Chemical engineering education ( Journal Site )

Material Information

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


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


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

Record Information

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

Full Text

chemical eg i a

235 of our people

left theirjobs last year.

We' proud

ofthat record.

Job hopping is something we encourage through our
Internal Placement System.
We happen to believe our most valuable corporate
assets are people. The more our people know, the
stronger company we are. IPS was initiated over three
years ago and in that time over 700 Sun people have
changed jobs using the system.
Here's how it works. Say you're an engineer.
You'd like to broaden your experience and feel that
you'd make a contribution in Marketing. You check
the weekly job opening notices. When there's an

opening in Marketing you think you can fill, you
apply-and get first consideration.
You have freedom to experiment and move around
at Sun. You learn more and you learn faster.
You want to learn more right now-about Sun
and IPS? Ask your Placement Director when a Sun
Oil recruiter will be on campus. Or write for a copy of
our Career Guide. SUN COMPANY, INC., Human
Resources Dept. CEE, 1608 Walnut Street, Philadel-
phia, Pa. 19103. An equal opportunity employer m/f.

A Diversified Energy and Petrochemical Company
Sun Company, Inc. (formerly Sun Oil Company)

Department of Chemical Engineering
University of Florida
Gainesville, Florida 32611

Editor: Ray Fahien
Associate Editor: Mack Tyner
Business Manager: A. W. Westerberg
(904) 392-0861

Editorial and Business Assistant: Bonnie Neelands
(904) 392-0861
Publications Board and Regional
Advertising Representatives:
William H. Corcoran
California Institute of Technology
Homer F. Johnson
University of Tennessee
Vincent W. Uhl
University of Virginia
CENTRAL: Leslie E. Lahti
University of Toledo
Camden A. Coberly
University of Wisconsin
Darsh T. Wasan
Illinois Institute of Technology
WEST: George F. Meenaghan
Texas Tech University
University of Houston
James R. Couper
University of Arkansas
Leon Lapidus
Princeton University
Thomas W. Weber
State University of New York
Lee C. Eagleton
Pennsylvania State University
NORTH: J. J. Martin
University of Michigan
Edward B. Stuart
University of Pittsburgh
NORTHWEST: R. W. Moulton
University of Washington
Charles E. Wicks
Oregon State University
D. R. Coughanowr
Drexel University
Stuart W. Churchill
University of Pennsylvania


Chemical Engineering Education

ehU 6OMwe. J64 47ed4me

126 The Chemical Engineering Profession,
R. Alkire

130 Plant Design: A Logical First Course for
ChE Freshmen R. Shelden

134 A Practical Introduction to Analysis and
Synthesis, R. Williams and W. Cosart

136 Process Model-Building: An Introduction to
Complex Design, T. Ward


114 How to Get the Most out of an Equation
without Really Trying, R. Aris

140 Ranking Chemical Engineering Departments,
R. Griskey

146 Organization of Reaction Engineering
Problems, J. Sommerfield and W. Ernst


108 Departments of Chemical Engineering
Iowa State

112 The]Educator
James Douglas
of University of Massachusetts

107 Letters

124, 125 Book Reviews

107, 145 News

152 Division Activities

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 DeLeon Springs, Florida. Correspondence
regarding editorial matter, circulation and changes of address should be addressed
to the Editor at Gainesville, Florida 32611. Advertising rates and information are
available from the advertising representatives. Plates and other advertising material
may be sent directly to the printer: E. 0. Painter Printing Co., P. 0. Box 877,
DeLeon Springs, Florida 82028. Subscription rate U.S., Canada, and Mexico is $10 per
year, $7 per year mailed to members of AIChE and of the ChE Division of ASEE.
Bulk subscription rates to ChE faculty on request Write for prices on individual
back copies. Copyright 1976. Chemical Engineering Division of American Society
for Engineering Education, 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.
The International Organization for Standarization has assigned the code US ISSN
0009-2479 for the identification of this periodical.


Industrial Sponsors:

The following companies donated funds for the

support of CHEMICAL ENGINEERING EDUCATION during 1975-76:


Departmental Sponsors:


The following 115 departments contributed

to the support of CHEMICAL ENGINEERING EDUCATION in 1976:

University of Akron
University of Alabama
University of Alberta
Arizona State University
University of Arizona
University of Arkansas
Brigham Young University
University of British Columbia
Bucknell University
University of Calgary
California Institute of Technology
University of California (Berkeley)
University of California, (Davis)
Case-Western Reserve University
Chalmers University of Technology
University of Cincinnati
Clarkson College of Technology
Clemson University
Cleveland State University
University of Coimbra
University of Colorado
Colorado School of Mines
Columbia University
University of Connecticut
Cornell University
University of Delaware
University of Detroit
Drexel University
University College Dublin
Ecole Polytech, Canada
University of Florida
University of Houston
University of Idaho
University of Illinois (Urbana)
Illinois Institute of Technology
Indiana Institute of Technology
University of Iowa
Iowa State University

Kansas State University
University of Kentucky
Lafayette College
Lamar University
Laval University
Lehigh University
Loughborough University (England)
Louisiana Technological University
Lowell Technological Institute
Manhattan College
University of Maryland
University of Massachusetts
Massachusetts Institute of Technology
McNeese State University
University of Michigan
Michigan State University
Michigan Tech. University
University of Minnesota
University of Mississippi
University of Missouri, Rolla
Montana State University
University of Nebraska
University of New Hampshire
New Jersey Institute of Technology
New Mexico State University
City University of New York
Polytechnic Institute of New York
State University of N. Y. at Buffalo
North Carolina State University
University of North Dakota
University of Notre Dame
Nova Scotia Technical College
Ohio State University
Ohio University
Oklahoma State University
University of Oklahoma
Oregon State University
University of Ottawa

University of Pennsylvania
Pennsylvania State University
Princeton University
University of Puerto Rico
Purdue University
Queen's University
Rensselaer Polytechnic Institute
University of Rhode Island
Rice University
University of Rochester
University of South Carolina
South Dakota School of Mines
Stevens Institute of Technology
Tennessee Technological University
University of Tennessee
Texas A & M University
Texas A&I University
University of Texas at Austin
University of Toledo
Tri-State College
Tufts University
University of Tulsa
University of Utah
Vanderbilt University
Virginia Polytechnic Institute
Washington State University
University of Washington
Washington University
University of Waterloo
Wayne State University
West Virginia University
University of Western Ontario
University of Windsor
University of Wisconsin
Worcester Polytechnic Institute
University of Wyoming
Youngstown State University

TO OUR READERS: If your department is not a contributor, please ask your
department chairman to write CHEMICAL ENGINEERING EDUCATION, c/o
Chemical Engineering Department, University of Florida, Gainesville, Florida


letters |

Quite recently Provost Gill of SUNY Buffalo has
visited upon us an evaluation of graduate Chemical En-
gineering efforts, in the spirit (indeed in carbon copy) of
the celebrated Cartter report et seq. That the "Gill Re-
port" has provoked comment, I have no doubt. That the
"Gill Report" has done justice to Minnesota, I have no
doubt whatsoever. They are "uno numero." But that, fair
reader, ends equity. Witness the "top 20." Look into your
minds, I plead. Permit me a few undemocratic observa-
As I am a professor at Notre Dame, I comment not
upon our statistically established status in the Gill re-
port. In fact, for reasons set forth below, we could not
care less, save for the obvious acknowledgment that the
University of Minnesota is rightfully ranked No. 1 and
several other quite distinguished departments hold an ele-
vated status.
But what is the nature of that properly first ranked
department? It is, pardon me, catholic in instinct and
implementation. The other 19 of the top 20? To be sure,
in catalysis and fluid mechanics, Stanford is pre-eminent.
In the several areas of chemical engineering science, sure-
ly Delaware emerges. One can go on, citing specific areas
of expertise and assigning particular departments the
role of "uno numero." My point, which I trust is virtually
obvious, is that the ranking of graduate departments of
chemical engineering must respect particular areas which,
though ignored in the past of the unit operations mentali-
ty, now yield to delineations and specializations heretofore
unanticipated. Which is to say, how do we rank a chemical
engineering department of strength in, say, surface
catalysis (e.g., Stanford) with one of signal merit in,
say, thermodynamics (e.g., Florida or Oklahoma)? Tis
the problem, dear reader, of contrasting oranges and
Permit me a further illustration: VPI boasts a rather

114 "l news

Professor Joseph A. Bergantz
State University of New York at Buffalo
Joseph A. Bergantz, Professor of Chemical Engineer-
ing at the State University of New York at Buffalo, died
June 5, 1976. He was the founder and first Chairman of
the Department of Chemical Engineering, which was
established July, 1961. He served in that capacity until
1969. He later served as Associate Provost of the Faculty
of Engineering and Applied Sciences at SUNY/Buffalo.
He also was a Vice-President of the Creative Education
Foundation, Inc. of Buffalo.
Memorial contributions can be made in support of the
Joseph A. Bergantz Memorial Reading Room by sending
checks, payable to the University at Buffalo Foundation
Inc. c/o The Department of Chemical Engineering, State
University of New York at Buffalo, Buffalo, N.Y. 14214.

strong chemical engineering group (in my opinion) in
the area of fundamentals of food sciences, including that
most glorious of inclinations-wine technology. Delaware,
a department of admirable scope and depth, claims not
such expertise. How does the Gill report rank these de-
partments? See for yourself. MIT boasts of a just reputa-
tion insofar as they and Michigan virtually invented "our
trade," at a time when Minnesota could claim naught but
Bronko N. No informed citizen of our chemical engineer-
ing group would or could place MIT and/or Michigan in
the same province of universal excellence as is now
occupied by Minnesota. Indeed, I, quite frankly, am very,
very, suspicious of a goodly number of rankings, ala Gill,
which place greats and near-do-wells within the top 20.
Indeed, the top 30 or 40.
Continued on page 152.

