Front Cover
 Table of Contents
 Transport phenomena: we have not...
 Professor E. B. Christiansen
 McMaster University
 Use of visual interactive display...
 Case problems in chemical process...
 An open-ended course in chemical...
 Computers and applied math in the...
 Thermo paradox explained
 An undergrad ChE laboratory
 An assistance program in Ecuad...
 Scaling initial and boundary value...
 Back Cover

Chemical engineering education
http://cee.che.ufl.edu/ ( Journal Site )
Full Citation
Permanent Link: http://ufdc.ufl.edu/AA00000383/00029
 Material Information
Title: Chemical engineering education
Alternate Title: CEE
Abbreviated Title: Chem. eng. educ.
Physical Description: v. : ill. ; 22-28 cm.
Language: English
Creator: American Society for Engineering Education -- Chemical Engineering Division
Publisher: Chemical Engineering Division, American Society for Engineering Education
Publication Date: Summer 1970
Frequency: quarterly[1962-]
annual[ former 1960-1961]
Subjects / Keywords: Chemical engineering -- Study and teaching -- Periodicals   ( lcsh )
Genre: serial   ( sobekcm )
periodical   ( marcgt )
Citation/Reference: Chemical abstracts
Additional Physical Form: Also issued online.
Dates or Sequential Designation: 1960-June 1964 ; v. 1, no. 1 (Oct. 1965)-
Numbering Peculiarities: Publication suspended briefly: issue designated v. 1, no. 4 (June 1966) published Nov. 1967.
General Note: Title from cover.
General Note: Place of publication varies: Rochester, N.Y., 1965-1967; Gainesville, Fla., 1968-
 Record Information
Source Institution: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
Resource Identifier: oclc - 01151209
lccn - 70013732
issn - 0009-2479
sobekcm - AA00000383_00029
Classification: lcc - TP165 .C18
ddc - 660/.2/071
System ID: AA00000383:00029

Table of Contents
    Front Cover
        Front Cover
    Table of Contents
        Page 105
    Transport phenomena: we have not gone far enough
        Page 106
        Page 107
    Professor E. B. Christiansen
        Page 108
        Page 109
        Page 110
        Page 111
    McMaster University
        Page 112
        Page 113
        Page 114
        Page 115
        Page 116
        Page 117
    Use of visual interactive display in process design
        Page 118
        Page 119
        Page 120
        Page 121
        Page 122
        Page 123
    Case problems in chemical process design and engineering
        Page 124
        Page 125
    An open-ended course in chemical plant design
        Page 126
        Page 127
        Page 128
        Page 129
    Computers and applied math in the engineering curriculum
        Page 130
        Page 131
        Page 132
        Page 133
        Page 134
        Page 135
        Page 136
    Thermo paradox explained
        Page 137
    An undergrad ChE laboratory
        Page 138
        Page 139
        Page 140
        Page 141
    An assistance program in Ecuador
        Page 142
        Page 143
        Page 144
    Scaling initial and boundary value problems as a teaching tool for a course in transport phenomena
        Page 145
        Page 146
        Page 147
        Page 148
        Page 149
        Page 150
        Page 151
        Page 152
    Back Cover
        Back Cover 1
        Back Cover 2
Full Text

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INDUSTRIAL SPONSORS: T allowing companeS hcwe domaed

Ud, &4 /4e ao 4dIj oj CHEMICAL ENGINEERING EDUCATION dai4 1f970:








DEPARTMENTAL SPONSORS: The llawif //7 depame4 ha

ca4h~ided to Me duptf.2 of CHEMICAL ENGINEERING EDUCATION in f970

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Chemical Engineering Education


106 Acknowledgements
107 Letters
108 The Educator
Professor E. B. Christiansen
112 Departments of Chemical Engineering
McMaster, M. H. I. Baird
106 Views and Opinions
Transport Phenomena: We Have Not Gone
Far Enough, E. N. Lightfoot

118 The Classroom
Use of Visual Interactive Display in Process
Design, T. Juul-dam, J. D. Lawson, L. A.
Maddox, and H. F. Rase

124 Case Problems in Chemical Process Design
and Engineering, C. Judson King

126 An Open-Ended Course in Chemical Plant
Design, F. P. O'Connell

132 The Curriculum
Computers and Applied Math in the Engi-
neering Curriculum, D. B. Greenberg and
E. L. Morton

137 Problems for Teachers
Thermo Paradox Explained, R. R. Davidson

138 The Laboratory
An Undergrad ChE Laboratory, C. C. Peiffer
142 International Chemical Engineering
An Assistance Program in Ecuador,
G. E. Klinzing

Feature Articles
145 Scaling Initial and Boundary Value Prob-
lems as a Teaching Tool for a Course in
Transport Phenomena, W. B. Krantz

CHEMICAL ENGINEERING EDUCATION is published quarterly by the Chemical
Engineering Division, American Society for Engineering Education. The publication
is edited at the Chemical Engineering Department, University of Florida. Second-class
postage is paid at Gainesville, Florida, and at DeLand, Florida. Correspondence
regarding editorial matter, circulation and changes of address should be addressed
to the Editor at Gainesville, Florida 32601. Advertising rates and information are
available from the advertising representatives. Plates and other advertising material
may be sent directly to the printer: E. 0. Painter Printing Co., 137 E. Wisconsin
Ave., DeLand, Florida 32720. Subscription rate U.S., Canada, and Mexico is $10 per
year to non-members of the ChE division of ASEE, $6 per year mailed to members,
and $4 per year to ChE faculty in bulk mailing. Individual copies of Vol. 2 and 3
are $3 each. Copyright (6) 1970, ChE Division of ASEE, Ray Fahien, Editor. The
statements and opinions expressed in this periodical are those of the writers and
not necessarily those of the ChE Division of the ASEE which body assumes no
responsibility for them. Defective copies replaced if notified within 120 days.


rImTa)_views and opinions



University of Wisconsin
Madison, Wisconsin 53706

It is time to take a hard look at what used to
be the field of unit operations, and, for most of
us at least, it is time to make some fundamental
changes. Our present practices overemphasize
analysis as opposed to synthesis, and this im-
balance seriously distorts both teaching and
academic research. The solution to this problem
is not to weaken analysis, as some have sug-
gested, but to provide a more powerful and
attractive framework for the synthesis aspect of
unit operations, which is equipment design. It
is also important to eliminate the artificial divi-
sion between theory and practice, so common in
the undergraduate teaching of physical rate
processes, but this is a separate problem. Most
attempts to combine the introduction of basic
principles with examples of practical applica-
tions have been based on the elegant but purely
descriptive framework of transport phenomena.
They have thus aggravated one problem while
trying to solve another.
The unit operations are a fundamentally
heterogenous collection, and their organization
into a single course sequence is an obsolete tran-
sition stage in the development of chemical en-
gineering curricula. However the vigorous at-
tempts of the last ten years to replace unit
operations by much more systematically organ-
ized courses in transport phenomena have not
been entirely successful. At Wisconsin, for exam-
ple, of ten semester credits allotted for physical
rate processes only four are devoted to transport
phenomena. The remaining six credits, are used
for rather conservative courses on fluid flow and
heat and mass transfer.
The department has consistently rejected sug-
gestions that these ten credits be reorganized
to a transport phenomena-based sequence in
which introductory of basic theory is immedi-

Professor Lightfoot was educated at Cornell University,
BChE and PhD. In 1953 he joined the Wisconsin depart-
ment, became active in curriculum revision, and colla-
borated with Bird and Stewart on the text Transport
Phenomena. His major research interests are in mass
transfer and separation processes and in the application
of transport phenomena to environmental and biomedical

ately followed by discussion of practical applica-
tions. I have been disappointed by this attitude
in the past, but I now believe that there is a
very sound basic objection to this otherwise
attractive idea: a well taught course in unit
operations was something more than a poorly
organized course in transport phenomena. The
something extra was an attempt to teach equip-
ment design. The equations of change provide
an effective basis for calculating the length of a
heat exchanger given the radial dimensions, flow
rates, and terminal temperatures. They are not
sufficient for determining the configuration or
coolant flow rate. They provide no basis for
answering such questions as: how would you
grind garnets to make sandpaper? They are
purely descriptive.
We have overlooked equipment design in part
because it was taught unsystematically, but also
because of our current emphasis on sophistica-
tion and elegance. Synthesis can never be as
elegant as analysis, and we can never develop as
impressive a framework for equipment design as
for transport phenomena. We can, however,
improve greatly on our present performance.
We must first recognize that analysis and
synthesis are fundamentally dissimilar and
should be taught in a course sequence based on
the organization of Transport Phenomena (Bird,
Stewart, and Lightfoot) or similar texts, and it


should proceed directly from fundamental princi-
ples to practical examples. The development of
such a course sequence is relatively straight-
forward and should not be further discussed
here*. The design aspects must be taught within
a much more flexible framework, comparable to
that recommended for process design in such
references as Strategy of Process Engineering
(Rudd and Watson). This framework does not
now exist, and a very high priority should be
given to its development.
Equipment design must, like process design,
be based on a strategy and general principles
rather than a set of generally applicable differen-
tial eqations. Problem definition is now the pre-
cise statement of equipment function. Thus in
the sandpaper example above the grinding device
must both reduce size and produce sharp-edged
particles of compact shape. The remaining
stages of the solution will generally require much
more detailed physical information than used in
conventional treatments of process design, and
transport phenomena can be expected to play a
key supporting role. The listing of alternative
solutions will require an extensive knowledge of
physical chemistry. Precedence ordering will
now often require ordering of experiments or a
mixture of experiments and computations, and
it must be recognized that a systematic approach
is useful even for very messy problems not
amenable to extensive computation.
Development of an undergraduate course in
equipment design is now being seriously consid-
ered at Wisconsin, and, I would expect, else-
where. Detailed discussion of such a development
is out of place here, but it does seem proper to
point out that this type of a course will affect
the rest of the curriculum. In addition to a sound
background in transport phenomena we must be
sure that the student has an adequate practical
grasp of applied physical chemistry. I am not
sure that this latter requirement is always met.
It is also desirable to provide a more extensive
historical background in both science and engi-
neering than is now customary, to give perspec-
tive and also the faith necessary to successful

*This must, however, be done with care. The analo-
gies and contrasts between the three transport processes
must be emphasized and a proper balance maintained
between theory and application. Simplicity must not be
achieved at the price of misrepresentation.

Scenario for the 1970's-January 1, 1980
Sir: This is a report on the decade of the 1970's. Ten
years ago, I note that I worried that the population
explosion would come to a climax in the 1970's and that
its manifestations would be a combination of mass starva-
tion, catastrophic war, uncontrolled pollution, widespread
epidemics and exhaustion of essential raw materials.
Except for catastrophic war, these things have all hap-
pened but not in quite the way I had expected them.
Mass starvation we have certainly had. Back in 1970,
we were used to hearing about starvation in India, Pakis-
tan, China and Biafra. During the decade it continued in
these countries on an ever increasing scale and to these
were added Egypt, the rest of southeast Asia, Brazil,
Mexico, Colombia, Venezuela, Peru, the central American
countries and all of black Africa. For awhile in the
early 1970's, new strains of rice and wheat held out a
hope of reducing starvation, but population increases kept
pace with the gains in food production. And by 1975 the
annual increases in food production, which seemed so
promising in the early 1970's, had slowed greatly so that
food production remained static after 1975 in most coun-
tries, and even declined in some countries, for a variety
of reasons.
It is estimated that during the decade, 200 million
people starved to death. An accurate count was impos-
sible. There were widespread epidemics in the poor coun-
tries, but they were so intermingled with starvation that
it was impossible to obtain reliable data on deaths from
starvation and from disease. Contrary to many predic-
tions, the "have-not" countries did not blame the "haves"
for the epidemics. Starving people apparently do not mind
seeing their neighbors die of disease; it reduces the com-
petition for food. Western medical teams won popular
support for their unstinting efforts during the epidemics.
Air pollution in the U.S. got no worse in the bad places
of 1970-Los Angeles, New York and Chicago-but it
spread to many other metropolitan areas. Emission con-
trols on gasoline engines and the widespread use of steam
and electric cars has actually made Los Angeles a better
place than in 1970. Low sulfur fuels and the development
of public transportation improved the situation in New
York, Chicago and San Francisco over what it was in
1970. Water pollution on the other hand is considerably
worse than in 1970. Lake Erie is a lifeless sump. Lakes
Michigan and Ontario are about as bad as Erie was in
1970. The open ocean itself is in poor condition being
polluted world-wide and not just from the U.S.A. The
Atlantic beaches from Boston to Virginia Beach are un-
safe for bathing. A new major cause of death in the U.S.
is poisoning from an accumulation of pesticide residues.
This affects principally middle aged and older people.
Marijuana is now legal and rivals tobacco in sales.
The fears concerning exhaustion of essential raw ma-
terials were largely unfounded. We now get 40% of our
oil from offshore wells compared to 15% in 1970. In the
past decade, we opened up vast deposits of low grade
copper and iron. We collect and recycle almost all of the
(Continued on page 116)


I educator


University of Utah,
Salt Lake City, Utah 84112

H ALF A CENTURY AGO, in a rural commu-
nity known as Richfield, Utah, "industry"
consisted of a bit of mining, some processing of
agricultural products, and a lot of farming. How-
ever, there was a boy who looked in growing
wonder at the production of cheese from milk,
flour from wheat, and at the beginnings of clay
and gypsum processing. The desire thereby
kindled in him to be a part of this exciting up-
grading of materials led him to enter the geologi-
cal engineering program at the University of
Utah in 1928. Nineteen years later, he was to
found the chemical engineering department at
that institution; but, in the interim, a budding
war, some proud Arabs, and a dynamic teacher
were to influence profoundly the life of Ernest
Bert Christiansen.
After two years at the University of Utah,
Chris deserted student life to serve three years
as a missionary in Germany, Switzerland, France,
and Alsace-Lorraine, where he witnessed the
struggles between the Nazis and the Communists,
the rise to power of Adolph Hitler, and the bur-
geoning of German industry. Before returning to
the United States, he and a friend purchased a
one-cylinder motorcycle and, riding double, com-
menced a two-month tour that was to lead them
through Italy, Greece, Turkey, Syria, Palestine,
and Egypt. One evening, happening upon a British
police outpost in the hills north of Nazareth, the
two young men were regaled with feats of horse-
manship by the Arabs manning the post. Though
Chris had ridden farm animals throughout his
boyhood, he had never before dreamed how beau-
tiful, intelligent, and responsive a horse could be
and vowed he would own an Arabian himself
someday. As many as five thoroughbred Arabians
at a time have since made their home adjacent
to the Christiansen residence, looking upon Chris
as their owner, trainer, exerciser, and chief vet.

Chris on Sammara, one of his registered Arabian horses.
His broadening experiences in Europe, Africa,
and the Middle East had convinced Chris that
geological engineering would not satisfy his in-
defatigable interest in the industrial upgrading
of materials. Accordingly, when he returned to
the University of Utah in 1934, he changed his
major to chemical engineering, then administered
by the Department of Chemistry, with all classes
taught by one man. By 1937, Chris had com-
pleted the requirements for a BS degree, married
Susan Mann, and begun to nurture the idea of
becoming an educator. As he pursued MS and
PhD degrees at the University of Michigan, the
idea grew into a firm decision under a dynamic
influence: "I don't believe that anyone could
have gone through the graduate program at the
University of Michigan and had an experience
with G. G. Brown without acquiring an interest
in teaching, combined with research and consult-
ing, as he practiced it. . . . Most of us felt we
would like to become a G. G. Brown someday."


Chris believes that a student must be taught the essence
the engine of social change; . . . the engineer must be
well as the mechanism". . .

