall issue devoted to graduate
education. It consists of 1) articles on graduate courses and research, written by professors at various
universities, and 2) ads placed by chemical engineering departments describing their graduate programs.
Anyone interested in contributing to the editorial content of the 1991 fall issue should write to the
editor, indicating the subject of the contribution and the tentative date it will be submitted.
SDeadline is June 1, 1991.

Random Thoughts...



North Carolina State University
Raleigh, NC 27695-7905

Being engineering professors, we all know about
the need to make assumptions and we also
know that if the assumptions are invalid, the results
can be worthless. We learn early in our careers to
check our results (Does the model fit the data? Does
the algorithm converge? Does the product meet qual-
ity specifications?) and if they are not satisfactory, to
question our assumptions (Is the solution ideal? Is
the reactor isothermal? Is flow laminar?), and we try
to develop the same critical, questioning mentality
in our students.
When it comes to education, however, our men-
tality changes. We generally do whatever it is we do
without much critical evaluation of how well or how
poorly it is working, and we accept without question
what Armando Rugarcial2' calls academic myths-
assumptions that have never been shown to have
any basis in reality and often defy common sense.
Here are some of them.


People who (1) don't have Ph.D.'s, or (2) have
spent their careers in industry and have no
research publications, are not qualified to be
engineering professors.
When filling faculty vacancies, an engineering
department benefits most by selecting the can-
didates in the hottest and currently most fund-
able research areas. How much grant money
they attract in the next five years is more
important than whether they know enough
engineering to teach the core courses and to
change research areas if their present one goes
out of fashion.
The best way to handle required courses that
Copyright ChE

no one wants to teach, such as the unit opera-
tions laboratory or the capstone design course,
is to rotate them among the faculty so that
no one gets stuck with them too often. An
inferior solution is to fill a vacant faculty po-
sition with someone who has the desire to
teach these courses and the expertise to teach
them well.
When selecting a department head, the faculty
benefits most by choosing the candidate with
the strongest research record, regardless of
administrative experience or ability. How he
or she runs the department in the next five to
ten years is less important than what he or
she does in research after that.


Excellence in research and excellence in teach-
ing are highly correlated.
Requiring EVERY faculty member to build
up a strong research program as a condition
for promotion and tenure is in the students'
(professors', department's) best interests.
Excusing new professors from teaching re-
sponsibilities so they can write proposals is a
good thing to do. Excusing them from re-
search responsibilities so they can develop a
couple of good courses makes no sense.
Professors who are excellent at research and
mediocre-to-adequate at teaching deserve ten-

Richard M. Felder is a professor of chemical eng
neering at North Carolina State University, where h
has been since 1969. He received his BChE fro.
City College of C. U.N. Y. and his PhD from Princeto.
"" He has worked at the A.E.R.E., Harwell, an

Divson, ASEE 1991


oDI uuna, l I vaI na aL aty, anIICIU a prseU b lt
courses on chemical engineering principles, reactor
design, process optimization, and effective teaching
to various American and foreign industries and insti-
tutions. He is coauthor of the text Elementary Prin-
ciples of Chemical Processes (Wiley, 1986).

Chemical Engineering Education

ure. Professors who are excellent at teaching
and mediocre-to-adequate at research don't.


Our graduates routinely say they never use
907c of what we taught them. Since we're
engineering professors, 90% of what they're
doing must not be engineering.
It makes sense educationally to teach stu-
dents a generalized theory (e.g., transport
theory) before teaching them anything about
the specific phenomena and devices that the
theory was invented to describe (e.g., unit
Tensor calculus, quantum chemistry, and
statistical mechanics should be taught to every
chemical engineering undergraduate; statis-
tical process control, project management, and
technical writing they can pick up on their
own-there's no room for those subjects in
our crowded curriculum.
The best thing to do with ethics, safety, envi-
ronmental science, and all those other impor-
tant things ABET says we have to teach, is
stick them all in the capstone design course.
I accomplish something useful when I spend
fifty minutes in class writing detailed deriva-
tions on the chalkboard for the students to
We can't teach students to think critically or
creatively-ither they can do it or they can't.
Students who complain that our lectures have
nothing to do with the real world don't know
anything about the real world-and we do.
IfI have covered the syllabus, I have done my
job successfully.

How well our students will do as engineers
correlates highly with (a) their undergradu-
ate GPA; (b) their ability to solve problems
with unfamiliar twists on 50-minute exams;
(c) anything else that we typically use to evalu-
ate them.
An average score of 40 on my final exam
proves (a) I set high standards; (b) they didn't
understand the material. There is no possi-
Spring 1991

ability that it proves (c) the test was lousy.
An average score of 85 on your final exam
proves (a) it was a trivial test; (b) you're a soft
grader; (c) there was widespread cheating.
There is no possibility that the result proves
(d) they learned the material.
Performance on the written Ph.D. qualifying
examination correlates with anything except
performance in courses on the same material.


All methods of evaluating teaching are unre-
liable, and student evaluations are the most
unreliable of all.
If you get consistently outstanding student
evaluations, it must be because you are (a) an
easy grader; (b) an "entertainer." It is cer-
tainly not because you are (c) an outstanding
Ifl get consistently rotten student evaluations,
it is because (a) the students are ignorant
and lazy; (b) I don't water down the ma-
terial for them; (c) they don't understand
what I am doing for them now but in later
years they'll come back and thank me. It is
definitely not because (d) I am doing a rot-
ten teaching job.

I could go on, but you get the idea.

When I classify these points as myths I am not
saying there's nothing to them; it's just that as far as
I know they've never been scientifically or even
empirically validated. (Mentioning someone who is
great at both teaching and research, for instance,
doesn't quite do it.) If you can justify one or another
of these assumptions, let me know and I'll set the
record straight. If, on the other hand, you conclude
that the assumptions might be faulty, then how about
considering whether some alternative assumptions
might lead to better ways of doing things? Couldn't
hurt. 1
'Before you attempt it, though, you might want to check out the
literature: McKeachie'l provides invaluable summaries of the
research on most of the topics in question, and Rugarcia'' makes
some interesting points specifically on the research/teaching di-
1. McKeachie, W.J., Teaching Tips: A Guidebook for the Be-
ginning College Teacher, 8th ed., Toronto, D.C. Heath & Co.
2. Rugarcia, A., "The Link Between Teaching and Research:
Myth or Possibility?" Engineering Ed.. 81, 20 (1991)





University of South Florida
Tampa, FL 33620

Courses addressing topics in biotechnology are
becoming more common in the chemical engi-
neering curriculum. Many departments offer a sen-
ior- or first-year graduate course in biochemical en-
gineering fundamentals, often following the curricu-
lum developed by Bailey and Ollis.'2'1 Tavlarides'I3
also describes a course in enzyme and biochemical
engineering for graduate students. However, the text
of Baily and Ollis, now in its second edition,141 ap-
pears to be the book of choice, due to the fact that its
orientation is towards chemical engineering while
most other books are aimed at biochemists or bio-
technologists. The only exception to this might be
the text of Aiba, et al.,'" which is (unfortunately) out
of print. There has been an increase in the number
of potential texts during the last few years, such as
the text by Bu'lock and Kristiansen.'"'
Basic enzyme technology is often addressed in
such an introductory course, and it usually includes
enzyme kinetics in some detail along with some ref-
erence to immobilized enzymes. More advanced
courses in enzyme kinetics are quite often handled
by chemistry departments at the graduate level.
However, selected advanced enzyme technology con-
cepts within chemical engineering are frequently in-
cluded as special topics in courses such as advanced

William E. Lee III is an assistant professor of chemi-
cal engineering at the University of South Florida.
He is the coordinator of the biotechnology and
biomedical programs between chemical engineer-
ing, the College of Natural Science, and the College
of Medicine. His current research interests involve
the application of chemical engineering principles to
problems in the life and medical sciences, including
research in sensory perception, metabolic aspects
of disease processes, and problems in citrus proc-

kinetics and reactor design. In most of these cases,
the topic of immobilized cells is given only passing
reference at best. One application example that is
sometimes addressed relates to biofilms which im-
mobilize microbes that form on the walls of fermen-
tation vessels, including the aeration tanks in waste-
water treatment. Biosensors may also be discussed.
Otherwise, applications are often only briefly cov-
ered, if at all.
The technology of immobilized enzymes and cells
has grown tremendously over the last decade. Chemi-
cal engineers are involved in the immobilization proc-
esses themselves in addition to the ultimate utiliza-
tion in some bioreactor configuration. The descrip-
tion of the kinetics and mass transfer aspects of
immobilized systems depends on a good foundation
in chemical engineering transport phenomena and
reaction engineering. Many enzyme applications
involve the enzyme in an immobilized form due to a
number of advantages (versus the free form) such as
ease of recovery, maintenance of the active form at
higher levels for longer times, more freedom in reac-
tor operation, and less potential product contamina-
tion problems."7
Economic considerations often favor the immobi-
lized system'8" for the same reasons stated above in
addition to the higher throughput rates (relative to
the free form) that can often be realized. However, a
detailed economic analysis must consider the costs
of the immobilization process itself since prepara-
tion for the more sophisticated techniques may be
Immobilized cells enjoy many of the same bene-
fits as immobilized enzymes. In the case of mam-
malian cells, immobilization is often the only way

SC(0pyriight ChE Diriim. ASEE 1991

Chemical Engineering Education

Immobilization technology has found its way into a variety of applications, including organic chemical
production, food processing, pharmaceutical production, environmental engineering, and (receiitly)
biomedical situations.... This article describes a course in chemical engineering which
addresses, in some detail, the technology of immobilized enzymes and cells.

that cells can be used in most reactor systems, due
in most cases to their fragility. For example, mam-
malian cells may not be able to tolerate even the
gentlest of mechanical agitation.
Immobilization technology has found its way into
a variety of applications, including organic chemical
production, food processing, pharmaceutical produc-
tion, environmental engineering, and (recently) bi-
omedical situations. Increased employment of this
technology will probably parallel the continuing suc-
cesses of molecular biology. Immobilized enzymes
and cells are also important in the biosensor area,
where very specific probes are now possible as a
result of this technology.
This article describes a course in chemical engi-
neering which addresses, in some detail, the tech-
nology of immobilized enzymes and cells. It is meant
to be an elective course for advanced seniors or gradu-
ate students in chemical engineering or some other
technical discipline. The course has been offered twice
at this writing, and will be offered in the future as
part of a series of chemical engineering electives in
the biotechnology area.


Table 1 presents the course outline. As can be
seen, the one-semester course (3 semester credits)
covers a variety of topics, including the basic immo-
bilization methods, transport phenomena and kinet-
ics of immobilized systems, reactor configurations,
and applications. An important application area
which received special attention involved biosensors.
The topic of basic microbe physiology and the impact
of immobilization procedures on viable organisms
was also addressed.

Two texts were required for the course. Process
Engineering Aspects of mmobilized Cell Systems, by
Webb, et al.,19' was used along with Immobilized
Microbial Systems: Principles, Techniques, and In-
dustrial Applications, by Kolot."101 In addition, a
number of journal articles and other readings (see
Table 2, next page) were utilized.

Each class meeting typically started with the
presentation of an application example, either by
one of the students or by the instructor. The presen-
tation and following discussion were limited to ten

Course Outline

1. Introduction to immobilized enzyme and cell technology
2. Immobilization methods
A. Entrapment
other methods
B. Binding
Carrier binding
physical adsorption onto surfaces (including physical
aspects of various carriers)
ionic binding
chelation or metal binding
covalent binding
C. Cross-linking
D. Analytical methods used to study the effectiveness of

3. Immobilized cell physiology
A. Importance of cell physiology prior to immobilization

B. Effect of immobilization on cell physiology
C. Activity of immobilized cell particles, including mass
transfer and control of cell growth and metabolism
4. Immobilized system kinetics
A. External mass transfer resistances
B. Intraparticle diffusion and chemical reaction
C. Simultaneous internal and external resistances

5. Reactor design considerations
A. Basic enzyme kinetics
B. Reactor configurations used for immobilized biocatalysts
C. Miscellaneous topics
biofilm formation
mixing and agitation approaches
oxygen supply
control schemes
6. Biosensors
A. Types of sensors and underlying principles
B. Applications

Spring 1991

minutes. The two texts included a number of appli-
cation discussions and were eventually addressed as
part of this series. Additional examples, beyond those
in the texts, were presented by the instructor during
the course and are listed in Table 3.
There were also a few supplementary exercises.
In the first exercise, students were instructed to con-
tact an industrial supplier of immobilized enzymes
and, if the supplier was cooperative, to obtain a
sample of the product along with any descriptive
literature. The samples thus obtained were displayed
in one session for all to see. We also viewed some of
the samples under a scanning electron microscope.

The second exercise involved the analysis of US
Patents involving immobilized systems, specifically
"Process for Preparing Biomass Attached to a Car-
rier" (Patent No. 4,560,479) and "Immobilization of
Microorganisms on a Plastic Carrier" (Patent No.
For the final exercise, students presented three
in-class presentations on the following topics:
A method of physical adsorption of an enzyme or
cell onto a surface, including the underlying
physical principles
An analytical procedure which could be used to
determine the extent of success of an
immobilization procedure
An application example
Students were told that the presentations should
last ten to fifteen minutes. The general class was
allowed to direct questions to the presenter follow-
ing the presentation.
The students also did simple experiments involv-
ing the immobilization process itself. They formed
alginate gels (no enzyme or microbe involvement)
starting with sodium alginate solutions,"1I and they
formed K-carrageenan gels by dissolving the mate-
rial in physiological saline, warming, and contacting
with a gel-inducing agent.1101


The two texts used in the course were good selec-
tions. Their technical depth is satisfactory, and they
are reasonably priced (the combined price is less
than $70). Neither book addresses immobilization
methods in any depth. Also, analytical procedures to
establish the success (or lack thereof) of an immobi-
lization procedure are not cited. As a result, both of
these important topics were addressed via outside

sources (see Table 2). Additionally, the topic of bio-
sensors is not considered in either text, so outside
supplementation in that area was also necessary
(noted in Table 2). The discussion on biosensors
stressed the underlying enzymatic principles involved
and did not emphasize any associated electronics or
probe hardware aspects. Finally, the texts do not
consider engineering economic analysis at all, but
this was easily handled by additional materials.
Application examples were presented through-
out the course, some by the students themselves but
most of them by the instructor. I found that mixing
in the applications with the technical material was
effective, and it helped the students to focus on the
concept that there are many real applications, i.e.,
that the topic is not just theoretical in nature. The
students also found the discussion on the patents to
be interesting, both as to the technical content and
as to the nature of the patent and patenting process

Selected Additional References

General Materials
Enzyme Engineering Case Study: Immobilized Lactasel141
Industrial Applications of Immobilized Enzymes: A com-
mercial Overview18]
Immobilized Enzymes: A Survey[15"

Immobilization Methods
Preparation and Properties of Gel Entrapped Enzymes1'lo
Microbial Adhesion in Perspective'17'
Adherence of Marine Micro-Organisms to Smooth Surfaces[t18
Mechanisms involved in Sorption of Microorganisms to
Solid Surfaces191
Microcarrier-Bound Mammalian Cells'201
A Range of Ceramic Biosupports[21'
Carriers for Immobilized Biologically Active Systems[221
Immobilization of Enzymes by Adsorption'23'
Covalent Linkage III: Immobilization of Enzymes by
Intermolecular Cross-Linking1241
Some Techniques Involved in Study of Adsorption of
Microorganisms to Surfaces[251

Mass Transfer and Kinetics
Mass Transfer in Immobilized Cellsl261
Oxygenation of Processes Involving Immobilized Cells127]
Diffusion and Kinetics with Immobilized Enzymes[28]

Reactor Technology
Design and Operation of Immobilized Enzyme Reactors[291
Reaction Engineering Parameters for Immobilized

Membrane Systems: Analysis and Designl321
Immobilized Enzymes for Clinical Analysis'331

Chemical Engineering Education

itself-something most of the students knew little

Most students who selected this course had pre-
viously taken the senior chemical engineering class
titled "Theory and Design of Bioprocesses," a course
which uses the text of Bailey and Ollis. However,
there are always some students who have not-typi-
cally, students in the environmental engineering
sequence of civil engineering. Their participation in
the course required several lectures on basic enzyme
kinetics. Also, the section on intraparticle transport
phenomena and kinetics required a presentation of
some preliminary background (Bailey and Ollis give
a good elementary treatment) in order to bring all
the students up to speed.

The weakest area of the course involved the labo-
ratories. Ideally, several experiments should be done
(at least as demonstrations) which cover a variety of
immobilization methods. A minimal series could in-
clude an example of gel entrapment, covalent cross-
linking, microencapsulation, and physical absorp-
tion. These should be supported by SEM or some
other appropriate analytical inspection procedure.
Several recipes are presented by Trevan'121 and by
Rosevear."113 Another good experiment could involve
a comparison of free and immobilized enzymes in a
simple reaction experiment. I intend to improve the
laboratory aspect of the course in future offerings.

Finally, the in-class presentations were effective
for two reasons: it made students more aware of the
available sources of information on the subject, and
it gave students good practice in organizing and
orally presenting a technical topic, something in
which most of them did not have much experience.

Selected Application Examples
(in addition to examples in the texts)

Antibody Production[341
Separation of L-Amino Acids from Mixtures of the L- and
D-Amino Acids'35,361
Hybridoma and Monoclonal Antibody Productiont37'
Drug Production from Immobilized Plant Cells381
Hydrolysis of Lactosel39
Encapsulation of Vaccines and Hormones1401
High-Fructose Corn Syrup Production[41'
Bioconversion of Lipophilic Compounds'42'
Effect of Biofilm Presence on Reactor Performance'41

In summary, the course effectively presents a va-
riety of new information regarding immobilized en-
zyme and cell technology. All the students claim to
have received new knowledge, and all could see the
potential and demonstrated significance of the tech-
nology. While this is a good stand-alone elective, it is
especially effective when the students have previ-
ously taken an introductory course in biochemical

1. Bailey, J.E., and D.F. Ollis, "Biochemical Engineering Fun-
damentals," Chem. Eng. Ed., 10,162 (1976)
2. Bailey, J.E., and D.F. Ollis, "Biochemical Engineering Fun-
damentals (Revisited)," Chem. Eng. Ed., 19, 168 (1985)
3. Tavlarides, L.L., "Enzyme and Biochemical Engineering,"
Chem. Eng. Ed., 8,188 (1974)
4. Bailey, J.E., and D.F. Ollis, Biochemical Engineering Funda-
mentals, McGraw-Hill Book Co., New York, NY (1986)
5. Aiba, S., A.E. Humphrey, and N.F. Millis, Biochemical Engi-
neering, Academic Press, New York, NY (1973)
6. Bu'lock, J, and B. Kristiansen, Basic Biotechnology, Aca-
demic Press, London, England (1987)
7. Atkinson, B., "Immobilized Cells, Their Application and Po-
tential," in Process Engineering Aspects of Immobilised Cell
Systems, by C. Webb, G.M. Black, and B. Atkinson, eds.,
Pergamon Press, Inc., Elmsford (1986)
8. Sweigart, R.D., "Industrial Applications of Immobilized En-
zymes: A Commercial Overview," App. Biochem. Bioeng., 2
9. Webb, C., G.M. Black, and B. Atkinson, Process Engineering
Aspects of Immobilised Cell Systems, Pergamon Press, Inc.
Elmsford (1986)
10. Kolot, F.B., Immobilized Microbial Systems:Principles, Tech-
niques, and Industrial Applications, Robert E. Krieger Pub-
lishing Co., Malabar, FL (1988)
11. Mattiasson, B., "Immobilized Systems," in Immobilized Cells
and Organelles, B. Mattiasson, ed., CRC Press, Inc., Boca
Raton, FL (1983)
12. Trevan, M.D., Immobilized Enzymes, John Wiley and Sons,
New York, NY (1980)
13. Rosevear, A., J.F. Kennedy, and M.S. Joaquim, Immobilized
Enzymes and Cells, A. Hilger, Philadelphia, PA (1987)
14. Ford, J.R., and W.H. Pitcher, "Enzyme Engineering Case
Study: Immobilized Lactase," in Immobilized Enzyme Tech-
nology, J.J. Weetall, S. Suzuki, eds, Plenum Press, New
York, NY (1975)
15. Goldstein, L., and E. Katchalski-Katzir, "Immobilized En-
zymes: A Survey," in Applied Biochemistry and Bioengineer-
ing. Volume 1, Immobilized Enzyme Principles, L.B. Win-
gard, E. Katchalski-Katzir, and L. Goldstein, eds, Academic
Press, New York, NY (1976)
16. O'Driscoll, KF., "Preparation and Properties of Gel Entrapped
Enzymes," Adv. Biochem. Eng., 4,155 (1976)
17. Marshall, K.C., and G. Bitton, "Microbial Adhesion in Per-
spective," in Adsorption of Microorganisms to Surfaces, G.
Bitton and K.C. Marshall, eds., John Wiley and Sons, New
York, NY (1980)
18. Fletcher, M., "Adherence of Marine Micro-Organisms to
Smooth Surfaces," in Bacterial Adherence, E.H. Beachey,
ed., Chapman & Hall, New York, NY (1980)
19. Daniels, S.L., "Mechanisms Involved in Sorption of Microor-
ganisms to Solid Surfaces," in Adsorption of Microorganisms

Spring 1991

to Surfaces, G. Bitton and K.C. Marshall, eds, John Wiley
and Sons, New York, NY (1980)
20. Hirtenstein, M., and J. Clark, "Microcarrier-Bound Mam-
malian Cells," in Immobilized Cells and Organelles, B. Mat-
tiasson, ed., CRC Press, Inc., Boca Raton, FL (1983)
21. Adams, J.M., L.A. Ash, A.J. Brown, R. James, D.B. Kell, G.J.
Salter, asnd R.P. Walter, "A Range of Ceramic Biosupports,"
Am. Biotech. Lab., October (1988)
22. Messing, R.A., "Carriers for Immobilized Biologically Active
Systems," Adv. Biochem. Eng., 10, 52 (1978)
23. Zaborsky, O.R., "Immobilization of Enzymes by Adsorption,"
in Biomedical Applications of Immobilized Enzymes and
Proteins, Volume I, T.M. Chang, ed., Plenum Press, New
York, NY (1977)
24. Zaborsky, O.R., "Covalent Linkage: III. Immobilization of
Enzymes by Intermolecular Cross-Linking," ibid.
25. Costerton, J.W., "Some Techniques Involved in Study of
Adsorption of Microorganisms to Surfaces," in Adsorption of
Microorganisms to Surfaces, G. Bitton and K.C. Marshall,
eds., John Wiley and Sons, New York, NY (1980)
26. Radovich, J.M., "Mass Transfer Limitations in Immobilized
Cells," Biotech. Adv., 3, 1 (1985)
27. Enfors, S.O., and B. Mattiasson, "Oxygenation of Processes
Involving Immobilized Cells," in Immobilized Cells and Or-
ganelles, B. Mattiasson, ed., CRC Press, Boca Raton, FL
28. Engasser, J.M., and C. Horvath, "Diffusion and Kinetics
with Immobilized Enzymes," in Applied Biochemistry and
Bioengineering: Volume 1, Immobilized Enzyme Principles,
L.B. Wingard, E. Katchalski-Katzir, and L. Goldstein, eds.,
Academic Press, New York, NY (1976)
29. Pitcher, W.H., "Design and Operation of Immobilized En-
zyme Reactors," Adv. Biochem. Eng., 10, 1 (1978)
30. Buchholz, K., "Reaction Engineering Parameters for Immo-
bilized Biocatalysis," Adv. Biochem. Eng., 24, 39 (1982)
31. Turner, P.F., Biosensors: Fundamentals and Applications,
Oxford University Press, Oxford, England (1987)
32. Vieth, W.R., Membrane Systems:Analysis and Design, Hanser

Continued from page 63

stations for the two-semester senior course. For twenty
years now we have continuously worked on upgrad-
ing the laboratory experiments and its format.