Editors Note:
The following response was received from Provost
Gill. (For another approach to the rating of departments,
see the paper by Griskey in this issue.)


If Professor Carberry (B.S. 1950; M.S. 1951, Notre
Dame; PhD 1957, Yale) is trying to say that peer evalua-
tions, which disagree with his opinion, are meaningless,
I disagree with him completely. It seems that Carberry
feels that one man's opinions are superior to collective
peer judgments. However, it has been demonstrated in
many studies (i.e., Bernier, et al, Chemical Engineer-
ing Education) that collective peer evaluations correlate
highly with objective measures of excellence such as
numbers of papers published, research expenditures, ci-
tations, PhD's produced, etc.
I'm sorry that the chemical engineering departments
are not viewed by other faculty colleagues the way Pro-
fessor Carberry would like them to be. But I can assure
him that no one at Buffalo, including me, participated in
any of the rankings, including those of Notre Dame and
Faculty members at all ranks from 19 schools other
than Buffalo provided useable responses. Some schools
provided more than one useable response. To my
knowledge no bribes of any kind were offered to in-
fluence the rankings one way or another.
It is worth noting that the introduction to the report
includes the following statement:
"An attempt was made to obtain what seemed to be
a reasonable mix of raters among the various
academic ranks of assistant, associate, and full pro-
fessor. However, this study is not purported to be as
comprehensive and has not been designed with the
care given to the details of statistical design that
characterized the two previous American Council on
Education studies. Therefore, the results should be
viewed in this context. That is, no doubt departments
which should have been included have been omitted
and the ratings of those departments which have been
included certainly are subject to significant, but unde-
termined, errors."
State University of New York at Buffalo
William N. Gill


mnB Ddepartment


Iowa State University
Ames, Iowa 50010

IOWA'S TRADITIONAL commitment to quality edu-
cation at every level was established in 1868
when Iowa State became the first institution in
the U.S. to qualify under the Morrill Act as a
land grant college. Since the founding of the De-
partment of Chemical Engineering in 1913, the
university and the department have grown to-
gether in scope and diversity from primarily
agriculturally based institutions into multi-facet-
ed and diverse entities. The College of Engineer-
ing now enrolls more than 3000 students annually
out of the 21,000 attending the university, and
has become one of the largest engineering colleges
in the U.S. Under the leadership of several out-
standing individuals, the ChE program now
occupies an eminent position in the college, en-
rolling over 250 undergraduate and 50 graduate
students annually. The faculty of 18 holds degrees
from a total of 25 schools, and the physical facili-
ties available for instruction and research now
occupy over 26,000 square feet of space.
Following the graduating of the first class
in 1914, the first graduate degrees were offered
in 1918, and the first Ph.D. granted in Chemical
Engineering in 1925. To Dr. Orland R. Sweeney
goes the credit for the development of the de-
partment from the 1920's to the 1940's. Dr.
Sweeney, who became a true Iowa State legend,
had a creative approach to research, and his en-

thusiastic promotion of the profession was re-
sponsible for the rapid development of the de-
partment during the 1930's. Sweeney truly be-
lieved that the condition of simply being a
chemical engineer endowed one with all of the
necessary qualities for success. On more than
one occasion he would extoll the virtues of a
student to a prospective employee and only after
finishing the testimony inquire as to the student's
name. His partial deafness was used as a weapon
by the simple device of turning off his hearing aid
at the appropriate moment. He was probably the
only ChE department head in the U.S. to make
frequent use of a fire pole to make optimal use
of his time.

D URING THE SWEENEY era the department de-
veloped a worldwide reputation in the areas
of the utilization of agricultural by-products,
water treatment and ion exchange, filtration
technology under Dr. B. F. Ruth, and in fertilizer
technology. During this period Iowa State College
itself was growing from an agricultural and
engineering school into a modern university. Fol-
lowing Sweeney's retirement in 1946, Dr. G. Leon


Bridger, now a department chairman at Georgia
Tech, led the department until 1955. His major
contribution was to use this experience gained
in fertilizer technology at TVA to establish a re-
search program that still continues today. Dr.
Morton Smutz, now an associate dean at the Uni-
versity of Florida, was department head from
1955 to 1961. In 1961 Dr. George Burnet became
head, and the department entered a period of
growth and expansion in faculty size and facili-
ties which was characteristic of much of the uni-
versity during the past decade. In 1964 the de-
partment celebrated its 50th anniversary by
moving into Sweeney Hall, a large three-story
building which now houses most of the depart-
ment's services and facilities. In 1971, Dr. David
R. Boylan moved from his position as a faculty
member in the department and director of the
Engineering Research Institute to become Dean
of Engineering. In 1973, administrative reorgani-
zation resulted in the department becoming com-
bined with the existing graduate program in Nu-
clear Engineering. The department now operates
with two separate faculties, and Dr. M. A. Larson
has been assisting in the administration of the
ChE program since the reorganization.
In addition to the facilities available in Sween-
ey Hall, which include a large number of gradu-
ate student research laboratories, a large reading
room, shops, classrooms and faculty offices, the
department also operates a large unit operation
teaching laboratory and a digital control labora-
tory containing a number of analog and digital

entering chemical engineering are from the upper
5% of their graduating high school class. It is
not unusual for one-fourth of the average gradu-
ating B.S. class to continue into a graduate school.
Curriculum design and development has therefore
been a continuous challenge, and the present
undergraduate curriculum has developed to main-
tain the department's traditional strong emphasis
in design and also provide a strong base for con-
tinuing study in engineering. The traditional se-
quences in unit operations and transport phe-
nomena were integrated in 1970 into a four
quarter sequence. Undergraduate courses in pro-
cess optimization, digital and analog simulation,
chemical reactor design, and an introductory
freshman level design experience supplement the
traditional sequences. A special feature is the op-
portunity for advanced undergraduates to desig-
pate up to 15 credits to concentrate in a
specialized area such as applied mathematics,
biochemical or biomedical engineering, polymers,
applied chemistry, or energy resource develop-
ment. A large number of ChE undergraduates
participate in the University Honors Program,
which allows exceptional students to develop in-
dividualized programs which fit their career goals.
The department sponsors a 4 day industrial plant
inspection trip in the junior year to the St. Louis
area. An extensive Cooperative study program
with several companies in the chemical industry
is available so that students desiring work ex-
perience can spread their education over a 5 year
period and gain enriching experience.

To Orland R. Sweeney goes the credit for the development of the department
from the 1920's to the 1940's. During the Sweeney era the department developed a
worldwide reputation in the areas of the utilization of agricultural by-products,
water treatment and ion exchange, filtration technology under
Dr. B. F. Ruth and in fertilizer technology.

computing devices. As a result of a long associa-
tion with the Ames Laboratory of the U.S. Energy
Resource Research and Development Agency
(formerly AEC) on campus, there are also ad-
ditional excellent research facilities available in
that area.
THE UNDERGRADUATE program at Iowa State is
distinguished in the breadth of educational
opportunities that are available to the student.
The quality of students entering Iowa State, as
measured by any of several national indicators is
unusually high. Over one-third of the students

A special opportunity is also available in the
Foreign Study Program, in which a group of 10
to 16 advanced students each year have been
able to complete up to 12 credits of required
work during a 6 week stay at University Col-
lege in London, England. This program, instituted
in 1973, has been very popular, both with
students and faculty. Since the course of study
takes place in June and July, students can com-
bine a period of traveling in Western Europe
following the program. Faculty at University
College, in conjunction with an Iowa State facul-


ty member, conduct the laboratory and lecture
ChE undergraduates participate in many
student activities on the campus. One such op-
portunity is provided by the very active student
AICHE chapter, which last year hosted the Great
Plains Student Chapter Conference. Also, the
local chapter of Omega Chi Epsilon, the national
chemical engineering honorary, is active in pro-
moting interchange programs with the faculty,
in the form of evening fireside visits and other
Generous support from a number of chemical
firms has enabled the department to provide a
large number of attractive undergraduate scholar-
ships, including a four-year scholarship spon-
sored by the Dow Chemical Company and award-

Graduate research laboratory.