However, Chris felt strongly that all chemical-
engineering faculty should have industrial ex-
perience so that they could present engineering
to the students realistically and could outline
with first-hand knowledge the requirements for
success in industry. Such a person, Chris felt,
could speak more competently and, thus, be far
more effective than someone who had not had a
responsible industrial experience. Therefore, upon
completing his PhD in 1941, Christ accepted a
position with the du Pont Company's rayon di-
vision in Buffalo, New York, at a starting salary
of $225 per month! (Chris: "This was somewhat
less than offered by some of the other corpora-
tions; but the innovations of du Pont in many
areas, such as nylon, had caught my fancy." Sue:
"I had been working on the Michigan campus for
$80 a month; $225 sounded like a fortune!") In
a succession of assignments, he developed and
designed equipment for producing an electrolytic
bleach solution to be used in the spin-bath con-
centration of viscose rayon; designed the process
and equipment for producing a special wartime
nylon polymer to be used in "bullet-proof" fuel
tanks for aircraft; and, as a member of the du
Pont team working on the Manhattan District
Project, solved problems relating to the produc-
tion of plutonium.
Because he had become so engrossed in work-
ing out solutions to important industrial prob-

For many years
Chris has been
'I trying to develop
a late-blooming
(to miss Utah's
late spring frosts)
F, ,English walnut.

of engineering - problem solving . . . "Engineering is
prepared to participate more strongly in the steering as

lems, Chris had almost set aside his earlier
ambition to become a teacher. However, when he
was offered the position of professor of chemical
engineering at the University of Idaho in 1946,
his latent interest was stirred; and he returned
to the West. A year later, he became the first
(and, thus far, the only) chairman of the De-
partment of Chemical Engineering at the Uni-
versity of Utah, with the charge to develop a full-
fledged department to replace the previous one-
man operation in Chemistry. He did so with
wisdom, his first major decision being to place
the department in the College of Engineering
rather than in a second college of applied science.
Also. Of the ten faculty appointees (all hold-
ing earned doctorates), only one has left to take
another position. Such a stable roster of ener-
getic and productive people is rare. The attrib-
utes for which Chris has looked in prospective
faculty members are a strong desire to contribute
to the growth of young people; a deep commit-
ment to the service of society; potential ability
to motivate students to achieve the utmost pos-
sible; and, perhaps most important, the intel-
lectual capacity to contribute to the fund of
knowledge. Furthermore, he has considered only
men who have had industrial experience in addi-
tion to their academic preparation. Finally, in
recruiting faculty, Chris has avoided hiring only
Mormons and local graduates, who were the im-
mediately available applicants. Of the nine he
has recruited, only three are of the locally domi-
nant religious faith; and only two hold doctorates
from the University of Utah. Chris has thus
ensured that the collective experience of the fac-
ulty is broad - socially and academically.
Chris has long been concerned with develop-
ing in bright young people an interest in chemi-
cal engineering, believing that it is necessary to
provide a means for junior-high and senior-high
students to identify with the profession. This,
he feels, can be accomplished by stimulating con-
tact between the students and practicing profes-
sional engineers and educators and by developing
positive attitudes toward the chemical-engineer-
ing profession in high-school teachers of chem-
istry, physics, and other sciences. Toward these
ends, he has encouraged his faculty to participate


Chris sees a bright future for ChE in water and food
supplies and environmental pollution . . .

actively in student tours, Career Day presenta-
tions, and science-club lectures and has sponsored
annual dinners and tours for local high-school
science teachers.
The future Chris sees for chemical engineer-
ing is bright. In fact, he feels that the chemical
engineer is beginning to have his "day" because
of his unique potential to solve such problems as
the depletion of the world's food and water sup-
plies, as well as the varied and currently alarm-
ing aspects of environmental pollution. His in-
tense interest in chemical engineering has influ-
enced all four of his sons. Magazines concerned
with science and engineering have always been
around the house, readily available for the grow-
ing children to read and examine; dinner-table
conversations have frequently turned toward
creative developments in chemical engineering
aimed at solving the problems of modern society;
and Chris has often taken his sons to professional
meetings so that they could have a first-hand
experience with active scientists and engineers.
The results of this immersion in a science-
oriented atmosphere cannot be disputed - two
chemists and two more chemical engineers bear
the name Christiansen!
AMONG THE MOST rewarding experiences
during his many years as an educator have
been Chris' opportunities to review the progress
of the many graduates of the University of Utah
Chemical Engineering Department. Many have
become important contributors to industrial prog-
ress, and a number have become educators them-
selves. Indeed, Chris' influence on chemical en-
gineering in Utah has been felt primarily through
the activities of graduates from the department
he founded. His influence, both locally and na-
tionally, has also been felt through his outstand-
ing service to the chemical-engineering profes-
sion, summarized in the accompanying table.
Chris has developed a philosophy of education
that is, perhaps, an outgrowth of his earlier in-
dustrial experience. He believes that a student
must be taught the essence of engineering;
namely, problem solving. In spite of many claims
to the contrary, Chris knows of no procedure
more effective than the use of a variety of experi-
ences in the solution of challenging, relevant
problems. He has also been a strong advocate of
the need for engineers to take courses in the hu-

manities, stating, "Engineering is the engine of
social change; but, from here on, the engineer
must be prepared to participate more strongly in
the steering as well as the mechanism." Easy for
Chris to say; throughout his entire professional
career, he has been dynamically active in both.

-National AIChE
* Director, 1966-68.
* Chairman: Technical Program, 38th National
Meeting; Humanities and Education Area Com-
mittee; ten symposia on basic chemical engi-
neering, chemical-engineering education, and
humanities at national meetings.
* Member: Nominating, Education and Accredi-
tation, Advanced Seminars, Research, Ethics
(ad hoc), Awards Policy (ad hoc), Environ-
mental Project (ad hoc) Committees.
* Council Liaison: Professional Development
Committee, Organizing Committee for Agricul-
tural Chemicals Division, Information Systems
Committee, five local sections.
* Member-at-large for liaison with Great Salt
Lake, Idaho, and Southern Nevada Sections.
* Official AIChE delegate, symposium chairman,
and lecturer at III International Congress of
Chemical Engineering, Chemical Equipment,
Construction, and Automation (CHISA '69),
Mariansk6 Lazne, Czechoslovakia.
-Great Salt Lake Section, AIChE
* Chairman: Organizing Committee, 1954; Sec-
tion, 1956.
* Liaison, 1966 to present.
* Chairman or member of many section com-
* Chairman: Chemical Engineering Department
Heads' Program Committee, 1959 and 1969.
* Member: Nominating, Utah Relations with In-
dustry Committees.
* Chairman, Local Arrangements Committee,
1971 Winter Meeting of the Society of
* Member, University of Utah Subcommittee,
XIII International Symposium on Combustion.
* Member, Utah Governor's Committee on Tech-
nical Education.
* Member, Professional Standards and Utah Re-
lations with Industry Committees, Utah Engi-
neering Council.
* Chairman or member of many local and
regional ACS meetings and symposia.
* Chairman, Salt Lake Chapter, Tau Beta Pi.
* Consultant to the National Science Foundation,
the U.S. Office of Education, the Artificial
Organs Institute of the University of Utah
Medical College, the Heart Test Facility of
Bio-Logics, Inc., and several industrial con-


would you like

to plan a plant

in Puerto Rico ?

Too late, the plant is planned! In fact
construction is already beginning on
Sun Oil's new $125 million refinery
complex and harbor at Yabucoa.
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An Equal Opportunity Employer M/F

McMaster University
Hamilton, Ontario

The visitor coming to the McMaster Chemical Engi-
neering Department for the first time is usually rather
bewildered. The main office on the third floor of the
Engineering building is small, crowded and noisy. In all
probability he will have to wait there while a free profes-
sor can be found. "Prof. A is giving a lecture, Prof. B
is at a meeting, Prof. C is on the telephone . . . etc." If
he is lucky, our visitor will find a chair to sit on, but
often the chairs are piled high with reports and memos.
The atmosphere is reminiscent of a newspaper office in
a 1940 movie. In short, things hum. The air of this article
is to present our philosophy on chemical engineering edu-
cation, illustrate its application, and perhaps correct our
visitor's chaotic first impression !

U ) il department




underlying philosophy of the department, it
is necessary to take a brief look at the recent his-
tory of chemical engineering in Canada. In 1958,
when the department was founded, there were
just eight other chemical engineering depart-
ments in the country. The emphasis was very
much on undergraduate teaching, with 236 BEng
graduates being produced in that year, while the
graduate student population was only about 75.
The undergraduate teaching load for faculty was
heavy; twenty contact hours per week were not
uncommon. The supervision of graduate students
was not considered to be part of the normal teach-
ing load. In the post-Sputnik era of the late '50s
and early '60s, both the demand for engineers and
the university enrolments soared, and many new
chemical engineering schools were created. Today
in Canada there are 23 such schools, of which 18
have graduate programs. The 1970 output of
BEng graduates is 490, and the graduate student
population is 608. This last figure reflects a major
change in emphasis since the late fifties.
On the industrial scene, there is and always
has been a strong demand for chemical engineers
at the bachelor's level. However, since many
Canadian companies are subsidiaries of parent
companies whose research and design depart-
ments are not situated in Canada, the level of
industrial research activity is comparatively low.
Some Canadian-owned companies have active re-
search departments, but many others do not. The
Canadian government has for some years recog-
nized this unbalance providing tax incentives and
other assistance for industrial research, and the
industrial demand for MEng and PhD chemical
engineers has been rising, though more slowly
than supply.


CEE features a developing Canadian department that emphasizes design and simulation (as well as fundamentals)
and whose unofficial motto is: "The whole must be stronger than the sum of the component parts."

In this department we work hard to main-
tain strong liaison with Canadian industry with
the prime aim of indicating the uses of new and
sophisticated problem-solving techniques, and
thereby encouraging companies to employ our
graduates, both at the BEng and higher levels.
The McMaster department has grown steadily
since its formation to its present strength of 13
Faculty, a 1970 BEng graduating class of 24, and
a graduate student population of 50. The average
faculty age is 40 (age range 28-55) and there are
seven full, four associate, and two assistant pro-
fessors. Our educational goal is to graduate an
engineer with a good grounding in fundamentals
(versatility), who is technically sophisticated and
can use up-to-date techniques of design and an-
alysis (adaptability), who appreciates the im-
portance of new research results and improved
knowledge in the field (continuing self-educa-
tion), who is aware of industrial problems and
constraints and who can formulate the right ques-
tions, obtain answers and select the most practi-
cal solution (relevance), who can communicate
with technical and non-technical people (inter-
action) and who is aware of his professional and
social responsibilities (social conscience).
This broad goal applies equally to the under-
graduate and graduate programs: we are con-
stantly examining and re-evaluating the pro-
grams so that they may better achieve this goal.
The departmental philosophy has evolved over
the past twelve years, and include the following
tenets. The emphasis is mainly on technical so-
phistication and fundamentals, as opposed to
teaching "technology" which may change com-
pletely in a few years. On the other hand, we
believe in an integration of fundamental science
with application. Graduate and undergraduate
programs are developed concurrently, and under-
graduates are thereby provided with an insight
into the vitality of graduate research. Indeed,
several of our undergraduate experiments are
performed on current graduate research appara-
tus or may be directed to obtaining peripheral
for a research program. All faculty members par-
ticipate in teaching, research and professional
activities-for instance there are no non-re-
searching teachers or non-teaching researchers
among us. There are many cooperative projects
involving several or all Faculty as well as grad-

uate and undergraduate students. The unofficial
motto of the department is "The whole must be
stronger than the sum of the component parts."
As well as communicating strongly within the
department, and thereby develop a philosophy
together, we continually interact with other de-
partments at McMaster, industry and the chemi-
cal engineering professions. We are acutely aware
of the dangers of the "ivory tower" mentality, and
for that reason a conscious effort has been made
to assemble faculty with industrial experience as
well as academic expertise. Innovation in teaching
and research are encouraged; indeed experiments
on teaching at the graduate and undergraduate
level take place every year. Originally, classes
were small and there was no tradition to stifle
new ideas; although classes are larger now, the
early spirit of innovation persists.
year of basic material, common to all engineer-
ing departments. In the second year, in addition
to further basic courses, there is an introductory
chemical engineering course which acts as a
bridge between the science already covered and
the engineering that is to come. For several years
this course has included a cooperative project
with local industry (see Fig. 1). Also in the second
year, we give one of our most important courses.
Information Management. This course runs the
gamut of the various means of communication:
use of library, computer programming, report

Figure 1. Dr. A. I. Johnson and a group of second-year students
discuss a problem in simulating a glycerine evaporator at the Procter
and Gamble plant.


writing and oral presentation (via closed circuit
TV) are included. There was a marked improve-
ment in our laboratory reports in later years after
this course was inaugurated. In our laboratory
courses, in third and fourth year, we have broken
away from the traditional set experiment to be
done in one or two periods. Instead, students are
faced with an in-depth project (sometimes the
problem is not even defined!) and are given four
weeks or more to produce a report. Usually one
faculty member is in charge of a given experi-
ment; two or at most three students work on any
given experiment. One of our other successful
teaching experiments has been the inclusion of
a design project near the end of our junior year.
Each student is given an objective to be achieved
in his experiment and then is guided through the
apparatus design by a faculty member and tech-
nicians. Several of the best designs have been

We are acutely aware of the dangers of the "ivory
tower" mentality, and for that reason a conscious
effort has been made to assemble faculty with
industrial experience as well as academic expertise.

constructed and used in our teaching laboratory.
In these courses, they draw upon the material
taught in Information Management and in addi-
tion they get a foretaste of industrial project
work and academic research.
Nowhere is our philosophy epitomized more
than in the undergraduate "simulation project".
As implied, the primary aim is to simulate a
given chemical process using the CDC 6400 com-
puter available at McMaster. The information so
obtained may be used in process improvement,
design of new plants, etc. Ten to twelve under-
graduates work throughout their final year on
each project, with usually three or four coordi-
nated sub-groups studying different aspects of
the process. There are weekly meetings of the
whole project team which would typically include
three or four faculty and six graduate students
as well as the undergraduates. These studies con-
cern real plants operated by Canadian industry.
Our weekly meetings may be attended by repre-
sentatives of the cooperating companies, and dur-
ing the project plant visits are arranged as
needed. We owe an inestimable debt of gratitude
to the companies concerned since the first project
in 1965.
These include: Aluminum Company of Can-
ada Ltd.; BP Refinery Canada Ltd.; Canadian

In our laboratory courses, in third and fourth year,
we have broken away from the traditional set experi-
ment to be done in one or two periods.

Industries Ltd.; Cyanamid of Canada Ltd.; Poly-
mer Corporation Ltd.; Procter and Gamble Ltd.;
Shell Oil Canada Ltd.
The simulations use two computer executive
programs, both developed in the department.
MACSIM (McMaster Sizer and Simulator) was
developed from the Dartmouth College PACER
Program. Further details may be found in the
book Chemical Plant Simulation by Crowe, Hamie-
lec, Hoffman, Johnson, Shannon and Woods, Mc-
Master University, 1969. A hard-cover edition
will be published by Prentice-Hall in 1971. Since
1969, we have also begun to use GEMCS (General
Engineering and Management Computation Sys-
tem), a system developed here in cooperation with
Canadian General Electric Ltd. GEMCS may be
run either on the CDC 6400 or on other time shar-
ing computers. The simulation project generates
enormous enthusiasm in all who take part, and
we are aware of the risk of overemphasis on com-
putation. We therefore urge our students to "com-
pute if necessary, but do not necessarily com-
pute", in other words to look for the consequences
of a solution rather than to regard the solution
as an end in itself.
This simulation work provides a focus for de-
partmental activities and is the key to our close
liaison with industry. It is a means whereby we
can apply the expertise of each faculty member
to the solution of real problems. It gives us a good
excuse to talk to each other about a given prob-
lem and thereby increase our breadth of knowl-
edge in chemical engineering. In this way we
come to realize each other's strengths. It pro-
vides us with an appreciation of industrial prob-
lems and perhaps of those areas which require a
better understanding; certainly many new re-
search projects have originated through the sim-
ulation projects, not only for the simulation group
itself but also for the experimentalist as well.
There is no doubt that the interaction among
faculty on the simulation project has been a major
factor in creating an harmonious team of faculty
and students.
The above outline has only given the high-
lights of the undergraduate program; for details
the reader is referred to the usual sources. At
the present time, the program is being reap-
praised, with the main objective of providing a


number of options in areas such as applied chem-
istry, applied mathematics (including simulation
and control), biochemical engineering, etc. These
options would comprise about 15% of the total
course units, and they reflect the diversity of
interests in the department. Many of the pro-
posed option courses would bring together under-
graduates and post-graduate students since
undergraduates would take some of the introduc-
tory graduate courses which are offered our
course-oriented MEng students. Another proposal
which is independent of the options program, is
for a five-year course in combined chemical en-
gineering and business administration. We are
discussing these changes with other departments
in the university, with our alumni (via mailed
questionnaire) and with our current undergrad-
uate and graduate students. An important input
is also provided by the departmental Industrial
Advisory Committee which comprises three mem-
bers from Canadian Industry and one member
(currently Dr. S. W. Churchill) from a large
U.S. chemical engineering department. We also
formed an Undergraduate Curriculum Advisory
Committee comprised of three faculty and two
student representatives from each of the under-
graduate classes and graduate school to undertake
studies of various aspects of our undergraduate
curriculum. This has proved to be a very success-
ful committee and the interaction with the In-
dustrial Advisory Committee is excellent.

OUR GRADUATE PROGRAM offers two routes
to the MEng degree: one is mainly course-
oriented, while the other has a relatively light
course load and a major thesis requirement. The
latter is the usual precursor to entry to the PhD
program, although it may be entered directly by
a student with a good Master's degree from an-
other school. Prior to presenting the PhD thesis,
the student must pass two qualifying exams.
These are aimed at ensuring a breadth of knowl-
edge at least as broad as that offered in our
bachelor's program, plus the ability to "think on
one's feet". The second part of this qualifying
examination is related directly to the candidate's
research project. Here, the candidate reviews the
present status of the research project (literature
review), the progress of his program to date and,

One of our other successful teaching experiments has
been the inclusion of a design project near the end
of our junior year.

Our graduate program offers two routes to the
MEng degree.

most important, the direction he has planned for
his research. He is then examined in detail on his
proposals. An integral part of the program, in
addition to course work and research, is the input
of practical problems and realism that results
from participation in undergraduate projects.
Working contact between graduate students and
industry is particularly important in the Canad-
ian context, since the opportunities for industrial
employment on fundamental research are almost
non-existent. A graduating PhD can rarely expect
to get a job which relates directly to the expertise
obtained in his research program.
The research activity of the department is
detailed in our Research Report and is sum-
marized here. The research projects cover a wide
spectrum from the most fundamental to the very
applied. Our policy is to concentrate on compara-
tively few research areas, with a back-up of two
or more faculty active in each area, rather than
having each man "doing his thing" in isolation
in one specialized area. The benefits of such in-
teraction far outweigh those of attempting to
have an expert in each area. The areas covered
* Applied chemistry: heterogeneous catalysis, poly-
merization and reactor design
* Applied mathematics: simulation, optimization,
computer-aided design
* Transport phenomena: heat transfer, fluid mechan-
ics, mass transfer with and without chemical re-
* Waste-water treatment
* Transport phenomena in iron and steel manufacture
Several faculty members act as bridges be-
tween these five areas, and through associate
departmental membership we cooperate with
Chemistry, Metallurgy and Mechanical Engineer-
ing. Figure 2 shows a typical joint project on
solids conveying in a 2 inch pipeline. We have
already started interdisciplinary projects with
the Health Sciences Centre which is due to open
soon, just across the campus, and we look forward
to increased activity in this area.
Industrial support for research is less wide-
spread here than in U.S. chemical engineering
departments, because of the relatively low level
of industrial research activity in Canada. One
major industrial project involves the development
of a file-oriented, information-handling program,
GEMCS, for use on time sharing computers, in


Figure. 2. The Department cooperates with the Mechanical Engineer-
ing Department in operating this 80 ft loop for slurry pipeline

cooperation with Canadian General Electric Ltd.
This program has been used in simulating alterna-
tive steel-making processes (Steel Company of
Canada Ltd.), and a fat hydrolysis unit (Procter
and Gamble Ltd.). A new dynamic simulation
program, DYNSYS, has been developed and used
in transient and control studies with Polymer
Corporation, Dow Chemical Co., and Aluminum
Co. of Canada. The Department has just pur-
chased a SUPERNOVA Computer to test in the
laboratory, via direct digital control on pilot plant
equipment, some of the ideas developed in com-
puter/equipment studies of the dynamic response
of this equipment. A number of industrial proj-
ects have been carried out through the agency of
CARED, the McMaster Centre for Applied Re-
search and Engineering Design (whose Director
is a member of the Department!). These include a
major study of heavy water separation for Atomic
Energy of Canada Ltd. and the simulation of a
polymer reactor train.
However, government agencies provide most
of our research support. The National Research
Council of Canada granted us a total of $205,800
this year. This amount allows for the fact that
the university provides overheads, professors'
salaries, and partial student support. The Depart-
ment of Energy, Mines and Resources is granting
$100,000 per year (renewable, for up to 5 years)
for a major research program on waste water
treatment plants.
All the faculty are active in one or more of
various professional societies (CIC, CSChE,
AIChE, ACS, etc.). The department contains the

editorial office of the Canadian Journal of Chemi-
cal Engineering, and several of us are examiners
for the Association of Professional Engineers of
Ontario. We initiated the annual meeting of On-
tario Professors of Chemical Engineering, a use-
ful clearing-house of education experience for the
eight departments in the province.
In concluding, it is interesting to look ahead
to the next 40 years, the working lifetime of our
present crop of graduates. What changes will
occur in chemical engineering? Will it even exist
in 40 years time? Certainly there is a discernible
broadening in the scope in which chemical engi-
neers are employed; originally in the 1930s the
profession was centered around oil refining, and
in recent years the "chemical industry" has been
the recognized employment area for chemical en-
gineers. Now in the 1970s we see that in Canada
chemical engineers are in demand in such areas as
pollution control, mineral processing, and in broad
systems studies which may have little formal
chemical engineering content. Overlying these
new technical needs, there is a growing aware-
ness in the profession that we are accountable
for our actions-not only to our employer, but
to society and the community. By precept and
example, we try to impart this attitude to our
students. Hopefully, the teaching and research
emphasis in our program will stand our graduates
in good stead throughout their careers.