During these years, together with colleagues in
the civil engineering department, Angie also initi-
ated cooperative efforts at the graduate level in en-
vironmental engineering. The first joint effort was to
secure an interdisciplinary water-pollution training
grant for graduate civil and chemical engineers,
funded by the Federal Water Pollution Control
Administration. This then led to the development of
an interdisciplinary program in environmental engi-
neering. Angie developed courses in unit operations
of water treatment processes and in solid waste man-
agement processes.

Angle and John Liskowitz developed other highly
successful joint research and programs that eventu-
ally led to numerous EPA research grants as well as

Publishers, New York, NY (1988)
33. Suzuki, S., and I. Karube, "Immobilized Enzymes for Clini-
cal Analysis," in Enzymes and Immobilized Cells In Biotech-
nology, A.I. Laskin, ed., Benjamin Cummings Publishing
Co., Inc., London, England (1985)
34. Nillson, K., "Entrapment of Cultured Cells in Agarose Beads,"
in Large Cell Culture Technology, Hanser Publishers, New
York, NY (1987)
35. Chibata, I., T. Tosa, and T. Sato, "Immobilized Biocatalysts
to Produce Amino Acids and Other Organic Compounds," in
Enzymes and Immobilized Cells in Biotechnology, A.I. Laskin,
ed., Benjamin Cummings Publishing Co., London, England
36. Chibata, I., and T. Tosa, "Industrial Applications of Immobi-
lized Enzymes and Immobilized Microbial Cells," in Applied
Biochemistry and Bioengineering. Volume 1. Immobilized
Enzyme Principles, L.B. Windgard, E. Katchalski-Katzir, and
L. Goldstein, eds., Academic Press, New York, NY (1976)
37. Goosen, M.F., "Animal Cell Culture in Microcapsules," Chem.
Eng. Ed., 22,196 (1988)
38. Brodelius, P. "Immobilized Plant Cells," in Immobilized Cells
and Organelles, Volume I, B. Mattiasson, ed., CRC Press,
Inc, Boca Raton, FL (1983)
39. Goldberg, B.S., "A Novel Immobilized Enzyme Reactor Sys-
tem," paper presented at the 24th Annual Spring Sympo-
sium, AIChE, East Brunswick, NJ, May 10 (1984)
40. Change, T.M.S., "Biomedical Applications of Artificial Cells
Containing Immobilized Enzymes, Proteins, Cells, and Other
Biologically Active Materials," in Enzymes and Immobilized
Cells in Biotechnology, A.I. Laskin, ed., Benjamin Cummings
Publishing Co., London, England (1985)
41. Barker, S.A., and G.S. Petch, "Enzymatic Process for High-
Fructose Corn Syrup," in Enzymes and Immobilized Cells in
Biotechnology, A.I. Laskin, ed., Benjamin Cummings Pub-
lishing Co., London, England (1985)
42. Tanaka, A., and S. Fukui, "Bioconversion of Lipophilic Com-
pounds by Immobilized Biocatalysts in the Presence of Or-
ganic Solvents," ibid. O

an Exxon grant that funded an environmental toxi-
cology option under the direction of Dick Trattner.
Out of all these efforts came the impetus for the
Institute for Hazardous and Toxic Waste Manage-
ment and the NSF-initiated Haz-Tox Center.

While Angie's research efforts have been in the
main environmentally oriented, his research inter-
ests span the spectrum from ultrasonic-aided mass
transfer to characterization of leachate from MSV
incinerator ash. His current interest is in MSW in-
cinerator residue, which he has been working on
jointly with Don Sundstrom and Herb Klei (Univer-
sity of Connecticut). This research is an outgrowth
of a two-year (1988-90) stint as a visiting professor
of chemical engineering and a research fellow at the
Environmental Research Institute at UConn.

A fellow of AIChE and ASEE, he is the recipient
of numerous citation certificates and awards, includ-
ing the ASEE/MidAtlantic Western Electric Award,
the DELOS Distinguished Service Award, and the
ODK Award of Merit.

Chemical Engineering Education

His AIChE activities include service on ten insti-
tute committees, Technical Program Vice-Chairman
of the 1977 NYC Annual Meeting, and Chairman of
both the Student Chapters Committee and the Edu-
cational Projects Committee. He has also served as a
Director of the New York City AIChE local section.
In ASEE he has served on numerous commit-
teess over the years, including Chairman of the 3M
and DELOS Award Committees, in addition to hold-
ing ten elective offices, including Chairmanships of
CHED, DELOS, and the Instrumentation Division.
In addition to the above professional activities,
he has also served as Chairman of the ACS Mobay
Committee, and as National President of Omega Chi
Epsilon (the chemical engineering honor society),
and President of the Association of College Honor
Societies. He is also the author of approximately
thirty-five papers, numerous presentations, coauthor
of a book, and coeditor of three proceedings.
Angie's role in Omega Chi Epsilon deserves spe-
cial attention. When Angie came to our department
as a young assistant professor in 1967, I was Faculty
Advisor of Omega Chi Epsilon, an honorary society
with relatively few members at the time. I seized the
opportunity to pass this advisorship on to our new
young faculty member-I had more seniority and
was being called upon with increasing frequency for
other faculty business. Little did I realize what an
impact this decision would have on the future of
Omega Chi Epsilon. When he became advisor to our
chapter in 1968, there were less than twenty na-
tional chapters in existence. After working inten-
sively with our chapter, he became National Vice
President of the organization in 1974 and then Na-
tional President in 1978. When he completed his
tenure as president he had expanded membership
organization in Omega Chi Epsilon to forty chap-
ters. He continued to work for the organization in
his capacity as past president, and there are now
forty-nine chapters nationwide.
His role as a national leader in Omega Chi Epsi-
lon also led to the office of President of the Associa-
tion of College Honor Societies, an umbrella group
for the nation's more than sixty different honor so-

These activities epitomize Angie's devotion to the
profession. His volunteer involvement has always
been intense, and he has given his time and talents
happily and without thought of reward-his real
reward has been his own satisfaction in having par-

Spring 1991

The multitude of people in our professional socie-
ties that Angie knows continually amazes me-and
he always remembers their names! He and I have
attended these meetings together for years, and al-
though we were at the same sessions, he somehow
always managed to meet many more colleagues than
I, or anyone else, did. He never tires of meeting old,
and new, friends and engaging in lengthy bull-ses-
sions with them at meeting after meeting. His en-
thusiasm permeates the air at check-in and lasts
long after everyone else is tired and ready to go
In addition to service on numerous department
and institute committees at NJIT, Angie has been
Chairman of the Faculty Council and President of
the Professional Staff Association. He has also been
a reviewer for NSF, EPA, AIChE, CEE, I&EC, Engi-
neering Education, and the IACT, jr. He has been a
consultant to the municipal and industrial sector,
and during the summer of 1989 he served as a con-
sultant and senior development officer to UNIDO in
Vienna, Austria.
Angie's activities in the department include a
stint as Acting Department Chairman (covering for
me while I was on sabbatical leave) and as indus-
trial fund raiser. During the 1970s his activities in
fund raising led to a tripling of funds donated to the
department and to the development of a Chemical
Engineering Department Merit Award Program with
its own endowment fund. At the present time he
devotes his energies to teaching and the develop-
ment of a Center for Municipal Solid Waste Studies.
When I was first contacted by CEE about the
possibility of writing this article, I asked Angie for
his permission and cooperation. He agreed with the
one condition that he would be permitted to write
the concluding paragraph for the article. It follows.
You know, I consider myself extremely fortunate
in having had a department and an institute
administration that has supported my activities
at a number of professional society meetings,
and I am appreciative of the large number of
colleagues I have had the opportunity to
interact with through the years. In many cases,
these associations developed into strong
friendships that I have grown to treasure. To
all of these individuals and their families I
would like to take this moment to express my
sincere appreciation for their support and for
the opportunity to have served with them, but
mostly for their friendship over the years. I've
got to say-I'm a very lucky fellow who has had
a rewarding career. o





University of Waterloo
Waterloo, Ontario, Canada N2L 3G1

Conventional wisdom holds that lower-year
courses in mathematics for engineers should be
taught by mathematicians, who can supply the nec-
essary depth and rigor that engineering instructors,
however adept in applying the subject, may lack.
Reality, however, tells us otherwise. Excessive insis-
tence upon uniqueness, existence properties and proof
of theorems, and unfamiliarity with engineering-
flavored problems, coupled with a reluctance to blend
lectures with practical examples, is counterproduc-
tive in lower-year courses. A large proportion of the
students lose interest in the subject; their indiffer-
ence, often mingled with hostility toward anything
mathematical, can make the instruction of higher-
year engineering mathematics and process control a
difficult task.
There is much to be said, as a consequence, for
the teaching of mathematics to undergraduate engi-
neering students by engineering instructors who
possess the required mathematical background and
motivation. Having taught third-year (compulsory)
and fourth-year (elective) courses (including process
control) over the years, I have often been frustrated
by the varying and unpredictable mathematics back-
ground of chemical engineering students entering
their third year. Depending on the whim of the mathe-
matician who taught the second-year course in ap-

- 71 ^__


Thomas Z. Fahidy received his BSc (1959) and
MSc(1961) at Queen's University (Kingston, Ontario,
Canada) and his PhD (1965) from the University of
Illinois (Urbana-Champaign) in chemical engineer-
ing. He teaches courses in applied mathematics to
engineenng students and conducts research in elec-
trochemical engineering. His major research areas
are magnetolectrolysis and the development of novel
electrochemical reactors. He he is the author of nu-
Smerous scientific articles.

Excessive insistence upon uniqueness,
existence properties and proof of theorems, and
unfamiliarity with engineering-flavored
problems,... is counterproductive
in lower-year courses.

plied differential equations, one stream of students
may have been given a healthy dose of certain topics
(notably Laplace transformation) while the next
group would have received little or no instruction in
the same subject. Recently, when an opportunity of
putting my thoughts of what this course should con-
tain into practice, I seized it with alacrity.
The framework and "infrastructure" was given to
me: 1) the course was to be administered by the
mathematics faculty (including the assignment of a
teaching assistant), 2) the traditionally-used text"'
was designated, and 3) the course designation code
and title was assigned. All this suited me fine. I was
eager to set about my goal of putting a strong em-
phasis on the solution of chemical engineering prob-
lems via ordinary differential equations (ODE) which
could be handled in the second year. The strategy
was to discuss the theory behind each technique
in a concise manner but without a formal proof
(except where the procedure was short and straight-
forward) and to supply a goodly number of numeri-
cal illustrations.
Homework assignments, normally consisting of
four to six non-elementary problems per set, were to
be handed out and graded every week. A two-hour
open-book midterm and a three-hour open-book fi-
nal examination would serve as formal measures of
student performance.
The course structure is summarized in Table 1.
The seven major topics follow a similar sequence in
the textbook.'11 In Part 1, the definitions, the gen-

Copyright ChE Division, ASEE 1991

Chemical Engineering Education

eral, particular, and singular solutions, and the ques-
tion of uniqueness are briefly covered, followed by a
more-detailed discussion of direction fields and
isoclines (in anticipation of nonlinear analysis in
future years). In Part 2 the separable-variables tech-
nique, transformation methods, homogeneous equa-
tions, exact differential equations, the integrating-
factor method, and Clairaut-type equations are
treated. This portion of the course is heavily dosed
with (elementary) numerical examples taken from
chemical kinetics, reaction engineering, applied bio-
chemistry, and heat-transfer theory.

Particular attention is paid to linear equations in
Part 3, where Laplace transformation techniques
are introduced and treated by anticipating later use
in fourth-year process control courses in terms of
transfer functions. Since the transfer function is the
bridge in transform space between the input and
output function in a linear system, its concept is in-
troduced early to emphasize its usefulness in solving
differential equations. The basic tools for handling
transform inversion (e.g., reduction to simpler forms
via partial fractioning, convolution theorem, trans-
form tables) are treated in detail, but contour inte-
gration is omitted due to the students' lack of knowl-
edge of complex calculus in the second year.
The treatment of series solutions deviates from
the conventional approach in that various classical
methods (e.g., the method of Frobenius) are covered
briefy- but sufficiently for the introduction of Bessel

functions as an important technique for solving a
class of second-order linear differential equations of
practical importance. Due to time limitations, only
the Bessel equation of the first kind is discussed,
with appropriate applications; emphasis is laid
particularly on the handling of the zeroes of
Bessel functions in view of physical considerations
(see Example 1).
In the next section, on orthogonal functions
and Sturm-Liouville theory, the motivation for the
orthogonality concept is emphasized and the general
technique for the expansion of functions into or-
thogonal series is briefly shown (the discussion of
Fourier series in solving partial differential equa-
tions in a subsequent third-year course is an exten-
sion of this topic).
Part 6 concerns a subject of growing importance
at lower-year levels but which is not traditionally
taught in this course: numerical techniques. I am
convinced that the numerical handling of all mathe-
matical problems of engineering importance should
be introduced as early as possible and that an undue
weighting of analytical techniques is outdated. The
obsolete philosophy of neglecting numerical solutions
at a lower-year level is also manifested in the text-
book, which deals only with the Euler techniques
and the Runge-Kutta method (in a surprisingly short
chapter). To remedy this, I added the handling of
second-order ODE's with two-point boundary value
problems (see Example 2) and initial value problems

Structure of Second-Year Course in Applied Differential Equations



1. General concepts and philosophy of ODE's
2. First-order and simple ODE's

3. Linear differential equations and Laplace transformation

4. Series solutions and Bessel functions

5. Orthogonal functions and Sturm-Liouville theory
6. The numerical solution of ODE's
7. System of ODE's and linear ODE's. Linearized systems

First-order irreversible batch reactors; mixing in a well-stirred
tank at equal and unequal inflow and outflow rates; second-
order irreversible batch reactions; radial heat conduction in a
cylindrical solid; flow through containers of various geometries;
growth and decay in simple biochemical reaction systems;
production of isotopes in a nuclear reactor
Countercurrent heater-cooler problems; second-order under-
damped control systems; two-element mixer cascades; elemen-
tary transfer function analysis
Flux distribution in a cylindrical nuclear reactor; radial temp-
erature distribution in a cylindrical conductor; buckling of a
vertical column (in an ecumenical spirit!)
Consecutive irreversible first-order batch reactions; mixer
cascades; flow through mixers equipped with valves

Spring 1991


as a step in (what I conceive to be) the right direc-
tion. (I would be happy to see a strong component of
numerical approaches in earlier calculus courses.)
Finally, Part 7 puts emphasis on the structural
properties of linear systems, e.g., eigenvalues and
eigenvectors. It introduces the state-variable and
state transition matrix concept, the decoupling of
state variables via canonical transformation, and
the solution of nonlinear systems for small excur-
sions about their steady states via linearization
(see Example 3). For obvious reasons, first- and
second-order systems only serve for the purpose of

Physical Importance of the Zeroes of Bessel Functions
The energy flux distribution in an upright cylin-
drical nuclear reactor of radius R is given by the
ODE2' 2
2 d2 + dO 2 2 (1)
dr2 dr
where y is a known physical parameter. At r = R, the
flux 4 is zero and the maximum energy flux, called
the design power level of the reactor, exists at the
axis: 4Om = )(0). Since )ma is finite, the Yo-function
(Bessel function of the second kind order zero) term
must be suppressed in the general solution. Hence
4(r) = maxJo(yr) (2)
where J is the Bessel function of the first kind order
zero. It follows that
Jo(yR)=0 (3)
There are, in principle, an infinite number of roots
which satisfy Eq. (3), but which one should be taken
This is where the physics of the problem must be
considered. We know that the flux decreases from its
maximum value at r = 0 to zero at r = R: so does
Jo(yr) on [0,ao], a, being the first zero of J(x). Since
Jo(x) is negative between a, and the second zero a2,
and negative energy flux is physically meaningless,
the correct solution of Eq. (3) is
yR = al = 2.4048
and the final solution to the problem is given by
)(r) = AJo(2.4048 r / R) (4)
The suppression of successive roots of Bessel
functions past the first one due to physical con-
straints is an often-encountered requirement. An-
other instructive example, albeit not in chemical

engineering, is the stability of a vertical wire prob-
lem'31 involving a fractional Bessel function of the
first kind (good for a homework problem?).

A Simple Two-Point Boundary Value Problem
Given the linear ODE
dy =-exp-y/2 (5)
with boundary conditions x = 0, y = 1, and x = 2,
y = 1, the problem is to estimate the values of y in
the interior of the [0,2] domain. Using the conven-
tional central difference approximation for the
second-order derivative, a grid structure with ele-
Yn 2yn + Yn-1 = -h exp(-y 2) (6)
can be constructed, where n is an arbitrary node (or
mesh point) position in the grid. This is a very good
problem for illustrating at the same time the useful-
ness of linear algebra as well as finite-difference
calculus and iteration strategies. In the simplest
case we take a single interior point at x = 1, and thus
n = 0 and n = 2 become boundary points. Conse-
quently, Eq. (2) reduces to the finding of y, via the
iteration scheme

yL 1 + (1 / 2) exp -y (7)

starting with an arbitrary estimate y10o'. If we choose
y(0) = 1, then yl(4' = 1.16954 and y15' = 1.16955
are obtained; with y 'O = 1, y(4' = 1.16955. If
we choose two interval nodes 2/3 units apart,
we obtain the 2 x 2 matrix A with elements
all = a22 = 2/3 and a2 = a2, = 1/3, connecting the
vector with elements y1(k+", y2k+l) to the vector with
elements 1 + (2/3)2exp(-y1(k)); 1 + (2/3)2exp(-y2(k). It-
eration quickly yields the values of yl = Y2 = 1.15193.
Smaller grid sizes can be assigned for a homework
problem, calling upon the students' computer skills.
The approach is an adaptation of Hamming's treat-
ment of two-point boundary value problems.l41
Linearization of Flow Through a Tank With a Valve in
the Effluent Line
This problem is often discussed in process control
texts'5' and in the author's opinion it serves as an
excellent and simple example to illustrate the con-
cept of linearization and the usefulness of deviation
variables in lower-level courses. The starting point
is the mass balance.
Adh Q h (8)
dt -k (8)

Chemical Engineering Education

where A is the uniform cross-sectional area of the
tank, h is the instantaneous liquid level in the tank,
Qi is the liquid inflow rate, and k is the valve con-
stant. At steady-state conditions

Qi = kV h
Hence, in terms of deviation variables y = h h* and
x Qi Qi*, Eq. (8) is rewritten as

A = X(t) = k(h (9)

For sufficiently small magnitudes of x, the nonlin-
earity is removed by the truncated Taylor expansion
Oh--h= 1 _y
2 h*
and the linear approximation

Ad+ k y=x(t) (10)
2y h
is obtained. The constraints on the validity of lin-
earization are illustrated numerically under a spe-
cific set of conditions as shown in Table 2. Having
discussed this problem in class, we then take up flow
through two tanks in series and solve by elimination
or elementary state variable theory, emphasizing
the stability of the linearized system with negative
real eigenvalues

-k /2A,1 h

- k2 / 2A2 h2

By and large, student response was what could
be expected in any course in engineering mathemat-
ics; those with a grasp of fundamental mathematical
principles were receptive to the application flavor,

Comparison of True and Approximate Solutions
in Example 3
for Step Inputs X(t) = XoH(t) [H(t): unit step function]
A = 0.28 m2; Qi, = 0.39 m3/min; k = 0.408 m3/min-m1/2
time x = 0.01 x = 0.1
(min) (m/min) (m /min)
Eq. 9* Eq.10 Eq. 9* Eq. 10
0.1 0.9174 0.9174 0.9483 0.9484
0.5 0.9288 0.9288 1.0632 1.0626
1.0 0.9390 0.9390 1.1678 1.1641
2.0 0.9508 0.9507 1.2963 1.2808
3.0 0.9564 0.9561 1.3638 1.3353
5.0 0.9603 0.9599 1.4195 1.3726
10.0 0.9614 0.9609 1.4416 1.3828
0.9614 0.9610 1.4423 1.3830
*Solved by an arbitrary numerical technique, covered in Section 6 (Table 1)

Spring 1991

while those with a weak mathematical background
were too bogged down in operational details to worry
about the physical nature of the topics and problems
discussed. There was, at any rate, not a single com-
plaint about the application side of the course, and
one of the two written comments supplied with a
computerized course evaluation by students states,
"Nice having some semi-real chemical engineering
On a scale of ten, 42 responding students in a
class of 69 gave 6.6 to the course and 7.5 to me
(second-year course critiques often give overall scores
below 5.0). Some students recognized their weak-
ness in linear algebra (in spite of a two-term course
taught in the first year) as a serious impediment in
following Section 7 (Table 1). Orthogonal functions
and Sturm-Liouville theory (Section 5) also proved
to be a "baptism of fire" for many, and numerical
techniques (Subject 6) made even the sleeping come
temporarily alive-a sure sign of the ubiquitousness
and appreciation of computers.