ed annually to the outstanding Iowa high school
graduate entering ISU in ChE, and a number
of scholarships for women students, sponsored by
the Celanese corporation. As in many chemical
engineering departments, the number of women
undergraduates is steadily increasing.
T HE 50 GRADUATE students pursuing Master of
Science and Doctor of Philosophy degrees at
ISU carry out research in a large number of areas.
Over 60 ISU alumni are now active as faculty
members in universities around the U.S., a fact
which attests to the quality and flavor of the
graduate program. During the last 15 years, ChE

research has become increasingly interdisciplin-
ary, and the work going on at Ames is no excep-
tion. Following a long period which saw ISU de-
velop a world-wide reputation in fertilizer tech-
nology and in the utilization of agricultural by-
products, resulting in well over 40 patents, new
research areas have developed in areas such as
coal technology under T. D. Wheelock and A. H.
Pulsifer; industrial crystallization under M. A.
Larson; and biochemical engineering under the
direction of P. J. Reilly. Large external contracts
have been developed in each of these areas. In
addition, research work at the Ames Laboratory
in interfacial mass transfer by L. E. Burkhart,
heterogeneous catalysis under R. G. Bautista, and
liquid metal technology with George Burnet has
become well known. Since 1966, the department
has been an active collaborator in the Biomedical
Engineering Program, with work on heat and
mass transfer in applied physiology under R. C.
Seagrave. Additional research areas include J. C.
Hill's work in fluid mechanics, W. H. Abraham's
program in process analysis, Kenneth Jolls' in-
terests in thermodynamics, J.D. Stevens' work in
emulsion polymerization, and D. L. Ulrichson's
program in thermodynamics and hydrogen as an
energy source. A recent addition to the faculty,
Dr. Charles Glatz, brings expertise in biological
mass transfer.
The curriculum leading to the M.S. and Ph.D.
degrees is based on core sequences in transport
operations, thermodynamics and reactor design,
and applications of mathematics in ChE. In ad-
dition, advanced courses in process dynamics, non-
equilibrium thermodynamics, biochemical engi-
neering, coal technology, crystallization, hetero-
geneous catalysis, and applied electronic instru-
mentation are available for those wishing to
specialize. Advanced sequences in transport
phenomena and simulation are also available for
advanced students.
Graduate students at Iowa State may also
participate in interdisciplinary programs in
Water Resources, Energy Resources, Technology
and Social Change, and Biomedical Engineering.
Excellent programs in chemistry, nuclear engi-
neering, computer science, physics, and me-
chanical engineering are also used as minor areas.
The Engineering Research Institute and the
Ames Laboratory have traditionally provided
strong assistantship support, and in combination
with a healthy grant program from private in-
dustry and successful research contract efforts by


Burkhart and Collins doing digital control.

faculty a broad base for graduate support has
been assembled.

In addition to their teaching and research ac-
tivities, Iowa State's ChE faculty have been un-
usually active in the areas of national and inter-
national service. A long list of research publica-
tions, patents, and textbooks which is characteris-
tic of many outstanding faculties is supplemented
by the extramural accomplishments of the group.
George Burnet is currently serving as President-
elect of ASEE and as chairman of the important
Engineering Education and Accrediting Commit-
tee of the Engineers Council on Professional De-
velopment. Maury Larson is serving as chairman
of the Division of Fertilizer and Soil Chemistry
of the American Chemical Society. Both George
Burnet and John Stevens have recently served
terms as national Presidents of Omega Chi Epsi-
lon. Burnet and Larson each spent two month
periods as NSF Science Improvement Program
consultants at The Indian Institute of Technology
in Karagphur, while Bill Abraham spent two
years on leave as a Ford Foundation Fellow in
Manila, the Phillippines, developing a graduate
program in ChE there. Allen Pulsifer spent one
year at Prairie View A & M college in Texas
helping to establish a ChE program while John
Stevens spent one year sponsored by AID visiting
in the ChE Department at Hacettepe University
in Ankara, Turkey. More recently, Larson spent
a year in residence at University College in Lon-
don as the Shell Visiting Professor and conduct-
ing crystallization research. He also participated

in an exchange program in Czechoslovakia and
Poland. Seagrave spent one year at the Institute
for Medical Physics in Utrecht, the Netherlands
doing research in anesthesiology. Currently, Bau-
tista and Pulsifer are spending one year periods
in England and West Germany respectively
pursuing research in their areas.
The department has been fortunate in recent
years to have had several outstanding visiting
professors. This year, Professor Henry Rojkowski
from Warsaw is in residence teaching and doing
research in crystallization. Other recent visitors
have included Dr. Ted White from the University
of Queensland in Australia and Dr. Norman
Harnby from the University of Bradford in
England. Next year Dr. John Garside from the
University College of London will be visiting.
The faculty have also been active in consulting
work, and in addition have received many honors.
George Burnet was named Anson Marston Dis-
tinguished Professor of Chemical Engineering in
1975. Professors Larson and Seagrave have both
been named recipients of the North Midwest
ASEE Outstanding Teacher Award, while John
Stevens was named as a winner of the Standard
Oil Outstanding teacher award in Engineering.
Compared to the legendary antics of the color-
ful Dr. Sweeney, our modern faculty activities
take on more pastel hues. Like many of our col-
leagues around the U.S., we have become affected

The quality of students at Iowa State ... is
unusually high. It is not unusual for one-
fourth of the average graduating B.S. class to
continue into a graduate school ... Over 60 ISU
alumni are now active as faculty members in
universities around the U.S....

by the physical fitness craze, and on any given
noontime several faculty may be observed
running, biking, or playing basketball, volleyball,
handball or tennis. Perhaps we are distinguished
more by the combination and range of our in-
terests, which find us with two licensed pilots
(Abraham and Wheelock), two gentlemen farm-
ers (Larson and Collins), a railway station
demolition expert (Ulrichson), a professional
musician (Jolls), a part-time political hack (Sea-
grave), and a host of quasi-expert bowlers.
Chemical engineering, as Dr. Sweeney would at-
test, is an exciting profession, and life at Iowa
State is no exception. IZ



University of Massachusetts'

fameS, Me 3",ac*

Prepared by Robert Laurence
University of Massachusetts
Amherst, Massachusetts 01002

the Johns Hopkins University didn't fold
while James M. Douglas loitered through his
undergraduate years at Hopkins. It was intact
even while Stan Middleman wandered through
Maryland Hall. It collapsed as we joined forces
at the University of Massachusetts. It may well
have been Douglas who precipitated the debacle;

The exodus of students (and faculty)
grows as they pass down the corridor, and among
others, Jim Douglas finds his way to the Top
of the Campus for the beers and Friday
afternoon advising session.

for that matter a few years at U. Mass. and the
Commonwealth nearly folded. The Hopkins days
may well have played a large role in the develop-
ment of our "enfant terrible." Long hard intense
nights at poker sharpened his killer instinct. The
warm Baltimore spring may well have brought
him to Homewood field to watch Morrill and
Webster and others show Maryland's Terrapins

*The family Douglas, according to Lang (History of
Scotland, vol. 1, p. 236), is "a great, turbulent, daring,
often treacherous house." After the demise in rapid
succession of the first and second earls of Douglas arose
an energetic border chief, a zealous protector of the kirk
of Scotland, Archibald, the Grim, third earl of Douglas,
dit the Black Douglas (1328-1400). A natural son of
James "the Good" Douglas, he was the instrument of Hot-
spur's demise at Otterburn (1388). The house of Douglas
developed two distinguished branches The Black (of
Douglasdale), the Red (of Angus). Internecine conflict
marked the ascendencies of Red and Black for many years.
The Black Douglas most often however wore the white

how to play lacrosse. These athletic talents be-
came nearly as highly developed as his skill in
emptying beer cans. In the latter day academic
profession, such skill is essential in maintaining
communication with students.
At U. Mass/Amherst, a migration occurs
from Goessmann Lab nearly every Friday just
after 4:00 p.m. The exodus of students (and
faculty) grows as they pass down the corridor
and among others, Jim Douglas finds his way to
the Top of the Campus for the beers and the Fri-
day afternoon advising session. A university, a
school, a department must strive to be a com-
munity of scholars. They must meet, they must
talk, exchange ideas. These sessions are one way
towards those goals. These sessions are of finite
duration, however; Betsy and the hills of Leverett
do need Jim. Robbie, his son, took to downhill
skiing this year and Jim, as accomplished a cross-
country skier as he is, still had a transition to
make. Changes are not new to the Black Douglas.
His career has provided enough for him.
A graduate of the John Hopkins University,
he migrated the short distance to Newark, Dela-
ware, in the late 50's and served his time as a
graduate student in the vigorous Chemical
Engineering Department at the University of
Delaware. His companions in crime of the time
were Forrest Mixon, Marty Wendel, Steve


Whitaker, Bill Abraham, and many others. The
tutelage of Bob Pigford did him no harm, but
he regrets to this day the anger which preceded
disposal of the classic text by Marshall and Pig-
I can't see Douglas having changed political
views in the last 20 years. His intensity may
well have mellowed. Douglas, would you believe,
served an Army tour. His stories mirror his
perennial frustration with ineptitude and red
tape, but more on that later.