LETTERS (Continued from page 107)
copper, aluminum, nickel and iron that we use. The im-
provements in technology kept pace with the decline in
quality of ores so that the cost of metals and fuels didn't
change much during the decade. Garbage and unusable
solid wastes are now being hauled considerable distances
from metropolitan areas for disposal.
In spite of technological advances the quality of life
in the U.S. went down during the decade. The U.S. made
little headway during the 1970's on its population prob-
lem although some encouraging signs are just beginning
to emerge. The ghettos are considerably bigger than they
were ten years ago. In spite of massive public housing
additions, there were always people waiting to move in
every time a ghetto dwelling was vacated. Attempts to
interest the poor in birth control were always met by
demagogic statements of "governmental genocide aimed
at reducing the ghetto dwellers political muscle." In spite
of massive expenditures for better schooling in the
ghettos, the education remains unable to train people for
useful roles in today's society. Crime and lawlessness run
rampant in the ghettos. The police do little more than
try to contain it at the borders. Drugs, alcohol and
marijuana are available at low cost in the ghetto in the
hope that it will dull the anger of the residents.
(Continued on page 152)


Beneath this soft and warm exterior,
there lies a heart of plastic.

So far, ifs only a valve. Eight-year-old
Janet Hemandez has one.
It may not be long before a whole
working heart will be made out of plastic.
Men in plastics research at Union
Carbide are working on the almost im-
possible job of designing plastics com-
patible with the body.
Their most crucial job is making an
ultra-thin polypropylene fabric for lining
the inside of the heart. A fabric coated
with parylene that will allow human tis-
sue to grow into and around it to keep
blood from clotting.
A plastic heart isn't the only part of
the body we're working on. Maybe some-
day there will be a little plastic in all of us.
Right now, we've got you surrounded

by our plastics. We were in plastics be-
fore most people knew the word. We
make more plastics than anyone else. We
haven't scratched the surface yet.
Why is a great big company like Union
Carbide so concerned about a little bit of
plastic for the body?
Beneath our corporate exterior, there

beats a heart.



For additional information on our activities, write to Union Carbide Corporation, Department of University Relations, 270 Park Avenue, New York, New York 10017. An equal opportunity employer.

1to i Pclassroom



L. A. MADDOX, and H. F. RASE
The University of Texas at Austin 78712

Both ChE students in process design classes
and practicing process engineers have long been
plagued by the necessity of doing many tedious
and methodical calculations before reaching the
more interesting and creative aspects of design.
The advent of high speed computers generated
great hope that both the professional engineer
and the student would be freed from tedium
and would be able to concentrate on the heart
of any engineering problem - the exercise of
engineering judgment and innovation. Unfor-
tunately, in practice this hope has not been
totally realized. Even if one assumes that the
programming and "debugging" are done by
others, several crucial issues remain which de-
tract from the real engineering meat of the
* Although the usual process design calculations can
be done in seconds, the actual time measured from the
time of submitting input data to the receipt of the
printed results can be many hours. The reason for this
is simply that large computers in any organization are
used by many people. Time sharing makes this use an
orderly, efficient process, but some kind of priority sys-
tem must be established which often relegates many
problems to longer waiting periods. This is especially
true in a university where involved research calculations
may take a large portion of computer time.
* The results when obtained consist of the familiar
long printout of masses of numbers which is essentially
unintelligible until one produces some sort of graph that
enables analysis of trends. This further delay is par-
ticularly annoying during the earlier stages of contact
with the problem when the student or designer has little
feel for the way variables interact to effect outcomes,
and is anxious to overcome this deficiency. Chemical
reactor design, because of the associated nonlinear sys-
tems of differential equations is an excellent example of
a problem requiring detailed calculations merely to ac-
quire a feel for the problem.
* In the early stages of a problem the designer must
decide how the stated purposes are to be accomplished. It
is during this aspect of the problem that he exercises his

creative abilities and makes some of the most critical
decisions of the project. Although the creative act re-
mains essentially a mystery to psychologists and others
who have attempted to study it, it seems rather clear that
it usually occurs most successfully when one is totally
immersed in the problem and is obtaining the results of
tentative ideas in a rather rapid and orderly fashion. This
climate is not provided by the usual mode of interacting
with the digital computer as described above. Relatively
long waiting periods for receiving results together with
the presentation of these results in long printed format
cause the mind to wander from the problem and require
that one renew his interests and reestablish his previous
viewpoints each time a series of results is received. Of
course, one can submit a number of different designs at
one time. In any real situation, however, one is apt to
submit a number of cases which are trivial and do not
necessarily converge to the desired result. This can be
a very common and natural consequence of an inadequate
intuition about the variables during the early stages of
attack on a problem.

An obvious and much more desirable begin-
ning on a design problem would involve toying
with the variables and immediately observing the
results in graphical form. An interactive visual
display is ideally suited for this purpose. We
have recently adapted such a unit for use by
members of the senior class in process design,
and the results have been most gratifying. Each
student in two separate twenty minute periods
was able to master rather complete understand-
ing of the impact of the several variables on the
problem and developed a feel for the issues
which enabled him to make major engineering
decisions. This encounter with the visual display
of profiles of variables was then followed by an
opportunity to accomplish study of a well planned
series of cases using the more common procedure
of submitting and receiving design cases from
the digital computer in printout form. The sec-
ond phase of work now, however, was intelli-
gently planned and executed for the purpose of
obtaining precise quantitative results for a rather
well-defined system, major decisions on operating
conditions having been fairly well decided by
use of the visual display.


The Authors

T. Juul-Dam was a teaching assistant and is now with
Atlantic Richfield Company in Dallas, Texas. He obtained
a civil ingenior degree in ChE at Danmarks Tekniske
Hojskole in Copenhagen and his PhD from The University
of Texas. He is a member of Omega Chi Epsilon.
J. D. Lawson was a teaching assistant and is now
with Pan American Petroleum Research Center in Tulsa,
Oklahoma. He received his BS in ChE from the Univer-
sity of Tulsa and his PhD from The University of Texas.
He is a member of Phi Kappa Phi, Phi Lambda Upsilon,
and Omega Chi Epsilon.
L. A. Maddox was a teaching assistant and is now
with Celanese Corporation Research Center in Clark-
wood, Texas. He received his BS in ChE from Texas
A & M and his PhD from The University of Texas. He is
a member of Tau Beta Pi, Phi Kappa Phi, Phi Lambda
Upsilon, and Omega Chi Epsilon.
Howard F. Rase is a Professor of Chemical Engineer-
ing at The University of Texas. He has been a process
engineer with Foster Wheeler Corporation and a chemical
engineer with Dow Chemical Company and Eastern States
Petroleum (now Signal Oil Company).

The proof of the efficacy of this procedure
can best be realized by observing the effect on
students. The encounter with the visual display
is essentially a teaching encounter in which the
student teaches himself about the problem. It is
rather inspiring and somewhat surprising to see
how rapidly a student becomes very knowledg-
able about the important issues. Students seem
to be overflowing with ideas at this stage and
become most anxious to proceed with testing
these ideas further. Even the average and below
average students are stimulated and their abili-
ties extended to the maximum. The use of visual
interactive displays has received a great deal of
attention in mechanical design, and it also now
seems to possess equally exciting potential in
process design.
In order to provide interested readers with
some insight into the issues involved in planning
and executing the use of visual interactive dis-
plays, we will present some of the details of a
reactor design problem and the issues involved
in selecting the variables for display.

The design problem was stated simply: Design a
catalytic reforming unit for producing 20,000 BPSD of
95 research octane number reformate.

Hydrodesulfurized Feedstock Analysis
The feedstock has API gravity of 51.90 and volumetric
composition of 43.4% paraffins, 40.0% naphthenes, and

16.4% aromatics. Data for the ASTM distillation are:
IBP-2400F; 10%-262OF; 20%-272OF; 30%-279OF;
40%-2840F; 50%-292�F; 60%-302oF; 70%-3110F;
80%-3220F; 90%-3350F; 95%-3460F; and EP-


The catalyst is Sinclair-Baker RD 150 (0.6% Pt-on-
alumina), 1/16" extrudate and has bulk density of 0.78
gm/cc; surface area of 471 m2/gm; and pore volume of
0.42 cc/gm.
Catalyst characteristics: Poisoned by sulfur, arsenic,
and nitrogen compounds. Coking occurs on the catalyst
and deactivates it gradually. Regeneration by burning
with air partially restores the activity. Catalyst life de-
clines with increasing operating temperature and decreas-
ing pressure.

Idealized Rate Equations7

A number of references on the process were sup-
pliedi-10 including kinetic data.7 The following equations
Each of the three hydrocarbon classes is represented
by a single compound having the average properties of
that class.

1. Naphthene g aromatic + 3H2; , 30,500 mole H12 liberated
-r cpl(PN - p---

(23.21 - 34750) b-moles naphthene
S e' T (hr)(lb cat) (atm)

Kpl i

e(46.15 - 46045 am3

2. Naphthene + H2 * Paraffin; AH12 = -19,000 mole 112 consumed

-r 2 � kp2 k (PNPH - Kp2

S(35.98 - 59600) lb-moles naphthene
p2 " T ' (hr)(lb cat) (atm)

S e(8000 - 7.12) atm-1

3. Paraffin + H, 2 Hydrocracked
Products; AH3 = -24,300 mole H2 consumed
Stoichiometry: CnH2n+2 + H2 * [c + c2 + C3 + c4 + c5]

-3 kp3YP

S (47.97 - 6200) lb-moles paraffin
Tp3 (hr)(lb cat)
4. Naphthenes + H2 - Hydrocracked
Products; AH4 = -22,300 mole of H2 consumed

Stoichiometry: C H 2n+ H2 [c + c2 + c3 + 4 + c5

r4 = k4 PT kp4Y

1p4 - Same as kp3


. . the creative act remains a mystery, but it seems clear that it occurs most successfully when one is totally

immersed in the problem and is obtaining the results of
display expedites the creative process . . .

ideas in a rapid and orderly fashion . . . the visual

The value of n is obtained from the molecular weight of
the feed and the mole fractions of the feed component
types as described by Smith.7

Balance Equations in Difference Form

(-r) AW= AX

(-r2) - = x

(-r34) = Ax4

F- [(-rl)(-AH1)(3) + (-r2)(-AH2) + (-r3)(-AH3)

+ (-r4)(-AHO)()] = - N. C AT (6)

The reason for use of adiabatic reactors in all
industrial installations of this process was first
established in discussions with the students. By
proper choice of initial condition Reaction 1 is
made to proceed to the right and Reaction 2 to
the left. These events are both highly endo-
thermic and demand staging and intermediate
The balance equations were programmed for
the iterative calculations necessitated by the
coupling of Equation 5A-D and 6. Variables
selected for appearance on the visual display are
limited by the capacity of the oscilloscope to pro-
duce a readable graph. Thus, items were chosen
that would contribute most to the students grasp
of the problem and understanding of the sensitiv-
ity of the more important rates to changes in
variables. The cumulative volume per cent aro-
matics in the Cs+ reformate, which is correlated
with octane number, and the rate profiles of
aromatics production and paraffin hydrocracking
were selected for visual display as a function of
W/F (reciprocal space velocity). These rates
have an overriding effect on octane number of
the finished product. Volume per cent aromatics
is not only affected by the amount of aromatics
formed but also by the extent of hydrocracking,
which acts to decrease the volume of C.+ paraffins
in the product and thus increase the net volume
per cent aromatics.

At the end of each trial design the designer
also needs to know the yield, which is most de-
sirably expressed for a product sold by volume,
as volume of Cs+ product divided by volume of

Use of the Visual Interactive Display
These variables were plotted as shown in Fig-
ures 1 - 3. All are graphical except the yield fig-
ure which appears as a number at the end of each
trial on the lower right hand corner of the screen.
The user selected the number of reactors, the in-
let temperature, average pressure and space
velocity for each reactor by punching the key-
board as shown in Figures 4 and 5. This simple
keyboard could be mastered by anyone, even a
person not familiar with the problem. Thus, it
was possible for a student to use the keyboard
freely and let his ideas develop without inhibi-

Fig. 4. Keyboard. The top row of keys is used to select the class of
variable, e.g., temperature, pressure, W/F, and numbers of reactors.
The particular reactor of interest and the magnitude of each variable
is specified using the lower array of keys.

Typical Trial Run on the Display
After initial random trials or prior study of
literature on existing reformer plants the stu-



[Il� RET

Q~ � 7

0 00C


Fig. 1. View of display for Trial 1.

Fig. 2. View of display for Trial 2.






0 2 4 6 8 10 12 14
Fig. 3. View of display for Trial 3.

X axis division 2. Y axis division R1 = 0.005, R3 = 0.002, VPAR
respectively. VPAR is volume per cent aromatics.

= 0.05 beginning at 0.4. R1 and R3 are rates of reactions 1 and 3

dent decides that a reasonable set of input values
would be as follows:
Trial 1: (Fig. 1) No. of Reactors 4
T 950 950 950 950
P 475 450 425 400
W/F 7 7 10 10
From the display the student realizes that a
volume per cent aromatics (VPAR) of 62.9 at
outlet of last reactor is above his product quality
specification (57% required) and that his yield
is not particularly good. The student reasons
that possibly eliminating the re-heating between
the 3rd and 4th reactor would cause less hydro-
cracking of paraffins which would lower his
product quality to a more acceptable value and
also simplify the design of the reformer. From
previous trials the student knows to expect a tem-
perature drop of approximately 250F in the third
reactor. The student then changes the inlet tem-
perature of the 4th reactor to give:
Trial 2: (Fig. 2) No. of Reactors 4
T 950 950 950 925
P 475 450 425 400
W/F 7 7 10 10

The student sees that the results of Trial 2
are a VPAR of 58.25 which is near the range of
product quality desired. He also is pleased to see
that the yield has increased to 85.8%.
Upon examining the rate of conversion of
naphthenes to aromatics (the top-plot-Ri) he
sees that R1 has become quite low near the end of
1st and 2nd reactor. He, therefore, reasons that
the 1st and 2nd reactor should be made smaller.
Also, since the product quality could still be
lower and be acceptable, he decides that he will
need less cracking of paraffins and can therefore
shorten both the 3rd and 4th reactors. These
inferences lead to

Trial 3. (Fig. 3) No. of Reactors 4




The student notes that R1 has not fallen to
as low a value as in Trial 2. He sees that his
product quality has dropped to a VPAR of 57.0%
which is quite acceptable to him and he is also
rewarded with a much higher yields of 87.5%.
He also recognizes that Reactors 3 and 4 can be


Fig. 5. Student operating display under observation of teaching
combined into a single reactor if vessel economics
so indicate.

Description of Computer Equipment and Program

Equations 1 through 6 were programmed to
calculate the rates of reaction, temperature pro-
files, and material balances through the length
of fixed bed catalytic reactors. An iterative tech-
nique was used to balance the heats of reaction
and reaction rates for small increments of cata-
lyst bed based on an arithmetic average tempera-
ture for that increment. Once a balance was
reached for one increment of catalyst bed, the
outlet temperature and component flow rates
were used as inlet values to the next increment of
catalyst bed. The computation continued until
the prespecified amount of catalyst had been used.
The program allowed the student to specify the
number of reactors and the inlet temperature,
average pressure, and space velocity of each re-
The program was modified to run on a Scien-
tific Data Systems Model 930 computer coupled
to a Model 9185 Scope Display having vector and
character generators. The unit had 32,000 words
of memory. The program was operated under
the special University of Texas Tape Monarch
system containing a custom multigraphics pack-
age for the scope.


It can be seen from the description of a series
of trials by a student that the student rapidly
acquires knowledge about the process. He is

motivated by the ease and rapidity to try new
ideas of all types. We have found that great
enthusiasm for the problem is generated by this
encounter with the visual display, and many of
the students have indicated genuine originality.


We are grateful for assistance and advice
from Dr. C. L. Coates, Dr. J. K. Aggarwal and
Messers Richard Wackerbarth, John Bradley and
David Hogan, all of the Electrical Engineering
Department of the University of Texas.