The real challenge in teaching this course was in
finding an appropriate balance between mathemati-
cal theory and engineering applications when stu-
dents had little knowledge of either. The course con-
tent may thus have been a bit too ambitious. It may
be more useful in the future to expand the numerical
techniques portion at the expense of ODE systems,
allotting at least as many formal lectures to the
former as to the latter. Recently-written books, tuned
more closely to the eighties, may also enhance the
The course was a source of great enjoyment for
me, and I look forward to teaching it periodically. I
hope that some of the students will subsequently
explore the wonders of applied mathematics on their

1. Spiegel, M.R., Applied Differential Equations, 3rd ed., Pren-
tice Hall, Englewood Cliffs, NJ (1981)
2. Farrel, O.J., and B. Ross, Solved Problems in Analysis, Prob-
lem 6, p. 343, Dover, New York, NY (1971)
3. Relton, F.E., Applied Bessel Functions, Section 5.3, p. 62,
Dover, New York, NY (1956)
4. Hamming, R.W., Introduction to Applied Numerical Analy-
sis, Section 8.11, p. 217, McGraw Hill, New York, NY (1971)
5. Stephanopoulos, G. Chemical Process Control:An Introduc-
tion to Theory and Practice, Example 6.1, p. 118, Prentice
Hall, Englewood Cliffs, NJ (1984)
6. Edwards, Jr., C. H., and D.E. Penney, Elementary Differen-
tial Equations with Boundary Value Problems, 2nd ed., Pren-
tice Hall, Englewood Cliffs, NJ (1989) 0

class and home problems

The object of this column is to enhance our readers' collection of interesting and novel problems in
chemical engineering. Problems of the type that can be used to motivate the student by presenting a
particular principle in class, or in a new light, or that can be assigned as a novel home problem, are
requested, as well as those that are more traditional in nature and which elucidate difficult
concepts. Please submit them to Professors James 0. Wilkes and T. C. Papanastasiou, Chemical
Engineering Department, University of Michigan, Ann Arbor, MI 48109.




University of Dayton
Dayton, OH 45469-0001

In industry there are many examples of absorption
of a gas with or without chemical reaction in the
liquid phase. In physical absorption, a particular
gaseous component is removed from a gas mixture
due to its larger solubility in the liquid phase sol-
vent. The removal of butane and pentane from a
refinery gas mixture by a heavy oil in the liquid
phase is an example of physical absorption. In ab-
sorption with chemical reaction, the gaseous compo-
nent to be removed transfers across the gas-liquid
interface due to a difference in the bulk chemical
potentials or concentrations in the two phases. The
transferred gas then reacts with a liquid-phase com-
ponent while simultaneously diffusing in the liquid
phase mixture. The gas purification processes, such
as removal of chlorine from nitrogen or air by means
of water, removal of carbon dioxide from synthesis
gas by means of aqueous solutions of hot potassium
carbonate or monoethanolamine, and removal of H2S
and CO2 from hydrocarbon cracking gas by means of
ethanolamine or sodium hydroxide, are some ex-
amples of absorption with chemical reaction.

Sarwan S. Sandhu is a professor of chemical engi-
neering at the University of Dayton. He received his
PhD from the University of London (England). His teach-
ing and research interests are in applied mathematics,
chemical engineering kinetics and reactor analysis,
transport phenomena, thermodynamics, combustion,
and electrochemical engineering including fuel cells.


Chlorine is to be removed from a mixture of chlo-
rine and nitrogen by absorption and reaction of chlo-
rine with water in a falling liquid film, where a
pseudo-first-order reaction takes place:
C12(g- e)+H20(0) Cl- (1)+ H ()+HOCl(g)
1. Develop mathematical expressions describing two-
dimensional concentration profiles of C12(A) in the
liquid film, the total chlorine removal rate for the
entire length of the film, and the mass transfer
enhancement factor defined as the ratio of the actual
rate of chlorine removal to the rate of chlorine removal
in the absence of chemical reaction.
2. Evaluate the two-dimensional chlorine concentration
profile, the total chlorine removal rate, and the mass
transfer enhancement factor for the following data:12'
System temperature: 24.5 C
Chlorine concentration in the liquid film at the gas-
liquid interface: CAo = 0.1746 x 10-5 mole cm-3
Width of the liquid film: w = 1.0 cm
Thickness of the liquid film: 5 = 0.008 cm
Height of the falling liquid film: L = 1.0 cm
Pseudo-first-order reaction rate constant:
k1'"= 13.6 s-
Molecular diffusivity of chlorine (A) in the liquid
solution: DA = 1.477 x 10-5 cm2 s-'
The chlorine removal process is to be carried out
under isothermal and steady-state conditions by
gently stirring the chlorine/nitrogen mixture as de-
picted in Figure 1.

Copyright ChE Dwiision. ASEE 1991

Chemical Engineering Education


A sketch of the process is shown in Figure 1.
Continuously flowing chlorine-nitrogen mixture is
stirred and a film of liquid water falling along the
vertical nonreactive plane wall is in contact with the
gas phase. The gas mixture is at temperature, T,
and pressure, P. The liquid phase concentration of
chlorine at the gas-liquid interface can be deter-
mined for the evaluation of the numerical data using
the methods given in References 3 and 4.
The solution'1 to the momentum equation for the
steady-state fully developed laminar flow gives an
expression for the velocity, vZ, profile as

vz(x)=vmr 1-)2] (1)

vm g 2 (2)

and vm = maximum velocity of liquid at the
liquid-film surface
g = gravitational acceleration
p = liquid density
g = absolute viscosity

To set up the differential model describing trans-
port and consumption of the species A(C12) in the
liquid phase region, we follow the generally accepted
approach given in Reference 1. The origin of the
cartesian coordinate system x, y, z is located at the
surface of the liquid film at its top end (see Figure 1).
Species A is assumed to be transported in the x and z
directions only. The concentration of the species A,
CA, is a function of both x and z coordinates. A mole
balance for component A is applied over the spatial
element in the liquid region shown in Figure 1. The





0z +Az-




x x+Ax

/ // / //
Figure 1. Sketch of the chlorine removal process by
absorption and chemical reaction in the falling
film of liquid water (not to scale).
Spring 1991

resulting differential equation is

NAx NAz +kl CA=0 (3)

Under the assumption of negligible transport of spe-
cies A by diffusion in the z direction relative to its
transport by the liquid bulk flow, and no bulk flow in
the x direction, NA and Nx are approximated by

NA =CAV,(x) (4)

NA =-DA x (5)

NAz and Nx represent the molar fluxes of species A
in the z and x directions, respectively.
Equations (1), (3), (4), and (5) are combined to
result in

DA2 CA +v l-x CA ()
-DA a2 +vm CAz +kCA =0 (6)
ax [ o z

The required boundary conditions are:

at z=0


for 0

at x=0 CA =CAo for 0

at x=6 A =0

for 0

If the region of the liquid film in the direction of the
x coordinate, where molecules of the species A pre-
vail, is thin relative to the liquid film thickness, then
the liquid velocity in the downward direction in that
region can be assumed to be close to the maximum
velocity, vm. This approximation results in the sim-
plification of Eq. (6), making it suitable for obtaining
an analytical solution. The simplified version of Eq.
(6) is
O2CA __A
-DA m OA2 m +k CA= 0 (8)

The boundary condition, Eq. (7c), is reduced to
x--o, CA=0 for 0 The assumption of constant velocity in Eq. (8) holds
under the condition that chlorine is rapidly removed
via chemical reaction in the liquid phase relative to
its diffusion perpendicular to the gas-liquid inter-
Using the Laplace transform procedure,15,'6
Eq. (8) is solved to obtain the following result:

CA -1 Le-4erfc z + e~ p erfc12 + r }p
Cz 2Szcca 2 rz a9





-" 2
k, x
Equation (10) describes the dimensionless
centration profile, CA/CA, as a function of both x
z. Under the limit of z -- (i.e., sufficiently lar
so that erfc in the first term becomes erfc (- o) ar
the second term becomes erfc (-), then Eq. (10
duces to

A= exp(- p
The molar flux of species A into the liquid film a
location is given by

x=0 -DA a xO x
The total removal rate of species A (i.e., of C12)
the gas mixture is given by
WA=WJ NAxx )dz

= wCAoVm D [( u)er u) e-u

k, L

Error and complementary error functions were com-
puted using the approximation technique from Ref-
(lla) erence 7. It is noted that erfc (x) = 1 erf(x). The
resulting two-dimensional dimensionless concentra-
tion profiles of chlorine in the liquid film are shown
(lib) in Figure 2. The calculated total chlorine removal
rate is WA = 0.278 x 10-' mol s-1, and the resulting
con- mass transfer enhancement factor is Et = 1.982.
ge z) Validity of the assumption of constant velocity in
d in Eq. (8) was verified by solving Eq. (6) numerically.
)re- Analytical solution of Eq. (8) and the numerical solu-
tion of Eq. (6) are compared in Figure 3 for two (z/L)


Figure 2 shows the profiles of the dimensionless
(13) concentration, CA/CAO, of chlorine as a function of the
dimensionless penetration distance, x/6, at a num-

-T = 0.8 0


The expression for the removal rate of species A
by its absorption in the absence of chemical reaction
is obtained by substituting k1 = 0 in Eq. (14) and
then applying the L'Hopital's rule to determine the
resulting indeterminate limit. The result is given by

1+u)erf +cu) e-U}
WAAo WCAoVm DA 1 -dk d 1/21
k -O k1

=WCAoL 4DV (15)

Finally, the mass transfer enhancement factor is
given by
Sf +u) erf -+ e-u
mts = W----( = L )

The second part of the problem is answered by
obtaining the numerical data by means of a Fortran
program that solves the above theoretical equations.



Figure 2. Two-dimensional concentration profiles of
chlorine in the falling film of liquid water

- 0.5


Figure 3. Comparison of the analytical solution of Eq. (8)
with the numerical solution of Eq. (6).
Chemical Engineering Education

ber of dimensionless depths, z/L. A rapid decrease in
the chlorine concentration is interpreted in terms of
its fast consumption via chemical reaction relative
to its diffusion in the liquid phase. Agreement be-
tween the analytical solution of Eq. (8) and the
numerical solution of Eq. (6) as seen in Figure 3
justifies the assumption of constant velocity in Eq.
(8). The mass transfer enhancement factor value of
1.98 is indicative of about double the chlorine re-
moval rate via its absorption without chemical reac-
tion. The model predictions suggest that the con-
tinuously flowing liquid films can, indeed, be used
for purification of gas mixtures, e.g., chlorine/nitro-
gen or air mixture, by absorption of trace species,
e.g., chlorine, with chemical reaction in the liquid

1. Bird, R.B., W.E. Stewart, and E.N. Lightfoot, Transport Phe-
nomena, John Wiley and Sons, New York, pp. 537-539 (1960)
2. Rosner, D.E., Transport Processes in Chemically Reacting
Flow Systems, Butterworths, Boston, MA., p. 393 (1986)
3. Smith, J.M., and H.C. Van Ness, Introduction to Chemical
Engineering Thermodynamics, McGraw-Hill Book Co., New
York, NY, p 332, 346 (1987)
4. Reid, R.C., J.M. Prausnitz, and T.K. Sherwood, The Proper-
ties of Gases and Liquids, McGraw-Hill Book Co., New York,
NY, p. 361 (1977)
5. Spiegel, M.R., Advanced Mathematics, McGraw-Hill Book Co.,
New York, NY, pp. 277,100, 73 (1977)
6. Oberhettinger, F., and L. Badii, Tables of Laplace Trans-
forms, Springer-Verlag, New York, NY, p. 264 (1973)
7. Abramowitz, M., and I.A. Stegun (editors), Handbook ofMathe-
matical Functions, (9th printing), Dover Publications, Inc.,
New York, NY, p 299 (1970) 0

REVIEW: Process Design
Continued from page 79.
the major types of equipment in the class, the basic
operating principle, literature references, and
sketches or photographs of the units. Short-cut siz-
ing techniques and rules-of-thumb are used through-
out the chapter for rough sizing. The major feature
of the chapter is a set of tables which provide criteria
for the preliminary specification of units within each
equipment class. The selection tables are organized
by principle of operation, applicable capacity range,
important data to that class of equipment (i.e., par-
ticle size for crushing equipment), material compati-
bility, type of service, and any other criteria useful
for differentiating alternatives within the class of
equipment. Qualitative ranking of the units is pro-
vided when numerical comparisons are not appro-
priate for comparing equipment, such as past expe-
rience in the suitability of the unit for a particular
Spring 1991

problem application. I tried to use the tables by
selecting some units that I was particularly familiar
with and found that they (and the text) provided
enough basic information to describe the unit and
give a size range. There is enough information to
select a unit given the feed characteristics, but not
enough information to do any analysis of the opera-
tion of the unit or detailed sizing.
The second section of the book (approximately
one hundred and fifty pages) covers "Economic Analy-
sis." Chapters cover capital and manufacturing cost
estimation, economic optimization, and cash-flow
analysis. The cost estimation techniques presented
are adequate for a preliminary estimate. Figures
provide capital cost estimates for different types of
units, but there is no information about the error or
spread of data used to create the figures. The chap-
ter on cash-flow analysis (time value of money) is
brief, and the coverage on the treatment of alterna-
tive investments could use more examples and dis-
The final, brief, section is a single chapter on
"Technical Reporting." There are many anecdotes to
encourage the student to write effectively. It would
have been useful to provide example outlines for
different types of engineering design reports to give
the student an idea of what information is expected,
depending on the type of study being done.
After I finished reading the book, there were a
number of things that troubled me. The design proc-
ess is not emphasized as an iterative process that
requires preliminary sizing and costing and then
more detailed study and operations analysis (which
may force changes in the original process concept).
Little reference is made to modern computer pack-
ages that can do both the short-cut and the rigorous
mass and energy balances (and sometimes the eco-
nomics), and which allow the student to do a second
pass at the design. The overall plant design is a set
of chemical operations for which one must make
decisions about unit alternatives as well as the proc-
ess configuration itself. Process units interact through
recycles so that design decisions in one unit can
affect the operation, size, and economics of the rest
of the plant. Some material and detailed examples
on process configuration alternatives (process syn-
thesis) would be useful for the student to see that
different process concepts are possible.
If the instructor has a design course that is based
on a well-defined case study, then the book provides
reference material that would be useful for prelimi-
nary unit design and economic analysis. O

views and opinions


Where Do We Go From Here?

Stevens Institute of Technology
Hoboken, NJ 07030

Chemical engineering undergraduate education
has undergone many changes and transforma-
tions over the years. It has moved from a curriculum
best described as industrial chemistry through the
unit-operations approach, to an emphasis on engi-
neering sciences (i.e., transport phenomena) with
greatly increased mathematical sophistication, and
ultimately to a heavy infusion of computer-based
methods and techniques.
The nature and background of the faculty has
also changed. Initially, the typical professor was ori-
ented toward practice and to what some called a
handbook-approach to teaching. Later, however, as
the unit operations approach took hold, faculty
(while still oriented to practice) began to involve
themselves in research that was designed to provide
an understanding of complex phenomena. The next
permutation saw faculty becoming both more mathe-
matically and more scientifically oriented. Further,
while engineering research had been mainly ex-
perimental in nature, it now began to take on a
more theoretical slant. Finally, the "computer revo-
lution" produced a new breed of professors, with
many of them geared almost exclusively to a com-
puter approach.
In addition to the above, the relationship of the
faculty to industrial practice has also greatly changed.
Where it was once common to encounter faculty
with industrial experience, there are now far fewer
such individuals, particularly among junior profes-

Richard G. Griskey received his BS, MS, and PhD
degrees from Carnegie-Mellon University. He has
held both professional and administrative positions
(department head, dean, provost, executive vice presi-
dent) at several universities. An active researcher,
She has over two hundred publications and has super-
vised over fifty graduate theses.

sors. It is not uncommon at some institutions to find
many, if not all, of the departmental core courses
taught by faculty whose experiences are wholly con-
fined to academia.
The changing curriculum and changing faculty
have obviously had a great impact on chemical engi-
neering education (in particular, on undergraduate
education). There is no question that today's bacca-
laureate graduates are considerably different from
their predecessors of twenty, ten, or even five years
ago. Today's chemical engineering graduates are
sharp, they are highly-sophisticated mathematically,
and they are quite proficient with respect to the
All would seem to be well. However, when engi-
neers in industry (including new hires) are asked to
evaluate today's undergraduate chemical engineer-
ing education, they raise a number of questions. For
example, newly-minted engineers complain about a
lack of "practical information" in their training. The
serious thing about this charge is that it even comes
from students who have graduated from institutions
which strongly emphasize practice rather than the-
ory. Complaints of older engineers range from an
inability of new hires to carry out well-known proce-
dures to their lack of even a rudimentary under-
standing of equipment.
At this point, a number of different opinions would
be elicited. One type of response would be that there
is no problem and that all is well. Others, however,
would probably recommend a massive reorganiza-
tion of chemical engineering education in order to
cure any and all perceived problems.
Actually, both camps are correct in their evalu-
ation. Massive changes in curriculum, courses, etc.,
are not needed; what is needed is a change in the
way the material is presented. We must move from
an over-balance and dependence on theory, mathe-

Copyright ChE Division, ASEE 1991

Chemical Engineering Education

One type of response would be that
there is no problem and that all is well. Others,
however, would probably recommend a
massive reorganization of chemical
engineering education ...

matics, and the computer, to a new approach that
not only recognizes and maintains those gains but
also clearly links them to engineering practice.

How do we do this? We do it by changing the
style and philosophy of teaching our undergraduate
courses. At the risk of oversimplification, the follow-
ing points should be considered:
Continue to teach fundamentals, but emphasize the
first principles even more strongly.
Make the greatest possible use of phenomenological
Clearly delineate the progression, use, and
relationships between theoretical, semi-empirical, and
empirical approaches.
Emphasize practice by continually interlinking
theory to actual or real situations. Do this
quantitatively; if unable to do so, use qualitative and/
or anectodal examples.
Build on first principles by using homework or
examination problems that emphasize applications in
different, new, or novel areas or applications (i.e.,
enable the graduate to move into new areas of
Put mathematics into its proper perspective (i.e.,
useful and important, but not the be-all or end-all).
Use the computer, but emphasize that it is a means,
not an end, and that garbage in gives garbage out.
Work into each course the concepts of process and
Emphasize innovation, creativity, and ingenuity,
remembering that an engineer is a "person who carries
through an enterprise by skillful or artful contrivance."

A response to the preceding might be that we
already do these things in academia, so why bother?
It should be evident that even if we are doing them,
as academics we are falling short and must there-
fore emphasize them even more strongly.
Another comment might be that these are admit-
tably worthwhile objectives, but how can they be
implemented? A possible scheme for implemen-
tation in chemical engineering departments would
be to:
Commit to a teaching philosophy that emphasizes
the preceding points as well as others that accomplish
the same goals.

Take advantage of the valuable resource of faculty
with industrial experience to track the undergraduate
core courses so that theory and practice can be
effectively interlinked.
Utilize, as well, those faculty members who
specialize in experimental research so that the aspects
of equipment and processes can be emphasized.
Develop good rapport with industry so that
examples, guest lecturers, etc., can be used to enrich
core courses.
Build on science and mathematics, but clearly
emphasize the fact that engineering is different.
Evaluate all of the preceding by contacts and
discussions with recent graduates and more mature
practicing engineers.
Keep the undergraduate curriculum dynamic,
recognizing that static situations produce deterioration.

Hopefully, this paper will stimulate discussion
and more detailed consideration of undergraduate
education in chemical engineering. This in itself
would be a rewarding and beneficial exercise. 0

book review

by Stuart Churchill
Butterworths, 80 Montuale Avenue, Stoneham, MA
02180; $52.95, 602 pages (1988)

Reviewed by
Stanley Middleman
University of California, San Diego
La Jolla, CA 92093-0310

Professor Churchill has produced a textbook
aimed at the student with prior background in fluid
dynamics, although he states that it has been used
with "surprising success" as a first course for under-
graduates when the material is presented at a slower
pace and with some deletion of detail. My own im-
pression is that this book could indeed be used in a
junior-level fluids course, but that its success would
depend to a great degree on the skill of the teacher
in choosing the topics to be included, and in supple-
menting the material of the text with ample class-
room discussion so as to provide a broader context in
which fluid dynamics is seen as an essential element
of chemical process engineering. In the hands of a
teacher whose main focus would be on the derivation
of solutions to various fluid dynamics problems, the
use of this text would be less successful in providing
Continued on page 111.

Spring 1991




The Amoco Resid Hydrotreater Process

J.F. MOSBY,1 I.A. Karimi,2 P.K. Andersen
Purdue University
West Lafayette, IN 47907

The senior chemical engineering laboratory is a
required part of most accredited chemical engi-
neering programs and is considered a "capstone"
course, drawing as it does on students' previous tech-
nical work. Furthermore, the senior laboratory typi-
cally requires the students to use their written and
oral communication skills and, since lab projects are
often group efforts, their interpersonal skills as well.
In Purdue's laboratory course students work to-
gether in groups of three, consisting of a group leader,
an experimentalist, and a design engineer. Each
group works on three month-long projects chosen
from a list of about a dozen experiments which in-
volve processes such as extraction, filtration, distil-
lation, gas- and liquid-phase reaction, ion exchange,
heat transfer, fluid flow, mixing, and diffusion.
In our view, the ideal laboratory experiment
should duplicate a real industrial process. The stu-
dents would use modern equipment to investigate a
complex problem, and would do so under realistic
time and budget constraints. Since universities can
hardly afford to construct or operate industrial-scale
plants, the next best alternative is to devise experi-
ments which closely simulate the operation of indus-
trial processes. With this in mind, we are developing
a series of computer simulations intended for use in
undergraduate chemical engineering laboratories.
These simulations model actual industrial chemical
processes and are being produced with the assis-

In our view, the ideal laboratory experiment
should duplicate a real industrial process. The
students would use modern equipment to
investigate a complex problem...

' Amoco Corporation; 2 Northwestern University

Dow Chemical
Tennessee Eastman
Air Products

Catalytic Reforming
Latex Emulsion Polymerization
Methyl Acetate from Coal
Process Heat Transfer

tance of various corporate sponsors. The first five
are listed in Table 1.

The first simulation that we have completed
models a hydrodesulfurization pilot plant (see Fig-
ure 1) built by Amoco in its Naperville, Illinois, re-
search facility. The hydrotreater takes a mixture of
heavy, high-sulfur hydrocarbons (called "resid oil")
and upgrades it by
breaking the long carbon chains to form smaller chains
adding hydrogen to increase the saturation
removing sulfur in the form of HS gas

R.cI Pump

R.Acy Pu

Figure 1. Amoco hydrodesulfurization pilot plant. The
three ebullated-bed columns are well mixed by the
recycle streams.