WHEN JOHN ELDRIDGE began to assemble the
personnel to build a strong department of
Chemical Engineering, his fundamental premise
was to provide a sound undergraduate program
through a faculty with substantial industrial ex-
perience. Jim Douglas was no exception. His ex-
perience with Atlantic Refining flavors his senior
design course. Jim's interest in design is in some
sense counter-cultural. A large fraction of design
teaching in chemical engineering has a focus in
computer aided design. Although Douglas is
aware and used computer aided design, a
significant fraction of his teaching and research
effort is directed towards simple design al-
gorithms . in a sense to offer credence to the
fabled design engineer who based his designs on
years of experience. Such a set of research in-
terests is not at all out of character for Jim. He
has managed to attack consistently difficult prob-
lems and arrive at simple solutions.
After several years at Atlantic, Jim had an
industrial sabbatical at Imperial College (Uni-
versity of London). Contrary to most views, he
did use his leave to good purpose. He lived in
Wimbledon and did not play tennis. He, Betsy,
Lynn, and Robby travelled through Britain, visit-
ing even the Borders of an earlier Douglas. From
Jim's work with Dave Rippin (now ETH, Zurich)
came periodic operation. He and Rippin showed
the marked improvements in performance which

He and Rippin showed the marked improvements
in performance which can be obtained in
chemically reacting systems through
forced oscillations. It was through
the work on periodic operation that Jim
began his two-volume text on Process
Controls and Dynamics.

Cooling a cup of coffee
may not sound like an exciting
chemical engineering problem, but it is
not unusual to find students in Jim's heat
transfer course measuring the temperature
history of a cup of coffee.

can be obtained in chemically reacting systems
through forced oscillations. This work opened a
new research area for him, work which continues.
It was through the work on periodic opera-
tion that Jim began his two-volume text on
Process Control and Dynamics. The books began
as one volume, but finished as two, the mass of
information to be distributed having grown con-
tinually. His ideas were tested on students, on
colleagues, on himself.
Cooling a cup of coffee may not sound like an
exciting chemical engineering problem, but it is
not unusual to find students in Jim's heat trans-
fer course measuring the temperature history of
a cup of coffee. This problem shows Jim's ap-
proach to things . define a problem in the
simplest description possible, make some experi-
mental measurements, and refine your model. This
pattern of analysis is what has led to Jim's latest
research efforts in simple design algorithms.
Douglas' office is at the back of Middleman's
laboratory, populated with aspiring rheologists.
They were sufficiently distressed by the frequency
of the question, "Is Dr. Douglas in?" that they
put up a sign with a movable arrow pointing to
In, Out, or Maybe. Another sign was soon
necessary to identify whether the first was true
or false.
One aspect that students see little of are his
continuing efforts in the development of a sense
of scholarship in his colleagues. He has not al-
ways been successful, but he does keep trying
and we all will discover soon that he was right all
along. His latest frustration came this spring in
the senior design course. Plagued with "seniori-
tis," the class was nearly in rebellion over the
workload. They expected to coast while Jim ex-
pected them to learn.
I suggested earlier that Douglas has little
patience with ineptitude and red tape. "Notre
enfant Terrible" mustered the forces of the uni-
versity administration against him in a valiant
attempt to expose the usual ineptitude of
Continued on page 145.





University of Minnesota
Minneapolis, Minnesota 55455

1. Cast the problem in as elegant a form as possible.
2. Choose a sympathetic notation, but don't become
too attached to it.
3. Make the variables dimensionless, since this is the
only way in which their magnitudes take on general
significance, but do not lose sight of the quantities
which may have to be varied later on in the prob-
lem nor forget the physical origin of each part.
4. Use a priori bounds of physical or mathematical
origin to keep all variables of the same order of
magnitude, letting the dimensionless parameters
show the relative size of the several terms.
5. Think geometrically. See when you can reduce the
number of variables (even at the expense of first
treating an over-simplified problem), but keep in
mind the needs of the general case.
6. Use rough and ready methods, but don't carry them
beyond their point of usefulness. (E.g. Isoclines in
the phase plane).
7. Find critical points and how the system behaves
near them or what is asymptotic behaviour is at
long or short times.
8. Check limiting cases and see how they tie in with
simpler problems that can be solved explicitly.
9. Use crude approximations, e.g. 1-point collocation.
Trade on the analogies they suggest, but remember
their limitations.
10. Rearrange the problem. Don't get fixed ideas on
what are the knowns and what the unknows. Be
prepared to work with implicit solutions.
11. Neglect small terms, but distinguish between
regular and singular perturbations.
12. Use partial insights and despise them not. (E.g.
Descarters' rule of signs).
13. These maxims will self-destruct. Make your own!

IT IS A COMMON PARADOX that one should only
start computing after one knows the answer.
Not to be taken to literally, it emphasizes that
one should learn as much as possible about a
problem before computing any case or sequence
of cases so that the output of the computer may

be critically appraised, for, without this critical
oversight, the computer can produce an output
more tedious and turgid than the so-called play-
boy philosophy. It is in any case part of the
'craft and sullen art' of the engineer or applied
scientists to bring his problem into its most re-
sponsive formulation and to explore the modes
of its solution as delicately as possible before pro-
ceeding to its complete analysis. From one point
of view it requires sensibilities which are 'nasci-
tur non fit,' but from another it is surely an art
we may all strive after even if we despair of
its mastery.
Of the texts on applied mathematics and en-
gineering analysis the best may perhaps instruct
by example, but only Segel and Lin's recent
masterpiece [1] attempts to unfold some of the
techniques of right formulation. There the ques-
tion of reduction to dimensionless form and the
scaling of equations is carefully and systematical-
ly explained. It will be clear that this essay is in-
fluenced by what they have done, both in this
regard and in the play they have given to per-
turbation methods. The maxims of modelling that
I have ventured to set down are a preliminary
attempt to codify some of the mental processes of
the chemical engineer as he probes and explores a
problem. Like all maxims they tend to have the
unassailable probity of "this ye ought to have
done and not to have left the other undone."

*EDITOR'S NOTE: In this issue, CEE begins a new de-
partment: ChE LECTURES. We intend to publish
seminars and lectures on important areas of modern
chemical engineering. If you feel that one of your
seminars or lectures on a certain topic would have peda-
gogical or tutorial value and would be of general in-
terest to our erudite readers, please send the manuscript
to the editor for review. We would appreciate comments
from our readers on this new department as well as
suggestions for authors of papers.


Dr. Rutherford Aris was born in England in 1929, studied mathe-
matics in the University of Edinburgh and taught it to engineers
there. He has degrees from the University of London (B.Sc. (Math);
Ph.D. (Math. and Chem. E.); D.Sc.). He worked a total of seven
years in industry, but since 1958 he has been in the Chemical
Engineering Department at the University of Minnesota enjoying the
liveliness of its interests, both technical and cultural, and endeavouring
to contribute to this vitality and communicate it to his students.

Nevertheless they should be looked on with a
quizzical eye and subjected to a more than usually
critical appraisal. They are dignified with
numbers merely to invite the participation of the
reader by pencilling them in the margin at the
stage or stages of the example where they are
most obviously invoked.

T HE EXAMPLE WILL BE the elementary and
familiar one of a single nonisothermal re-
action in a catalyst pellet of arbitrary shape for,
though it might be argued that I am getting
the benefit of a good deal of hindsight, its very
familiarity will allow us to concentrate on the
method rather than be preoccupied with the
matter. If the reaction is between the S species
Aj it may be written SajAj = 0 giving a positive
sign to the stoicheiometric coefficients of those
species which are regarded as the products of
the process. In the Knudsen diffusion regime the
effective diffusion coefficients Dej may be regard-
ed as independent and mass balances for over
an element of volume within the catalyst pellet
for each species lead immediately to the S equa-

DeaV2cj + ajPbSjf(cl,c2,...,cS,T) = 0 (1)
where cj = cj (r) = concentration of Aj ,
T = temperature,

pb = bulk density,
Sg = catalytic area per gram,
= reaction rate per unit catalytic area.
The Laplacian is with respect to the position
variables r = (x,y,z) within the pellet which is
assumed to have uniform properties. Into the
formulation of this equation have gone the
principle of the conversation of matter and two
constitutive relations. One is a generalization of
Fick's law which asserts that despite the physical
complexity of the porous medium the flux can
be related to the concentration gradient by an
effective diffusion coefficient. The other is the
kinetic law that may be embodied within the
rate expression f. With the validity of the model
we are not here concerned but though a suspension
of disbelief is called for it should be remembered
that it is ever temporary. An energy balance leads
to the equation for the temperature
keV2T + (-AH)pbSf (cl,c2,...cs,T) = 0 (2)
where AH is the heat of reaction and is credited
with a negative sign since the exothermic reac-
tion, being more interesting in its effects, is taken
as the norm. The simplest of boundary conditions
will be taken at the boundary of the pellet, namely