Cp = heat capacity
FT = total fresh feed, lb-moles/hr
AH = heat of reaction, see text
kp = velocity constant based on partial pressure,
see text
Kp = equilibrium constant in pressure units, see
n = number of carbon atoms
P = pressure, atm
r reaction rate, lb-moles converted
lb cat-hr
W = weight of catalyst, conversion
x = conversion, moles converted
mole total fresh feed
Y = mole fraction

A =
H2 =
i =
N =
P =
T =

any component in reaction mixture

1. Bozeman, H. C., Oil and Gas J. 61 (51), 50-58
2. Davidson, R. L., Petrol. Processing 10 (8), 1170
3. Decker, W. H., and D. Stewart, Oil and Gas J., 54
(9), 80-84 (1955).
4. Decker, W. H., and C. Rylander, Oil and Gas J., 57
(6), 88-9 (1959).
5. Hettinger, W. P., C. D. Keith, J. L. Gring and
J. W. Teter, Ind. Eng. Chem., 47 (4), 719-730
6. Hydrocarbon Processing 45 (9), 195-204 (1966).
7. Smith, R. B., Chem. Eng. Progress, 55 (6), 76-80
8. Smith, R. B., and T. Dresser, Petro. Refiner, 36
(7), 199-202 (1957).
9. Stanford, G. W., Petrol. Refiner, 34 (9), 190 (1955).
10. White, E. A., Petrol. Processing 12 (7), 122-4


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You'll start out facing practical situations and
using your academic knowl-
edge and skills to solve real
problems. You may even have
to improvise and develop
new approaches to specific
We rotate the assign-
ments of young professionals.
You will be able to work
with different groups of

experienced colleagues and sharpen your skills on
a variety of projects.
Talk with our representative when he comes
to your campus about the
opportunities we have for
you. Check your placement
office for more information or
write to: D. C. Reid, Coordi-
nator, Professional Employ-
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of California, 225 Bush Street
-Room 105, San Francisco,
1i California 94120.

Standard Oil Company of California
An Equal Opportunity Employer





University of California
Berkeley, California 94720

A major challenge to chemical engineering
education is the need to develop students' abili-
ties in the art of engineering. Present-day cur-
ricula concentrate upon analysis and the under-
standing of physical and chemical phenomena. A
chemical engineer must necessarily have a strong
background in these areas; yet engineering is
inherently an active, problem-solving function,
for which analysis and scientific understanding
are only the tools. We devote considerable time
to developing the tools, but usually spend much
too little time developing skills in the integrated
use of these tools for the synthesis of new proc-
esses and for coping with other real, complex
and loosely-structured problem siutations.
Universities can and should provide the train-
ing to bring out talents of application and prob-
lem-solving in students. Leaving this job to in-
dustrial experience runs the risk of these talents
never being developed at all, and results in spe-
cific methods and customs being passed on from
one generation of engineers to the next without
the young engineer being encouraged to question
and to bring in a fresh approach.

These conclusions have led this department
to stress chemical process design and engineering
as an important portion of the available graduate
program. This portion of the graduate program
is under the principal direction of four full-time
faculty members: Professors Alan S. Foss, Ed-
ward A. Grens II, C. Judson King, and Scott
Lynn. Courses are available in Process Simula-
tion in Chemical Process Design, Chemical Proc-
ess Synthesis, Design and Engineering of Inte-

t classroom

C. Judson King is Professor of Chemical Engineering
at the University of California, Berkeley. His principal
teaching and research activities lie in the fields of process
synthesis and development, separation processes, food
dehydration and mass transfer. He is the author of a new
textbook, "Separation Processes," to be published by Mc-
Graw-Hill in late 1970. He holds the BE from Yale Uni-
versity and the SM and ScD from MIT. Since 1967 he
has been Vice-Chairman of the Berkeley chemical engi-
neering department.

grated Chemical Process Systems, and related
areas. The first three of these courses emphasize
not only techniques which are available, but also
the application of these techniques in specific
chemical processing situations. The fourth course
is built around a sequence of short case problems
of the sort described below, and the development
of these problems is an important aspect of the
program. MS and PhD degree requirements are
equivalent to the rest of the graduate program,
and a thesis is required for each degree. Theses
in the process design and engineering program
represent original and potentially publishable
work in the development and improvement of
design concepts and techniques, or of specific
processes. Thesis research and the creation of
case problem material for use in class are often
closely connected. Ties with industry are main-
tained through short-term (typically one quarter)
visitors to the program and through the previous
industrial experience of the faculty involved. The
program is currently supported by a short-term
initiation grant from the Division of Graduate
Education in Science of the National Science



The case problems generated and used in the
program are for the most part short enough so
that they can be handled through class discussion
in a relatively few class periods, with intervening
homework assignments. They are not the sort of
course-long problem typically taken up in a
senior-year design course or in the AIChE Stu-
dent Contest Problem; instead they are shorter
and more qualitative. They are intended to in-
crease the student's abilities in synthesis, in
basic process understanding and in coping with
open-ended engineering problems. The student
must solve the problem himself; he does not read
a history of someone else's solution. The prob-
lems are similar to those presented by Thomas K.
Sherwood in his book, A Course in Process De-
sign, and to those presented in Chemical Engi-
neering Case Problems published by the AIChE
Education Projects Committee in 1967.
At Berkeley these case problems are used as
the entire subject matter for the aforementioned
graduate course and also for a senior-year elective
undergraduate course which follows the required
senior design course. It is also possible to use
one or more of the problems as a portion of a
lecture course, for example as a means of tying
together and showing application for subject
matter at the end of a course.


Through the grant from the National Science
Foundation, these Case Problems are available
to faculty of other universities for the cost of
Xerox duplication. Each problem consists of a
short descriptive introduction with references, a
suggested Problem Statement for issuance to the
students, and an extensive discussion or "Solu-
tion" of the problem for faculty use. This "Solu-
tion" constitutes 80 to 90 % of the pages involved.
The problems may be obtained by college and
university faculty members and by those in
charge of industrial or governmental training
programs. They will not be published in a form
such that the "Solutions" are readily available
to students, so as to preserve the atmosphere of
a new and challenging problem situation in the
Classroom. Copies of any or all of the prob-
lems listed below may be obtained by sending
payment or a purchase order to Professor C. J.
King, Department of Chemical Engineering, Uni-
versity of California, Berkeley, California 94720.

Checks should be made payable to "Regents of the
University of California." Overseas orders should
add 600 per problem for extra handling and


Announcements of Problems CP-1A, 1B, 2,
3 and 4 were distributed to chemical engineering
departments in the U. S. and Canada this past
winter. Three additional problems have become
available since that time. The full list of prob-
lems available as of June, 1970, is as follows:

CP-1A.* Production of Benzene and Xylenes by Hydro-
dealkylation. Process Analysis and Synthesis
(King). 29 pages ($1.00).
The aim of this problem is to develop an understand-
ing of a chemical process, starting with a simplified flow
sheet. The student is asked to determine reasons for the
choice of particular operating conditions which have been
given in a brief process description. He then must de-
velop reasonable values for other operating conditions
which are not given and must consider the possibility of
modifying the basic flow scheme in various ways. Finally,
a major elaboration of the process is suggested, and the
student is asked to synthesize an ordering of process
equipment for the new process.

CP-1B. Simulation of a Hydrodealkylation Plant. Proc-
ess Simulation (Alesandrini, King and Foss).
34 pages ($1.00).
This problem is designed to give the student some
understanding and familiarity with the requirements of a
plant simulation on a computer. The student is asked first
to generate a list of independent variables for a mod-
erately complex chemical process. He then must select a
sub-group of these variables upon which to base the
simulation and present a block diagram of his approach
to the solution of the heat and mass balances throughout
the process. The selection of independent variables so
as to eliminate iterative calculations connected with re-
cycles is stressed.

CP-2.* Continuous Drying of Air. Trouble-Shooting
(King). 41 pages ($1.25).
This problem involves the analysis of operating data
for a fixed-bed, continuous air drying unit. The student
is given a smattering of information on the current per-
formance of the unit. On the basis of this he must design
an appropriate and discriminating performance test. The
results are real data, obtained from a past test on an
actual, operating dryer system. From the data the stu-
dent is asked to identify the source or sources of mal-
function and to suggest ways of improving the operation
of the unit.
(Continued on page 135)
*CP-1A,-2 appeared in "Chemical Engineering Case
Problems," AIChE, New York (1967).





University of Detroit
Detroit, Michigan 48221

Editors Note: CEE joins the profession in
mourning the recent death of Professor

Over the years a number of views have been
presented on plant design, and each has had its
own concept of what design is. Some have concen-
trated on small problems related to design. Others
have concentrated on design calculations. Others
have concentrated on the preparation of drawings
and specifications. Here at the University of De-
troit we have tried to take in the broad concept
of design1, 2, which starts with the conception of
a chemical process and ends with the preparation
of the drawings and specifications suitable for
purchase of equipment and for contractors to
make bids on engineering construction. The func-
tions with which the chemical engineer is chiefly
interested are emphasized.

The design sequence consisted of two quarters
of ten weeks duration each. In the beginning of
the first term a process was assigned, which would
consist usually in simply writing a chemical com-
pound, but not necessarily the chemical reaction,
for obtaining the compound. The criteria needed
for design were worked out during this term. In
the second term, then, after the criteria had been
worked out through preliminary studies and ex-
perimentation, the actual plant design procedure
was simulated by the students.
This design sequence was essentially an open-
ended course, in that nothing more than a chemi-
cal product was assigned to the class. -It was a
case history approach-the students must decide
by what process, chemical reactions, and other
modes of procedure that the design should be
carried out.


Francis P. O'Connell was at the University of
Detroit for many years, where he was Professor of
Chemical Engineering. Over the past 30 years he was
engaged in research, development, process design, project
engineering, plant start-up and operations. A graduate
of Villanova University, he had the MS and the PhD
degrees in chemical engineering from Lehigh University.
Dr. O'Connell was a licensed professional engineer in
Pennsylvania and Michigan.

The classes have consisted approximately of
twelve to fifteen students who where divided into
groups of three to five students each. It is the
author's judgment that the optimum group would
be somewhere between three and four students.
We found that if the group were too small, the
students would not be able to cover enough
ground to make the assignment worthwhile, and
if the group were too large, the more eager stu-
dents would tend to dominate the group.

During the course of this plant design exercise
emphasis was not placed solely on calculations,
important as they may be. The students had to
decide which direction to go, for instance, whether
their control valves are to fail open or closed.
Here is a list of typical decisions which the stu-
dents have made:
Whether to use a spray, packed, or plate tower
How much hold-up time for a surge tank
Should reflux be pumped or fed by gravity
Select equipment for separating a liquid-vapor mixture
Should material be shipped by water, road, or rail
Should mounted spare pumps be provided
Mounted spare control valves vs. hand operated by-
pass valves


. . . The survey work just described was coupled with
in the laboratory on a bench scale an operation of the

experimentation. The students were expected to set up

Can plain carbon steel be used instead of stainless
Is an explosion wall necessary
How large should an escape exit be made
Selection of a fire extinguishing system
Selection of nitrogen, helium, argon, or carbon dioxide
as an inert gas
Should spring loaded safety valves or rupture discs
be used
Method of removing heat from a reactor
It is hoped that engineering judgment and
creativity were developed through this decision
making exercise. If a student put forward an idea
that was half way reasonable, it was never dis-
couraged, but he was encouraged to discuss his
idea with others. Synthesis, as well as analysis,
of all concepts had to be emphasized.

One way to encourage this was to have the
class assemble about once a week and give a brief
written and oral progress report. This was done
in the groups in which they were assigned, so
that possibly once a week one member of each
group would report on the work progress. This
gave him a chance to defend his ideas and the
ideas of the group against the criticisms of the
other groups. And to a certain degree it developed
a healthy sense of competition among the groups.
We found that this did not tend to make the
groups copy one another. Perhaps this is true be-
cause right in the beginning of the course the
groups selected a particular path to follow as re-
gards such things as reactions and patented proc-
esses, and they tended to deviate from one an-
other as time went on. Nevertheless they could
exchange ideas with one another, and this was
healthy. It is somewhat of an art, trying to de-
velop healthy discussion among the various
groups at the weekly meetings. The teacher must
not inject himself too much nor too little.

One of the more difficult chores of the teacher
is to find a suitable process for the students. The
following pitfalls stand out in the choice of an
1. The right amount of data must be available to the
students. If there is too little data available in the
literature or otherwise, they are forced to do an undue
amount of guessing. If there is too much data avail-

able, they are unable to digest it in the time allowed,
and they tend to copy previous designs. This would
be the case with any of the old heavy chemicals, such
as sulfuric acid or caustic-chlorine.
2. The number of technological steps should be optimum.
Too few steps would lead to a trivial study. Too
many steps would 'render the project too complex
for the time allowed.
3. When laboratory investigations are included in the
project, the following limitations prevail:
a. Safety of the students must be assured.
b. Pick a process which will allow the students to
take meaningful data in the time allowed.
c. Work is limited by laboratory equipment available.
4. The process must be such that it can be run at a
suitable capacity. If the capacity is too small, the
students will only be designing pilot plants. We try
to shoot for about 100 tons per day.
5. Pick a process that is profitable. This is hard to do,
and nothing is more discouraging to the students
than to find out that their plant will not be able to
make money. Unfortunately today most profitable
operations have multidepartment plants and multi-
plant industries, whereas the students are necessarily
limited to one process.

In the first term, or first phase of the program,
the students simulated what happens in the
process development stage of plant design in
industry. This consisted of learning and practic-
ing a number of techniques associated with the
problem. The students had to make a market
survey to form some idea, at least qualitatively,
of what demand could be expected for the pro-
posed product. The first week the groups were
given a chance to go over the process, consult
literature, and decide with the best judgment
they had available at the time which process they
wanted to follow through.
This got them started in a given direction,
so that they could go through the entire develop-
ment and design experience. They then developed
a rough flow sheet and went into estimation of
fixed and operating capital. Then from capital in-
vestment they went to manufacturing cost esti-
mate, profitability estimates, optimization studies,
and various economic studies, such as variation
of capital cost and profitability with capacity.
The survey work just described was coupled
with experimentation. The students were ex-
pected to set up in the laboratory on a bench
scale an operation of the process. In the ten weeks


. . . it is hoped that in developing this sequence
further, we shall be able to expand the use of various
optimization and operations research techniques.

or less allotted for this experimental work it has
been found that the students had all they could
do to merely set up a demonstration of the process
itself. This meant that their work was usually
confined to reactor studies, which might have
given them an opportunity to match mathemati-
cal models for the process through the use of
kinetic and thermodynamic principles. This also
gave them a chance to compare literature data
with their actual experimental data, and gave
them some conception of problems met in scale-up
of processes.
For the most part the mathematical tools used
were those the students had in engineering school
and consisted mostly of algebra, calculus, differ-
ential equations, and error theory. However, it is
hoped that in developing this sequence further,
we shall be able to expand the use of various op-
timization and operations research techniques,
such as dynamic programming, linear program-
ming, stochastic programming, nonlinear pro-
gramming, evolutionary operations, game theory,
and any other concepts and techniques that may
appear in the future.
An attempt was made to have the students go
through economic studies a number of times at
various stages in the development of the informa-
tion on the process. This was to allow them to get
a feel for the increasing accuracy of their cost
estimates as the project progressed. This also
allowed them to go through the iterative process
of re-evaluating and remodifying their studies, an
experience needed in design.
In addition to their written and oral weekly
progress reports, which were not allowed to be-
come too time consuming, the students had an
interim report and a final report for this process
development stage. The interim report was due
after about four or five weeks. Format or stan-
dards of this report were not made too rigid.
The quality of the final report due at the end of
the first quarter, or term, was more rigidly con-
trolled to assure that the students had developed
all the essential information. Also effort was made
to encourage completeness, clarity, usefulness,
and workmanlike appearance.
This report contained a process study, includ-
ing heat and material balances, chemical flow
diagrams, and sample calculations. The economic

studies mentioned previously were included.
Plant location was also shown. Tied in with these
studies was a write-up on the experimental find-
ings in the laboratory with an interpretation of
the data. Chemical and physical properties of the
various materials processed, and needed for de-
sign purposes, were required, and salient design
problems which the students were able to antici-
pate were discussed. Also included was a discus-
sion of safety considerations specific to the pro-
cess. This report ,then, containing the students'
conclusions and recommendations, constituted the
design criteria which they would use in the second
phase of the program concerned with the plant
design proper.

In the second term the students, remaining
in the same groups that were assigned in the first
term, continued with more specific- studies on de-
sign, where they actually took the criteria they

. . . An attempt was made to have the students go
through economic studies a number of times at various
stages in the development of the information on the

had developed and went through the project work
required. This work consisted of roughly two
aspects. One aspect embraced project planning
and administration. There were instructions on
acquisition of equipment and services for the
erection and start-up of the plant, on engineer-
ing law, erection supervision, and plant commis-
The other aspect of this term was the process
design. This included equipment design calcula-
tions. The tools used in these design calculations
were very varied and actually drew on every
course that the students had in their engineering
program. They included calculations in fluid flow,
heat transfer, mass transfer, reactor design,
economic balances, mechanics of materials, ther-
modynamics, and many other disciplines. Other
disciplines are being introduced as time goes on.
For example, the students are showing increasing
interest in process control theory. In addition to
these design calculations the students were made
to simulate, as much as possible, all the services
which a chemical engineer and related professions
would have to perform on a design project. In
their final report they included an engineering


work progress schedule with the help of critical
path planning. The site selection made in the first
phase had to be expanded from general geogra-
phical considerations to the specifics of exact loca-
tion of a site. The material balance had to be
worked out in more detail. A more exacting and
usable chemical flow diagram was prepared, and
the students were shown how to prepare a me-
chanical flow diagram as well. However, piping
drawings, piping specifications, and pipeline des-
ignation lists, while discussed, were left optional,
because it was felt that this peripheral detailing
did not fit in the allotted work time. Selection of
materials of construction was included. Equip-
ment specifications had to be included on all
process equipment. For vessels this meant draw-
ings showing wall thickness, temperature and
pressure requirements, location of nozzles, and
other process details, but fabrication details were
not required. For other pieces of ready made
equipment, such as heat exchangers, pumps, and
agitators, they had to fill in standard check lists
of specifications with proper back-up informa-
tion. More complete physical and chemical prop-
erties of materials used in the process were in-

In the second term the students continued with more
specific studies on design . . .