Copyright ChE Division, ASEE 1991

Chemical Engineering Education

Process Simulations and Industrial Sponsors

R-a orV2

Pmd-lx Ra-vr


Non-Catalytic Reactions

+H, H2 +H2 +H2
R -> G ---- D N -w-> L
\k k2 k 3

Catalytic Reaction
Sulfur + H2 -- H2S

Figure 2. Hydrodesulfurization reaction scheme. Each of
the components R, G, D, N, and L is a mixture of many
different compounds, lumped together by boiling point.

The reaction scheme is shown in Figure 2. Each
of the components R, G, D, N, and L is a complicated
mixture of many different chemical species, the ac-
tual composition of which would be very difficult to
specify exactly. R, G, D, N, and L are characterized
by their average boiling points and their sulfur con-
tent (see Table 2).

The hydrogenation reactions (reactions 1 through
7) are modeled as a set of sequential and parallel
first-order reactions. The net generation rates are
given by

R.G. Squires is a professor of chemical engineering at Purdue University. He
received his BS in chemical engineering from Rensselaer Polytechnic Institute
in 1957 and his MS and PhD from the University of Michigan in 1958 and 1963,
respectively. His current research interests center on the educational applica-
tions of computer simulation.
G.V. Reklaitis is Head of the School of Chemical Engineering at Purdue
University. He earned a BS from Illinois Institute of Technology in 1965 and a
MS and PhD from Stanford University in 1969. His research interests include
process systems engineering, process scheduling methodology, and the de-
sign and analysis of batch processes.
N.C. Yeh is a post-doctoral research in chemical engineering at Purdue
University. He received a BS from National Tsing-Hwa University (Taiwan) in
1978 and a PhD in chemical Engineering from Purdue University in 1987 His
research deals with process simulation and optimization.
J.F. Mosby is a Senior Research Associate at the Amoco Research Center in
Naperville, IL. He received his BS and PhD in chemical engineering from
Purdue University in 1959 and 1964, respectively. His research interests
include petroleum refining process development and simulation.
LA. Karimi is an assistant professor in the chemical engineering department at
Northwestern University. He received his BS from IIT Bombay in 1980 and his
MS and PhD from Purdue University in 1982 and 1984. His research has dealt
with computer-aided design, scheduling, and optimization of batch chemical
P.K. Andersen is an assistant professor in the Department of Freshman
Engineering at Purdue University. He earned his BS from Brigham Young
University in 1981 and his PhD from UC Berkeley in 1987, both in chemical
engineering. His research has dealt with transport in multiphase flows and the
educational applications of computer simulation.
Spring 1991

rR =-(k +k5+k + k7)R
rG =-k2G +CRGk1R
rD =-k3D + CRDk5R + CGDk2G
3 RD5 GD2
r -k4 RN R + CDNk3

where R, G, D, N, and L are the weight fractions of
the sulfur-free components; k1, k2 .. ., are rate
constants, and CRG, CRD ... CRL are stoichiometric

The desulfurization reaction (reaction 8) is cata-
lytic. It is first order in hydrogen, second order in
sulfur, and inhibited by resid:
-r 1 + K9R

Here A is a catalyst deactivation factor (A = 1 for
fresh catalyst), i is the partial pressure of hydrogen,
kg is a kinetic rate constant, and K, is an equilib-
rium constant.

The rate constants for reactions 1 through 8 are
given by Arrhenius-type relations
ki = ai exp(-Ei / RT), i= 1,...,8

where a is the pre-exponential factor and Ei is the
activation energy for the ith reaction.

The reactions are carried out in well mixed, ebul-
lated-bed reactors, which are modeled as continuous
stirred-tank reactors (CSTRs). Under some condi-
tions, the simultaneous solution of the mass and
energy balances for a CSTR may exhibit multiple
steady states (see Figure 3). The reactors usually
operate at the intermediate steady state, which is
unstable with respect to temperature; at the lower
steady state the conversion is too low and at the
upper steady state the temperature is too high.

The program consists of more than 10,000 lines
of FORTRAN and C code. It can simulate the steady-
state behavior of one, two, or three reactors in series,


Component Average B.P. (F) Sulfur (wt. %)
Resid (R) >1200 5.0
Gas Oil (G) 827 2.0
Distillate (D) 514 1.0
Naphthas (N) 280 0.5
Light Gas (L) <200 0.0

or the dynamic behavior of a single reactor. The
program currently runs on the Sun 3/60 worksta-
tion, although it can be readily modified to run on
any machine that supports the X Window System.
A graphical user interface makes the program
easy to use, even for students having minimal expe-
rience with Sun computers. The user employs
a mouse to select from options presented on
"pull-down" menus. Should the user get lost or for-
get what to do, he or she can get help from the
program itself.

Eight three-hour lab periods are allotted to each
project. In preparation for the first scheduled lab
period, the students are asked to study a written
description of the process and to view a short video-
taped "plant tour" supplied by the corporate spon-
sor. They also attend an orientation meeting with
the instructor, where general questions about the
process, the simulation, and the lab are answered.

In keeping with our attempt to provide realism
in the project, the students are given their assign-
ment on official Amoco stationery. They are required
to do the following things:
Determine the values of the pre-exponential factors for
the hydrogenations
Check activation energy for one of the hydrogenations
Determine the pre-exponential factor a8 and activation
energy E8 for the desulfurization
Check the form of the catalyst deactivation equation
and measure the catalyst deactivation rate
The assignment letter authorizes the students to
run the Naperville pilot plant and two small labora-
tory reactors.

Contributing to the sense of realism in this mod-
ule is a requirement that the students work within a
budget. Initially they are given $150,000 (simulated
money, of course!) with which to work. Table 3 lists
the time and money required for various tasks in-
volving the pilot plant and laboratory reactor. Note
that the students are charged a fee each time they
seek help from the "consultant" (i.e., the instructor).

The students spend the first two lab periods pre-
paring a plan of attack, which they must present to
the instructor in a planning conference before the

Figure 3. Mutiple steady states in a CSTR. The system
usually operates at the intermediate steady time.

third period. In this conference the instructor asks
the students to describe, in order, the experiments
they intend to carry out. At each step they must
justify their plans. The instructor asks questions
and gives hints where necessary, but is careful not
to reveal too much about the solution to the problem.
The students are faced with a number of choices
regarding the type and number of reactors, the cata-
lyst age, the feed composition, and the reactor tem-
perature. In making these choices, they have to keep
in mind a number of constraints:
It takes five days' and $75,000 (half the budget) to
clean and prepare the pilot plant.
It costs another three days' and $50,000 to replace the
catalyst in the pilot plant; obviously, the students cannot
afford to change their minds on the catalyst selection.
Each pilot plant run takes twenty-four hours.'
The pre-exponential factors a,,..., a, must be measured
in the pilot plant.
Other constants can be obtained from the lab reactor,
but their values must be checked in the pilot plant.
It makes sense to use the lab reactors as much as
possible, since they are considerably cheaper to op-
erate than the pilot plant. Furthermore, the lab re-
actors are easily refilled with catalyst, permitting
the students to take data related to catalyst age.
However, all constants that are determined from
laboratory data must be checked in the pilot plant.
(By "checked" we mean that four or five points over a
reasonable range should agree with the previously
determined values.)

Once the students have demonstrated to the in-
structor's satisfaction that they have a good grasp of
the problem, they are shown how to operate the
computer program in the steady-state mode. This
enables them to simulate the operation of the labo-
S imulated time
Chemical Engineering Education

ratory reactors and the pilot plant, from which they
can obtain the required kinetic constants.
The students are permitted to take data from the
third through the sixth lab period. During the sixth
period the group leader is required to give a fifteen-
minute oral progress report, which is videotaped
and critiqued in private with the speaker.


After the group leader's progress report, the in-
structor shows the students how to run the simula-
tor in the dynamic mode. The students are then
given a second assignment letter informing them
that they have been selected to act as consultants
during the start-up of a resid hydrotreater at Amoco's
Texas City refinery. They are asked to simulate the
start-up of a single reactor, controlling the operating
conditions manually to reach steady state. Then they
are to cease controlling the system and to note the
time that elapses before automatic shutdown occurs.
The start-up problem is especially challenging
because the operating conditions within the reactor
can only be controlled indirectly, by setting the tem-
perature, flow rate, and composition of the feed
stream. Furthermore, instantaneous changes in these
variables are not permitted; the students must wait
fifteen minutes between changes in the feed set-
tings, and they are limited to changing feed tem-
perature by no more than 100 F at a time. Finding
a suitable control strategy is typically a trial-and-
error process. (Dynamic simulation runs are not
charged against the students' budgets.)
Two lab periods are allotted for the start-up prob-
lem. The students then have one week to produce a
full written report, including the results of their

I Expenses

Initial preparation and start-up of
pilot plant (includes cost of initial
charge of catalyst
Replacement of catalyst in pilot plant
One pilot plant run (includes labor,
materials, analysis, etc.)
Three reactors in series
Two reactors in series
One reactor
One laboratory reactor run (includes
catalyst replacement)

5 days $75,000
3 days $50,000

24 hours
24 hours
24 hours


24 hours $5001
? $500

'Multiply by 1.5 for Saturday runs; by 2.0 for Sunday runs
Spring 1991

steady-state experiments and an outline of their rec-
ommended start-up procedure.

The instructor has four important parts to play
in a simulation project:
1. Mother Nature-sets the mean values and random
variability of all parameters used in the simulation
2. Boss-receives the oral and written reports from the
3. Consultant-helps with specific technical questions,
but charges a fee that must be paid from the budget.
4. Instructor-assigns the grades, of course.

Although it would be possible to design a senior
laboratory made up entirely of computer-simulated
experiments, we believe that students should also
gain "hands-on" experience by working with real
laboratory equipment. For this reason, we allow only
one of the three required experiments to be a com-
puter project.
We have used the Amoco module here at Purdue
for five semesters, with great success. As an alterna-
tive to traditional lab experiments, computer simu-
lation offers a number of significant advantages:
Processes that are too large, complex, or hazardous for
the university lab can be readily simulated on the
Realistic time and budget constraints can be built into
the simulation, giving the students a taste of"real world"
engineering problems.
The emphasis of the laboratory can be shifted from the
details of operating a particular piece of laboratory
equipment (which may not be representative of current
industrial practice) to more general considerations of
proper experimental design and data analysis.
Computer simulation is relatively inexpensive compared
to the cost of building and maintaining experimental
Simulated experiments take up no laboratory space and
are able to serve large classes because the same computer
can run many different simulations.

Anyone interested in obtaining more information
on the Purdue-Industry ChE Simulation Modules
should contact Professor Squires. An NSF-sponsored
workshop on the modules will be held at Purdue on
July 26-28, 1991.

This work has been supported by the National
Science Foundation (Grant No. USE-888554614).
Technical assistance was provided by Amoco Oil
Company and the CACHE Corporation. I



An Interesting Experience in the ChE Laboratory

Universidad de Antofagasta
Antofagasta, CHILE

The economy of Chile is strongly based on metal-
lic mining activity. However, large reserves of
salt and brines available in northern Chile have led
to a significant increase in the amount of research
effort expended on non-metallic mining exploitation
and processing. Wealthy reserves of lithium, potas-
sium, nitrates, sulphates, boron, etc., including var-
ied crystalline forms, are found there.
The Universidad de Antofagasta has played an
important role in the development of these non-
metallic mining research projects. Crystallization has
been one of the chosen subjects and has been taught
during the last three terms in the department of
chemical engineering.
Crystallization is offered as a four semester-hour
course, including lecture and laboratory work which
consists of four experiments. The one described in
this paper is aimed at the study of sodium-sulphate
crystallization in a MSMPR continuously-agitated
crystallizer tank. It is intended for the study of crys-
tallization kinetics of decahydrated sodium sulphate.
The nucleation growth rate kinetics were
evaluated by measuring the crystal size distribution
(CSD) and using the mass, energy, and population


Industrial crystallization is defined as a tech-
nique aimed at producing crystals with specific char-
acteristics of purity and size distribution. Crystalli-
zation is an extremely complex process which is af-
fected by a number of variables, such as supersatu-
ration level, temperature, agitation, impurities,
mechanical effects, etc. Important advances related
to analytical description and process understanding

have been achieved since the 1960s.
The population-balance approach to the descrip-
tion of crystal size distribution is the most widely
accepted approach, and it has proved to be the most
fertile in germinating new developments for describ-
ing and modeling crystallizers.
The population-balance equations were first for-
malized by Randolph and Larson.11' They allowed us
to get the nucleation and crystalline growth kinet-
ics. Two phenomena are involved in the crystalliza-
tion process: the formation of new particles by nu-
cleation processes and crystal growth processes. They
both depend on supersaturation, but in different
During nucleation, small regions are formed
within the homogeneous phase that consist of vari-
able numbers of ordered atoms or molecules, called
clusters or embryos. Some of these are in equilib-
rium with the mother liquor. This cluster, termed a
critical nucleus, is converted during further growth
into a macrospecies which forms the new phase.
Kinetics data on crystallization processes are of
basic importance for the design of industrial crystal-
lization equipment. These data determine the size of
the crystallizer and the crystal size of the product.

Tedfilo A. Graber is an associate professor in chemi-
cal engineering at the University of Antofagasta. He
received his BTech (1975) from the Universidad
Tcnica del Estado and his MS (1988) from the Univer-
sidad de Chile. He has presented courses in chemical
/ reactor engineering and transport phenomena. His re-
search interests are in chemical processes.

Maria E. Taboada is an assistant professor of
chemical engineering at the University of An-
tofagasta. She received her BTech (1980) from the
Universidad del Norte and her MS (1989) from the
Universidad de Chile. She has presented courses
on heat and mass transfer. Her areas of interest
are in process crystallization.

Chemical Engineering Education

Copyright ChE Division, ASEE 1991


A population balance general relationship valid
in a crystal size range Li to L2 (AL) and in the period
of time At, is the starting point in the analysis.

N of crystals
entering the
reactor with
size AL

N of crystals N of crystals
+ entering range = exiting the
AL because reactor with
of growth size AL

Crystals exiting
+ the range AL
because of

a) The number of crystal seeds entering the crystal-
lizer having a size range (L,, Li+AL) during At
interval, is given by
Q ns AL. At (1)
where n. is the population density at the inflow,
n AL represents the fraction of crystals with size
AL, and Q, is the volumetric inflow.

b) The number of crystals entering to AL range in
the At interval due to G1 growth is given by
V-G1-n1-At (2)
where V is the volume of the crystallizer. The
growth function of G crystals is represented as a
supersaturation and crystal size function.
G = G(L, AC) (3)

G = Gc (C) .(L) (4)

c) The number of crystals having a size range
(L1, L,+AL) which are removed from the reactor
during At interval are given by
Q2 n AL-At (5)
where n is the population density at the exit and
Q2 is the volumetric exit flow.

d) The number of crystals growing outside the size
range (L1, L1+AL) at At interval is
V-G2 n.At (6)

Then the population balance [using Eqs. (2) to (5)
in the size range (L1, L,+AL)] is
VGinlAt+QlnsALAt=VG2nAt+Q2nALAt (7)
Carrying out the appropriate arrangements in
Eq. (7) and considering that there are no crystals
in the feeding, yields

d(Gn) Q2
dL V
Defining the half-time residence as

The population-balance equations were
first formalized by Randolph and Larson. They
allowed us to get the nucleation and crystalline
growth kinetics. Two phenomena are involved
in the crystallization process: the formation
of new particles by nucleation processes
and crystal growth processes.

and assuming steady state

d(Gn) n=


Integrating Eq. 10, by separation of variables
when G # G(L), yields
n = no exp(-L / Gt) (11)
in which no is the nuclei population density.
Therefore Eq. (7) represents the crystal size
distribution (CSD) of the process, where the dis-
tribution function n represents the number of
particles having a certain size range per unit
volume and a characteristic size.

Number of particles with size
between L and (L + AL)
n(L)= (Volume) (AL)


This size distribution function can be directly
obtained by determining the number of particles
associated to each size range, as

Mass of crystals retained in a sieve / p,
(average size particle volume)(volume)


where pc is the crystal density. Using an average

L- L1 +L2
L =-
and defining the particle volume as
in which kv is the crystal shape factor
AL = L2 L1




where L, is the lower mesh opening (through
which the particles enter) and L2 is the retaining
mesh opening of the sieve. Therefore

n= AL

n= W
pckvL3 ALVs



() where Vs is the volume occupied by the solution.
Then it is possible to interpret the population

Spring 1991

density of zero particle size, or nuclei number den-
sity, n, as
n=B/G (19)

resulting in Eq. (11)

(n)= tfn L (20)

This equation is very important, since by using
experimental distribution functions (obtained
through screening tests) it is possible to find the
adequate system kinetic model. Representing gra-
phically (n) versus L we obtain a straight line of
slope -1/Gt and intercept B/G from which the growth
velocity G can be determined at specific values of t.
In addition, it is possible to obtain the value of nu-
cleation velocity B.


The experimental equipment used in this study
(see Figure 1) was a translucent acrylic MSMPR
crystallizer, cylindrical in shape and 15.2 cm diame-
ter by 39 cm height. Inside the tank there were three
baffles and a 10 cm diameter by 15.2 cm height
concentric tube, located at 6.5 cm distance from the
bottom of the tank. The overflow volume is 3.250 ml.
The system was provided with agitation similar to a
perfect mixed crystallizer proposed by Randolph.13'

Due to the significant decrease in solubility
exhibited by decahydrated sulphate sodium solution
with decreasing temperature, the crystallization was
carried out by cooling. The feeding solution was
pumped from a storage container provided with a
heater (25 0.1 C) to the crystallizer (using a double-
head peristaltic pump in order to obtain a perfectly
regulated flow). The crystallizer was maintained at
18 C inside a 20 1 thermostatic bath, obtaining the
supersaturation by cooling. The feeding flow was
monitored with a Gilmont rotameter provided with a
precision valve.

One of the experiments was carried out at 500
rpm for a residence time of 0.62 hours. The solution
flow for this experiment was established measuring
the solution density in order to reach the steady
state. After steady state was reached, the outlet flow
was vacuum-filtered and the product was washed
with acetone to eliminate residual water and avoid
agglomeration of crystals. After the drying stage the
crystals were screened in a Rotap provided with
standard Tyler sieves with mesh of 16, 18, 20, 30, 40,
50, 70, 100, and 140, by which the crystal size distri-
bution was obtained.

Table 1 shows the experimental steady-state data
for an experiment at 500 rpm with a residence time
of 0.62 hours and the conditions mentioned in the
previous section.
Equations (13) to (18) were used in order to ob-
tain the values of the crystal size distribution func-
tion. The former results were plugged into the popu-
lation balance from which the experimental results,
plotted in Figure 2, were obtained.
To determine the crystal shape factor under the
conditions used in this work, small samples of known
crystal size were counted and weighted, determining
the shape factor by the relation

k P ( W
pc(L)3 AN


1.- Constant head reservoir
2.- Pump
3.- Rotameter.
4.- Refrigeration Unit.
5.- Cristallizer vessel.
6.- Filtration Unit.

Figure 1. Experimental equipment

Experimental Data

Q^ (cc/min)

r, (g/cc)

top (min)

Mesh Sieve Opening Sieve Mass
L (mm) (g)




Sample Mass M,(g) = 490.99

Chemical Engineering Education

where AN is the number of crystals in the sample of
mass W. An average shape factor of 0.553 was ob-
From the data plotted in Figure 2, we obtain the
slope and interception values by applying a linear
regression method to Eq. (20), obtaining
1 4.9951 (1/ mm)
B / G = 2.7154 x 107 (crist./1 mm)

with a correlation factor = 0.979.
Clearing the equation, we obtain the growth and
nucleation velocity
G = 0.3216 (mm / h)

B = 1.04451 x107 (crist./1h)


The laboratory experiment described above al-
lows a good understanding of the crystallization proc-
ess. The key factors affecting this process (i.e., agita-
tion, size distribution, nucleation) are better grasped
by the student when theoretical equations are worked
out together with real-life processes.
Even though this work presented only one set of
experimental data, the experiment itself is very flex-
ible since it is possible to work out various situations
under different conditions (temperature, concentra-

Inten=ptl T

- Slope=-Y/Gr

T=0622 h
N= 500 RPM
M= 240 68 9/1

01 02 03 5 06 07 09 t10 1.1
Size T(mm.)
Figure 2. Crystal size distribution obtained from a
laboratory-scale MSMPR crystallizer

tion, spatial time, agitation velocity, etc.). For in-
stance, the parameters affecting the B and G values
can be determined by testing B and G under differ-
ent operating conditions. Thus the students can find
a kinetic equation of the studied system, through
B = k(G)b. Furthermore, it also allows the student to
understand the influence that each variable has in
the crystallization process, i.e., agitation velocity. In
industrial processing this has great importance since
a homogeneous crystal size distribution is required
by connecting processes such as centrifugation,
among other things.
Due to its simple phase diagram, the Na2SO, -
H20 system is a good example for experimental study
and teaching purposes. In fact, this system exhibits
direct and reverse solubility between 0 and 60 C
with formation of different hydrates. For the reason
stated below, the experiment allows a good versatil-
ity in crystallization products when working under
different operating conditions.
The graphical representation of the equilibrium
phases we well as the distribution of crystal size is
an effective way to understand the phenomenon from
a physical point of view. Also, the solubility diagram
allows the student to calculate theoretical output by
means of simple material balances.
By analyzing the experimental data (presented
in Table 1) the crystal mass turned out to be
490.95 g, and the predicted value was expected to be
500 g. This result means a 2% accuracy when the
crystal performance is considered. The resulting dif-
ference may be due to the fact that some of the
crystals produced remain attached to the crystal-
lizer walls and to the losses in the drying and filtra-
tion processes.
Since in the former graph a linear relationship
was obtained, it can be stated that the experiment
was performed under the basic assumptions of crys-
tal growth independent of its size and steady-state

The authors appreciate the financial support
given by FONDECYT to Project 89-0775.

1. Randolph, A.D., and M.A. Larson, "Transient and Steady
State Size Distribution in Continuous Mixed Suspension
Crystallizers," AIChE J., 8, 639 (1962)
2. Sehrwin, M.B., R. Skinnan, S. Katz, "Dynamic Behavior of
the Well Isothermal Crystallizer," AIChE J., 13, 6, (1967)
3. Randolph, A.D., and M.A. Larson, Theory of Particulate
Processes, Academic Press, New York (1971) O

Spring 1991

[ classroom




A Simple Algebraic Approach Using Solvent Extraction

University of Bath
Bath, BA2 7AY, United Kingdom

traditionally, graphical techniques such as the
McCabe-Thiele and Ponchon-Savarit methods
have been used to introduce undergraduate chemi-
cal engineering students to the design and analysis
of multistage separation processes. While the stu-
dents have quickly grasped the concepts of simulta-
neously solving the material balances and phase
equilibrium relationships, their understanding of
transforming such principles into graphical methods
has often been slow to develop. A strong emphasis on
the use of computers from the beginning of the first-
year course at Bath has resulted in students who
find it increasingly difficult to adapt their minds to
solving complex problems by graphical methods.
Building on the mathematical expertise of fresh-
men, a simple liquid-liquid equilibrium (LLE) sys-
tem has been used to demonstrate most of the essen-
tial features of multistage contacting, whether cross-
or counter-current. Solutions to the material bal-
ances and phase equilibria are all algebraic and
simple to derive and only an elementary knowledge
of series summation is required to derive the solu-
tion for minimum solvent-to-feed ratio. The simple
LLE system can then be used to introduce students
to the graphical techniques which are necessary for
complex equilibria.