The maxims of modelling that I have
ventured to set down are a preliminary
attempt to codify some of the mental
processes of the chemical engineer, as he
probes and explores a problem. Like all
maxims they tend to have the unassailable
probity of "this ye ought to have done and
not to have left the other undone."

c, = cj, T = Tf. (3)
The notation for the basic equations is an
obvious one with cj immediately suggesting the
concentration of the j t species and T the tem-
perature. Similarly the suffix f in the boundary
value suggests quantities associated with the
fluid phase around the particle or, for the teu-
tonically minded, with the surface. As a problem
grows one often runs out of really sympathetic
letters for the various quantities and compromises
often have to be made. However, when the ob-
vious suggestiveness of an initial letter (e.g. c,T)
is abandoned, those quantities that hang together
should have letters that hang together; thus
dimensionless c and T may become u and v but
the barbarity of and W should be avoided. Well-


established conventions should be observed and
of course there are publishers' house styles which
may ultimately override a preference for Re and
insist on NRe. The practice of using two letters
for one quantity is open to objection even though
one in upper and one in lower case give it a
pleasant literary favor.
However notation is somewhat a matter of
taste and "de gustibus non est disputandum."
Since it is also a vehicle of communication it is
important not to become so attached to one's own
version that the sensibilities of others are offend-
ed or communication impaired.
These basic equations presume a consistent set
of units for each variable and parameter and our
first task is to render the variables dimensionless.
This does not derogate their physical significance
in any way, for it is always important to keep
the physical meaning of a variable or parameter
in mind; rather it is intended to confer a meaning
on their magnitude that is independent of the
particular system of units. This point is important
for the significance thus attained is universal in
a deeper sense than would be conferred even by
a universal agreement on units, such as the SI.
Philosophically it is akin to Lonergan's in-
dependence of time and place [2]. But more than
this, it measures the quantities in terms that are
intrinsic to the problem rather than those dic-
tated by an arbitrary external system. In general

However notation is somewhat
a matter of taste and "de gustibus
non as disputandum." Since it is also
a vehicle of communication it is important
not to become so attached to one's
own version that the sensibilities
of others are offended or
communication impaired.

the objective should be to keep the dimensionless
variables of the order of magnitude of 1 and al-
low the parameters to be just that-quantities
which give the measure of the situation. How-
ever this should not be done at the expense of in-
troducing unnecessary dimensions. For example,
when the tubular reactor is considered without
regard to any longitudinal dispersion there is no
boundary at the far end of the reactor and it is
artificial to introduce the length of the reactor
just to make the dimensionless axial coordinate
go from 0 to 1; it is preferable to use a combina-

tion of velocity and rate constant with the dimen-
sions of length. It is however often possible to
choose between putting a parameter in the equa-
tion or in the boundary conditions as we shall see
In the problem under consideration r -= (x,y,z)
is the coordinate system within the pellet of
which we have some natural dimension, dp, to
render these independent variables dimensionless
as p = ({,,) = r/dp = x/dp,y/dp,z/dp). (Here
a notational problem is raised by the traditional
use of 71 for the effectiveness factor. We should
probably go to (x1,x2,x3) as coordinates with
ef = xi/dp. However so little use is made of the
cartesian space coordinates that we will not be-
labour this. When there is symmetry and r can
be taken as a scalar its dimensionless form is p.)
It is dangerous to take uj c= /cjf since we may
want to consider cjf = 0 for some products of
the reaction. Rather we take c( as characteristic
of the cjf, perhaps as Yjcjf, and set uj = cj/cf,
uJi = cjf/cf. Then equation (1) becomes

V2u d + 2bS (cu,T) = 0, (4)
where the Laplacian is with respect to the
dimensionless space variables. There is only one
characteristic temperature in the data, namely
Tf, and it is in no danger of being zero. We there-
fore take v = T/T, and the second equation is
V2v + bSt(cru,Tfv) 0. (5)
The second terms in these equations is now di-
mensionless and could be written as say Rj (u,v)
and R (u,v). However this would confound the
importance of the various factors that enter the
functions and overlook the fact that they are all
proportional to one another. It is better to render
the reaction rate dimensionless first by setting

R(u,v) = t(Cfu,T)/f(cjr,Tf) (6)
so that R (uf,1) = 1. Then the coefficient of R in
equation (4) would be ajdppbSgf(cjf,Tf) /Dejcf
and this only depends on j through aj and Dej.
If we let Aj = Dej/De where De is some charac-
teristic value of the diffusivities then dP2PbSgt
(cf,Tf) Decf emerges as the characteristic dimen-
sionless parameter. We will not rush to fix the
characteristic value De since it may be advan-
tageous to fix it-or rather the combination Decf
-later. But

2 = dp2pbSg (Cf,Tf) /Decf


. . Our first task is to render the variables dimensionless. This does not derogate their physical signifi-
cance in any way, for it is always important to keep the physical meaning of a variable or parameter
in mind; rather it is intended to confer a meaning on their magnitude that is independent of
the particular system of units. Philosophically it is akin to Lonergan's independence
of time and place. But more than this, it measures the quantities in terms that
are intrinsic to the problem rather than those dictated by an arbitrary external system.

is in fact the general form of the modulus intro-
duced by Thiele and commonly bears his name.
This is appropriate enough for of the three in-
dependent workers in the late thirties he solved
this problem the most completely (see historical
notes in 3, 4). Calling this parameter 02 we have
V2u + (a/A/,) 2R(u,v) = 0 (8)
V2v +42 R (u,v) = 0 (9)
where 3 = (-AH) Decf/keTf. These equations
hold in 0, the region occupied by the pellet, whilst
on the boundary an
uj = u, v = 1. (10)
Let us pause a moment to see what we have.
There are three dimensionless independent
variables in p occurring explicitly only in the
differential operator, (S+1) dependent variables
and one reaction rate expression, R. There are
(S+2) visible parameters, of which S are
stoicheiometric coefficients modified by the diffu-
sion ratios (it is assumed that none of these is
zero). 8/ is clearly a dimensionless heat of reac-
tion, on which more later, and there may be one
or more parameters, such as a dimensionless ac-
tivation energy or Arrhenius number, concealed
in the dimensionless rate law. The Thiele modulus
can be written
42 = dPlpbSs (cjf,Tf) /d, Do (c,/dp). (10)
The numerator is proportional to the total reac-
tion rate at surface conditions since the volume
is some multiple of dp. Similarly in the denomina-
tor dp2 is proportional to the surface area and
(cf/d,) characteristic of the gradients in con-
tration, so that the whole denominator is a mea-
sure of the total diffusion rate. The Thiele modulus
is thus a ratio of the reaction rate to the diffusion
rate and, when it is small, the reaction rate is
the limiting whereas, when it is large, diffusion
controls. But why call it )2 rather than
4? This is certainly legitimate since the Thiele
modulus is always positive, but it is not altogeth-
er a product of hindsight. For the Laplacian is a

second order operator and hence we might ex-
pect solutions to be functions of Op, which is
rather neater than OPp.
But at this point the mind should question
whether (S+1) equations are really necessary
when there is only one reaction in an adiabatic
system. This is the import of the maxim "Think
geometrically." Geometry is here being used in
a sense which is loaded with even more overtones
than the cyE:wieTpnrTOS over the archway of the
academy. It embraces the idea of degrees of free-
dom and of what we may expect in the way of
characteristic dependencies. In this case we ob-
serve that we can eliminate the reaction rate be-
tween any pair of equations and that the linear
combinations (3Ajuj--aiv) are all harmonic func-
tions. Since their values are constant on the sur-
face aft they are constant throughout a and so
each concentration can be expressed in terms of
the temperature
u uj f U+ (aj/fPAj) (v-1)
This would allow us to reduce all the equations
to a single equation in the dimensionless tempera-
However, once having perceived the idea of
reducing the equations to a single equation, we
might try to do the reduction more symmetrically.
There is a risk here since it is sometimes an ad-
vantage to stay with a physical variable such as
v rather than move to a more mathematical
variable. Let us brave this danger in the hope
of comprehending the mysteries of the equation
and set

uj = uif + -Aw, v = 1 P3w


P(w) = R(ujf + ajW/Aj, 1 + fw). (12)
Then all the equations reduce to the single equa-