Operating instructions in reasonable detail
were prepared for use by production supervisors.
These included a process description, start-up,
operation, and shut-down procedures, and main-
tenance instructions. Diagnostic instructions were
prepared for anticipated operational difficulties.
Also included were safety instructions suitable
for supervising operators to prevent injury and
losses due to chemical and mechanical hazards.
The students were shown how to prepare an ex-
tended equipment list, which also fills a function
in acquisition and cost control.
A final economic study was made showing a
manufacturing cost estimate in as much detail
as possible. This included a final study of return
on investment as it varies with the capacity.
Our students did not become involved in more
detailed civil, electrical, and mechanical engi-
neering. Their work, for example, would be con-
fined to specifying weight loads without design
structures, specifying electrical loads without de-
signing distributions, and specifying steam re-
quirements without designing boiler plants. In

. . . Operating instructions in reasonable detail were
prepared . . .

lectures, however, they were made aware of the
need and significance of these other engineering
We have made some attempt to have the stu-
dents work with engineers designing in industry.
Success in this direction depends greatly on geo-
graphical location. We have had limited success
with architect-engineer firms in our area, and we
hope to have greater success in the future.

The full morphology and anatomy of design
was followed in this program to a reasonable de-
gree. The students' operations matched with the
seven basic phases outlined by Professor
Asimow', 2 in his Morphology of Design.

While lectures were given during this program
on principles and helpful information useful in
design, the students' main exercise was the design
of a specific chemical plant. We found that many
of these ideas emphasized during the project are
difficult to lecture in an interesting manner. Some-
times the students do not see the light until years
after they have graduated, at which time they
come back and thank the teacher. Lectures on
theory and practice of design should be timed,
if possible, so that the subjects discussed come
up at the same time they occur in the project
As regards computers, it is not recommended
that it be made into strictly a computer course.
The policy has been to encourage the students to
use computers when a computerized problem is
indicated. This might occur where there are long,
detailed iterations required, or where some logical
decision network is needed. Computers should not
become the be-all and end-all of the program, but
rather they should be presented as a valuable
tool of serious philosophical portent.

1. Asimow, M., Introduction to Design, Prentice-Hall,
Englewood Cliffs, N. J., 1962.
2. Rosenstein, A. B., and Heinz, W. B., UCLA Workshop,
Proceedings of Third Conference on Engineering De-
sign Education, Carnegie Inst. of Technology, Pitts-
burgh, Pa., July 12 and 13, 1965.






Louisiana State University,
Baton Rouge, Louisiana 70803

T HE INSTRUCTIONAL USE of analog and digital
computers in today's engineering curriculum
is assuming an ever increasing role. This situa-
tion has apparently arisen out of necessity,
mainly because we tend to emphasize more so-
phisticated mathematical techniques as the basic
key to comprehension and learning. Whereas in
the b.c. era (i.e., before computers) undergradu-
ates lived primarily in the "steady-state world",
the contemporary student investigates the dy-
namics of processes in which the "steady-state"
assumes its proper perspective as a limiting con-
dition. Therefore the introduction of computers
into the curriculum has been a major factor in
fostering the evolution of engineering instruction
from the art into the science stage.
In developing the full potential of computers
and associated mathematics to meet the challenge
of present day curricula, the possibility can exist
that too much time is devoted to the tools and not
enough to the subject matter. Therefore our
purpose in this article is to indicate how we at
LSU are attempting to bridge such a gap. Toward
this end we require fundamental courses in ana-
log and digital computation at the sophomore
level, followed by advanced (hybrid) computa-
tion and applied mathematics for qualified stu-
dents. We not only provide instruction on the use
of these tools, but encourage such usage through-
out the educational program with suitable appli-
cations in other coursework.
Employing practical demonstration examples
in these advanced courses which submit readily
to analysis by a variety of methods from classical

*Presented at the ASEE Gulf Southwest Regional Meet-
ing, Texas A&M University, March 22, 1968.

mathematics to computer implemented numerical
techniques, we stress the problem solving ap-
proach in each case. Thus a student's academic
training provides the following two-fold method-
ology to support his professional capabilities:
* He must develop the ability to study a situation,
evaluate facts and formulate the problem to be
solved based upon sound and fundamental engineer-
ing principles.
* Once the problem has been defined quantitatively
in engineering terms he must know, and be able
to apply the tools with which to effect a reasonable
Obviously one without the other is less than satis-
In order to stimulate our students and to
gage their progress in adapting to new situations
it is instructive to challenge them with a "realis-
tic" problem of a normally non-academic origin.
The following example is of this type, having
been culled from an article in the literature. We
first describe the problem, develop the mathe-
matical model subject to reasonable assumptions,
and then outline several solutions applying ana-
lytical methods as well as various computer

In a continuing effort to improve both the
quality and performance characteristics of its
packaging, a soft-drink corporation desired to
consumer field test a newly designed returnable
bottle for one of its products. Specifically, it
wished to ascertain whether or not the new
bottles would have a significantly longer service
life than the bottles presently in use.
During the field test new bottles were inserted
into the filling line at a specific daily rate over a
period of several days. The filled containers
(both new type and old bottles interspersed)
were displayed for sale as usual in the market-
place. The "empties", returned by the consumer
to the market after a reasonable delay period,


David B. Greenberg obtained his BS, MS, and PhD
degrees all in ChE from Carnegie Tech, the Johns Hopkins
University, and Louisiana State University, respectively.
He is an Associate Professor at LSU in Baton Rouge and
is Associate Editor for the journal, SIMULATION. His
research interests include analog, digital, and hybrid com-
putation, bioengineering, and transport phenomena.

Larry Morton is currently Director of the Computer
Research Center at LSU. He received the BSChE from
the Georgia Institute of Technology and the MS and
PhD ('65) degrees from Louisiana State University. He
has taught courses in computer science, unit operations,
and engineering use of digital computers. His interests
include computer operations, software, applied mathe-
matics, and unit operations. (left photo)

were then sent to the plant for refilling. Data
collected consisted of a daily count of the new
type bottles as they passed the capping station
during the bottling process. At this monitoring
point both newly inserted bottles as well as bot-
tles that had completed one or more field cycles
were included in the count.
In order to obtain a quantitative evaluation
of the test results it is necessary to model mathe-
matically the complete cycle, then define and
evaluate the performance parameters. To facili-
tate the development of a mathematical model the
following simplifying assumptions are made:
a. The rate of purchase of test containers is directly
proportional to the number of these bottles in the
marketplace at any time.
b. The losses at the plant and market are negligible
compared to the losses sustained in the home by
the consumer.
c. There is a constant (average) time delay between
purchase and re-insertion of the bottle in the mar-
ket. This delay accounts for consumption of the
product by the purchaser.
d. Time delays in the bottling plant are negligible
compared to that by the consumer described in
(c) above.
With these assumptions the modified process


Figure 1. Flow Diagram for the Mathematical Model

cycle is described by Figure 1 from which the
model is to be derived.


An overall material balance for new type
bottles on the market yields:

Rate of
accumu- Rate of Rate of re-
lation - sale + insertion +
dH(t) - A(t) + A,(t) +

Rate of new


Focusing on the right hand side of Equation (1)
the functions are evaluated as:

Rate of sale. If H (t) represents the number
of bottles in the market at any time t, then by
assumption (a) above

A2(t) = kH(t) (2)
where k is the constant of proportionality.

Rate of new insertion. For purposes of the
field test, bottles will be inserted at a constant
rate C (bottles per unit time) over a given period
0, thus
Al(t) =C for 0 and,
A1(t) =0 for t> 0 (3b)
Rate of re-insertion. If f is the fraction of
bottles lost per cycle, the input to the bottling
plant becomes the product of the fraction re-
turned (1-f) and the number of empty bottles re-
turned by the consumer, or
A4(t) = (1-f) A, (t) (4)
But noting that A, is evivalent to the rate of



sales A2 displaced in time by the delay period r,
we have
A4(t) = (l-f) A2,(t-r) = (1-f) kH(t--) (5)
The substitution of these terms into Equation
1 yields:
dH - kH (t) + (1-f) kH (t-r) + A, (t) (6)
Equation 6 is the mathematical model describ-
ing the process and is characterized by the three
parameters k, f, and T which must be evaluated
by field test data. Clearly from the model it is
obvious that k is a first order rate constant and
the term 1/f represents the average number of
cycles a bottle makes in the field before becoming
lost. This latter term becomes, therefore, the
criterion for comparison between old and new
type bottles.
Data (Field test data is given in Table 1)
1/f (old type bottles) ~_ 3-4 cycles.
C = 200 new bottles/day inserted into cycle.
0 = 5 days (at a rate of 200/day for 5 days, a total
of 1000 new type bottles are put into circulation for
the test).
r = 7 days (this represents the normal time be-
tween shopping trips for the average family).

Table 1. Field Test Data

Time Carrier Count Rate
(days) (per week) (cumulative)

7 0 0
12 56 56
19 164 220
26 183 403
33 178 581
40 140 721
47 145 866

Because of the transport delay term, H(t-T),
the solution can be most readily handled by La-
place transform methods. It should also be noted
that Equation 6 lends itself to solution by finite
difference methods on the digital computer by
which the authors of the original article obtained
their results. We define the Laplace transform
of each term and make appropriate substitutions
in Equation 6 to obtain the following algebraic

sh(s) = -kh(s) + ae STh(s) + (le- ) (7)
where a = (1-f)k, and H(0) = 0 for this situation
Equation 7 when solved for the transformed
dependent variable h(s) becomes:

h(s) = - (8)
(s+k -ae-7
The analytical solution follows by first rearrang-
ing, then expanding Equation 6 using the bi-
nomial theorem, and inverting term-by-term to

-� : (1i-f "a 0-n) k o k(t-.T-e)' ( t- e-) j 5:'( 21 n(t -T) (9)
where u( ) = 0 fr < -0
where (t- fo-9) - t is the Heaviside unit function.

The complete solution to this problem requires
that parameter 1/f, the average number of cycles
per bottle, be evaluated. To obtain this term we
must first compute both Hr = H (t-r), the time
displaced bottle concentration in the market, and
Hc(t-r) the cumulative total of bottles progress-
ing through the bottling plant. By calculating the
absolute value of the difference between Hc(t-r)
and He the cumulative field test data, an error
function E (t) can be obtained. The correct values
of k and f are therefore determined by varying
these parameters systematically so as to mini-
mize the criterion E(t) over the entire test
period. With Equation 9 as a starting point it is
evident that such a task can be quite formidable
in terms of time even for the digital computer.
A more reasonable approach using statistical-
numerical methods follows:


We first define an expression for the cumula-
tive total of bottles in the bottling plant in terms
of the bottle concentration H(t-r)

Hei = I (1-f) kH(t.-T)
1-1i -


where the summation ranges over daily values of
concentration up to time ti. As before the error
function is calculated as the difference between
Hc, the analytical, and He, the cumulative field
test data. We require values of k and f to mini-
mize E(t) summed over all data points.

E(t) - Z (Hei-Hei)2 (11)
where the index m represents the total number
of data points collected in the field test and E (t)
is a function of f and k. By the method of least
squares a pair of equations may be derived by
differentiating E(t) with respect to both f and
k and setting the results to zero. Before differ-
entiation Equation 11 is expanded by Taylor's
series about some point z. We then differentiate


E (t) with respect to each parameter, equate the
resulting partial to zero, and obtain the follow-
ing linear equations:

feii) ^- ^ 2 + n ( a ^) ) (12a)
m gIii ) k
ai, . f ( 1I+ 6ki -2' (12b)

where Af = f-fz and Ak = k-k,.
Initial estimates f, and k. of the unknowns f and
k at some arbitrary point z, but sufficiently close
that convergence will occur, are used to evaluate
all sums in Equations 12, from which Af and
Ak are computed. Application of these incre-
mental changes results in estimates fz+, and
k,+, which should converge eventually to f and k.
By taking derivatives of Equation 10 with
respect to the parameters f and k we obtain the
following expressions:

= -c [ (n+l) -(1-f)n fu +e-kaj(ekvaj- ) (13a)

ag Hic i -kaj n k b.
j 1 n 0cr
k - 1. 0 _1f),, k ke 'r 3 +
S(6-a l - -l)u - J ] (13b)

n k'(t.-nT-0)r n kr(t -nT)r
uere a.- ---1---- a - E I
S rJ 0 ;- r -0 r
a = t - nT ; b = t - nT-8
Hleaviside unit functions:
u. = u(t. - nT) ; v = u(t - nT- )

Equations 12 and 13 are in a form which permits a
digital computer solution. Given m cumulative field test
data points and reasonable initial estimates for fz and k.,
the partial in Equations 13 may be calculated for each
point. Cross products of these partial at each point are
accumulated according to Equation 12.
In order to test the convergence of this method, initial
values f, and k, were taken at values given in Table 2
following. This Table also shows the final approxima-
tions f and k and the number of iterations required to
achieve 3-place accuracy. The time required on an IBM
7040 computer for each case is given.

Table 2. Convergence Values, Digital Solution

Initial Iterations Time Final
Estimates Required Required Approximation

f. k" sec f k

.058 .0293 22 61 .1636 .03701
.239 .043 21 59 .1643 .03704
.1 .01 26 72 .1636 .03701

Today's engineer must have a solid foundation in
applied math to avoid absolescence in the light of
advances in science and engineering . . .

In all cases above the computing time to con-
verge to a satisfactory result was on the order of
one minute. Certain steps could be taken to speed
up convergence, but unless the problem is one
which would be used frequently, there is little
incentive for the extra programming effort. (Pro-
gram documentation and sample problems are
available from the authors for interested read-


From the student's point of view analog
solution methods are often the most interesting,
for the system model is programmed directly on
the computer which responds (hopefully) to per-
turbation as does the real physical system.
Furthermore, in this case there is considerable
man-machine interaction, because the student
forms an integral part of the information feed-
back loop.
In programming this problem for the analog
the basic equations to be considered are Equa-
tions 6, 10, and 11. We perform the task of mag-
nitude and time scaling and rewrite them in in-
tegral form below.

[.01H] = - t{l10l (10k)[.01H] + 10-l<10k(l-f)>[-.01HT]+(10-3Al)[-10]}dt (14)

[.OlHc)= - t1o_1

[e] = - {[-.01Hc] + [.OlHe]l (

[E] t .2 dt (17)

The parameter [e] represents the instantan-
eous difference between model and experimental
value of the cumulative total of bottles, and [E],
the criterion function, is proportional to the
accumulated total error between these terms.
In the mechanization of these equations an
electronic switch, triggered by the polarity
change of a ramp function signal, was used to
generate the discontinuous function A1(t). A
variable diode function generator provided an
approximation to the experimental field test data,
He, and the transport delay was simulated by a
fourth order modified Pade circuit. As indicated
by the output curve, H (t-r) of Figure 2, this
approximation is quite adequate for the low fre-


Time, days

Figure 2. Output Curves, Final Run

quencies involved here (time scale for this ex-
ample was chosen as 1.0 seconds of compute time
per day of problem time).
The analog procedure, a global search tech-
nique, is relatively straight forward. Computing
in the repetitive operation mode, the parameters
k and f, each isolated on a potentiometer, are
varied in alternative fashion, one discretely and
the other continuously and E (t) values are ob-
tained visually on the oscilloscope. When an ap-
proximate absolute minimum has been estab-
lished, a few real time computer runs can be
made to obtain a more accurate value of the cri-
terion function. Three place accuracy in the
answer is readily attainable with a digital volt-


The analog output for the final real-time run
is presented in Figure 2. For purposes of com-
parison the analytical solution which was eval-
uated on the digital computer has also been in-
cluded. As the figure shows both results predict
accurately the peak of the H (t) curve and the
slight dip beyond that point. In general, the
agreement between these two results is excellent.
It is also apparent that the analog and analyti-
cal solutions for the cumulative field data,
Hc (t-r7-) curve, also show close agreement. In com-
paring these results with the analogous experi-

mental data points also plotted in Figure 2, we
observe that for these final k and f values the
mathematical model provides a reasonable curve
fit except initially where the rate of slope change
is greatest. The difference here is due in part to
the imperfect nature of the transport delay simu-
lation circuit employed; the initial transients of
which are clearly evidenced on the curve of
Figure 2.
A comparison of the final parameter values
is given in Table 3. The approximately 7% lower
value of the parameter f obtained from the analog
solution arises from the fact that experimental
field data points were fit by a series of 10 straight
line segments with the VDFG. On the other hand
an almost exact fit using a 7th degree polynomial
was employed to fit the data for the analytical
solution. Despite these differences the final result
in all cases suggests that the new type contain-
ers have a service life of more than 50-75% longer
than the original carriers.

Table 3. Comparisons of Final Parameter Values


Analog Digital Analytical

k 0.036
f 0.152
1/f 6.0



In this article we have attempted to show by
a specific example how digital and analog com-
puters are being used in the undergraduate engi-
neering curriculum at LSU to enhance instruction
in applied mathematical methods. This particular
problem, although relatively elementary from a
mathematical point of view, has been useful in
developing and exercising student proficiency in
the following areas:
* The use of Laplace Transform techniques to obtain
an analytical solution.
* The use of a statistical numerical method (least
squares) to effect a digital solution.
* Finite difference methods (presented in the original
publication) for the digital computer.
* Digital programming logic for the analytical as
well as the two numerical methods.
* Analog programming techniques: the use of analog
logic, switching, and other non-linear equipment,
the development of a method of transport delay
* The use of a simple optimization method.


Analog and digital computers are needed in today's
curriculum because we emphasize more sophisticated
math techniques as the key to comprehension and

Of equal importance from an instructional
standpoint in the fact that this exercise, of an
interdisciplinary nature, is a very practical indus-
trial problem that any professional engineer
might encounter. It follows therefore that the
problem is completed when an interpretation of
the mathematical solution invokes a practical
engineering decision. We have found with this
problem as with others which we have developed,
that this "practical flavor" or realistic aspect has
been an important factor in eliciting a most fav-
orable response from among our students. As a
follow-up to the problem presented here it was
interesting for our students to discover that simi-
lar mathematics were reported by T. Wood,, who
investigated first order irreversible chemical kine-
tics in a series connected well-mixed and tubular
reactor system.

1. Barnes, B. G., R. E. Fuchs, and R. A. Somsen,
TAPPI, 50, 72A (1967).
2. The analog computer solution: Simulation, Vol. X,
No. 4, 157 (April 1968).
3. Wood, T., Nature, 191, 589 (1961).