Barry Crittenden obtained his BSc and PhD de-
grees in chemical engineering from the University of
Birmingham. He is a senior lecturer in the School of
Chemical Engineering at the University of Bath. His
teaching interests are in separation processes and
heat transfer. His research and consultancy interests
are in fouling of heat exchangers, novel forms of heat
transfer equipment, adsorption, environmental con-
trol, and hazardous waste management.

At the University of Bath, lecture programs in
separation processes are given in each of the three
taught years in the BEng Honours degree courses in
chemical engineering and chemical and bio-process
engineering. Most students elect to spend their third
year on industrial placement, working effectively as
graduate engineers with leading process engineer-
ing companies. Thus it is important that all the core
material in separation processes is given in the first
two years of the BEng courses.
In the first year, students are expected to gain an
understanding of the fundamental principles of phase
equilibria and their application (with material and
energy balances) to the design and operation of com-
mon separation processes. Examples are drawn es-
pecially from binary distillation, solvent extraction,
batch adsorption, batch crystallization, etc.
In the second year, the principles of continuous-
phase contacting are presented, using examples
drawn especially from gas absorption, stripping, dis-
tillation, and solvent extraction. The selection and
sequencing of separation processes, together with
the principles and practices of multicomponent sepa-
rations, adsorption, membrane processes, and other
highly-selective separations are reserved for the fi-
nal year lecture course.
Modern textbooks in chemical engineering con-
tinue to adopt the use of graphical techniques to
explain stagewise separation process calculations.
The main advantage of using such techniques at the
outset is realized by the lecturer, who can easily cre-
ate visual aids to explain concepts such as cross-
current multistaging, countercurrent multistaging,
minimum solvent flowrate, minimum reflux ratio,
total reflux, etc.
Copyright ChE Dwiision, ASEE 1991
Chemical Engineering Education

However, while some students readily understand
that graphical methods are based on the fundamen-
tal material balances and phase relationships, there
are many students who find the use of hypothetical
pole points or difference streams to be mysterious
techniques. In addition, with the advent of modern,
powerful computers and supporting software, the
use of graphical methods (with their inherent in-
accuracies) should be discouraged for all except check
calculations or for systems with complex equilibria
which are difficult to model thermodynamically.

Most freshmen already appreciate the basic con-
cepts of partitioning a solute between a solvent and
a diluent. They are also mathematically competent.
With these points in mind, the first-year course in
separation processes now commences with a totally
algebraic approach to stagewise contacting, using a
simple liquid-liquid equilibrium system to illustrate
a number of important aspects of stagewise contact-
ing. For solvent extraction, these are
the equilibrium stage model
simultaneous solution of single-stage material balances
and phase equilibria
multistage cross-current contacting
efficient use of solvent in multistage cross-current
multistage counter-current contacting
advantage of counter-current contacting over cross-
current contacting
minimum solvent-to-feed ratio

The use of solvent extraction to explain impor-
tant facets of stagewise contacting is particularly
apt since this process is one of five which have been
identified by the UK Science and Engineering Re-
search Council as requiring special research atten-
tion under its Separation Processes Initiative. Oth-
ers include membrane processes, selective adsorp-
tion, highly-selective separations, and the opportu-
nities for exploiting centrifugal fields.


The algebraic analyses are restricted to the sim-
plest case of extraction of a solute from a diluent by
means of a solvent which is immiscible with the
diluent even in the presence of the solute. The distri-
bution coefficient K for the solute is constant and is
given by
mass of solute per unit mass
K Y of solvent in extract
X mass of solute per unit mass
of diluent in raffinate

In the first year, students are expected to gain an
understanding of the fundamental principles of
phase equilibria and their application (with
material and energy balances) to the
design and operation of common
separation processes.

pure solvent
S = mass flow

F = mass flow of diluent
Xf= solute mass/diluent mass

F= mass flow of diluent
X = solute mass / diluent mass

S = mass flow of solvent
Y1= solute mass I solvent mass

FIGURE 1. Single equilibrium stage with pure solvent.

The use of mass ratios in place of mass fractions
is readily understood by the students. The simple
conversions are given later in this article.


Students are encouraged to read about discrete
stage solvent extraction equipment such as the mixer-
settler. A single equilibrium stage is shown sche-
matically in Figure 1. To keep the problem as simple
as possible, a feedstock containing only solute and
diluent is contacted with a pure solvent. The per-
formance of the unit is calculated as a function of the
following parameters:
S = mass flow of solvent

F = mass flow of diluent in feedstock

X, = mass of solute per unit mass of diluent in feedstock
X, = mass of solute per unit mass of diluent in raffinate

The material balances for diluent and solvent
are trivial because these two components are immis-
cible. The solute material balance is
XfF = XlF + YlS (1)
The assumption that the stage behaves as an equi-
librium stage means that the phases leaving are in
equilibrium, i.e.,
Y1 = KX1 (2)

Hence the performance of the single stage is given

Spring 1991

by the simultaneous solution of Eqs. (1) and (2)

Xl 1
Xf (r+1)



r=KS/F (4)

It is readily seen from Eq. (3) that the amount of
solute extracted can be improved by one or a combi-
nation of the following:
increasing the solvent-to-feed ratio
increasing K either by changing the temperature or by
using another solvent
passing the raffinate as the feedstock to second and
further equilibrium stages, i.e., cross-current extraction
shown schematically in Figure 2.


Provided that an equal flowrate of pure solvent S
is fed to each stage, the solute balance for the gen-
eral stage n is
Xn_1F = XnF + YnS (5)
Applying the equilibrium relationship yields
Xn 11
Xn- 1 (6)
Xn_1 (r +1)
Hence for a battery of N equilibrium stages
XN 1 (7)
Xf (r + 1)N
From Eq. (7) it can be seen that X/Xf tends to
zero as N tends to infinity.


Equation (7) can be used to show that a greater
extraction of solute can be obtained
if the total flow of solvent is split
between a number of equilibrium
stages rather than all the solvent eed
being used in a single equilibrium
stage. This general result is most
easily demonstrated by the example
of splitting the solvent equally be-
tween two equilibrium stages. For FI

this case
X2 1 1 (8)
Xf r}2 I 2+r+l

Comparison of Eq. (8) with Eq. (3) confirms the
improvement in the extraction of solute, but at the
additional expense of providing an extra equilibrium
stage. The general result for splitting a total flow of
solvent S equally into N stages is
XN 1 (
Xf r+N


The counter-current extraction scheme is shown
in Figure 3. A solute balance across stage 1 gives
XfF + Y2S = XlF + Y1S (10)

Y = KX1

and Y2 = KX2

X1 -Xf =r(X2 X1) (11)

Applying solute balances across each stage in turn

X2 X1 = rX 3 2 )

n n 1 r(Xn1 -Xn)

XN-XN1 r(XN+1 XN)

Eliminating X. from Eqs. (11) and (12) gives

X2 Xf = r +r2 (X3 X2)





With further eliminations of intermediate raffinate
compositions, it can be shown that




Yn S

2. Multistage cross-current extraction with pure solvent.


f 1 1
F X- F X1 F Xa

S S +

F X,.-1 F Xn

FIGURE 3. Multistage counter-current extraction with pure solvent.

Chemical Engineering Education

Xn -Xf = r+r2+r3 +...rn}(Xn+-Xn) (16)
Xn Xf = {Xn+-Xn r' (17)

and hence i=1
XN -Xf ={XN+ -XN} I r' (18)
Since XN, would be nominally in equilibrium with a
pure solvent stream S,

to infinity as N tends to infinity, and therefore XN/X,
tends to zero. Thus complete extraction of the solute
is possible with an infinite number of stages. This is
clearly shown in Figure 4.
Reducing the solvent flowrate reduces the value
of KS/F. When KS/F becomes less than unity, rN,1
tends to zero as N tends to infinity, and hence Eq.
(21) becomes

XN =l-r


XN+= 0
Hence from Eq. (18)
XN 1 1
Xf N N
1 ri 1ri
i=1 i=0

The performance of a battery of counter-current
extractors (Eq. 20) is compared with that of a bat-
tery of cross-current extractors in which the solvent
is split equally between all N stages (Eq. 9) in Figure
4. It should be noted that for the same total solvent
flowrate S and the same number of stages, the per-
formance of the counter-current battery is always
superior to that of the cross-current battery. Figure
4 can be used to demonstrate that the amount of
separation that can be achieved on each successive
stage decreases as the number of stages increases.

For the counter-current system, Eq. (20) may be
simplified by summation of the series to give
XN 1-r for r#l (21)
Xf 1 rN
When KS/F is greater than unity, the term rN** tends


c-ross current
-- counter- current

0-6 ------r=0-5


1= 2 ,r=5
0 1 2 3 4 5 6 7 8 9 10
number of stages. N
FIGURE 4. Comparison of multistage cross- and
counter-current extraction.

(19) It is clear from Eq. (22) that complete extraction
of the solute is not possible (even with an infinite
number of stages) when KS/F is less than one. The
(20) limiting performance is given by Eq. (22), and this
result is also clearly shown in Figure 4. The highest
flowrate, at which the limiting performance expressed
by En. (22) occurs, is given by

r=1 (-- 23--
r=1 (23)

i.e., by



Solvent flowrates in excess of this value would
allow X,/X, to tend to zero as N tends to infinity. The
concept of minimum solvent-to-feed ratio for a given
specification, i.e., to reduce a solute concentration
from X, to XN, is thus clearly demonstrated by the
simple LLE system.


The above algebraic analyses enable the princi-
pal features of multistage contacting to be
demonstrated quickly, although the liquid-liquid
equilibrium system is hypothetical. The equilibria
for real systems are more complex, particularly
when the solute concentrations are high. The above
LLE system can be used to introduce students to the
graphical solution methods. For convenience, the
solute ratios Y and X should be converted to mass
fractions. Thus, since the solvent and all extracts
contain no diluent, the mass fraction of solute is
given by

y Y
Y 1+Y


Similarly, since the feed and all raffinates contain
no solvent, the mass fraction of solute is given by

x iX (26)
The locus of extracts solutee and solvent only) is
clearly the hypotenuse of the right-angled diagram
shown in Figure 5, while the locus of raffinates (sol-
ute and diluent) is clearly the abscissa.

Spring 1991

0 solvent

mass fraction
of solvent

0.4- 1

02 -

0.2 I

\oed locus of raffinates
,0-, n ,


y, fraction
of solute
in extract



0.4 0.6 0-8
mass fraction of solute

0 0-2 0-4 0'6 0'8
x, fraction of solute In raffinate

FIGURE 5. Single stage extraction with simple LLE

A single stage calculation of the extraction by a
pure solvent of a solute from a mixture with only the
diluent is shown in Figure 5. The value of the parti-
tion coefficient used in this example is K = 1.5. When
written in terms of mass fractions rather than solute
ratios, the equilibrium relationship is no longer in
linear form. Substituting Eqs. (25) and (26) in the
equilibrium relationship Y = KX gives the revised
form of the equation

f 1 y1 -y Ixx1 (27)
{li-y} Kl-x} (27)
Students are encouraged to derive the inverse
lever arm rule from the material balances and to
apply the rule to the single stage calculation. Analy-
ses of cross- and counter-current extractions, includ-
ing minimum solvent-to-feed ratio, can also be stud-
ied using the system shown in Figure 5. However, at
this point in the first-year course, students would be
expected to be using real chemical systems in which
either one pair or two pairs of the three components
are partially miscible, and the corresponding graphs

would show the extract and raffinate loci not to be
the sides of the triangle.


A simple liquid-liquid equilibrium system involv-
ing a constant partition coefficient, which is based
on solute ratios, is used to develop an understanding
of multistage contacting in the first-year separation
processes course of BEng degrees at Bath. The alge-
braic solutions are used to demonstrate the advan-
tage of counter-current operation over cross-current
operation, to demonstrate the effectiveness of split-
ting the solvent in cross-current operation, and to
demonstrate the problem of minimum solvent-to-
feed flow ratio in counter-current operation.


F = mass flowrate of diluent in feedstock
K = distribution or partition coefficient expressed in
mass ratio units
N = number of stages in solvent extraction battery
r = parameter defined by Eq. (4)
S = mass flowrate of pure solvent
x = mass fraction of solute (in feed or raffinate)
X = mass of solute per unit mass of diluent
y = mass fraction of solute (in extract)
Y = mass of solute per unit mass of solvent

f = feed
n = phase leaving stage n
N = phase leaving stage N
1 = phase leaving stage 1
2 = phase leaving stage 2 O

Books received

Organic Reactions: Volume 38, edited by Beak et al.; John Wiley
& Sons, 1 Wiley Dr., Somerset, NJ 08875-1272; 805 pages, $89.95
CAE: Computer Modeling for Polymer Processing, by Charles L.
Tucker, III; Oxford University Press, 2001 Evans Road, Cary, NC
27513; 623 pages, $99 (1990)
Biotechnology Focus 2, by R. K. Finn and P. Prave; Oxford
University Press, 2001 Evans Road, Cary, NC 27513; 543 pages,
Fermentation: A Practical Approach, edited by McNeil and
Harvey; Oxford University Press, 2001 Evans Road, Cary, NC
27513; 226 pages, $65.00 (1990)
Polymer Characterization, by Schr6der, Muller, Arndt; Oxford
University Press, 2001 Evans Road, Cary, NC 27513; 344 pages,,
$47.50 (1989)
Chemical Engineering Education

S II I I I I I l I

- I

I I with K=1'5




REVIEW: Viscous Flows
Continued from page 97
an appropriate background in fluid dynamics. Since
there are those among us who do bring this focus
into our undergraduate classes, some thought must
be given to the selection of this book for a first
undergraduate course.
Professor Churchill has laid out the book in a
logical and attractive manner. It begins with several
chapters on one-dimensional laminar flows. These
flow fields are physically appealing and mathemati-
cally tractable for the undergraduate, and they pro-
vide a foundation for some of the later material. As
is the case with most fluids texts, the flows illus-
trated are almost entirely newtonian (though there
is a short chapter on non-newtonian flow through
channels) and flows in which surface tension plays a
dominant role are barely mentioned. This is a choice
an author must make in order to keep the size of the
text manageable, and it is a defensible choice. Ex-
tensive referencing makes it possible for the intro-
duction of additional material by the teacher or by
the self-motivated independent student.
Following this introductory material there is a
presentation of the Navier-Stokes equations and a
discussion of the special cases of creeping flow and
inviscid flow. Several subsequent chapters treat
boundary layer flows in great detail, with special
attention given to a comparison of experimental re-
sults with the mathematical models for these flows.
Similarly, flows over solid cylinders and spheres are
discussed with extensive comparison of theory to
observations on the structure of the flow (wakes,
eddies, etc.) and on drag coefficients for these bodies.
A long chapter on bubbles and drops, illustrating the
role of the deformable interface (here, of course, sur-
face tension enters) is presented. There is almost too
much material here-I found myself bogged down in
the seeming repetitive presentations of data on ter-
minal velocity of rising bubbles.
On the whole, I think this text is a viable option
for introduction into the undergraduate curriculum,
with the reservations regarding the importance of
the instructor that I have indicated above. It would
be an excellent choice as the basis for a second course
in fluid dynamics.
One criticism of this textbook arises first upon
reading Chapter 10, which presents a long (seventy
pages) description of various flow fields that are
exact solutions of the Navier-Stokes equations. Here
the author has an opportunity to introduce a num-
ber of practical applications of theory (note the sub-
Spring 1991

title of the book) but this is not done either through
worked examples within the chapter or through the
introduction of problems at the end of the chapter.
Of the 105 problems that follow Chapter 10, most
are of the form of "reduce the equations," and "derive
an expression." Only four of the problems are stated
in a form that implies a clear practical use of the
theory presented in the chapter. I am disappointed
that in a text with this prominent sub-title there is
so little illustration of the practical use of theory.
If the feature of the text which I have just cri-
tized were only a matter of author's choice and style,
one could accept the text as it stands since there is
so much of it to applaud. Unfortunately, the failure
to give more attention to practical applications, in
favor of derivations of solutions, leads on occasion to
comments that are at least confusing and which are
potentially misleading.
For example, a derivation is presented on pages
182 and 183 for the radially outward flow field gen-
erated by pressure within a porous cylindrical reser-
voir of fluid. This is an extensional flow field, and
extensional flows are important and are often ne-
glected in typical fluid dynamics texts. The solution
for the radial distribution of pressure is derived and
the statement is made that the pressure is inde-
pendent of viscosity because there are no shear
stresses. To most students this would imply that
extensional flows do not exhibit viscous effects, which
is clearly at odds with experience and intuition. The
introduction of an example at this point, showing
how to calculate the pressure required to drive this
flow at a specified volumetric flowrate, would serve
to clarify this point, with the bonus that the student
would be introduced to the concept of balancing the
total radial stress (which includes the radial viscous
normal stress) at the boundary of the flow. This
would permit the student to learn and appreciate
the distinction between shear stresses and normal
Practical applications of the theories presented,
as well as of the empirical correlations of data de-
scribed so extensively in many chapters, do appear
in several chapters more than in others. For ex-
ample, in Chapters 19 and 20 the topics of flow
through porous media and sedimentation and fluidi-
zation are covered in considerable detail, and a
number of problems at the end of each chapter pro-
vide an opportunity for the reader to explore the use
of the material in several practical contexts. Thus,
this text is not devoid of practical applications. I just
would have hoped for more of them in view of the
implication of the subtitle of the text. O

classroom )



University of Pennsylvania
Philadelphia, PA 19104-6393

Chemical equilibrium problems with simultan-
eous reactions can be solved by direct minimiza-
tion of the Gibbs free energy or by algebraic meth-
ods.'11 Direct minimization using optimization tech-
niques such as steepest descent is slower but has the
advantage that the minimization can be carried out
adiabatically as well as isothermally.'2' Algebraic cal-
culations are very fast but require elaborate pro-
gramming to ensure convergence.'3'
Whatever solution method is used, chemical re-
actions are not required as input data. The input to
the program consists of temperature, pressure, and
a list of chemical compounds expected to be present
at equilibrium with their initial amounts.
The Turbo Pascal (MS DOS) program used
to solve the examples in this paper by alge-
braic methods may be obtained by mailing a
3.5-inch diskette with a self-addressed, stamped
return envelope to the author, or by E-mail
( A minimization
program running under Microsoft Windows is avail-
able from O'Brien.121
The Pascal program uses matrix algebra for the
atom balance. The list of chemical compounds is
converted to an atomic matrix A (see the Appendix)
by a subroutine that parses the chemical formulae of
compounds in terms of the number of atoms of each

Alan Myers founded the series of International Con-
ferences on Fundamentals of Adsorption and is the
author of several monographs and one hundred pa-
pers. He is a graduate of the University of Cincinnati
(BSc) and the University of California at Berkeley
(PhD). His current teaching and research interests
are in statistical mechanics and molecular simula-
tions of adsorption.

element. The amount of each compound is expressed
as a vector n. The atom balance is
m=An (1)
where m is determined by the starting concentra-
tion n .
The stoichiometric matrix N for the set of chemi-
cal reactions is obtained from the atomic matrix A
by solving the equation
AN =0 (2)
for N (see the Appendix). An element of N is v., the
stoichiometric coefficient of compound j in reaction i.
For C chemical compounds containing E
elements, the number of independent chemical reac-
tions is R = C p, where p is the rank of A. The
amount n. of compound j at equilibrium is expressed
in the terms of its starting amount n ;
n =n +- vijni (3)

where i. is the extent of the ith reaction. The Newton-
Raphson method is used to solve the R nonlinear
algebraic equations:
0 n.
nKi-vj = iv n( +1v n j (4)

for the unknown extent of each reaction 4. Ki is the
equilibrium constant of the ith reaction. Possible di-
vergence of Newton's method is avoided by dividing
the compounds into two groups: primary and secon-
dary. Each secondary compound appears as a prod-
uct in one and only one reaction (see the Appendix).
The algorithm sequentially examines all possible
combinations of primary and secondary compounds
to find a set of reactions with equilibrium constants
less than unity. Then the starting concentration is
recalculated from Eq. (1) in terms of the selected set
of primary compounds. Convergence is assured be-

Copyright ChE Division. ASEE 1991

Chemical Engineering Education

cause each reaction must proceed to the right to
form a finite amount of secondary compound, but
not too far to the right because the equilibrium
constant K < 1. The search for the convergent set of
reactions is accelerated by selecting the most stable
compounds as primary, and the least stable (highest
values of Gibbs free energy) as secondary compounds.
This program is limited to reactions of perfect
gases. Condensed phases (liquid or solid) may be
present if they are at unit activity. Under these
limitations, it is legitimate to view the software as a
black box to which the input is thermochemical data,
composition of feed, and state variables. The
output is the equilibrium composition. The details
of the algorithm are less important to the user
than the program's speed and the conditions
under which it fails, such as high pressure or simul-
taneous phase and chemical equilibria. Computer
output can always be checked by substituting the
equilibrium mole fractions into the chemical equilib-
rium constants.