V2w + 2P (w) = 0 in 0
w = 0 on ail



But R (c,T) has a zero on the path
a_ (-AAH) Decf
c, -= c + Dcf w, T = T, + k w

for either the reaction reaches equilibrium or, if
it is irreversible, a least abundant reactant is ex-
hausted. We may now choose Decf so that this
corresponds to w 1. Then if the reaction is ir-
reversible, O become negative. If the reaction is reversible
then 0 beyond equilibrium and the rate change sign.
Physical intuition would dispose one to doubt
if the reaction could go beyond equilibrium but
the following argument (due, to Varma (5))
proves the case. For suppose there is a region
f_ within fl where w>1 and P(w) <0, then it is
bounded by a surface aIL on which w = 1. But in
_-, V w = -42P (w) >0 and so w is subharmonic.
This implies that w<1 in l- and contradicts the
assumption that w>1 there.
We have reached the point of knowing that
the system can be reduced to a single equation
(13) in a variable w bounded between zero and
1; also the reaction rate expression P (w) has
been normalized so that P(0) = 1, P(1) = 0. By
equation (11) the fact that w steady state temperature cannot exceed Tf (1-+-)
a result which in its generality is due to Prater
and justifies attaching his name to the parameter
P8. It was the way in which Thiele expressed the
useful result of the solution of the equation that
distinguished his work from that which had gone
before. The mathematician commonly uses a norm
of the solution, which in this case might be
Max w|, but the useful functional of the solu-
tion is not a norm but rather the average reaction
rate as a fraction of the reaction rate at surface
conditions. This is known as the effectiveness
factor where V, = vdp3 is the volume of the

f ff f(c,T) dV
= = ff (w())d=
V, f(ct,T,)

Sff d (14)
v o

particle and dy = dV/dp3 and d5 are the elements
of volume of f1 and area of Zu respectively. The
external surface area of the particle is Sx =
o-d,2 and D/Dn denotes the derivative along the
outward normal. Note that for any shape 71 will
be a function of(t/, f3 and whatever parameters are
concealed in P(w).

When the tubular reactor is considered without
regard to any longitudinal dispersion there is
no boundary at the far end of the reactor and
it is artificial to introduce the length of the
reactor just to make the dimensionless axial
coordinate go from 0 to 1; it is preferable to use
a combination of velocity and rate constant
with the dimensions of length.

T HUS FAR WE HAVE only set up the equations
that govern the system and it would be re-
latively safe to proceed immediately to the solu-
tion by some respectable numerical technique.
We want, however, to get more of a feel for the
form of the solution. To do this we can go in
several directions:
a. simplify the geometry and with it the
differential operator;
b. simplify the kinetics so that an analytical
solution is possible;
c. use a crude numerical method;
d. consider limiting cases.
Let us consider these seriatim.

T HE SIMPLEST FORM of a Laplacian operator is
the second order derivative in one variable.
To make the equation one dimensional we may
consider the case of a slab of porous catalyst with
two exposed faces a distance 2dp apart and with
its other edges sealed. Then there is a single
spatial variable p, the dimensionless distance from
the central plane and the exposed surfaces are
p =- 1. To make things even simpler, we con-
sider only symmetrical solutions for which the
derivative vanishes on p = 0. Then the equations

dp2 2P(w),
dp 0, = 0,




w = 0, p = 1,

f -1( dw
71 =- P (w) dp =]p--1
Though the sphere could have an equally
metrical solution and is more natural, sin
does not need sealed edges, its Laplacian is
complicated and p enters explicitly.
The second order autonomous form of
tion (15) suggests the phase plane might
some insight into the solution. Let W denote
derivative -dw/dp, then

=-W, w(1) =0,

d-= + 42P(w) W(0) =0.

In the w, W plane this means that the traje
w(p), W(p), 0 Figure 1, which starts (p 0) at some poi
the w-axis and ends (p = 1) on the W-ax



ce it

e the

The isoclines could be drawn in the plane and
we could sketch the solution curves, but they
would have to be redrawn for each value of ).
However p is only acting as a parameter along the
solution curve and there is no reason why should not be the parameter instead. Let Op T,
s(r) w(Tr/), S(r) = W(Tr/)/4) then

ds = -S, s(4=0,

dr F P(s), S(0) O,

1= S .
71 := S( )V




(19) Now the isoclines can be drawn once and for all
in the s, S plane, for suppose dS/ds -w then
(20) dS P (s) 1
_ S - or S=-- P(s).(25)
ctory ds
M in But this means the isoclines are all derived from
nt on the curve P (s) which represents the reaction
is. rate expression and that for a given slope w the
curve for wo = 1 is simply redrawn with a ver-
tical scale of 1/1o. Let us suppose that the curve
S = P(s) is like PQ in Fig. 2. Then it can be
crossed with a number of short lines of slope -1.
The curve RQ whose ordinates are just twice
those of PQ is ticked with lines of slope -1/2,
whilst TQ at half the height of PQ is the iso-
cline of slope -2. The s-axis and the vertical
s =1 correspond to infinite and zero slope re-
spectively. Quite clearly then any solution curve
such as LM will take off vertically from L and
go in an arc of decreasing slope to M. In fact


FIG. 1
The curve is a solution of the first-order non-
linear equation for W (w) which can be obtained
by dividing (20) by (19), namely

dW P (w)
dw W


This equation can be solved for any value of 4
and will give a solution if the path LM cor-
responds to going from p = 0 to p = 1 i.e. if
M = L dw -
SL dp= M W(w) =1.

FIG. 2


if So is the value of s at L, the arc S (s) is given

S2(s) = 2 P (s')ds'

and M is the point

Once this curve is determined the value of 4
which corresponds to it comes from the integral

=fo d, = S ds (27)
s S(s) (27)

Thus each trajectory can be made to yield a point
on the q,o-curve by equations (24), (26) and
But what can we learn of the behavior of
-7 (4) without actually doing any of the integra-
tions. First we see that for a solution curve L'M'
lying underneath LM the corresponding value of
4 must be smaller. For the integral can be

f S( ,) dS
Jo --o(S)S

and in comparing the contributions of the seg-
ments AB and A'B' to their respective integrals
we see that (-cw) is greater on A'B' than on
A B so that the integrand is smaller. Moreover
the path LM is over a greater range of S than
is L'M' so that on both counts the value of 4)
corresponding to LM must be greater than that
which corresponds to L'M'. The trajectories can-
not cross one another (except at Q) hence a se-
quence of trajectories with increasing so give an
increasing sequence of values of 4).
When () = 0 the equation gives the solution
w = s = 0, so that so = 0 corresponds to 4) = 0.
Does so = 1 correspond to P = co ? The answer
must depend on the behavior of P (s) near its
zero at s = 1. Let us suppose that P (s) = -P'
(1) (1-s) + 0 (1-s)2 in the neighborhood of s = 1.
Then the indeterminacy of dS/ds near s = 1, S
0 is resolved by noting that
dS P(s) P'(1) (1-s)
ds S S
can be integrated to give

S2= -P'(1) (1-s)2.
The trajectory that starts from Q therefore takes
off tangentially to the line S = -X (1-s) where
X2 = -P'(1). If this is substituted in the in-
tegral (27) with so = 1 we see that the integral
diverges. It follows that the trajectory through
Q (QN in Fig. 2) does correspond to an infinite
value of 4). What is remarkable however is that
the solution curve QN does not go to infinity but
reaches s = 0 for a finite value of N. This is
clearly the case since if it sneaked up the S-axis
it would have to have an increasingly large slope.
But near the S-axis for large S the slope of the
trajectories gets increasingly small, so that QN
must finish at a finite point N. Let the value of
S here be S ; then, since the trajectories LM
move up under QN as ) increases, S(4)) ap-
proaches S. as 4) gets large. But equation (24)
then shows that T1 ~ S / P for large values

of 4. Moreover the value of
lated from equation (26),

S can be calcu-


S2 = 2 j P(s')ds'
Thus a rough sketch of isoclines can be made
to yield a lot of information without really solving
any equation. However, it should be mentioned
that some of these arguments depend on the
rather straightforward shape of P (w) and
would not carry over quite so easily to a more
general shape. In particular a family of nonin-
tersecting curves of the type LM could be found,
approaching 0 for )-+00 and QN for 4-+oo but
they would not necessarily correspond to a mono-
tonic sequence in ). The arguments about QN
would also have to be modified if P'(1) were not

lies in the kinetic expression P(w) which is
limited only by the normalization P(0) = 1, P(1)
= 0. If we take an isothermal (f8 = 0) first order
reaction P (w) = 1 w and the equations become
linear. In particular we have analytical solutions
for simple shapes such as the sphere. In particular


1 d 2 dw +) (1w)
d p + (1l-w) = 0
p2 dp dp
w(1) =0, w' (0) = 0
has the solution

w(p) = 1 sinh
p sinh 4)
Thus the effectiveness factor is

= -- coth--7


1 d (p dw
pq dp \- dp

and with this trial function for w it is
2 (q+l) a = -2(q+l)w(p)/(1-p2).

(29) Thus the differential equation would be satis-
fied at the point p = pi if the value of a, and so
of w =- w(p,) = a (1-p2), were chosen to


which again has the asymptotic property that
'4q) tends to a constant (in this case 3) as

It is not suggested
that the maxims or their illustration . .
provide an infallable recipe which when followed
will open the portals of any problem.
Rather, they are adumbrated
as a framework.