(Continued from page 125)
CP-3. Removal of Water Vapor in Freeze-Drying.
Process Synthesis (Kumar and King). 89 pages
This problem requires that the student generate and
give a rough, evaluative screening to different approaches
to the removal of water vapor which is being continually
generated in a vacuum chamber, in this case a freeze-
drying process. Initial attention is given to the concep-
tion of various techniques for removing water vapor.
Then preliminary analyses are made of the proposed
schemes to check the feasibility of each process, to gauge
its requirements in terms of materials and energy, and
to determine the merits and drawbacks of the proposal.
CP-4 Desalination by Reverse Osmosis. Process Syn-
thesis and Optimization (Thompson and King).
60 pages ($2.00).
The student is presented with the basic physical con-
cepts underlying reverse osmosis and is given some indi-
cation of the difficulties which may arise and the factors
to be compromised in a reverse osmosis desalination proc-
ess. The principal problem is to determine the best con-
figuration of a reverse osmosis unit so as to achieve
minimum energy consumption. The student must recog-

nize the mechanisms by which design parameters influ-
ence pressure drop and water flux. He must ascertain
which decisions can be made on the basis of qualitative
or common sense thinking rather than through the opti-
mization of formal mathematical equations. Finally, he
can determine optimum values of the remaining decision
variables through either mapping or a formal optimiza-
tion procedure.

CP-5. Sulfate Removal from Brackish Water. Process
Synthesis (Forrester and Lynn). 50 pages
This problem concerns the synthesis of a process
which removes sulfate from a brackish water supply and
which permits the recovery of both the potable water and
its previous mineral content. The student is given several
existing processes with which to work and is asked to
combine them in the best way. Several different elements
of process engineering are involved, including develop-
ment of process flow sheets and mass balances, considera-
tion of the heat requirements of different processing se-
quences, thermodynamics of reactions in aqueous solu-
tion, and consideration of pollution potentials during a
process design.

CP-6. An Evolutionary Problem in Process Simulation.
Process Simulation (Grens). about 55 pages
In this problem a number of basic aspects of
process simulation are incorporated in a series of com-
puter implemented projects, which evolve from basic
equilibrium vaporization calculations to simulation of a
process with material and enthalpy recycle loops. The
problem is based upon a hydrocarbon absorber-stripper
system, with absorber and stripper each having only one
stage. First the student is asked to develop efficient
procedures for equilibrium flash computations. Then he
must develop simulations for the absorber-stripper sys-
tem, with alternative convergence techniques being used
and compared. Finally interstream heat exchange is
added to the problem, and simulations of the dual loop
system (material and thermal recycle loops) using both
direct substitution and convergence accelerating tech-
niques are sought. Development of efficient modular
simulation programs is stressed throughout.

CP-7. Removal of Inerts from Ammonia Synthesis Gas.
Process Synthesis and Analysis (Alesandrini,
Sherwood and Lynn). about 60 pages ($1.75).
The purge of methane and argon from ammonia syn-
thesis recycle gases causes a substantial simultaneous
loss of hydrogen and nitrogen. This problem pursues the
question of somehow obtaining a partial or complete
separation of methane and argon from the other gases,
by taking advantage of the unusual vapor-liquid equili-
brium behavior of the system of these gases mixed with
ammonia. Successively better process modifications are
developed and are explored through energy and mass
balances, followed by preliminary equipment sizing and
economic evaluation. A computer calculation of the be-
havior of an absorber-stripper may be included at the
discretion of the instructor.


There are more than 100 billion
barrels of potential new oil on the
North American continent. But it
will have to be dug-not pumped-
out of the ground. It's in the form of
low-grade hydrocarbon solids. Yet,
the world needs so much more

oil in years to come that Atlantic
Richfield is already working on
ways to extract it and get it moving.
Projects like this take imagination
and fresh viewpoints. The kind that
come from young innovators like
yourself. We need you-and your

kind of ideas-to keep making
great things happen. Talk to our
interviewer when he's on your
campus. Or write to:
Manager Professional
Recruitment, 717 Fifth Avenue,
New York, N.Y. 10022.

the new AtlanticRichfieldCompany *

problems for teachers

Professor R. R. Davidson of Texas A&M
University comments on Professor A. J.
Brainard's problem in the Spring issue
of CEE.

After hearing Dr. Brainard's talk "Does the
Entropy of a Compound System Always Reach
Its Maximum?" at the February meeting of the
AIChE in Atlanta, I gave my graduate thermo
class a quiz containing the following pair of
1. Given the first and second law and that internal
energy and entropy are state functions, show that for any
process in an adiabatically isolated system AS>O.
2. Given a system comprised of two chambers sepa-
rated by a freely moving adiabatic wall or piston. The
entire system and each chamber is adiabatic. Both cham-
bers contain gases, but the pressure is higher in Cham-
ber I and the piston is kept from moving by a stop
(Brainard's Figure 1). If the stop is removed so that the
piston can move freely until it comes to rest with the
pressures in the chamber equalized, will the change in
entropy be less than, equal to, or greater than zero in
(a) The entire system
(b) Chamber I
(c) Chamber II
(d) Is the entropy of the entire system necessarily
at a maximum?
The answer to (a), (b), and (c) follows
directly from the results of Problem 1. Since the
initial pressures in Chambers I and II were
unequal, the process was irreversible, and since
the entire system as well as Chambers I and II
were each an adiabatically isolated system, the
entropy change in each case was greater than
The answer to Problem (d) is no, because the
maximum entropy is reached when thermody-
namic equilibrium is reached and this system is
not necessarily in thermodynamic equilibrium
because the temperatures in the two chambers
are not necessarily equal. The word necessarily
is used because one might, by manipulating the
initial temperatures, obtain a final state in which
the temperatures are equal.
The final state in this problem cannot be
obtained by thermodynamics. Given the weight
of the piston, its coefficient of friction, the
dampening factor for the gas and its PVT prop-
erties, the final position of the piston could be
calculated, but this is a problem in mechanics,

not thermodynamics. Thermodynamics can only
say that the final entropy is greater than the
initial value and less than the value that could be
calculated if heat could flow freely through the
piston giving a uniform temperature throughout
the system.
I think it should be stressed that our inability
to obtain a thermodynamic solution for the final
adiabatic state is not due to a lack of thermo-
dynamic rigor, but to the fact that the solution
does not lie within the realm of thermodynamics.
In general thermodynamics can only give an-
swers for equilibrium states and this means,
among other things, that the temperature is
uniform throughout the system.
After the quiz a student posed a good question.
What if different gases were on each side of the
piston, wouldn't we have to let the gases mix before
thermodynamic equilibrium could be obtained?
The answer is yes and no. It is true that if we
punched a hole in the piston the entropy would
further increase. While we might consider this
final state to be the global maximum of the
entropy, the final state without mixing, but at
uniform temperature, is a local maximum hav-
ing a thermodynamic solution. It is unlike the
state in which only mechanical equilibrium is
reached for which there is no thermodynamic
solution at all.
The system at uniform temperature is at a
definite state before and after the hole is punched
in the piston, and so the entropy of adiabatic
mixing can be thermodynamically calculated.
However, with the adiabatic piston, the final
temperatures are undefined because the internal
energy of the total system, though known and
constant, can be distributed in an infinite num-
ber of ways. Thus we see that imposing an
impermeable wall is not like imposing an adia-
batic wall.
It was interesting to note that while many
students missed part (d), a number also missed
part (b) and (c). They seemed intuitively to
want to conserve entropy, and they found it
hard to believe that it increased on both sides of
the piston even though they had just proved it
in Problem 1.




N J1 laboratory



Pennsylvania State University
University Park, Penn. 16802

Various views have been presented about the
ultimate educational aspects of an undergraduate
Chemical Engineering Laboratory course. In
most cases, the questions of prime importance
* The size of equipment to be used?
* Should all experiments be functioning normally?
* At what point in the curriculum should the course
be taught ?
* What theoretical aspects should be covered?
* The type of reports required and the basis for
grading ?
Some chemical engineering faculty members
feel the laboratory should involve equipment of
pilot plant size mainly to provide the student
with a feeling for the problems he may encounter
in industry. Yet, does the student actually benefit
from operating equipment requiring a full labora-
tory period to attain steady state conditions? Or
would the student obtain a better insight to the
problems he will eventually face in industry if
sufficient data can be obtained to enable him to
tie together the loose ends of theory dangling
in his subconscious?
Other faculty members feel that the equip-
ment should contain "bugs", thus requiring the
student to determine the reasons for poor per-
formance. Thus, before the student can obtain
meaningful data he must locate and fix the
trouble. This procedure again may consume
much of the available laboratory period and re-
sult in insufficient data for writing a meaningful
report on the experiment.
Another method would be to have the equip-
ment functioning normally at the outset of the
experiment. After the student has obtained
sufficient data, the faculty member can demon-
strate the effects of these so called "bugs." The
student, if confronted with similar problems at
a later time, would then know the necessary

Dr. Charles C. Peiffer graduated from Lehigh Uni-
versity in 1951. He worked with Atlas Chemicals and the
U. S. Army before joining the Petroleum Refining Labora-
tory of Penn State in 1956. He was awarded the PhD de-
gree in 1962 .and joined the faculty at Penn State in 1963.

steps to be taken to correct the malfunction. In
this way he not only ties together loose ends of
theory but also obtains some practical experience.
Some ChE Departments conduct their labora-
tory courses during the summer vacation period
between the junior and senior years. A program
of this type will permit the utilization of larger
and more complex equipment by operating such
units continuously for 16 to 24 hours. However,
the same principles can be covered in smaller
equipment in two eight-hour laboratory periods.
This would then leave the summer between the
junior and senior year available to the students
to obtain summer employment in industry. Since
chemical engineering is so diversified, such indus-
trial experience is invaluable to the student in
helping him decide which area of specialization
would best meet his interests. Other departments
incorporate the laboratory with the unit opera-
tions courses, thus limiting the experimental pro-
cedures covered to the theory covered in these
courses. If the majority of theoretical aspects
covered in the ChE curriculum are to be incorpo-
rated in a laboratory program, a course separate
from the theory courses is most suitable. A ChE
laboratory could be given during the senior year
in two separate courses. This would permit
sufficient time to incorporate experiments per-
taining to the unit operations courses, as well as
kinetics, process dynamics, and other theory
After having been in charge of an under-
graduate ChE laboratory course for the past six
years, under varying instructional conditions and


while utilizing various sizes of equipment, this
author has developed the following views.
During the first two years, the writer while
in charge of the laboratory, required each student
to perform a total of sixteen experiments related
to the unit operations theory courses. These
experiments were performed during two ten-
week terms with the students meeting two four-
hour laboratory periods for each experiment.
Some of the equipment was of sufficient size
and complexity that two-thirds of each labora-
tory period was spent obtaining steady-state con-
ditions. Other experiments were performed on
smaller pieces of older equipment in which cer-
tain "bugs" would inherently be present. As a
result of both types of equipment, it was impos-
sible for the students to obtain more than one
set of data in each laboratory period for these
particular experiments. Thus, the students sim-
ply became familiar with the operating proced-
ures and gained no insight as to the optimum
operating conditions. How can a student write
a meaningful report with one set of data?
Early in 1965 plans were made for an addi-
tion to the then existing facilities of the ChE
Department which had been completed some five
years earlier to accommodate the graduate pro-
gram. The ChE Laboratory, previously housed
in a classroom building separate from the ChE
facilities was to be located in the new addition.
It was necessary to plan a room of sufficient size
to house the experiments in use, or to design new
experiments for the allotted space, which would
adequately coincide with the theory covered in
the unit operations and related courses. The
latter approach was followed. The new unit was
completed in August of 1968 with the first labora-
tory course taught the fall term of 1968.
During the interim period between 1965 and
1968 new experiments were designed with their
incorporation into the then existing program.
The older experiments were first replaced, at the
rate of two to three each calendar year.
Concurrently, it was decided to have the stu-
dents perform the required experiments during
one eight-hour period rather than two four-hour
periods. This change allowed the students to
obtain more sets of data on the larger and more
complex equipment. However, in some cases,
the data were yet of insufficient quantity for the
student to determine optimum operating condi-
tions. It was, therefore, decided to design equip-
ment on a smaller scale where possible, and less

complex. When the complexity or size of the
experiment could not be lessened, two eight-hour
periods were allowed for it.
These changes coupled with the new equip-
ment, relatively free of "bugs," permitted the
students to obtain sufficient data to make a com-
plete analysis of the situation confronting them.
The program now in effect consists of two
two-credit courses taken during the senior year.
The first course involves the following experi-
ments that can be completed in one eight-hour
laboratory period and covers areas of chemical
engineering involving (1) vapor-liquid equili-
brium, (2) filtration at constant rate and con-
stant pressure, (3) nucleate and film boiling,
(4) continuous transport of solids, (5) catalytic
dehydration of an alcohol combined with analysis
of products by gas chromatography, Figure 1,
(6) analog computation, (7) batch reaction ki-
netics, and (8) continuous stirred tank reaction
systems (Figure 2).
The second course involves experiments per-
formed during two eight-hour periods and covers
areas of chemical engineering involving (1) ve-
locity profiles and pressure drop studies, (2)
mass transfer coefficients by use of wetted wall
columns, (3) liquid-liquid equilibrium and ex-
traction, (4) distillation in a sieve tray column,
(5) process dynamics (Figure 3), (6) heat ex-
change coefficients for both heating and cooling
in 1 - 2 pass shell and tube heat exchangers
under laminar and turbulent flows, (7) economy
studies in a multiple effect evaporation system,
and (8) batch and continuous stirred tank reac-
tor systems.
In the first course each student performs all
of the listed experiments with the results re-
ported by each student in the form of a technical
letter (short form report).
In the second course each student performs
four of the two-period experiments. Since a
required course on reaction kinetics appears in
the curriculum, the experiment on reactor sys-
tems is a part of both laboratory courses so that
each student performs this experiment. Each
individual presents the results in a long form or
formal report. The schedule of experiments is
so arranged that duplication of theory is not
encountered. As an example, a student perform-
ing the distillation experiment will not do the
one on extraction. Also, a student who has not
taken the theory course in process dynamics does
not perform this experiment.


The program consists of two two-credit courses taken during the senior year . . . the first course requires eight
eight-hour experiments . . . the second course allows the student to elect four sixteen-hour experiments . . .
Both technical letters and formal reports are required.

With the various changes made during this
five-year interval, both instructional and equip-
ment wise, it was found that the quality of the
reports improved tremendously. It was also evi-
dent that the students' attitude toward the labo-
ratory improved greatly when it was possible for
them to obtain sufficient data to apply the theory
they had previously studied. The overall result
was excellent laboratory performance, thus allow-
ing the laboratory instructors to place more im-
portance on report writing for determining over-
all performance in the course.
In summary it is felt that
* The equipment in an undergraduate ChE
laboratory should be of a size and complexity
to allow the student to obtain sufficient data in
the allotted time so that he can properly analyze
the situation confronting him.
* The laboratory course should be a separate
entity in the curriculum and should contain a
reasonable variety of experiments to illustrate
the majority of theoretical aspects covered in the
ChE curriculum.
* Both technical letters (short form reports)
and formal reports should be required with prime
importance for overall performance being placed
on report writing since poor laboratory perform-
ance is directly reflected in the final report.

1. Experiment on Catalytic Dehydration and Analy-
sis by Gas Chromatograph
An alcohol is catalytically dehydrated in an
electrically heated tubular reactor packed with a
basic alumina catalyst. Determinations are made
at two temperature levels and three different
liquid hourly space velocities to determine the
effect of each variable on reaction rate.
Per cent conversions are determined by vari-
ous analytical methods with the final analysis of
products formed being determined by gas chro-
matographic analysis.
2. Experiment on Continuous Stirred Tank Reactor
This is part two of an experiment on the
saponification of ethylacetate with sodium hy-
droxide. Two five-gallon polyethylene storage

Figure 1. Equipment for catalytic


tanks contain the two reactants which flow by
gravity through the respective rotameters into
the first stirred vessel. The overflow from reac-
tor one can be directed to the drain or to the

I I ,I u
Figure 2. Continuous stirred tank reactor.

second reactor. Similarly the overflow from reac-
tor two can be directed to reactor three or to the
The first week's work involves the determina-
tion of order of reaction, the reaction rate con-
stant, and the energy of activation by obtaining
batch data at three different temperatures. The
results are used to predict what should happen
in a continuous flow system, as the one depicted
above, at a flow rate and temperature selected
by the students.


The world of Union Oil

salutes the world

of chemical engineering

We at Union Oil are particularly indebted to the colleges
and universities which educate chemical engineers.
Because their graduates are the scientists who contribute
immeasurably to the position Union enjoys today:
The thirtieth largest manufacturing company in
the United States, with operations throughout
the world.
Union today explores for and produces oil and natural gas
in such distant places as the Persian Gulf and Alaska's
Cook Inlet. We market petroleum products and petro-
chemicals throughout the free world.
Our research scientists are constantly discovering new
ways to do things better. In fact, we have been granted
more than 2,700 U.S. patents.
We and our many subsidiaries are engaged in such
diverse projects as developing new refining processes,
developing new fertilizers to increase the food yield, and
the conservation of air and water.
Today, Union Oil's growth is dynamic.
Tomorrow will be even more stimulating.
Thanks largely to people who join us from leading
institutions of learning.
If you enjoy working in an atmosphere of imagination and
challenge, why not look into the world of Union Oil?
Growth...with innovation. Union Oil Company of California.


3. Experiment on the Process Dynamics of Liquid
Level Control
The dynamics involved in liquid level control
of a simple one-tank system, and a two-tank sys-
tem involving interaction are investigated.
The students first determine the relationship
between proportional band setting and controller
sensitivity or proportional gain. The transfer
functions for the transducer (converts liquid
height to psi), the control valve, and the process
are then determined.
After all transfer functions are determined,
the student then proceeds to determine the best

J _ I. II

Figure 3. Liquid Level Control.

eC 9Ale~cMaowda

mode or combined modes of control which will
result in bringing the system to the desired
operating level in the least amount of time with
minimum overshoot and oscillations.
The appropriate control equations are ob-
tained from the complete process block diagram
and experimental results are compared to theo-
retical predictions.