We will illustrate the procedure for coal metha-
nation using steam and hydrogen. Coal is simulated
by graphite. Gases present at equilibrium are H2,
H20, C CO2, and CH4. In addition to the amount of
each compound and its state (solid, liquid, gas), the
program calls for the pressure, feed composition,
and dimensionless Gibbs free energy (G/RT) at the
temperature of interest. The feed is entered as the
amount of each compound, but the equilibrium com-
position depends only upon the atomic composition
(C,H,O) of the feed. In this example there are six
compounds and three elements, so the number of
chemical reactions R = C p = 3. The program prints
a set of independent chemical reactions with their
associated equilibrium constants to facilitate check-

ing the results.
The thermochemical data may be calculated
either by thermodynamics or by statistical mechan-
ics. The thermodynamic expression for the dimen-
sionless Gibbs free energy obtained by integrating
the Gibbs-Helmholtz equation is

_G f Ho-I(To)i (T dT (5)
RT RTR J R )-To T I J RT^ ^
where G and H are values of the molar Gibbs free
energy and molar enthalpy of formation at the refer-
ence temperature T and reference pressure Po, and
I(T) is the indefinite integral of the molar heat ca-
pacity of the compound at the standard pressure P :

I(T)= Cp(T)dT (6)

For example, for the commonly used polynomial[41
Cp = A + BT+CT2 +DT3 + ET-2 (7)
we have

I(T)=AT+ -T2 +CT3 +- 4 E (8)
Tf (T) dT= AenT + (T-To)+ (T2 T-2
RT2 R T 2R 6R

+D 3-T3 -E-1 1
12R( 2R 2 2

Heat capacity data[41 for the compounds under con-
sideration are listed in Table 1.
The dimensionless free energies of formation
tabulated in Table 2 were calculated using Eq. (5).
The feed contains hydrogen and water in the ratio
H/H20 = 2 with excess carbon.

Spring 1991

Free energies (Go) and enthalpies (Ho) of formation at To = 298.15 K;
heat capacity coefficients (A,B,C,D,E) for Eq. (7).
Cor- Go Ho A B C D E
pound State kJ/mol kJ/mol J/mol-K J/mol-K2 J/mol-K3 J/mol-K4 J-K/mol
CO, (g) -394.65 -393.77 19.795 7.344E-2 -5.602E-5 1.715E-8 0.0
H20 (g) -228.77 -242.00 32.242 1.924E-3 1.055E-5 -3.596E-9 0.0
CO (g) -137.37 -110.62 30.869 -1.285E-2 2.789E-5 -1.272E-8 0.0
CH4 (g) -50.87 -74.90 19.251 5.212E-2 1.197E-5 -1.132E-8 0.0
t (g) 0.0 0.0 27.143 9.274E-3 -1.381E-5 7.645E-9 0.0
C (s) 0.0 0.0 16.873 4.773E-3 0.0 0.0 -8.541E5

Input to computer program
for finding equilibrium of coal
methanation reactions at 800K.
pound State Gi/RT ni, mol
CO2 (g) -61.3410 0.0
H20 (g) -32.5318 1.0
CO (g) -28.6855 0.0
CH, (g) -3.4398 0.0
H, (g) -1.2607 2.0
C (s) -0.5925 2.0

Additional data supplied to the program are the
pressure (P = 0.5 MPa) and the number of moles of
inert gas (zero in this case). Table 3 gives the equi-
librium state computed for the feed composition in
Table 2. Computation time for the equilibrium point
in Table 3 is 0.5 second on an 80386/80387 personal
computer rated at 0.075 MFLOPS Megaa floating-
point operations per second). This includes the time
for reading and writing to a file. Therefore, enough
points for a graph can be generated in less than a
minute. For example, Figure 1 shows the effect of
the H2/H20 feed ratio upon the equilibrium yield,
expressed as moles of methane per mole of carbon

The program's output includes the chemical re-
actions with their equilibrium constants in Table 4.

Results of chemical equilibrium calculations for
coal methanation are given by Sandler'51 for the case
of no hydrogen in the feed stream. Helfferich161 solved
for the amount of hydrogen feed required to produce
0.9 mole of methane per mole of carbon consumed.

Ethane can be added to the list of compounds in
Table 2 to find out if it is present in detectable
amounts at equilibrium (it is not). Or, iron and iron
oxide can be added to the list to find out if the
process conditions favor oxidation of the reactor ac-
cording to the reaction Fe + H20 = FeO + H2 (the
result is no FeO at equilibrium).


Chemical equilibrium problems that require

ratio, 0.5

Feed ratio, H2/H20
Figure 1. Equilibrium yield of CH4 per unit amount of carbon
consumed as a function of ratio H/HI0 in feed.
T= 80 K, P= 0.5MPa

computers for their solution arise in high-tempera-
ture chemistry. For example, combustion of hydra-
zine (NH2NH2 + 02 2 N2 + 2 H20) generates OH,
NH, NO, H2, 02, N, H, and O as well as the principle
products N2 and H20. For this problem it is conven-
ient to use the formulae of statistical mechanics. For

Chemical equilibrium for coal methanation reactions
at 800 K, 0.5 MPa.
No inert gases; amount in feed, n,; amount at equilibrium, n,;
mole fraction in gas phase at equilibrium, y,.

Compound ni, mol ni, mol y,
CO, 0.0 0.13258 0.05808
H20 1.0 0.70954 0.31080
CO 0.0 0.02530 0.01108
CH, 0.0 0.87494 0.38325
H2 2.0 0.54058 0.23679
C 2.0 0.96718 0.0
Total 5.0 3.25012 1.0

Chemical equilibrium constants at 800 K

Reaction K
C(s) + CO2 > 2 CO 0.01043
2 C(s) + 2 H20 => CO, + CH4 0.23041
C(s) + 2 H,0 <- CO2 + 2 H, 0.16635

Molecular constants
Molecule MW, g/mol ,, K 0,, K Do/k, K o a

H, 2.016 87.55 6332 51,970 2 1
02 31.999 2.07 2274 59,360 2 3
N2 28.013 2.88 3374 113,350 2 1
NO 30.006 2.41 2740 75,390 1 2
NH 15.015 24.03 4722 39,460 1 3
OH 17.007 27.21 5378 50,970 1 2
13.40 2295
H20 18.015 20.90 5254 110,360 2 1
40.10 5404
N 14.007 0 4
H 1.008 0 2
O 15.999 0 5

Chemical Engineering Education

a diatomic molecule modeled as a rigid rotor, har-
monic oscillator in its electronic ground state, the
dimensionless Gibbs free energy is

G -n kT )-n (e+n I e-x _D -n
NkT p3 ) r ) kT

Translation Rotation

TVibration (10)
Vibration Electronic

where A is the deBroglie wavelength of the molecule
A= h (11)
V27 mkT
and x = J/T = hv/kT. The rotational symmetry num-
ber is o and the degeneracy of the electronic ground
state is e The energy of the molecule in its elec-
tronic and vibrational ground states relative to the
isolated atoms at T = 0 is Do, and the characteristic
temperature for rotation is 0, = h2/82Ik.

Chemical equilibrium for combustion of hydrazine at
3500 K, 1 MPa. Input to program, n,;
amount at equilibrium, n,; mole fraction, y,

Monatomic species (N, H, O) have no rotational
or vibrational terms. For nonlinear, polyatomic mole-
cules (H20), there is a separate term for each vibra-
tional mode and the rotational term is replaced by
SG n T3 0
[NkT ]r l 2n i T3- (12)

For NO another term must be added to account
for excitation from the ground electronic state (1) to
the first excited state (2)

[NkT]ee --n [+ +e2 e r l)/kT (13)
NkT eLec 0el I

where oe, = oe2 = 2 and (E2 e)/k = 172 K. Constants
extracted from Herzberg47' and NBS181 are given in
Table 5.
Computation time for the equilibrium state re-
ported in Table 6 was 1.5 seconds on a computer
rated at 0.075 MFLOPS. The results are that the
equilibrium concentrations of N and NH are low
enough to be neglected under these conditions.

1. van Zeggeren, F., and S. H. Storey, The Computation of
Chemical Equilibria, Cambridge University, New York,
NY (1970)
2. O'Brien, J.A., Department of Chemical Engineering, Yale
University; personal communication
3. Myers, A.K., and A.L. Myers, "Numerical Solution of
Chemical Equilibria with Simultaneous Reactions," J.
Chem. Phys., 84,5787 (1986)
4. Reid, R.C., J.M. Prausnitz, and B.E. Poling, The Proper-
ties of Gases and Liquids, McGraw-Hill Book Company,
New York, NY (1987)
5. Sandler, S.I., Chemical and Engineering Thermodynam-
ics, 2nd Ed., p. 531, John Wiley & Sons, New York, NY
6. Helfferich, F. G., "Multiple Reaction Equilibria-With Pen-
cil and Paper," Chem. Eng. Ed., 23, 76 (1989)
7. Herzberg, G., Molecular Spectra and Molecular Structure,
2nd Ed., Vol I-IV, Prentice Hall Book Company (1950-
8. NBS Circular 467, Atomic Energy Levels, U.S. Govern-
ment Printing Office, Washington, DC, Vol 1-III (1949)


atomic matrix
number of chemical compounds present
heat capacity
electronic energy
number of elements present
Gibbs free energy at Po
enthalpy at Po
Planck constant
function of heat capacity, Eq. (5); rotational
moment of inertia

Spring 1991

G/NkT ni, mol ni, mol y,


H20 -61.2859 2.0 1.40718 0.40850
N2 -60.9791 1.0 0.96259 0.27944
NO -52.6323 0.0 0.07465 0.02167
02 -47.4720 0.0 0.14014 0.04068
OH -41.3420 0.0 0.17333 0.05032
NH -38.4545 0.0 2.95E-5 8.57E-6
H2 -35.8107 0.0 0.39011 0.11325
O -22.5047 0.0 0.06456 0.01874
N -22.0821 0.0 1.29E-4 3.76E-5
H -17.4415 0.0 0.23205 0.06736

3.0 3.44478 1.00000


Chemical equilibriuum constants at 3500 K and
standard pressure Po = 1 atm.

Reaction K
0.5 H20 + 0.2502, <= OH 0.31069
0.5 0, = O 0.29191
0.5 H20 = 0.2502 + H 0.26357
0.5 N, + 0.502 4= NO 0.20326
H,0 0.5 N, 2> N 2.23E-4
0.5 H20 + 0.5 N2 < 0.25 0, + NH 2.02E-5

k = Bolzmann constant
K = chemical equilibrium constant
m = element vector
N = number of molecules
n = compound vector
n = amount, mol
P = pressure
Po = reference pressure
R = gas constant
T = absolute temperature
x = dimensionless frequency of vibration = hv/kT
y = mole fraction in gas phase
Greek Letters
Or = characteristic temperature of rotation
90 = characteristic temperature of vibration
A = deBroglie wavelength, Eq. (11)
v frequency of vibration
S- extent of reaction
p rank of A
o rotational symmetry number (integer)
coe degeneracy of electronic ground state (integer)

o refers to feed composition (initial state)

o refers to standard state at 298.15 K, 1 atm.
i refers to ith reaction
j refers to jth compound


Matrix operations are illustrated for a reaction
system consisting of nine compounds (C = 9) and
four elements (E = 4). The E-by-C atomic matrix is:
2 2 2 2 2 2 2
C 1 0 0 0 1 1 1 0 0
O 2 2 1 0 1 1 0 0 0
S 0 1 0 2 0 1 2 1 0
H 0 0 2 0 0 0 0 2 2

The rank of A is p = 4, so there are C p = R = 5 inde-
pendent chemical reactions. A particular set is found
by dividing the C compounds into p primary com-
pounds and R secondary compounds. The stoichiom-
etric matrix N is obtained from Eq. (2) as follows:
The atomic matrix is written with the p primary
compounds in the first p columns of A so that the E-
by-p atomic matrix A for the primary compounds is

at the left and the remainder of the A matrix con-
tains the E-by-R matrix for the secondary compounds
A=IA,, As

For A as written above, the secondary compounds
are CO, COS, CS,, H2S, and H2. After selecting the
secondary compounds, a unit matrix as large as pos-
sible is formed in the upper left-hand corner of A
using elementary row operations, so that a new
matrix A is generated with the following reduced
row echelon form
0 0

where I is a p-by-p identity matrix and B is a p-by-R
matrix. The number of rows of zeros is E p. Zeros
are present when the rank of A is less than the
number of elements E. In this example E = p.
The stoichiometric matrix N is constructed by
appending an R-by-R identity matrix Is to the R-by-p
negative transpose of B
N= -BT, Is

The result from A as written above is

2 2 2 2 2 2 2
-1 0.5 0 -0.25 1 0 0 0 0
-1 0.5 0 -0.75 0 1 0 0 0
N= -1 1 0 -1.5 0 0 1 0 0
0 0.5 -1 -0.75 0 0 0 1 0
0 0.5 -1 -0.25 0 0 0 0 1

The rows of N are the chemical reactions
CO2 +(0.25)S2 = (0.5)SO2 +CO

CO2 +(0.75S2)= (0.5)S02 +COS

CO2 +(1.5)S2 = SO2 +CS2

H20+(0.75)S2 = (0.5)SO2 +H2S

H20+(0.25)S2 = (0.5)SO2 +H2

The secondary compounds (CO, COS, CS2, H2S, H2)
appear in one and only one reaction. There are
sets of reactions, each containing a different combi-
nation of R secondary compounds. In this example
the number of reaction sets is
5! 4!

Chemical Engineering Education


This guide is offered to aid authors in preparing manuscripts for Chemical Engineering
Education (CEE), a quarterly journal published by the Chemical Engineering Division of the
American Society for Engineering Education (ASEE).
CEE publishes papers in the broad field of chemical engineering education. Papers generally
describe a course, a laboratory, a ChE department, a ChE educator, a ChE curriculum, research
program, machine computation, special instructional programs, or give views and opinions on
various topics of interest to the profession.
Specific suggestions on preparing papers.
TITLE Use specific and informative titles. They should be as brief as possible, consistent
with the need for defining the subject area covered by the paper.
AUTHORSHIP Be consistent in authorship designation. Use first name, second initial, and
surname. Give complete mailing address of place where work was conducted. If current address is
different, include it in a footnote on title page.
TEXT Manuscripts of less than twelve double-spaced typewritten pages in length will be
given priority over longer ones. Consult recent issues for general style. Assume your reader is not a
novice in the field. Include only as much history as is needed to provide background for the
particular material covered in your paper. Sectionalize the article and insert brief appropriate
TABLES Avoid tables and graphs which involve duplication or superfluous data. If you can
use a graph, do not include a table. If the reader needs the table, omit the graph. Substitute a few
typical results for lengthy tables when practical. Avoid computer printouts.
NOMENCLATURE Follow nomenclature style of Chemical Abstracts; avoid trivial names.
If trade names are used, define at point of first use. Trade names should carry an initial capital
only, with no accompanying footnote. Use consistent units of measurement and give dimensions
for all terms. Write all equations and formulas clearly, and number important equations consecu-
ACKNOWLEDGMENT Include in acknowledgment only such credits as are essential
LITERATURE CITED References should be numbered and listed on a separate sheet in the
order occurring in the text.
COPY REQUIREMENTS Send two legible copies of the typed (double-spaced) manuscript
on standard letter-size paper. Clear duplicated copies are acceptable. Submit original drawings (or
clear prints) of graphs and diagrams, and clear glossy prints of photographs. Prepare original
drawings on tracing paper or high quality paper; use black india ink and a lettering set. Choose
graph papers with blue cross-sectional lines; other colors interfere with good reproduction. Label
ordinates and abscissas of graphs along the axes and outside the graph proper. Figure captions
and legends may be set in type and need not be lettered on the drawings. Number all illustrations
consecutively. Supply all captions and legends typed on a separate page.

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  • idor...,.,.,,oo o nd thomathemo,ti&porto---id~r-r/a/0.~t Thermodynami
    PAGE 17

    --wtuct,t.aoopttiallundaofpon..J.....,...,. .,_ ..... __ ~......., ...... n.._.....,.._ .. ,_o1,1,o _______ ..., .. -""""'"ot.1,,, .... ,;u.u-...... ,__. ond1"'rel1--.""'1,....1uo,.,-Jl>Mdi1h lhotMIUof\/lenoocb"namoc,,. n.-,..,., ..... ndonlfonno ..... f(wh,.IOric,.I .........,.."dr.-.n,U,.p""'lem "hitobod;. n,ctly...,rul ... c::.:~~:::~t::..=. ...,,...i ................. .....-,,_ri...., va1-ot, ... o1-..............-1o1,....... Hriololoo T ondr,............ -oat,oTvatiobloV-,oloo booxptNM<1;,a,.,i-,-~ fun<1.-b-llb)-_outh_,,,..., .. IJ!T.Plond :~~~l~t"~"':'~:~i:~,::,r:::~~ IHT P 1;1(ivenb)'le:q,O). thtnitr ollowothot H IT.V) T 1 Tlot:(V) I') wh,d,io-thooa,...ul',q.(l)ond,oil!-aiv.lho ,equ,..,..voluob\l01Eq.mwillwher,1l>e1up ..,.;.,.....,,,dual>otl,tha1""or 11 "' T 1 ,1Tio.iT/V) Noto al .. tha,,ol,...,uchull"l213.llond 11,..\273.~. 0 ,.,i..,,ndunombiguouo.

    PAGE 18

    ~7,[;.::ionfol"Eq.llltt.. .. a ... two -iblo.;e. f,,.ntiol 1 dT,dH, o <>ddl' u qu,-ntt inw hoH in .!,ual fa,hkm lfwed,v\de:; :7f ;~:.f,:P : .i: ~( f(T+6T,:, /t(T, P )] (S) ,...,,. weem~ ,: ;~,:~~ a,,d last.,~:) ~~J,~;:::=.r-~::::= ""''""' we may :i!.~"'lytherat.,.oft~od ;lfo,.nti a l o ..,.d,rivo,,;.;. Thio1>0Utioniofuundtoi,,,>00;.ler11blylleofbothlf"' nd atf"'m',ofexactiylheoo""'"""'"'T W e0t,.... the.-dtouad,"'"""'""""' I"""' hon.wh.,hU..>tnd Wedefinody andd,wbeony twov o ri o bl, o wh;.,h N ti,fythe equation dy fdx (6) ondwo .. whieA ofU-quontit;o. 11; :::,;~.:.~:,::,d,t ::~r;-( : ~;:-whKh i o Ublain ( 9 ) Juo, ,o thed,!l\,....,tiol,oO:t,. ( 6)dcli .. ,tangent linolOthocurv,y l'l ), thtdHffl'>nti o!a ofEq,(7 ) "'l'..,.,,,,.,..,m,n1on pla.,whilthelel'l-hond oideofEq ( 9)ioonolgebrai,notohm,t oo in t,i (~).This;,, di""" "'Otfonthot1J,,dilfe,.n li&loa,....,,,..,,,_,.;1y,mallq""ntit "'"Thtim l)Ortant,eo ult i,thtllMu,..manipu laUon ~ill beol,.....,.k;thtSlroiot o 1>0<;.ntoothel,,ltoO)q. (9 ),lheuh,,..ofdll o nd ~;;e.nok>nirerorbil,ory,Mweho..,""" U oi nsti-oonttpu, t .. pe-eweemphNiuthottMtwowm ro,.tioool diJferentiolo ,..,. derivatieo.Now,con oi dt,-f)q.(10 ) :::,~:~~~if[Ldi~n,nt,ol:ll) l'l WU ,,,, wemay,fromthe,ituotionwhendP 0,..,..;nth e woll,koowo"'li ~~ (IS) c1,,,.,,.,;,:,.,,.,.n,.,1'4o
    PAGE 19

    -NoW/OrllOOtation wh;ch ~ohav,lloujlh<1..,t; tiono l ..,. o hon) W o m oy .. e...,,., ffon ond,i-, byodopton.go>honhondinwhi.tou,.,h0tation'"")"..,,,ily bee,,.y .. tho limilota,urn.Th>1i o. ~""""'P"'h\l,\l(S)from S,toS J.T" ds 12-( tT"' ls,v(sJJ~.) .,t,.,...,N~ S,-S..(The,.iono o mbiguityobout dSwhen....dinoor\junrtionwiththoint,graloign. ) c.,,,,..i.,ofun.yuniquely s s"' (I~J Wom ay1 ubolitulv, .. .oo ibi..Jrv. ~ h ,ll".,.co n-n,quely ol,'. to obtain T Of" l' wo looe infonnn""""u>''fromU"' ,i...,.1honhond !'>Ota bon.,ploinedobov< 05 ) ~~~~:~:{rl:~:'.!!~~~~:;; dU U'"dSU "' dV T"' ond 1 ,.,. ,u"'" thenobviwoly Th,,enewfunof.,hith ore inde::~~~;'.::i :'=~~ '"i:;:i1 .. ~~:;::., rot"oen..youffk,.J A,maoy,.de,.w i lll:...,,..v.eowlhal w ,.,,._...,.""r""",i-...i.r.o itionolllbov< s,,,;"''"''

    PAGE 20

    ;i ~ !Pi,< ( _c: 9~1;t !,f ~i !ji,l_r F!~-~i: : &. f hi' "-:: r p:f 'j~' 'P~I "'F" ~-cf p1, l i, ;JH L!!!f~--t i c: c: !h f i!Ii .. '!';r ~ii 1fr; l',i,,1-t i 1 ,ir [,' J. .. ,.,,H ,,,.! 1 :,1 ,;;H; < I , 'Ii !!ll4,~,q,,! tH;..-"!
    PAGE 21

    REQUEST FOR FALL ISSUE PAPERS ~ach year CA,m.,.I ,vii11ttri"lf &Juoo,..,,. publ;,h.,. a >ped2)od>p]a.ei~"""'p,'OframO. Anyonoin""""lll-.eod1torio l oootenloftl>el991falliowe1""ldwritet<>1ho od ; tor.ind i m,,..111<,ubjodoft=::::.t.;'::;.:'O:"i~\';~"'"';..,dot<;twmbm;tted dUTdS-PdV I ~,dN, (37) ol'l<"t<> h .-th .. mepn>b l emoof und.,,i.ndingthattlloM.nitK>ll o ofTandPo.,nod;lfn1 unde,yraduolN :~~~:': :;:.;,:-;,,~ A U TSA""K, i ondllandGon,fHh;on r,.,. '":,': :..::~:'.~::~.::. '.~':':'."O:::. :'.'!.: ofo,., new~:~:::~ ::~7'~~7,' i,.,,, ...... inge,..,,..ldonotturnwttobou .. ful :~;oo,, .. weohollnoplo,,,thio vnuefurWemoy olooOOl,!lm oowedidobov<,,ooetof Maxwell r,lotlooo, for.,.omplt, from the_,..d d,ri,ohVttofU.w,moy""'m 1 1<,_w, .. c'"-"A>tlJ-11"""-W .. c........_ 8 ,.0!ESIGNAN0EC0NOMICS t,'ictl Jol,t,Wlloy&Som;472-,S33.95(19114} W. -~y r"'"' I K >l -P S "X;I v.-hol,fromAWU,...pouibl,. ~-}H;, ~. , H,,. It perhopo' '- Otrt1in Ol 1h;, po;n,,h.,oll11>eoix,,.,,,""'\op,nonl;.pun,ly""'the '""'kal.All1ho f<]ouonov.~ hA,..d<,,,elope,J follow fromthep,_ni .. offunct..,...ondthoirderi ~--:-1::~!7:."".;.:";-:i'.!f~:;:i:. -::;.\~'.,"""' Thedev.lopm,n1th.,moybe;.lont;f"'o(;onofouroymbolo TondP~iththoiruoualmuni..,)willformtho1ul> jodento......i;1y.,..;m n ou,th i omotte,tf.,.., oou ... u,ina-co..,.,.,.i, .. ,uehuti.-from tho A ChEd<,ignnel:proc,,.de,irn. oconomillonddeoignofindi.;du,1,,-ofoqu1? ""'"'lnChopt"Oduep.-..ondob1aon,11g1yp;,,a tnowo11 tor...,...,h< hurotu,..and ~i:= :,:-:::;:n>H llowoheet p,_nuion and Chopttll< opttif"'"'""''"""""rnof;ndivid"'1lp',ooeoofp""' ::.:."~".:,~~ ,~':."':,':;~,::~. d:~'. "'"'"'""' lMh...,._K>llgiv .. abriofO"o"
    PAGE 22