In this case the complete solution can be ob-
tained rather easily and one might use this as a
starting point to explore other variations such
as those of shape or in the boundary conditions.
In any case it ties in with what we learned from
the method of isoclines about the general be-
havior of the planar case. From the simple form
of solution we see that the value of w (p) rises
from its zero boundary value with exponential
sharpness near the surface p = 1. In fact if
P = 1-y
w(T) = 1 exp ) y
so that w quickly rises to a constant value of 1
when ) is large.

OFTEN SOMETHING CAN BE learned from an ex-
tremely crude numerical method. This was
first shown for this problem by Stewart and Vil-
ladsen [6]. At any rate for small values of ),
w (p) = a (1-p2) is an approximation that satis-
fies the boundary conditions for a symmetrical
solution. We can deal with all three symmetrical
shapes (the slab, cylinder and sphere) by writing
the Laplacian as

2(q+l)w,/(1-p12) = 02P(w).


There is a full-scale theory, that of collocation
methods, to say where the point pt is best taken,
but we can use our experience with the sphere in
the previous section. When q = 2, for the sphere,
and P (w) = 1-w, for the first order reaction,
equation (31) gives
w, = 2 (l1-p.2) /[6--2 (1-p2)].
Since the approximation should be good for small
4 we might hope that this would agree with equa-
tion (29) for small ). In fact the expansions are
identical in the first term )2 (1-pt2) /6 and
agree in the term of order 04 if pi2 = 3/7 or
p, = 0.6547. A more general analysis would show
that pl2 = (q+l)/(q+5) is a good choice.
Let us use this value of pi but return to a
general P (w). Then with q = 2, pt2 = 3/7, equa-
tion (31) is

21w p (wl),
24)2 -


Before exploring this equation let us note that
to the same approximation

e dp )

Hence, by (14),

-2a 2w,

21w = 2 P(w).


Equation (32) lends itself to a graphical solu-
tion, as is shown in Fig. 3, for the right hand
side of the equation is the fixed curve P (w) and
the left side the straight line through 0 of slope
21/202. When (A is small the line is steeply sloped,
like OA, and 7j is close to 1. In fact, if the part
of the curve P (w) near P (0) = 1 is approximat-
ed by the straight line P(w) = 1+P'(0)w),
then equation (33) can be solved for w, and


P ='(1 0)2- 1 2P' (0) 2 + 0 (2)

On the other hand if 4P is very large the same
kind of straight line approximation gives

21 [1 + 21 -1
7-- 2 [ 1 2[-P'(1)]402

This is not a very good approximation since we
know that 4o) tends to be constant for large
). However this is not surprising since w(p) =
a (l-p2) is not a good approximation for large ).
Much more important is the revelation of the
possibility of multiple steady states that is made
in Fig. 3. For if the curve P (w) is as shown
then for values of 4 giving lines between OBC

time one must be cautious not to push conclusions
based on crude approximations too far.

T HE LIMITING CASES of large and small (A have
already been considered in the partial solu-
tions we have obtained. However they can be
approached also from the equation itself. If
() = 0, V2w 0 giving the solution w = 0
and -q = P (0) =1. Let us see if a solution can be
generated in powers of P)2 by setting
w (p) = 02w, (p) + P4w. (p) + ...
The function P (w) must be expanded similarly
P(w) = l+2P'(0) w+
4[P'(0)w,+j/2P"(0)w,2] +
Then comparing powers of 2 we have

V w7 = -1

Fig. 3

and OGH there will be three intersections such
as D, E and F which will give three values of 71.
We cannot expect much accuracy beyond the point
G, but Stewart and Villadsen showed that a sur-
prising accuracy was maintained [6]. The im-
portant thing is that it gives notice of the multi-
plicity of steady states. Furthermore the variable
w, can be made a parameter in the computation
of the 1,4)-curve, since -q = P(w,), 42 = 21w,/
2P (w,). This suggests that some internal value
of w, such as w(0) or max w(p) may be taken
as the parameter along the 7,0-curve in more
general cases.
On the basis of this understanding computa-
tion by more exact methods, such as those de-
scribed by Villadsen and Stewart [6] and Fin-
layson [7], can safely go forward. At the same

in fl, w, = 0 on afl

V w2 = -P'(0) W in f, W1 = 0 on Zn, ...
These equations are linear nonhomogeneous equa-
tions and are easier to solve than the nonlinear
equation (13). Moreover we can see the form
which r7 will take, for first w, can be found and
averaged to give k, (say), then w2 can be found
and its average, k2, calculated, and so on. This
then gives
7= 1l+k,P'(0) 2+[k,2P'(0)+ l/2k 2P"(0)]4+ ...
which accords with equation (34).
This solution for small 4) is obtained by a
regular perturbation in powers of 42 and a regular
perturbation does not involve a change in the
character of the equations. The situation for large
4 is quite different for, if we put e2 = 1/42, we

e2V2w + P(w) = 0.


The limiting case e = 0 is here quite different
for it has changed a second order differential
equation into a non-differential equation
P (w) = 0 whose only solution is w 1. This
makes sense since it claims that when ) is large
(i.e. the reaction rate is vastly greater than the
diffusion rate) the reaction is virtually complete
everywhere. But it cannot be true near the sur-
face, for w = 0 on the surface itself and the
solution is a continuous function of position.
This is the classic situation of a singular per-
turbation problem in which an "inner" solution-
in this case a solution near the boundary-has to


be matched with an "outer" solution-in this
case w = 1. Singular perturbation problems have
a large literature [8,9,10,11] and this is no place
to try to survey it, but mention should be made
of the unusually lucid introduction that Segel
and Lin [1] give in their book. In the present
case we know from the experience of Section 2b
that for large t, w can rise with exponential
sharpness from the boundary. In fact the solu-
tion we found there suggest that we should intro-
duce Oy where y is the normal distance from
the boundary, as a new variable. This is known
as a "stretching transformation" since it stretches
y proportionately to ). If we introduce an or-
thogonal coordinate system in the boundary sur-
face, say {,ij, and take C -= -y as the third co-
ordinate then the Laplacian in equation (36) is

2 w + 72w

where V22 is a second order operator in e and q.
Substituting this in (36) and letting e 1/4A
tend to zero gives

d2- + P(w) =0.

But this reduces the problem to the one
dimensional case that we explored in Section 2a.
Nor is this surprising since when all the change
is confined to a thin shell on the outside of the
pellet the curvature is not important and it might
well be unfolded as a flat plate. Now the flat plate
analysis gave

[S (4)]2 = 2fP(s')ds'

and when So approaches 1, as in this

S So .= [ 2

and so by eq

case, -> oo


dw dw dw
dTj dy dT

uation (14)

) a S(, /vcp

S ~ S(.


This accords with all that has gone before. In
particular if, for a sphere, dp is the radius a- =
47r, v = 47r/3 while for a first order reaction

P(s') = 1-s', S% = 1 Thus ? 7 3/4 as

we see also from equation (30).

This is the classic situation
of a single perturbation problem
in which an "inner" solution-in this
case, a solution near the boundary
-has to be matched with an
"outer" solution ...

The use of the phase plane and perturbation
methods has been stressed in illustrating the
value of the qualitative study of equations. These,
of course, are not the only methods available-
the maximum principles [12] and some of the
theorems on the behavior of the solutions of
equations come immediately to mind. Amundson's
papers in general, and some of those with Luss
[13] and Varma [14,15] in particular, show how
the skillful use of such tools can give insight into
much more complicated systems than the one con-
sidered here.
It is not suggested that the maxims, or their
illustration in the above example, provide an in-
fallible recipe which when followed will open the
portals of any problem. Rather are they adum-
brated as a framework within which one aspect
of the craft of mathematical modelling may be
"Exercised in the still night
When only the moon rages
And the lovers lie abed
With all their griefs in their arms."
Sufficient will be the reward if for a few moments
we find that it is "by singing light" that we have
haply laboured. 5

1. Lin, C. C. and Segel, L. A. Mathematics Applied to
Deterministic Problems in the Natural Sciences.
Macmillan Pub. Co. New York 1974.
2. Lonergan, B. J. F. Insight: A Study of Human
Understanding. Philosophical Library Inc. New
York. 1958.
3. Aris, R. Chem. Engng. Educ. 8, 19 (1974).
4. Aris, R. The Mathematical Theory of Diffusion and
Reaction in Permeable Catalysts. (2 vols.) Clarendon
Press. Oxford. 1975.