4. Experiment on Heat Transfer Coefficients
Two 1:2-pass shell and tube heat exchangers
are interconnected to permit procurement of the
overall heat transfer coefficients resulting from
a 1:2- or a 2:4-pass shell and tube heat ex-
Individual inside and outside coefficients for
both heating and cooling can be calculated from
the data obtained in the experiment. The stu-
dents can also determine the correction factors
involved between true countercurrent flow heat
exchangers and multipass exchangers.

5. Floor Plan of Laboratory
The new Penn State laboratory occupies a
100 ft. by 30 ft. room, partitioned into cubicles
10 ft. by 8 ft. constructed from transit sheeting
and Unistrut channels.


University of Pittsburgh
Pittsburgh, Penn. 15213

At the present time there are three universi-
ties that are offering degrees in Chemical Engi-
neering in Ecuador. There is one other university
that offers a degree in industrial chemistry based
on the European system. Two of the schools of
chemical engineering are located in the capital
city of Quito and the other is in the port city
of Guayaguil. Having two schools in the same
city producing chemical engineers in a country
where the chemical industry is next to nonexist-
ent is a bit unusual and one may question why
this development. The Politecnic University in
Quito is under the UNESCO auspices and most

George Klinzing received his BS degree in Chemical
Engineering from the University of Pittsburgh and his
MS and PhD from Carnegie-Mellon University. He spent
three years teaching and consulting in chemical engineer-
ing at Central University in Quito, Ecuador. His interests
are transport phenomena and engineering education in
and technology transfer to developing countries.
of the advisors who have served there have been
Europeans. The program of assistance to Cen-
tral University was one of the total development
of the University. To have left the School of


Chemical Engineering from this program would
have had severe consequences.
Central University has a student body of
some 5,000 students. Most of the classes are held
in the early morning from 7 to 9 a.m. and in the
late afternoon from 5 to 9 p.m. This is necessary
since the majority of the students and professors
are part-time. The part-time situation arises
from an economic need. Some of the students
must work to live and the professors must aug-
ment their meager University salaries by addi-
tional jobs. For the most part teaching at the
University is a highly prestigious matter. The
professors who thus elect to teach in the Univer-
sity are usually concerned with the education
of students.
In Chemical Engineering the number of part-
time students is not very great. Most of the
students in Chemical Engineering are full-time
although the faculty does not operate on a full-
time system.
Students in Latin America play a more active
role in University affairs than students in the
United States. At Central University in each
faculty of the University there is a student repre-
sentative on the University Council, and each of
these students has a vote on an equal basis with
deans and administrators in establishing Univer-
sity policy even in financial transactions and
possibly the hiring and firing of professors.
Temporary closure of the University for a period
ranging from a few days to a few weeks because
of political instability is anticipated at least once
a year.
In 1963 when the University of Pittsburgh
began its contract with Central University, the
School of Chemical Engineering was a part of
the Faculty of Natural Sciences and Chemistry.
The other components of this faculty were the
School of Geology and Mines, the School of Bio-
chemistry and the School of Pharmacy. The
arrangement of schools in this faculty seems like
an odd combination but this type of arrangement
often arises in Latin America. The School of
Pharmacy preceded the others in age and thus
when chemical engineering was enacted as a
school in 1950 the obvious place to put it in the
university structure was where the chemists

were. In the majority of Latin America Chemical
Engineering is a relatively new field. In 1966 the
Schools of Chemical Engineering, Civil Engi-
neering, Geology and Mines were combined into
one Faculty of Engineering. The Faculty is
headed by a dean and each school is supervised
by a director.
The program of study prior to 1966 for Chem-
ical Engineering required six years. The first
year of study was a preparatory course intended
to make up the deficiencies that existed in the
student's preparation in the secondary schools.
Chemical Engineers in developing nations do
need a different program from those in the de-
veloped countries although a certain basic core
is needed in order to call a program Chemical
In viewing the curriculum at Central Univer-
sity as well as at any of the Latin American Uni-
versities one must continually keep in mind that
state of the technology of the developing nations
is different than that of the developed. The engi-
neer in the developing nations must be educated
along avenues that are much broader so that he
will be able to cope with more of the total prob-
lem. The student must employ his ingenuity to
a greater extent when he leaves school in order
to apply the principles of his engineering educa-
tion to his developing country.
The engineering student must know some-
thing about the laws of his country in relation to
business practices, and accounting and mana-
gerial abilities are additional areas where the
student must be proficient. He will have to be
able to deal with many unskilled laborers, some
not even speaking his language.
One area that must be emphasized to the
student for progress in the developing countries
is the utilization of products natural to the coun-
try. Food processing and preservation is essen-
tial for development. This is first necessary on
a national basis then with time creating an in-
ternational market for the products. Extraction
of chemicals and drugs from local vegetation is
a very profitable endeavor and provides an eco-
nomic international market almost immediately.
A very thorough and complete geological study
must be done for the exploring of new areas for
Modifications were enacted in the curriculum
of the School of Chemical Engineering after
three years of meetings, discussions and debates


on the relative merits of most every point and
professor. The number of total hours present
in the curriculum was decreased. The program
was also modified in order to present courses in
a much better manner with the preparation of
syllabi and detailed laboratory programs with
assistants to aid with the latter. One major
change was the regulation regarding the thesis
requirement and graduation procedure. The old
regulations required that the student on com-
pletion of his course of study of six years would
prepare a thesis on a subject that was usually
an economic and engineering analysis of the pro-
duction of a material natural to Ecuador. Be-
cause of this long and involved process very few
students who finished their courses "egresados"
ever completed the tedious remaining tasks and
thus never completed the requirement for the
title of "ingeniero." This requirement was elim-
inated for the more practical program where the
student in his last year of study would choose
a thesis topic and an advisor under whom he
would work. At the finish of the thesis he would
have an oral examination. At a prescribed time
the people completing the above requirement had
a graduation. During the first of these gradua-
tions eleven people received their degrees. Most
of these had finished their course work within
the previous six years. This practical procedure
thus permits in principle the assimilation of the
graduate into the technical structure of the
country the quickest way possible after gradua-

The equipping of new facilities was accom-
plished via the funds of AID under the contract
of the University of Pittsburgh and Central Uni-
versity. Along with this grant fund Central
University also received a loan from the Inter-
american Development Bank. These funds were
used to develop the laboratories and libraries of
the School. The equipment purchased represented
a distribution of experiments in Unit Operations,
Transport Phenomena, Control and Kinetics.
Equipment for analysis, machine shop and ex-
pendable items such as glassware, chemicals and
solvents were also bought. All the books in Span-
ish in the field of Chemical Engineering and re-
lated fields were purchased. It might be noted
that this amount was quite small; thus the re-
mainder was ordered in English. These books
were catalogued and placed in the library for

Programs of assistance . . . should have high aims; . . .
and must be adapted to the culture where they are
applied . . .

student use. This is quite unique for most li-
braries in Latin America. In general, libraries
are poorly organized and students rarely can
use the books since they are under lock and key.
The reason for the latter is the ugly phenomena
of "caucion" which is a national law admin-
istered by the government whereby the person
in charge of the library and laboratories is per-
sonally financially responsible for all the items
in these facilities. If a book is lost or in bad
condition, the librarian must pay for the loss or
damage. If a piece of laboratory equipment is
broken or damaged then the same applies. The
result in this system is that the librarian and
stockroom keeper rarely let things out of their
storage areas.
The basic principle behind laboratory work
is to reenforce the classroom theory with prac-
tical experimentation. Rarely if ever did this
exist at Central University on an individual basis
prior to 1963. The normal operating procedure
was for the professor to do the experiment in
front of the class or to have a large group of
students attempt the experiment which resulted
in one or two doing the actual work. The "cau-
cion" system was one thing to hinder individual
work because of lack of equipment. When indi-
vidual work was initiated at the University, the
students progressed rapidly because for the first
time they were given the responsibility of items
of equipment. They learned to respect the equip-
ment and treat it as their own. With the enaction
of the individual laboratory early in the student's
academic career it is believed that this gap will
be eliminated.
Programs of assistance to Latin American
Universities should have high aims but should
realize that it takes time to achieve these aims.
Programs must be adapted to the culture where
they are to be applied. Imposing standards of
the developed nations on the developing is all
wrong. Curriculum changes were enacted in
Chemical Engineering at Central University
keeping this premise in mind. Student class hours
(Continued on page 152)



VALUE PROBLEMS as a Teaching Tool

for a Course in Transport Phenomena

University of Colorado
Boulder, Colorado 80302

IN THE COURSE of my chemical engineering
studies, one point of continual confusion to
me was the manner in which we simplify the
exact equations describing a process so that they
are amenable to an analytical or numerical solu-
tion. For example, in many flow problems we
can assume that the flow is fully developed. If I
had any doubt as to whether this was a valid
assumption I would consult some reference book
to find what the entrance length was for the par-
ticular flow in question. However, it was not
long before I faced the problem of determining
the validity of the fully developed flow assump-
tion for flow geometries for which the entrance
lengths were not determined; for example, coun-
tercurrent gas-liquid film flow in a duct. At this
point I was faced with the formidable task of
solving the boundary layer equations for the en-
try region flow.
Consider another example: we all have some
feel for the fact that flow through a duct can be
considered to be a two-dimensional flow if the
aspect ratio (height/width) is small. But, then
the question arises, "how small is small?" Again,
for many conventional flows we can find the
answer to this question in standard references.
However, "how small is small" for countercur-
rent gas-liquid, or liquid-liquid flow in a duct?
Time usually does not permit us to solve the
entry region flow problem or the three-dimen-
sional flow problem in order to ascertain the
validity of the fully developed flow, or two-
dimensional flow assumptions. If the solutions
to these flows were trivial we would not be
trying to justify simplifying assumptions for the
full equations describing them.
It is at this point that the more experienced
engineer attempts to invoke some physical in-
sight into the problem in order to have some

William B. Krantz is a graduate of Saint Joseph's
College in Rensselaer, Indiana (BA '61), the University
of Illinois at Urbana (BS '62) and the University of
California at Berkeley (PhD '68). He is now an assistant
professor of chemical engineering at the University of
Colorado at Boulder.
He is particularly interested in chemical engineering
education and has been active in curriculum development
at the University of Colorado. His research interests
include ecological engineering, fluid dynamics, and inter-
facial phenomena.

reasonable certainty that the assumptions he
proposes to make are valid. He probably will
scale the full equations describing the flow and
seek some criteria for discarding terms which
will simplify the system of equations to those
describing fully developed flow or two-dimen-
sional flow.
Although the practicing engineer is continu-
ally faced with justifying the simplifying as-
sumptions he invokes to solve the system of
equations describing some process of concern to
him, the conventional chemical engineering cur-
riculum has given him little or no practice in
doing this with any certainty. Even some of our
widely accepted and highly acclaimed texts such
as "Transport Phenomena," by Bird, Stewart
and Lightfoot' are quite prone to say "neglect
axial diffusion," "neglect viscous heating effects,"
etc. The chemical engineering graduate has had
little experience in determining when such as-
sumptions can be invoked in practice.
A systematic method of scaling a problem to
determine when a simplified set of equations may
describe a process has been described in an
article by Hellums and Churchill.2 However
their article is mainly concerned with using this
method to determine similarity variables for
partial differential equations. Although these


authors mention the applicability of their method
to achieve "minimum parametric representation"
of a problem, they offer no examples to illustrate
the method for this purpose.
In an attempt to use this method as a teach-
ing tool in my first year graduate course in trans-
port phenomena, I have developed several
example problems illustrating the utility of this
method for obtaining the minimum parametric
representation of a problem. Once having the
minimum representation, it is easy to ascertain
under what conditions the set of equations will
simplify to a form more amendable to solution.

N PRESENTING this material to my class, I first
attempt to apply it to problems for which the
students have a good physical feel. A typical
example here might be the highly viscous flow
(lubrication flow) between two slightly inclined
flat plates. The student immediately realizes that
many of the assumptions we make for flow be-
tween two parallel flat plates can probably be
invoked for this flow problem as well. However,
he is not quite certain of how much relative
inclination of the plates he can tolerate or how
high the Reynolds number can be, before these
simplifying assumptions begin to become ques-
tionable. I use a systematic approach to scaling
the equations to give him a firm feel for the as-
sumptions he proposes to make.
After a few problems such as this, I present
an example for which the student's physical
intuition is somewhat shakey. A typical example
here might be judging when convective heat
transfer can be neglected in heat transfer with
accompanying viscous heating in fully developed
laminar slit flow. A few examples such as these,
convince most students that the method has real
utility in practice.
In what follows, I consider four example
problems which I have developed for my trans-
port phenomena course, which illustrate the ap-
plication of scaling differential equations to
obtain the minimum parametric representation.
The first two problems are ones for which the
student has some physical intuition, namely: 1)
when can the lubrication flow assumptions be
made for flow between two slightly inclined flat
plates, and 2) when can the boundary layer as-
sumptions be made for flow over a flat plate.
The last two problems are ones for which he has
relatively poor physical insight, namely: 3) when
can convective heat transfer be neglected in heat

transfer with accompanying viscous heating in
fully developed laminar slit flow, and 4) when
can penetration theory type arguments be made
for film flow down a wall with a soluble con-
The first example will be discussed in detail
to illustrate the method, whereas the remaining
examples merely will be outlined to indicate their
applicability to a transport phenomena course,
and to illustrate a few of the more subtle con-
cepts involved in scaling.

1. Highly Viscous or Lubrication Flow:
CONSIDER THE VISCOUS flow between two infinite
flat plates shown in Figure 1. At the point defined
by r - 0, x = 0, a semi-infinite thin baffle is inclined
at an angle 9 to the centerline. We wish to predict the
drag on the baffle and therefore need to derive an expres-

Figure 1. - Lubrication flow over a baffle inserted between two
infinite parallel flat plates.
sion for the velocity profile in the baffled region (0 < x
< L). Our physical intuition tells us that if the baffle is
short (i.e., L is small) we have an undeveloped flow. On
the other hand, if the baffle is very long and the Reynolds
number very small, the flow locally (at a given x) may
be similar to flow between two infinite parallel flat plates.
In this latter case, we might suspect that the simplified
equations of motion would be identical to those for fully
developed flow between two infinite parallel flat plates.
Only the boundary conditions would be altered. Despite
our good intuition in the problem we do not know "how
long is long" or "how small is small." Scaling the com-
plete, two-dimensional equations of motion will enable
us to ascertain the validity of our assumptions.
The two-dimensional equations of motion in rectangu-
lar coordinates are as follows:

S6V Vx __P + x . , 62v (

v v --- -
Vy 6y P x 6x y 6y2 6x2

0 + - = o (31
6y 6x
The appropriate boundary conditions for the flow on the
underside of the baffle are:

S= 0, v =0 aty = 0

v = 0, v =0 at y = B - (-L )x, 0 x s L


v = V [1 - (1 - y/B)2], v = 0 at x = 0

v = v (y), v = v (y) at x = L
x x y y

Boundary conditions 4 and 5 are just the no-slip condi-
tions at the solid boundaries. Boundary condition 6
assumes fully developed slit flow at the entrance to the
baffled section. Boundary condition 7 just states that to
integrate these differential equations we need to know
the velocity profiles at some other value of x, say x = L
in this case. The fact that we really do not know these
velocity profiles has no bearing on the problem.
We now introduce dimensionless variables involving
the unknown scale factors Vo, Wo, Po, yo, and xo:

v* -. , * - p* P y* = ; X* =- (8)
S- V X - W0' 0 ' YO X0
These dimensionless variables are introduced into equa-
tions 1 - 3 and the coefficient of one term arbitrarily is
made unity by multiplying through by the reciprocal of
its dimensional coefficient. The resulting set of dimen-
sionless equations is given by:

"* V y* v pWoy2 * x 2 52 2* 2 *2 *
P-v -- -v o,- 8;* + --'-- -i- -- (9
R Y. 8y 1O x 2x 6x 2
Xy 0 z
* 2* o* 2 *

Y W o 6o * - pVo2 6* V� + (10)
Y o* 0x 0, X %2 6Y* Y2 pVoxo ex.2


W y 6v
00 =
Vx *
oo 5x

The dimensionless boundary conditions are:

v 0; = 0 v= 0 aty =0
x y

v * B Bh- ~xo * L
v =0; v =0 at y - - ( )- x ; 0 5x
x y Yo yo = 0

v = - [1 y - - yy ) ; v* =0 at x* =
x w v 0
* * * * * * * L
v =v (y ); V v (y) at x
X X Y Y 0

Nondimensionalizing the equations has introduced five
arbitrary scale factors given by equations 8. These may
be considered as five degrees of freedom which we can
choose such that the demensionless terms in equations
9 - 15 have the same relative magnitude. The scaling of
these terms is dictated by the boundary conditions and
the physics of the problem. That is, for example, the
boundary conditions give us the length scale over which
the dependent variable vx goes from its minimum value
(vx = 0) to its maximum value (vx = Vm).
We therefore begin determining our scale factors by
utilizing the dimensionless boundary conditions. Note
that the boundary conditions introduce four dimensionless
groups: B/yo, [(B-h)/L][xo/yo], Vm/Wo, and L/xo. We
are free to set these groups equal to zero or unity since
they involve the arbitrary scale factors, y., x, and Wo.

(6) Our only limitations here are that we do not introduce
any mathematical contradictions or violate our physical
intuition. Therefore, let us arbitrarily say:

B/yo = 1; Vm/Vo= 1; L/x, = 1 (16)
This implies that y, = B, V -= V,, and x. = L in agree-
ment with our physical intuition on the appropriate
scale factors. For example, we could not say L/xo = 0,
for this would imply that x, was infinite which disagrees
with the fact that the baffle is of finite length, nor could
we also say [(B-h)/L][xo/Yo] = 1, for this would intro-
duce a mathematical contradiction.