    Random Thought .. WE HOLD THESE TRUTHS TO BE SELF-EVIDENT l b<: tt ,um M t l:ult!.fl N,,,..c ...i, ... s,,,,,u.,""""" R"""",NCnJ6.79116 B =-.:=~=!:--:! k...,.1M1,t'tho_,.p1...,..,.;r,.-.1"too,-lu ,-,.i,.,-"''ol,,om,.nJ'i""''"'"",.' <1>fon 11t,o,.,,,,h.,rono,rg,/Do,11Mpn,d_,, qkOI 11,-/!>10on1/)aodif t lo,yon,"' .. '"fo,,idtonalhatha..,_boen_'"toh.ovo r 1 ':'" ... ~!..~::::""def, ___ ,,..,........,,,1""",,..,,.n,_o.,.,.,.,i111G,~ .,.,,.1,,, ........... ,..t_,,,_...,,..,,..., ,_,....""""_,_..,. _,~,.,,., _._,, .. ,,,..,,_._ v.,.,,,,w,,.,-.10,--,.,,._,.,.., """"1--fl,.-~-,,..,i,,,,.,. d,dolN,..,M,__,a..t .... ,,,.,1,-(i<..t ,.. __ .,,,,.,,,,_,\._,. .. ,,., .. ., ..... ..... _...,..,,,.,_...,,, ___ .... _, __ ,,.,,-,.u, .. ,-, ,.._.,,,,._.,,.,.,__ofl,,,_A,. =:... ~:;::';'.;-:;;~~ :Z:!1::',_,..,. .,.,,,.,,_..,..,.. .. \l '""'""'"''""""'P""""'"'Mad.tMfi,, i,,,,,r,,.,_,,.,,,,.....,.,.,,,,.,1u,,...,,d,dotrllh ,,,, .,,_., ,...,,,., ... """"' "11",-,Jt,,."' """"""'"''"~up,,v,.,.,,,,-abd,o,. /lo,,lt, .,,.,.,,..,,,.,tl,por,-"' ... ..,r,,~1<1 ...,_,..,,,..;_,.,.,,,.,,,..,,.,,,.,., .,,,,,,_....,~, ..... MvntSAIIQUT RESEAllalANO ffACMNG &,,1i,,,,,,,,..,._,,.r, .,.,am1aott,.,_. ,,.,,,.,.h...,A/y,.,,.,../oted. R ,.,,m,wJ:VA"RY(M,;lo,nvmO,,/o,,._lld po,i,..,.,,,.,.,..,w,p"'f1'"<'maoacond,Mn r,,,,,,.......,.aodr,n""'"'"'"'""d'"" 1,,,..,,_.-,.,,,.,,_,.,.,,_,,,,,,..,, ""'"""'_,,,..,,_.,,_.......,,..,,... _i,.,i,, __ ,,.,,...,,_,,,_i, ... ,-,d ........ .. -1'-,... _,.1.,_ .. ,,.,,.. ....... _,_.,,,_,,.,.,.,._ ........ a&u,.,..,w, ....,.. 11 ,,..,m....,\1,.,<---,. -"-~f..::0~::~~E,z~~:~ =:-_::: =::-,:::.::~-1/
    PAGE 23

    ""' Prof,,_, uho or, ,.ffl'l/e>1/ al l""h'HR and""'1wcr,.,_,qor,01r,_,.....,.d,.,,"1 MYTHSAllOUT C UR R IC UI. UMDl::SIGNANOPEDAGOGV 0.,,,,.,,,.,,,..,,..,.... ,,,,, ..... ,~, ... 90', of .... .."'"lfhl 1h,oo. ;;,.,.. .,..,., .....,_,, ... ,,,.,,,_,_91>'",,ft<.,,,,..,,..,., .,., ........ _,,,..,,._,."" ,,,,, ..... ,.,.,..,,<1.,,,,,_,,11_.,,,, ...... .,. deo1,orernli1,r,,,.,-h,-Wh1.,.,,,_, ,.,..,,,...11<,.,_.,..i.i.,....,.,...,,,., ==-'"""'"""'dnn.t,,-1,,, .. ..,, ..-,,.,,,.,.,/u,. yuomu,.,h,m<>"ry, ""'"'"'/_.,.i,.,n.-. ..... /dbr1a,,,i.,.,,.,.,. ,i,,,.,,,,,J,,...._,, .... ... ,,,.,,,,., ,,,. ___ _,ro1,_.__,,_ tttA ..,., . .,,,,,,,..,,.,.,.,,.,-1.p .... ,.,.,, ,..,,.:.,1,,1c,,,..,,..,,,.,!;--l>.Jm n.,_,,, ..... do . ,,~ ... -,.,,,,. .... ,., __ ___ ,,,.,,"",_,,,.,..,.,,_... IHlto-,\flf:T... .,.,4o, ... ,,,-,.." ,.,...,-.11,.,1,,,.._"""'1lomp/,,i,.....,,1h,...., .,,., ...... ,.,,,.d filhoo,w.,,..,,,,:-1,,u .,,.,,,.._,1,,,,. ,_ ... ,.,. __ ,.,,,,,,.,.., .... ,. .. "',., ... ;"'1rld...,."'1ndo. lflho, ... ,,,. ... ,-,dtl,,-,llot,,,,./1,a, ... d,...,..,., ""''""""'/fr MYTHSA80UT ~VA l UATIONOf'STVOENH (G RADIHG ) / /00, .. .-11 .. ,.,.d,-r,u,l/doo"-""...,.. .... ,.,,1., ... .,.,.,, .... ... 1,..,,,.,,.,. -,,Gl'A;i1Jo,i,oi,,/,tyro,o/, ... """""", _,,,.,..,.,' r...-,..,,0..,,,..h :~~"t!'"'""'"""-~11-"'"""" Ano, ... ,_.,,,,,of4'),,..,..yfinaJ.,,,,.. ,.,.,,...,.,, .... ,.i, ... _,.,,_,i,,,.,..,,1..,., ,..-.,.,.,,,., __ n,,-,.,.,._ llp,, f:1991 M11.,1ha,,1pn.o,-r,t.llfyoocanw"fy.,..,o,onutlltt olthe..,..,.ump,w.,,.k-t,,,.k,,.,...,ndnl.,tll> ...,...,i,.,.,at,, lf .,..,11,.,,-h nd.)'OIINlll
    PAGE 24

    curriculum A COURSE IN IMMOBILIZED ENZYME AND CELL TECHNOLOGY W cuAME.Lt:F. Jll u~""'""yo{S.,,,1hn,,,.,do Tornpo.fL3J620 c ::.:.:~=:.=.~-.~-::=:: -" .. .. ,. .. .......... ------- ... ,. .. __ ;.......... ... ... ,._ ............. __., ........ ,,._ :-.:= .~;:!7. ::,~~:.:. :".:.':::-' .. ,_.,.._,.,._._11,.. .... .. o1-.,;y-,ICll,,.,.,.,.;--"-'.. ............... o1,-..,_ .... .._,.ot , ::::.: :.:::~.:::::.:: .. -:-.~.:-:~ ............ r., ,, ,..,. ........... , ... ~::.~=~::~.~.-~7~::.'7.:~::::!'~:: "'_ .... 1 ..... .. .............. ..... ... ................ Knot,o II .,,,._,., ........ ;, .. ,, -io :::~= ~:~:-:=::.:~~~~: :~!, =-= ~=~~.f.;~~=:.:7:-::~:~::~~:= 11"" ::~~:::.:.'::~;=~~:::::: ::.":.'::~!! .. tol .. ... "" "'--1; ...... 11. ;, ........ ,,.; ===:~==~ ..'.1:~~~~'::.~~~~'::":~ .... ...... .... .......... -, .............. ... ~';~~~Ir.,, .,.,_,""' .,.., -.n.,,"'" ....... "''"'"""" .......... ,,.11 ._..,.~ . ,.,,,,.__,, ...... ,..,.,,.,._,_c1,o,,;. <01=-~,..;.,:~"'"'"' i :::.-:'"li'"'""'":""' .. i, -.,_.,., .,. ... i; .... ,..., """'""" ,_o1, ............ .., ................ o1 .. -.; ..... ... ....................... ,_ ;., ... """"' Y '"')- ppl i ,ot;., ;. ... .. ........ _,.,. ; .,-1, .... ..... .. .., .. ,o1 ........... .... .... c, .......... ......... . .. :::~;:.':' ...... .!,'.:: :;:r~:!:;'".:,i: .. ~,:: .... ,... ..... ,._._.,.,. ....... r .. ..-u,.; .. -. i;,o,1,, ......... ,,..,._.,_,.,.,o,1,_;, ::;:.:.::.:.~:~t.:~;"~'::~ 1 '.::'.\;:;,:::.~ .... ; ... ....... ,.., ., ... ...... ._,. ,_,. ,..,.,. .,. .. ,,.._,..,..;,,,,.,..,_,.,..,~-r"'

    PAGE 25

    ,_,;_,..,.,,~ .. ,f-"J1>..-.y-.,;,,,y-f<>pp/ic-,-.1ooc1, .. 1;,....,_;.,-...i ,,....,__,,_,..,..,-s.,..~... ,,,,.,1p,9ft<,;.,-,;-a1-1-., .... o11-.uy1 -,o1.a.,.,...,~ ... n;,.,.ickde>thor ___ ,.,,,..,,.. ___ .....,.,_ ,,lhoownu,..Md..,llb,coffe,H;et1,oM.,,. .. """"'"-"'"""'""" .... ---"',,-. --1:= ~::rt~'.::..";"=~ _,...,...,,,,._,;...i...i;ncthe*""" bili..,._.,..-.,,._.~...i1uicoali-"""'---"'"'' .... wl>
    PAGE 26

    m;n .,..The!wo..,, .. indonmbe,olapp l i ndl;.,.. :~::..":~~-:.:='7: ~::~ ;nstructo,during In ,I!'fi'!,\~ ':.~ ~-;:~~~n,~~== tou0<>l;.,.,., o """"""tive , o oam plolduct oJon.cwithony"-"rip!iv" \~':~~:"'.r1':':.'; 0 :a~: .:. ":.::~:! !ho ..,mp l .. u nde,-aoo,.nn;ngloct,onm~ Theoorond,..,..,...involvedhan l yiofUS Poton ia inv01>m...i oyoto""'. opoom<0Uy ~!:.~~~.~;;;'=:~1 ::.=:i.:.:.;;; !~~'7it '"" on a Pl ... .., c,.,.;.,. ( P,1en1 No Fo,thofinolexerd1<,lludenupreo,entedth..,. indo .. p,e,,n .. tiorulonthofollowingtopilogkal .. hn,,wanning,ondrontaOd.,I tiono.Their1hniuldi o a,oll,but thi,-aaeuilyhoodledhyad,faHHtalmaUtiolo. A~pli.
    PAGE 27

    ~':;,~mhrns moat of a1uden1> knew little ~ l oototuwbo.,lect,,dthiorou'90hodpre viou,lyi.kenthe .. niorp0rt pheoomenoaodkinet..,.r,quireiop"""n"'t;.,,,or ..,.,,.prel,minl')'b.e"3round(B.ileyandOlli,gi.., :h~..:=~~:,;:.::ment) ;n order to brina, all Th<~ .. kfftoreaofth<<,>riateono l yt,,;olin,pO,>11...,hnology.Allhtotuden'"dai m to have,_,...,,.,now k """lodge,ondollrou l d,.. t l>< po<""h nology. \\ 'hilehioioogoodotand k>t>elttt i vo,itio ,.p,,< m icol

    PAGE 28

    2:1.-,R.Alor! .... .... .... _ _____ .,,. .. .. .... .., ,, "" -,..o.-.. ,-;....,.,...,,_.,._ ,,,,._,.,,,.,..., ...., _,,t,_..,...J.,..,._. .... ,_ VolI. T.>I. a-c ..... .,_,. l"r-. """ ... -,,o.-..-c.. ..... ,,_rn ,-.r .....,_.,., ___ ....... ..... ""C--.J,W,.-T-lo,ol,..lo&...,..r :;-:;;:":~~::"' : =.;,,,.v..::_ .... ~~~~..e: ~~i'.~:;.~~ EDUCATOR: Perna "~"'lhllutHOnContt<> l Adminionment.olen.g; ,_,;nc.Ang'.thnLlokowitzdeve~othnm
    PAGE 29

    HioAICllt:,a;.;.,............,..,..;o...,w,,,inoci. u...,_.,,_Tocl,noc.i~\/ioo-Cl,o,....a ,/tholt77NYCA.ooual.W-.,..a ... Che,.....,,I =-"~=~-C.:.-:.~-~~~ o,...,..,,ottJ,eN-YortCityAJet,EloohoooJoo..-.l.uCba>,-,,itboAC8MoboJ, c-,.. ...i .. Natiooool-1,ia....,Chi po,loo,Ul-I .,.;_,.. ...,_ and-o/tbo"'-io,-o/Collopl SoridHeitola>tbou..i-o/oppn,>1-..l;f ,i,;..,,_n ... 11"-"" ......... _'"._"'"uthor olo-,ondo,td,l(W(JC1hn,oJll'O<""d, ..... An,;ie.,n>loinOmqoChi !;poiion-l"Yff OJ>e' rialot .. nt,otl WhOUrdtpO,tm
      ;,,_ AA,.wort,.1"11"""" .,.,lywilh..,oorJ!niutiooinl914ond\MnNo tkonol l._;do,nt in 1918 \\'ho1I he -.pletI h1& ,. ... ,. .. ,,....idonthel,o,dupondod-bo.-.!up o,pni,..btrdilfe-t.:,,,o,,... TMNOo pn,(-;,,,,. Hio V<>luntttr ,nV<>l.-nt hN ol"O)"I beh;,u,..,ndt&~ .. ho!>l"IJ,wlwilhwtthou&h\ol-,,,d-hio...i ......-,lhoo.....,...,....,,.....,_..,.,;aho,,ofll,a" --~~,::.~,::::.:.=-~ he,t-., ... ...-11eonc1111o~ .... .---;--"" .... ,....., ....... .......,....,_.,tbo ..... -i.. ,1 .. .,... .... ...,...iu,_.....,._OolMiohfNond....dr1<1eo lnaddit_lO_"" .,,_,_.,....._nl u.dinolll~ta.-..a._ats.llT.A,._;ehooboffl ~~~""=:.'.~=::!""..'! -foo-SS1'. EPA.AIC1't.C,/IH!C."1lt -n"'u--.ondlMIACT.j,.lle"""'-"" ---.,hantu,tbo,nun!Opolondinduwial-. ondduri"!ttboumnw,oll!Nlllho...-vedNo""' ~%~:~-""-:;1 ,::_1or cloV<\oi)md\\1oen!w ufim..,..,...tedt,yCF.F.ot,o,,,111>o -1lH lity ofwrit1 .. 1h11 o,ti<:l<, l ..i.o,IAnpf.. hio,,.,..,iNionond-roUon. llo,.-w,lhtho -
      PAGE 30

      M classroom A SECOND-YEAR UNDERGRADUATE COURSE IN APPLIED DIFFERENTIAL EQUATIONS TtoO>W!Z.FAHrDY ~.:;:~:Yi,~::1-:-,.,..i,. ,W l,3G! c ::-::'f:~.~!:~.,.htd:.~h.:~:~rd: laU11htbymalhoron,"ppJythoM< ...._,yddp,ool oftheorem,.ondonfmilioritywith<"(i,,..ri"II navorl p robk,ma,roupJod ~ ililarelueta,_toblend ~urnwithpreUndood motivHoon .ll a.;n,gt,.ugl,tth1,d.yeulota"lfhll ho...ondY,or"""""'"'Pb"xc.,,./w:ln,;.,,,a,ul""'uni9u e n .., ,..;enonopportunilyof puttini1mytho,,,gh,.ofwho~i.!ooi,;1witholacri1y Thefrom,workaoo;,.r, .. ,,uctun, ,. .. ~,.,,,"' m e: I) tho coo,... ~oo to ho odm;n;ou,.-.d by th< mathomatie>O/utionofohem;., 1 ,ng;,_,;ngp,oo. l ,movioon!in.o,,.d il!" .,,,.,,. 1 .. ,,.., ...... (0Dt;Jwhkh rouldbohandllmthet"-,behmdeaohthniq" ;norontioeman,,.,-bu1wil...,1ofonnolprool' l""'ptwh,r,1h-"" ~-hool< m;dlOrm ~d th~":'i"""hool< '.:. uden,

      PAGE 31

      ral.particulor.mdoinl!'-'l"'oolut.,....,ndii..Q.~7.:~~1:-:-:u::.'~7,~'7,~~ol~~t ~: i00K ( in a nticipotionofoonli,...,onaly,i ,n futore~a,allnl'>rt2ll> ., parabl,,.vribleowh niQue.t,ans!"<,,-mot;o.,,,...,hod,_~,...,....., tioM....,,dHf.,,..n t '"l""uoliono.thoi ntoW"'h"II fotn ,hem.,. l kmet..,._~;o.,,"11'-nng.ppl;..:tt,;,,. ,hem .. ,.,. o ndheoMron,rertheory l'>rt0<0l.,ottenlw,n"po"ltoh,,..,..,.,.,iln Part3,"'-"'tron fonnotionthiq "'introdu!dandtnee"'b<,niua ) attr',,fy-b,,toumo:ientlyfoo-theintrod""'""'of-1 fun,;t.,., ,., ,mport o ntocooahty""""p< ioe mph,,,iiedadvinnum,ri< a lNlru:lhngofallmothe mo1icalpn>l,l< w,,gh,;gofonolytk o lwhniq,... o oot
      PAGE 32

      .,.tntintmforillu.,tatit!i:attheNmetimetheuotful nu "''7U moU>y "' lf"tfinaloolution10thepn,l,lem;,~""l>Y (r) AJ (2.40.Sr/R) (4) n..,upp....,.ionoC,..,,,..,;,.,.,.,..,of-1 function,,...11,t>,f,,.,....,d.,tophy,;,al
      PAGE 33

      ,..h,reAis11>tuniformcrou-1iooala,.,or,t.. tank.hi>tll,,;n,tanta...,...liquidl<,,,elintl>ttank, l:.~~:t/;~:=.,:: k;. '"" ,,.., <00 Q: hh. ller.e,,;nt,nn,ofdeviatkm-.riablHyhh "o nd .. t4,(8JiOJ'ewritt,n .. A* X (t) +h-~hJ (9) t"orouff>tnonlin ,.,;tyioremovlbytl>ttn,n<0tedTaylor""ponoion ,h-\h ;,71 o ndtl>tl i,.... ,opp-imation whil0bopedme (otde n ts _,,;,oc1 their weak "*~ y- (1) nes,inlineo,o lg,,b<,,lmopit,o/ otwo-tormcooroe taughtin11>tfi"'Y"rl"' .. rioory ( Stioo5) a l..,pnwI """"''netvalidityoflm. oari1ntionor,illuot"'tednu'""rintf'OOpc,o,.wowhotrou l d bohpt<>thoopplicauonn~o, T ..., andApp}',OndnunlOriffl6ubje<16)modeev,nth< o lpin,..,,.. t,mporarily o l;,.._.,u,..,ignofll>tubiqui'"''""" ndopp,..;ia1oonof=pun.,,...1,hall,na,,in"8chm1thiocoo""'"'' .. in findi"Canappropriot,ba)or.cebot"',""'li ,.. 1,hoor), a nd~,,..n"llPPlifith o mbiI thniqu .. po,<>enhnceU!och; l i.,,,..,m,of(hootudontowill ubeeq""nlly e,pkH'>tho~ofoplilmoth ....... o~ .. .-.s.,,-:,.,_; ,.....,__.....,_ ~--:t0::t"'"-',..__- ... rd~;.~.:= .. :--~..:~J!::=;=::r:t;;::_

      PAGE 34

      M c/assandhomeprob/6ms ~-,..,,.,,,.,,, ...... ,, ..... ,,,,, .. ,......,,..,.,,,,,.., .... ., . ,,,.,.,-"II.,..,,_.,,,,_,,..,-. , .. i,alr"lflHri, P_/,,..of1 r1yp,-1ht""""'"''"'""'""'' ,thr,tdrl .. p,.,.,01 o ..,.,, ,,.,,.,. .,,,,,.,, .. .. ,,,,.,...,-hi. ,,,. ,, ., ...,. ..,..,,,.,,_p,.,,,, .... ,. ....... .. 11.,,. ... ..... ...,,..,,.,..,,,'6 ... 1, ,.,., ... ,, .... ,,.,, ,,.,,,,,,,,,,,.,, ,., ,,,,..H 06 .. 11, .. ,...,,_ ro Ja..,,w11 ,. J .P.,... .,.,,.,,.,.._, _.,.., ,., ,,,,...,,..,., .u ,.,,. ~orM . .... A,...,_.,,.,. REMOVAL OF CHLORINE FROM THE CHLORINE-NITROGEN MIXTURE IN A FILM OF LIQUID WATER $;JtWA..~ $. $,J,;DH U u.;,~,.,,yo(Dayton Oa1ion,Oll454Gfl-(J(JQ1 1 ::r~;:~:::-::~h=~:.-:::~~~=:: l iq u;dph ... l nphy,itoloboorpt"'1> op,,rtitular ru,o,, 1 rompon,nl is tt...,...1,.., doetoiularg,rool>1bilityinthll lnob o orphonw ;th< homit o l.-. oll,,_.,..,h .. .-v lofohlorinofrnmn;l"'C"n""oi;bymHn o or,..,..,._,....,. 1orondmid.ll o ol"hot,_. .. ;um '""'"""'"'""""""'nolom,,..,ond-Olol"II,$ ondOO fromhy,;h,,c ,. "'"~k;"l. 1"7,W,-'o' Th<ti,,.,..""" IP n>
      PAGE 35

      Aouoch.tlllo,,_i, ......... iV'oSUnl c-_...,._, .. .................... .. Hffoadllle ......... ly--" -"ifi...,in-lThtorir,no .. ,.,._ol',l>eliquidfolmotilOIOflond(oe,ond1 d""PO""-"ninl'ipNITht ~ .: : .' .... +P, ,.,,,,,. I ,.,..., __ .,.,.. ___ ..,. __ _,, _._ .. .,..,..,,. ,...,""""'_/_ .. Unclttlllo-p1ional...,iicibletramportol'6NAl>:,-d;rr....,.,;.,1,o,cli-ionr,lat"""''"' tra-b)"1l>tlMtuidbulkn.,... a nd,..bulkllown tl>td-ion.N .,a ndN.,,re,ppn;,imaudby s .. n.~ :.,~~~~::::-..:::;::-dlllioll>ecli__,e.,..;,.._u,,. ,oloooimph f"'1,,,. .,o.,o(l::Q ,,.. ...... ,. .... .,_._,. .. EQ, (8)loolda .......,.,1,o.-,,_ ... ,t.a.mlorino;orapodly-..i ...,thtto_,.1...,..;o..,nll>eliquidpha...,l,ui ... 1<1 ~:..dilf""ioo .,..,...,.i;,,,i., to tloo ..,..i_, ud inu,,. u,;n1 th ~,p 1 ,.,, """'''"' pn><
      PAGE 36

      t:,.,,..,.ondromplementaryerrorfunct;on ., . ,.ron,. puted ,..;"11'.lhoappro,;m.,W)Othniq""f""" R,f. (Ito) ...,...,,1_u;,.....,,.,hatrfc(x lerll).Tho ~ (llb) >:quat;.o (IO) <1,..,,;1,e, toe dimen,W)O'~~2-:q!i!r.~?=::~i;t~~~ ~':.,.":"'1 i,,rm ....... ,,ml"), then >:q.(IOJ~ ~.. ~-,,) (121 ,.,ulting1wo--)tlleo,.,....,.ntct. l""'P..,r,i..o10hlori,..iolholiquidfolmore,l>Own inF~re2.U..,..ll o' .andthere,ulting m,,noferenhonoementf""";,~ l.982. V alidityoftho ... umphonolronoU,.ntV<'l,;,,;ityin >:q. 18)oodthenu-.loolu :::,:::l6)oreoomporedioF~,.3f..-two (v'L) Thomol,,flu olopi<,foingtheou,...ri
      PAGE 37

      Ottofdimen,ion N:N dep1h, vJ A,op;dde<,. .., in :~ :.i;,lori.,:.:;;:.'".<;:; ~ ;:::.7'=~~ ':.~,"! 1<> i 10dHf._.ion;n1heliquidph .... Ag,ttmenll,e. ,......,thean o lyt kto l ool utoonof!;q, ( 8 )o 00the nurr.eritu ,....,, Jl,.chlori...,tnitn,. ll"Oor o irmoxtu,. byaboorptionoftro .,. < .g .. chlorine,withllintheliqu;d ph ,. ..... K, B., W .. .... .. N .....-_....__ ..,., .. ,N V ....... '37-Ml(II D X .. ,.,_,,,.,,,,_,, ._,,.. REVIEW: Proc ess De s ign C ecla ... th, boo i,, .,,,.,.,ng pn<"ple l"te, 0 1uu nee ,, and k<1epif.,.tk>nofuni ,. within< oc h equipn"10nleuni ,. ; ,,...,. vide,,.. ,-;,,-inlh<1uitabilityof1l>euni1rorop..-tirtideomhotl>eumt o nd g;., ,. izen>.np.The,. ia nooghinformauonto .. i ttto unit lJi ,..nthofut""' enoogh;nrormat.,.todoony o naly,i,of11>e.,,.,.., toonofthe book ppro>.imatd...tandfiflypapo ) .,.... nl "Eai.,,.,,-,Analy i o Cl,;"""""'' ""~l ndmonuf":'uri~~ onaly oi, .The..,.totimationthniqUd oro>et1,,ot,11entof o ll ~:,~otmen "' oould ,... mon,exampleoonddio Thefinal.l>riampltl l>e ty .. of,tud y beingdone Alterlfini o hee~nolpro,:,N<0neeohon-<:utondthn o f..-whi"""'boYepN< .... roruljrttmionitaell".r-u,,;u;nracttlt-" ""'f< k:s 10lh01de,.;gn
    1. n0mi
      PAGE 38

      UNDERGRADUATE EDUCATION Where Do We Go From H ere? c ::-:::.:.."':=~ ,__lho,-,._lthaa-.df,-o..,mnol --... ;..i........ithe ,..;,._notiom ~"'"" omphaw"" .,.;. _,,,,. "''""""' ~ .,,._....,.... ~ wilh ,...t1,i1>or.c,.,l.,.IIM aloo_._!~IOilm>I,.. .....__..,_o..._ .. .....,..i ... _.. ........... ,.-; .. .,,_,,~~.n..-, .............. .... 1, ,-., .. bolll .............. m111irthMIO..nm pen.....,talinnot u ... itno,,,bo(,tn"'"'~"""" -<11ooN,t,COlolon1. Fin ally.lho""""P'-'...,.,.* lu\lOllprod<><1anew"'-'IJ.,,.,._.,.,;1h -"'--...io1... 1 ....... 1y .... -1 ..w ....... ""' ..... -""' .... '""""''"'""' -.. .. -pn,ct,ol.__...,cha,..I \\'boni---l0_,..,fa<111lty ....o,-.,.1.,._,"-"""'-'"'re-. ...,.,,.,..,.,..,..i.,pon.,..1,r1y,.,....;., .. -p,o( ... -~-----~:=== -. ,, .. -----__ .. __ irnotoll.ollbo...,,._ .......... ,_ ~.:::-... =~-.. -... holl,Tho0,<1.M'""'lttolq-,;.,,,,. f or uamplo ,n .,..\y,,01nled,..,....,..romploinobou1 la,;ko("p;a1.,. "i n,i..,,, ,. ,n inJ,Tho ...-',o,,,11hln,(1 0"" 11hi1n>lnot ilul "h...i,o1.....,_pl,MiN,.-"<'lnU-tl,.on\i... ..,..c-,,a,,;nuo1o1c1o,""".,....,.....r,_.,. ;-~tyol,_..h,rw"<""l'out....Uk- ....,_..,0w,,1oc1,<,1-twlimot1tacJ'_,,."'--' "'"""-~-"'--beolo
      PAGE 39

      0-1)M-J,_..,..S,1i.,u.o, lkftlloM,,...,._..,..,,_.,,,,.....,Jj_'"' ._., __ ,....,ld""""' 'Y-- ... ..,, .. ......,.,.1,.,,;.,,,of<""'"'"'"' ~n1l....,....,,od..,o t""' ...,. ..._ n.thooon,put,,r,toone" PP"'Khth,t -on1y_,,1-andmoin10m1\l-,ai"'but ,1.,,,1oa,1yhnUthitto,,ct,,,_,;Olltho .. yloondplt,loMplMMr(llbook ......... ......,.wi..,P'n"--ndionOli1withomplo!clo ... """'"d;.,,,,"'""'"""PR"''" _,.""".,.,;n """',noo,M>Oio-nun-iollo!.,.nt =:-~::::=i:~~=:.= .r,.,i..,_..,.__n.iclc1yno,n ... ,..-.u.. -"'"''"""'.....WbolNo-lm~"f ~ --'''

      PAGE 40

      PURDUE INDUSTR Y COMPUTER SI MULATION MODULES The Amoco R e sid Hydrot r eater P rocess R.G SQ,.,,u:a, 0.V. Rau...m$, N ,C, YtH, J_ Mour. 1 I.A. Karimi ,' P K. And~....,, """'..,u.,......,,, 11'..,Lofa,,ff,, IN47907 T'" ,_":".: ~':... -=.: ~= -,,._,. .... ,,.. .. _,,_ .... p.t.on,,. _,,.., d ,.,.. ,.._ .. ;,doooon"'..t.o""~in ,...,..,.,_.....i,.,.. .. ,....,_ __ ~1.,.,,-d .. ,;1 latioll,po-Of>dh,quid-phuo,_.,,MMl,_ouho~. ...,,,,.,..r.,,n.;.in-, .. ;.,,.., ,no1 d,ff\, 1;o.. In our vi< id ..,l l obonol<>r)' o ,pooimlrialp""' :n,,, .,..11<,,,,,,._ldu .. -"'fl-l!o TA8L ----S,0,-0 -_,., __ r,,.. n..~ .......... ,-lhat ........ -,,,..... -h,..._rw...,_p;1otpioM(-'lf u..,Hbuol,..,_;o,,rnu,,m.-,,. -N'hfoahty.Tho~.llod .-..1,,;n """""""'"i,.., ...... ... ... ... ,. ............. .... .... ...... -, ........ ...._ ... ..._ .. ... __ ,. ..__., a s., /8-1,., .,_,,,iu,.,-..... i,.,., .-~-,-,,,...,.n,. -::;:;::,;:::::::;; ,_ ::;;;;:::;; ,, ;;;; ,. ;. ==..:.:;;:;-':":':'.~--=---""' ..

      PAGE 41

      C a ll!y!k:llue11oo s..,t,.,,.H,...'.!... H ,S n.,,....,.;.,,,,.,hon,oi M~ n;n !'igu,..2 Eaturoofmanydiff,..,,.leleri..0 ::,.: i;-;. ~~i;,._ po;nu and tht;r ,nlfu, """ Thohydrogl l e l lfirtnb)' ---_., __ ... ._ ... :-:-..;:..-; ___ ., __ ~.:.;= :::: ----=--!';",.. ;.-_, ... ... :::---=-~~==-:,= ===-=----!lpri .,. 1991 --( k 1 + k i< ,+ k 1 ) R r G -k 2 GC ac k,R r 0 k D C. ,,k R CGl,k 2 G 's -k,N c._~k,R Co~k D .csck,N C., .,R whSot tOO,ulfor-f,..>m?O'H'n ll: k ,. k.,. a ,orallure; to<>high Thoprolfnlmron o ;,10Jmorethonl0,OOOh of!'O~'-i':;dCoode,0lt
      PAGE 42

      ...... .,.___,_.,., ....... _,,,. _........,11y,.... ....... s..n.,.w--. __ ... ......, ......... -;i,,-.11oc1ion10 ... ..,._..,.,.,....,..,""""",1wx 11 ,.-s,,...,n. A,,...a_,.;n----heprosn ,.,1io,...,--1o,.,.......,,,..,.vi.,..m,ni1Ml .. pe rinco w,ih Sun compulero, Th UMr cmplO)' a mOu N Lo oolect f n opt'ono .. ..... 11..iown menu,.S....,H11ho .... ,ploo10,fo,,. '"'"'""'"'do,ho~ohocon ... helpfromthe _,...,; r. ... ,.-.-lab ............. ..i1oo...ito--1, __ ,,,, ..... ft .. --..slab ,.,..,., ..... .,........,areaokodto,t...JJ,a_,,,..., -.;p1;.,,ol'tl,opN>danorid1holab aro In k-..-witl, ...,..,....,ple3h"' thot1meond..,...1'""'"""'ro,-.._.,........,k,in oolvin11hop;1otplon1or,dl...,....,..,._.Not< 1ha\U,.ot"6ontoorecho"S"ofM..,.htimothey _,.htlpf,,,..,,t...coo..,ltant(;,,.,1heinotructorJ. Thoot....,.opn,dlhoft,_,_lab...,__ pon.,..,plan.,.011kt.,whomt""7"".. ,... __ ifloplaHo,. ___ tl,o ....,..__,.. __ i,,.c:mr.n., _,,,_ ...... _....,,,._ thordpono,,l.lnt1,to_,_,...,_.......,....._ .............. __ ; ...... ,Lhe .. pen_,,,. tllt-y.... ny-.Al-otopheyuot j,oot,f),.....,,p1, ... ,,,,.,_ ...... __ r>d~ ... hinu .. ht ... .,.._.,.,i..,,,. .. ee
        Oondnumbe,/ll,oacton,,the<010 1, .. __ ... _,,,.,.,....,.,r,,:1,1,e,_.....,. =::::.i~~~".:'i!:.~~=""'1"'"'"'M"il ...... _..,.. ____ .... _,, .. _._ .... ,.... __ =--~:::..:-~~= .... ...... __ ..... __ ___ .. ,t;::;:;::''"",--.. ,o,,_ ~ .... ..... -, ..... .......... __ .. ................ ..... Umalloo-iou .. 1holab-.... umucl,u _. ........... u..,,...,_,,...,,l,jy,._per ...... ,nt,thonthep.lotplan1--f\o..i--.,...i..i,,.. .... -, ................. ~_ .. .,,. !i""...:=.':i:~~hat~=-:::r: lalN>rMowy ...... -loochod'oMtiof......,hotU,,yluowo,ood""p.,. Lhep,,:,bi,,n,the)' ... -... .,..,. .. tho .,_pultt-nthe_y_,._..TI,;,, ......... ......... ... u.._.,.lhe_ ~-

        PAGE 43

        ::~~-=.:~i~ r,~~:::,::-:/hothlohperiod.Durina;thtmth ]>!riodt..,grouplooderi,"'lu rltoei"'fflttn minuU!oralptmo l'ind,ng o,uitoblocon1n'.N1tn,t,1P'istypi .) Twolabp 0 ful l .,rittollhtir T A BLE3 =':.i'c!:;:""-.i"""" ..,,_ .. ...., ................ ,. "'"'"""'""-1--__ ....,,...,,..,I ,i,ody-,tateo,ponmentaondanouUinoof1t,,;,,... ommende,d,ta,t-upp_u,.. ROLEOFHIEIKSTAUCTOA in-~~':::::""~ R,,,r ;mp0tta.nt aru W p l oy ,_ .. .i.. ..... . ....... ,-. ....... ~.d .. .. ,__ ... _,, ........... ,..,..,,._ .. ,.c....---.............. __ __ . ~"::.:.':':.'" .. -:.:.:"'..::. .. -COMPIITEASlMUl.lTIONSFOR EDIJC.lTION .llthooghi1.,ouldbo-ibk110dooign0Mn,or ~=::;::.-: ~l~~:;af .. ':'~::-~~I:~ prn"hondo-on",xp,Mnooby.,o,-Kflllwith-l labontoryoquopmen~h,,.,h;,,.....,,.,,...,,llowonly ';:'1e':p1::::;.r
        PAGE 44

        . ,.oon, o,y CRYSTALLIZATION An Interesting Experience in the ChE Laboratory l'f:(lriw A. Gua.u S . M AIWI E. T..-11A M u,,.,,,.,,,l;,,ld,Ao..,-........ ~-.emu:. ~===~~~~loIM~ too....,.,r,.._otinn.<1<.,in< l udi<>11at ltdcryoUoll, .. """""~ro,,,n,1,.,_.., 1'ho1Jnn,,o,.i.ddoA"""opot,1hupbl,-don iportaM,...,nthe~ntolU--. -..11;,...,... _,_cryou,11_._1Mo botn-olu.o-....,b,on,oo!,< ........,thelNlthr,e..,,_;nthe ...... ,,_,,. ,ho-, ................ Cryot.oll-;,offefduorow--i-, ....... indudi"(lenino M $ J.ll' Rdyolcryo tolliuuonkinot,..oldoaol\ydrated...t,un10ulphate. Tllonutoll,ut'" ;, dtol,,"i1hopo,ntln.Cryotolh Hti<>ni1ano>lremoly.,,..,ple,p1"00N1wh;ohloaf fOn1lcloom.,._....i,....._u-.....,,. i....i-...i,oev,,d.,,-t1M,J900o 'flle-""--holonnto~IOlhocloomp t--..,.oal--.,1,u,-,.t1M,-.....i.i1 _,.....~.-.:li1hu_....tobothe r..t>loin....,., ............. ~-i"ll".-.:1--1, .. ...,-fl,,llin. n.,_1 .......... ,.,_,:q .............. r,,..1o,. ""'l i oeelOnno 1"'"ot""wportill,.,l,q._.Th,.duoter,tttmodo
        PAGE 45

        ,._..,_........,.__.,. ....... .... inonyotthe .. .. ,....-yo .. lo 1n,11or<,t,-,Jy """"""t,y.._,n..,.llwn<1111be,o(....,.,.._ .. ............ ..,-;.::;:::-...:::::11=:, (13) ;,:""p,ilth<
        PAGE 46

        ,_,utCinEq.~;~)tft,8-t,L (70) TI,,.oq,..tion ;, ,.,, om)'.IOrt8nt, ,;,... byu1 n, porimen111d;,.,;buhonlunetlon1(ot,\.,nod 1hm.1rt,...,....;Rf.....,);1i1-i>leU>find1ht odoq...,,-,...,.,klnet0nl .. ')"l,.M8~IPR "YIIOlli-,cyhndn<1lin .... pe1ndl6.i,mdl,me ... br.Wle he..:tpe.....,1t;,p,.,mp;non1e,t0 ..... ,n ,pe rfldly "Clll-lluwl.Tho,.,,....1h..,,..,_,n.._inod11 18C, ..... ,2Ul"--tlu-h
        PAGE 47

        -.1.'l .. lhe-bttolayotal,ioi, ... _,...ol :::."."'""'-""""-"'~-r-u.. ........ lOdiafitt,1 .. 2 .... obwnlho olopoondi"'---bj,appl)'>ncOI,_, ,,.,._...,,,.,..l,odlOEq 120).ot,t.,,n;na d, .99~ 1 (1/,. m l 11/G 2.llll4xl0 1 (rritt.nmm) Cleari .. lbo---..,._,., ... _, .. ,nd _,_,......,,1 ll l.lM45hi0 1 (cnot.llhl Thol-"'1 P" ri .,.ndeOn<1.,.,... Tholl'O ? hittwllubo d .. ributNN1of
        PAGE 48

        M clsssl'QOm PRINCIPLES OF STAGEWISE SEPARATION PROCESS CALCULATIONS A Simple Algebraic Approach Using Solvent Extraction BAHH> !). C~1tte,N1:N u~"rnlyo{'lla1h &U,.IIA27AY.llaoi,,IK;"(/"io olmu l lo~ .. ,..,.,..,.,p __ \\"hilOi ri ... themau,ri o l bo l ph o .. oquihbrium,ol o !io,uh,p,.1he;,underotand,n,:ol t to nofonni..uoda h.,ollenbo.lhh a ,r, o ultlinotu&doptthei,mmd,1<> >Oivin.gromple.xproblem o by gn,. phi1ho v,, phi< o l...,hn,quttwhiopend1i,,i,1h1,-d f.:E,~E;f;~.~=F.:;1~~!: mat-'"";""" nde...,.,ndi"11"ofthefundomentalp-,,..,;p1<,,.o1pt,a. o ond 11,e;,opplitoede.,gnondop,r-o1;ooofrom """',.l"''"'"'"l"(lt,oct1on, bottl>ook o in
        PAGE 49

        tto.. __ whil<-"'""""'-'d da""'n talmoteriolbolo"""'andphooe,.,lotoon,hl"'.U-. otemanyotod< n 1a"l>ofondthteriwl 1erio whkho,..d i ffi.., l 1u,mod<,lthttmodyn.omiadyappn:.,,ioteth01,entond ~d~""i":They,.. "",";."'':'."!'klyrompOtapv,, .. oontart,t)jl, ... ,"ll. oimplehQuid-h~u i d,qui h brium,y,wmlO;llu,t,ot, anumbofimpon,,.ntMpt,et,ol'Olafnlan.1....._a,. .,..., __ .....::::...:..::J-+---"'""'"' Theu.,of>Ol.on .,,tracti<>ntoexploinimpor, tontfonlawhithooim =~:;; = :=.":h!: :1~:1:i:i:. d~~ ;t,~ ~::.:~:::::-it:':::':;~:::=~~~::: .. :: f :;q:p~~~ ::: lnth e f,,_, ,.,,,,.,ud,,n1><1,o._.,-:,edtu & ainan und .,,,and;ngQ/li,., f undam}lalh o d.,; g nond::;.;;:,;:,"{.::;=. flG U ~ t1 S,,W,,qulliMu-.,;fm,.,fra ;,readilyun.,.,..toodl,ythe,t""'u.n..o,mpl< oon.,.. oor;;eOlu,.,,..,.uni,....,..ofdai..,..i..,,., .. ., Thema1<,r\albalo""'fo,di l uentond>01,
        PAGE 50

        bythtroct,dronbeimp=lbyooeo,ocoml;,; f\Olionofth,follov.,,.. ':;7.;'!:,~'.':'..!:'"-"' .. .. ..,.._ .. .,. .... ,_..._.,, .. ...,.__, .. __,, .. ,..._ --i.. .-. ; ...,,,,._....,.1a, u ,1o,.,._,., MULTIST A GECROSS.CURREtllEXTRACTIOtl Pro,.;dl1hat an,q...,1 nov. ,,u,ofl>""'""''""'S ::;-::,:-:~,~.lh&ooluU,be]a"""fo,ther,n x .,r x .-.v.s Applyin;;tbeoquu,brium,.lot,oooh,p)'M,ld i.;";r.+rr ll,..,.f,,.obe tteryofNuTl,briumo1a.g .. ?. ~ t'romF,q,<7Jitconbe ... n1h,.1)(,l'(.tend,1-0 zeroo,Ntendotoinfinlly ~ H ~ (8) Comp.,rioonoft;q.181withl,;q.(3)eo,ctn>rt...,ofooluu,.butottbe addit"'11,., ... ofp=iding,next,aoquilibnum Olaa,,_Tho,.nl.-..ul1fo,-spmtin~-0taln.,.,.of ooln
        PAGE 51

        x, X r ,, , .. ~x 1 X, ) (16 ) 1<1 i nfin i ty as N..,nds,.,infonot,oet..,.ol'theoolute "'poowninfigu,e, Thehgheot l!ona,from&q 08 ) ----+~ (20) r ; ; Theperfonnonoeof o botra1m,ntbot .. ,y ;gu,. ,.,.nbeuoee..,; g; ,. ?. ~ fu,-r,] (21 ) \\' henKS/1-'iol""""'hnunity.thel.""'e>~ t,yt,a. ( 2l! ) ct .. ol'hi 1 , h .. woold al lowXJX,,.,tendto.,ro o, Ntendroed .. t,ofo.o (iv, po<0 o oolut,"'"""'i from x ,.,x_.; 0 1hu o nHJn"l'J)Olenu N aflh
        PAGE 52

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