W JE HAVE GAINED all the information we can from
the boundary conditions and have determined three
of our five scale factors. The remaining two scale
factors will be determined by applying our knowledge to
the physics of the problem to the equations of motion.
We know, for example, that mass must be conserved;
hence our continuity equation continues to be valid in its
dimensionless form given by equation 11. If our dimen-
sionless derivatives 8v,*/8y* and 8vx*/8x* are to be
equal we must demand that:

WoYo VmB
W.y- V -1 (17)
Voxo VoL
Hence our scale factor for vy is given by:

Vo VB (18)

This result was not obvious and we naively might have
(11) assumed Vo = Vm had we not scaled the continuity
equation properly.
In order to determine our remaining scale factor Po,
we must consider the physical situation for which we are
scaling the flow, namely, high viscous flow. This implies
that the pressure forces are balanced by the viscous
(12) forces rather than the inertia forces. Hence, if our
dimensionless pressure gradient in equation 8 is to be
of the same order of magnitude as the dimensionless
(13) viscous term 82v1*/Sy*2 (The reason for "arbitrarily"
making the coefficient of this term unity is now obvious!)
(14) we must have
Poyo2 PoB2
o -- - i (19)
(15) /WoWx. VmL

tV L
This implies that: P = ( - m) (--) (20)
Note that the scale factor on pressure is just a measure
of viscous shear multiplied by an aspect ratio. This
again agrees with our physical intuition for a highly
viscous flow, but certainly is not obvious. We naively
might have assumed Po = pVm2 which is the scale factor
appropriate to a nonviscous flow.
Introducing the known scale factors into our dimen-
sionless equations of motion yields:

S * * 2 *
Re tLy + Re(--)v - -- +
eY 8 , L x W x y

2 2 5vx

*V 1 .L . _ 31 L ,L, +
vY 7* x * Re B * 6y* 2 Re L 2


where the Reynolds number is defined by:

Re =-

Equations 21 and 22 represent the minimum parametric
representation of the problem under the conditions being
considered. For limiting values of the two parameters Re
and B/L the equations can be greatly simplified. If, for

B 2
(-) << 1 and Re (-) << 1 (24)
Lthe equations L
the equations reduce to

2 *
d v


* - a constant

6P -
* = 0
with the boundary conditions

* *
v = 0 at y =0

* h * *
vx =0 at = 1 - (1 - --)x , 0 =< x 1





We were able to make these simplifications under the
conditions given by equation 24 because our dimensionless
terms have been scaled such that they have the correct
relative magnitude dictated by the boundary conditions
and the physics of the problem.
The approximate physical conditions under which the
above simplified equations can be applied, can be deter-
mined from equations 24. We can say, for example, that:

B 0.1 and Re() 0.1 (29)
(-) 0.1 andReT

thus assuring that the terms these parameters multiply
will be at least an order of magnitude smaller than the
terms we have retained in equations 21 and 22. These
conditions then imply that:

BL = 0.32 and Re = 0.32 (30)

Physically these conditions say that the flow must be
highly viscous to insure that it can adjust rapidly to the
local infinite flat plate flow solution indicated by the
solution of equation 25. The aspect ratio B/L must be
small to assume that the entrance effects represent an
insignificant portion of the total flow regime.

2. Boundary Layer Flow Over a Flat Plate:

THE CONVENTIONAL WAY of arriving at the ap-
proriate form of the boundary layer equations is to
either pull the appropriate scale factors such as the
boundary layer thickness "out of thin air," or to make
"hand-waving" arguments for their validity based on the
results of the exact solution for the impulsively oscil-
lated flat plate in a quiescent fluid. The boundary layer

a^ 8(x)

Figure 2. - Boundary layer flow over a flat plate.

concept can be rendered far less obscure if we attempt
to arrive at the form of the boundary layer equations
by scaling the complete two-dimensional equations of
The complete two-dimensional equations of motion
describing the flow over the flat plate shown in Figure 2
are given by:

5v 6v 6 vx
6V x xx 6P
pv --+ pvy -y -x \ x
x 6x r 6y 6x \, 6 2

by bvy
vx x y 6vy
Px 6x py 6y




v 6by
S+ --- = 0
6x 5y
The appropriate boundary conditions are:

v =V , v =0 at x=0
x o0 y

v = (y),' y = Vy(y) at x = L

v =0, v =0 at y = 0

vx = V , v = 0 at y = 6(x), 0 5 x S L
xC 00 y-




This example illustrates two concepts in scaling which
were not involved in the first example. First, we note
that this is a problem for which we are asking whether
there is a region of influence wherein viscous forces can
be confined, namely the boundary layer. This region of
influence, defined by the boundary layer thickness 8,
must be introduced into the problem via the boundary
conditions, such as was done in Equation 37. Second, the
example involves the concept of local scaling. This im-
plies that the equations are scaled at a local x, distin-
guished by x = L, which may be treated as a constant
in the transformation of variables.
Introduce the dimensionless variables:

- v * vy * x * y_ * P
SY; v = ; = y; x= -; y = ;p= -- (38)
x W y V x y P0

The dimensionless groups arising in the boundary condi-
tions and continuity equation enable us to conclude that:

x = L; y= 6; W = V; Vo = - (39)

The fact that boundary layer flows are those in which
the pressure forces are of the same order of magnitude
as the inertia forces enables us to conclude that:


p 2 = (40)

The resulting dimensionless form of the equations of
motion is given by:

* * 62 2 *
XVx * 6Vx 6P* 1 5 6X + 2 e L 6 bv
6x x y 6x 6 * 6 X (1
*x *
* 2 * 2 *
6 + v V= - ()2 2
Vx ,Iy L Y +._. - (L ) Y (2)
V * * Re L) R *2
6x Y y 6 6y* 6 6x* y
where the local Reynolds number is defined by:

pV 6
6e uL


The fact that viscous forces must be at least as important
as inertia and pressure forces in the boundary layer if
we are to satisfy the no-slip conditions at the wall,
enables us to conclude that:

ary layer equations. The former is a class of problem
for which it is not possible to determine the scale factors
for all of the independent variables as is done in the
problems discussed here. In such cases a similarity vari-
able is suggested. The method for treating such prob-
lems is discussed in the article by Hellums and Churchill.2

3. Viscous Heating in Laminar Slit Flow:
N THIS CASE we wish to find the conditions under
which axial conduction and convection of heat can be
neglected relative to radial conduction and viscous
generation of heat for the fully developed laminar slit
flow shown in Figure 3. If we assume that there is no
coupling between the momentum and energy equations,
the latter is given by:

pC V [1 - (y/B)2]- k2 +


1 (L) 1
Re 6

6k 2T 4Vm 2
y 2 B

This implies that the boundary layer thickness is given

S" _ 1/2
p(i )

. R 1/2

Hence, we have arrived at the correct functional form
for the boundary layer thickness if we identify L as the
local axial coordinate.
We see from equation 44 that:

L - O 46)

Therefore, if Re 10 we might expect the following

simplified boundary layer equation to apply:

. 6vx

* 2 *
* x 6 v
+ v y
Y 6y

S= 0 (48)
Note the Re __ 10 implies that ReL = pV L I/ 100
' o0
for the boundary layer analysis to apply. This is in
agreement with the analysis of Janssen3 who showed that
the error in the drag coefficient would be approximately
40% at a Reynolds number of 100 and negligible at a
Reynolds number of 1000.
The boundary layer equations can be simplified further
by rescaling the dimensional form of equation 47, the
continuity equation, and the appropriate boundary condi-
tions. However, scaling these equations is a vastly dif-
ferent problem from scaling the full two-dimensional
equations of motion which led to these simplified bound-

Ti \ T. \
T1 V,=VM[l-(y/B)2]
Figure 3. - Viscous heating in laminar slit flow.

The appropriate boundary conditions are:

T = T. at x= 0

T = T(y) at y = L

T = T at y= � B, 0 5 x - L

- = 0 at y = 0
Introduce the following dimensionless variables:

(47) * T r * y_ *
T T ' y ; x x
0 0 0

The reference temperature Tr is included as an arbitrary
constant in order to make one of the boundary conditions
homogeneous. The boundary conditions indicate the fol-
lowing choices for our reference temperature and scale

T r i = T - Ti; = B; x = L (55)

The resulting dimensionless form of the energy equation
is given by:
pGcV T B 2 2 * 42T Vm 2 2
x L2 *- k-+ __ y (56)

The criteria for neglecting axial convection and con-
duction are seen to be:


pC V B2 B
m- = PrRe () = Pe () << 1


() << 1

where the Prandtl number and Peclet number are defined
Pr = (59)

Pe - (60)
Under these conditions the simplified energy equation
yields the solution given by Bird, et. al., in "Transport
Phenomena," page 345.1
This example illustrates the connection between the
lubrication flow assumption (small Re) and the small
Peclet number assumption made in heat transfer prob-
lems. Scaling the complete equations describing a trans-
port process provides the link between somewhat ana-
logous assumptions. This connection is not nearly so
apparent when a less systematic approach is used to
arrive at the simplified equations describing the process.

4. Solid Dissolution into a Falling Film:
THE PENETRATION THEORY concept in mass trans-
fer is as obscure as the boundary layer assumption
in momentum transfer. We will scale the convective
diffusion equation in a manner similar to that used in
the developing the boundary layer equations, for the case
of solid dissolution into the falling laminar film shown
in Figure 4.


Figure 4. - Solid dissolution into a falling film.

The complete convective diffusion equation for this

case is given by:

Vm& 2 cA
V -(y) 1 6
*m [H *H' J z

6 CA
DAB 6y 2

+ DB6 CA
AB 6x2

and the appropriate boundary conditions are:

S 2 6CA D 682CA 6 2CA (61)
Vm -H ] AB 6y2 +DAB (61)x2

cA= cAi at x = 0 (62)

CA = cA(Y) at x =L (63)

cA = cAw at y = 0, 0 < x 5 L (64)

cA = Ai at y = 6 (x) (65)

Introduce the following dimensionless variables con-
taining the arbitrary parameters cr, co, Yo, and x0.

* CA - Cr * * x
S= ; y = ; =- (66)

The boundary conditions indicate the following choices
for the arbitrary parameters:

cr= cAt; co = Aw- cA; Yo =c; xo = L (67)

The dimensionless convective diffusion equation then
assumes the form:
[/- , 2 V *, 2* 2 2 a 68*

Since the convection term must be of the same order of
magnitude as the cross-stream diffusion term if we are
to satisfy the boundary conditions at the wall, we must

DThis implies that:L

This implies that:


In order for the penetration theory equations to apply
we must have

(0)2 << 1 (71)


( 2 < 1 (72)

where H is the film thickness. This implies that:


,! ( DABL 1,/2
ac - V. )

( ReL "1/2

V H2 H SPe\HI7)
Hence we see that the ratio of the contact time to the
characteristic diffusion time must be small if the pene-
tration theory analysis is to apply. Most transport
phenomena texts state that merely the contact time
must be small. Scaling the equations tells us that the
relative contact time is the important parameter which
must be considered to ascertain the validity of the pene-
tration theory assumption. Note that equation 73 im-
plies that the penetration theory arguments will ulti-
mately break down at large L, (x).
The simplified dimensional equation that describes the
mass transfer under penetration theory arguments is

2V y 6cA
Hm A
H Ox

6 CA2
- DAB 2

The simplified boundary conditions are:

cA = cAi at x = 0
A Ai

A = Aw at y = 0, 0 x 5 L

cA = CAi at y = 0o




The last boundary condition follows from the fact that
8, is so small that for all practical purposes the boundary
condition at the gas-liquid interface can be considered
to be at infinity. The solution to this simplified problem
is outlined on page 551 in "Transport Phenomena," by
Bird et. al.1
This example illustrates the connection between the
boundary layer assumption (large Re) made in momen-
tum transfer and the penetration theory assumption
(large Pe) made in mass transfer.

A systematic approach to scaling the mathe-
matical description of transport phenomena can
be summarized as follows:
1. Write the complete differential equations and
boundary conditions describing the process. In problems
involving a "region of influence" such as boundary layer
problems, the bound on the region such as the boundary
layer thickness must be introduced in the boundary
2. Form dimensionless variables by introducing arbi-
trary scale factors on all dependent and independent
variables. Arbitrary reference factors may be introduced
to make certain boundary conditions homogeneous.
3. Introduce these dimensionless variables into the
differential equations and their boundary conditions.
4. Arbitrarily make the coefficient of one term in each
differential equation and boundary condition unity by
dividing through by its dimensional coefficient.

5. Attempt to determine the arbitrary scale factors
and reference factors by setting appropriate dimension-
less groups equal to zero or unity. Which groups are
chosen in this step depends on the physical conditions
for which the equations are being scaled. Characteristic
lengths can usually be determined from the dimensionless
groups generated by the boundary conditions. However,
characteristic times, velocities, etc., more frequently
are determined from dimensionless groups generated by
the differential equations. The guideline in determining
the unknown scale and reference factors is to avoid intro-
ducing any mathematical contradictions and to not violate
one's physical intuition.
6. In problems for which all the scale and reference
factors can be determined in this manner, the resulting
dimensionless form of the differential equations and
boundary conditions is the minimum parametric repre-
sentation of the problem. Problems for which not all
the scale factors on the independent variables can be
determined in this manner suggest a similarity solution.
7. The minimum parametric representation of the
problem can be used to ascertain under what approximate
conditions the mathematical description of the problem
can be simplified to yield a more feasible analytical or
numerical solution. It also suggests the appropriate pa-
rameters for a perturbation or a symptotic solution for
the complete mathematical description of the problem.
The systematic approach to scaling the mathe-
matical description of transport phenomena is
an effective teaching tool for a transport phe-
nomena course. It provides a means by which the
validity of various simplifying assumptions in-
troduced in the mathematical description of
transport phenomena can be quantitatively ascer-
tained. It also can be used to illustrate the
analogy between the assumptions made in sim-
plifying heat, mass, and momentum transfer
problems respectively.




half width of slit
concentration of component A
heat capacity at constant volume
diffusivity of component A in B
height of baffle at x = L
film thickness
thermal conductivity
axial length
Peclet number
Prandtl number
Reynolds number
Schmidt number
maximum velocity
axial velocity
transverse velocity
approach velocity
axial coordinate
transverse coordinate


momentum boundary layer thickness
concentration boundary layer thickness
angle of inclination of baffle

The author acknowledges his many students in trans-
port phenomena at the University of Colorado whose
constructive criticism helped him to develop this method
in its present form. In particular, he expresses his ap-
preciation of Don Guadagni, Jan Kreider, and Breck
Owens, all graduate students at the University of Colo-
rado, whose comments on the final manuscript were very

1. Bird, R. B., Stewart, W. E., Lightfoot, E. N.,
Transport Phenomena, Wiley, New York, 1966.
2. Hellums, J. D., Churchill, S. W., A.I.Ch.E. Journal,
10, 110, 1964.
3. Janssen, F., J. Fluid Mech., 3, 329, 1958.

KLINZING: ECUADOR (Continued from page 146)
were reduced from 40 or 50 per week to 25 or
30 per week. The complicated thesis regulations
were modified to a more efficient system. Scholar-
ship programs for students and professors to
improve their knowledge and return to their
Universities seem to be the salvation for many
Latin American Universities. Responsibility
needs to be fostered in the students in Latin
American Universities. This cannot be accom-
plished unless they are given the opportunity to
practice it in and out of the classroom. In En-
gineering assistance programs the work is much
easier than in other areas such as History, Ad-
ministration, Education, etc. The reason for this
ease is because the amount of physical equipment
that can be employed in this type of assistance.
People are anxious to change and accept new
ideas when they see one of the means of change
physically before them. Cooperation was excel-
lent and enthusiasm for improvement notable.
The School contains many capable and dynamic
professors and administrators. It is believed
with this leadership the School will progress at
a steady rate. One working in these programs
of assistance should be flexible in operation and
ideas. He should not concede on ideals. For full
effectiveness in such a program a tour of duty
should be no more than two years. Speaking the
language of the host country is an invaluable
asset in the entire endeavor.

(Continued from page 116)
The wild areas of the U.S. have had a bad ten years.
Visits to most of the National Parks are rationed. This
caused people to flock to adjacent wild areas. The use of
motorized bikes, snowmobiles and helicopters has opened
even the most remote regions to hordes of people. No
species became extinct during the decade but the grizzlies,
eagles and condors are very close to it.
Politically the world of 1980 is farther than ever
from "one world" but is closer to two worlds. The Viet-
namese war was never officially ended. Neither was the
Korean war for that matter. The U.S. slowly withdrew
its troops during the early 1970's. Control of all of
Vietnam slipped into the hands of a government con-
tinually more Communist oriented. Red China gained
more control over the country with the aim of securing
the benefits of the Mekong rice bowl for herself. Then
pressure was exerted against Laos and Thailand. These
countries asked for U.S. help from the aggressor. The
U.S. declined, however, having heard this cry before.
In India and Pakistan, food riots, epidemics and gen-
eral misery made their national governments almost pow-
erless to guide and control these countries. Red China
now virtually controls southeast Asia, but is no better off
for it. She inherited more people than food. Her border
clashes with Russia always were followed by a pull-back
when Russia acted tough. Israel stands at the same bor-
ders she had at the end of the 1967 war. The Arab na-
tions of Egypt and Syria are overflowing with starving
people, having increased by 12 million in the past decade.
They are much too weak to pose a military threat to
Israel and Russia apparently decided back in 1972 that
nothing was to be gained by continually arming the
Arabs. Russia appears to be having considerable difficulty
just feeding her own population, now 270 million, and
doesn't seem to have any food to spare for starving
partners. Latin America now exceeds North America in
population but in not much else. Most of the countries
of Central America and northern South America have had
a succession of military coups and "popular" uprisings.
Back in 1970 I thought that homo sapiens was about
three generations from extinction. Today, in 1980, I am
not quite so pessimistic. Two hopeful signs have emerged.
Almost all of the countries of the world have massive
educational campaigns advising "Replace Yourself Only."
Birth control is available and cheap worldwide. This
alone won't do the job since large pockets of resistance to
limited families still exist in South and Central America,
India and Southeast Asia, and in the Arab countries. The
other development is the recently introduced method of
pre-selection of the sex of offspring. In the countries
where there is the greatest resistance to family limita-
tions, there is also the greatest desire for sons. In India,
sons are social security; in Latin America, the measure
of a man's "manhood." With these countries in such a
chaotic condition, statistics are difficult to obtain but
there is evidence that a great preponderance of male
births is beginning to occur. It will take another 15 to
20 years until we know whether this creates more prob-
lems than it solves and also whether the world population
is actually starting to decline as some observers claim.
Lloyd Berg, Montana State University




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