5. Varma, A. Chem. Engng. Sci. 29, 1340 (1974).
6. Stewart, W. E. and Villadsen, J. Chem. Engng. Sci.
22, 1483 (1967).
7. Finlayson, B. A. The Method of Weighted Residuals
and Variational Principles. Academic Press. New
York 1972.
8. Acrivos, A. Chem. Engng. Educ. 2, 62 (1968).
9. Cole, J. D. Perturbation Methods in Applied Mathe-
matics. Blaisdell. Waltham. 1968.
10. Murray, J. D. Asymptotic Analysis. Clarendon Press.
Oxford. 1974.
11. Van Dyke, M. Perturbation Methods in Fluid Me-
chanics. Academic Press. New York. 1964.
12. Protter, M. H. and Weinberger, H. F. Maximum
Principles in Differential Equations. Prentice-Hall.
Englewood Cliffs. 1967.
13. Amundson, N. R. and Luss, D. Can. J. Chem. Eng.
46, 424 (1968).

book reviews

Mathematics Applied to Deterministic Problems
in the Natural Sciences
By C. C. Lin and L. A. Segel
MacMillan, New York, 1974
Reviewed by R. Aris, University of Minnesota
It is generally agreed that it is all very well
to teach students the methods of solving different
types of equation, but that it is much more dif-
ficult-yet even more essential-to teach them
how to develop a mathematical model, to assure
themselves of its reasonableness and to get as
much insight into it as possible before trying
to compute a solution of its equations. Of the
available books on the methods of applied mathe-
matics the one under review is unique in ad-
dressing the more difficult task without neglecting
the easier. As an introduction to the craft, as
well as to the skills, of the applied mathematician
it is as distinguished and valuable as the distinc-
tion and accomplishments of its authors would,
in any case, lead us to expect.
Like that well-known province of the Roman
empire, "liber est omnis divsa in tres parties "
The first part introduces the scope and range of
applied mathematics in a dramatic fashion by
outlining the way in which the physical descrip-
tions of galactic structure and the chemostactic
behavior of slime mold amoebae lead to challeng-
ing mathematical problems. Deterministic sys-
tems and the generation of ordinary differential
equations and random processes and their connec-
tion with partial differential equations are the sub-

14. Amundson, N. R. and Varma, A. Can. J. Chem. Eng.
50, 470 (1972).
15. Amundson, N. R. and Varma, A. Can. J. Chem. Eng.
52 580 (1974).

A preliminary version of this paper was given as a
seminar in the UNESCO project of postgraduate educa-
tion (VEN 31) at the Universidad Oriente, Puerto la
Cruz, Venezuela under the local coordination of Prof.
Hassan Elmayergi. It is a pleasure to record my in-
debtedness to Ray Fahien for many valuable conversa-
tions in which we probed the nature of the mathe-
matician's "magnificent grasp of the obvious." I am also
indebted to Professor Arvind Varma for some valuable

jects of the next two chapters and Fourier analy-
sis, illustrated by problems of heat conduction,
that of the two that follow. These five chapters
provide a survey of the interaction of mathematics
with physical phenomena for, besides those men-
tioned above, planetary orbits, the pendulum,
Brownian motion, coagulation, twisted beams and
DNA molecules all come into the picture. Nor are
the mathematical notions confined to the pedes-
trian, for the authors do not hesitate to take up
Poincar6's perturbation theory of periodic orbits
and allude to the Gibbs phenomenon.
The second part of the book would be called,
in the argot of our day, "very unique" for here
some of the fundamental modes of applied mathe-
matical thinking are explained in detail. Indeed
the detail is often "painful,' not in the contempor-
ary connotation but in the older and more honor-
able sence of 'painstaking.' I know of no other
place where the beginner and proficient alike will
find a systematic account of the way in which
the model and its equations should be handled and
of how intelligent simplifications, dimensional
analysis and the understanding of scale can be
used to bring the problem into its most responsive
form. This is the foreplay of mathematical
analysis and, as might be anticipated by analogy,
calls for sensitivity and intellectual tact. These
techniques are admirably illustrated by formulat-
ing and solving a problem in osmotically driven
flow. But the second part also contains a chapter
on regular perturbations and an introduction to
singular perturbation theory that is a model of
all that an elementary exposition of a deep sub-
ject should be. Chapter 10 takes this exposition


further by treating Michaelis-Mention (or Lang-
muir-Hinshelwood-Hougen-Watson, not to men-
tion Briggs and Haldane) kinetics in detail.
Finally the phase plane, multiple scale expansions
and linearization are introduced in connection with
the simple pendulum.
After the virtuosity of this second movement,
the third movement (just to mix my metaphors
absolutely and uniformly) is relatively traditional.
It provides an introduction to the theory of con-
tinuous fields and their associated partial
differential equations, considering first the elastic
vibrations of a bar, then continuum mechanics and
inviscid flow and, finally, potential theory with
an acoustical example. In a second volume we are
promised more continuum mechanics, with Carte-
sian tensors viscous flow and elasticity, dispersive
wave theory and variational methods.
In short it is a book that can be recommended
without reservation both for its style and content.
It can be recommended for chemical engineering
courses; for the chemical engineering student-
the least parochial of the engineering family-
will welcome the catholicity of example which the
chemical engineering teacher will find much in-
struction in working up further examples of his

An Introduction to Nonlinear Continuum
by Gianni Astarita
Societa Editrice di Chimica, 133 pp.
Reviewed by Martin Feinberg,
University of Rochester
Since the turn of the century anyone who has
set pen to paper in an attempt to advance thermo-
dynamics has come under attack from one quarter
or another, and the only thing upon which we all
agree is that Gibbs was a very smart fellow. So,
not knowing what to make of the battles raging
around us, we opt for neutrality: we confine our
teaching to the substance and style of 19th cen-
tury thermodynamics. Although this course of
action has served us reasonably well and, inci-
dently, lends the subject an undeniable charm, at
some point we must ask if such a state of affairs
is to prevail forever.
It might be argued that, before we commit
our classrooms to anything new, we ought to sit
back and wait until the relative merits of various
20th century theories are settled by experiment.

Well, I don't think things work that way for a
subject as broad in scope as thermodynamics.
What happens, I suppose, is that a theory is
offered by Professors A,B, and C, is learned and
found compelling by Professors X,Y, and Z, who
in turn teach the theory to students, write text-
books, try their best to make converts of col-
leagues, and so on. If the theory has appeal
and/or the political climate of the day is favor-
able, it penetrates into and diffuses through the
mainstream of scientific thinking and ultimately
flourishes if, in a sense difficult to make precise,
that theory is "successful" in applications.
In 1963 Bernard Coleman and Walter Noll
published a paper1 which articulated a simple,
yet powerful, line of thermodynamic reasoning
based upon the Clausius-Duhem inequality and, by
way of example, demonstrated how that line
renders results for familiar classes of materials-
e.g., linearly viscous fluids which are Fourier heat
conductors. In 1964 Coleman published a remark-
able paper2 in which he used the methods pro-
posed a year earlier to deduce results for materials
with fading memory (e.g. polymer solutions and
melts). Since then the theory has been explored
and used extensively by others (notably Gurtin)
in an explosion of papers generally endowed with
high technical excellence. One can never be cer-
tain of these things, but I believe the body of
theory precipitated by the Coleman-Noll paper of
1963 will, in fact, be "successful" and will come
to play a permanent role in the way chemical
engineers think about thermodynamics.
If this is so, then Professor Astarita's mono-
graph must certainly be regarded as an important
step in the coming assimilation process. Although
it is not the first volume which describes modern
methods based upon the Clausius-Duhem in-
equality, it is, I believe, the first written by a
chemical engineer with other chemical engineers
predominantly in mind. As such, the book is like-
ly to be a critical, if not decisive, factor in the
manner with which our colleagues and students
respond to the theory, at least in the immediate
Before I discuss the monograph in detail, let
me state my own biases plainly. I admire the work
Astarita admires, probably for the same reasons.
Plausible premises are stated clearly at the out-
set (to be accepted or rejected as one sees fit) and
conclusions are drawn from these using standards
of logic, rigor, and linguistic precision normally
insisted upon in all other areas of science we deem
Continued on page 133.


A Freshman Course


University of Illinois
Urbana, Illinois 61801

IN ORDER TO PROVIDE better and earlier aware-
ness of the nature of chemical engineering, a
freshman course has been developed at the Uni-
versity of Illinois at Urbana-Champaign. The ob-
jective of the course is to provide a qualitative
picture of ChE and to describe the scope of pro-
fessional activities into which chemical engineers
enter. Too often, choice of a curriculum is difficult
for beginning college students because they do
not have good information about the consequences
of their choice. For example, the traditional first
technical course in ChE (material and energy
balances) is at the end of the sophomore year.
As a consequence, important career decisions are
often made by prospective chemical engineers
on the basis of their interest, or lack thereof, in
chemistry, physics and mathematics instead of on
the basis of knowledge about ChE.
The content of a freshman orientation course
depends upon such things as the individual teach-
ing the course, the class size and composition,

TABLE 1: Course Outline
(a) The Nature of Chemical Engineering: chemical re-
actions, separation of chemicals, large-scale processing
Nitrogen fixation
Synthetic rubber
Soap and detergents
(b) The Activities of Chemical Engineers
Research and development
Process evaluation and design
Plant operation
Sales and Marketing
(c) Defining Engineering Problems: common sense, the
scientific method, and economic awareness
Engineering and chemistry
Economics of alternative reaction paths
Material balances and species allocation
Choosing separation methods

Professor Alkire studied Chemical Engineering at Lafayette College
and at the University of California at Berkeley. He has been on the
faculty of the University of Illinois since 1969. In addition to teach-
ing, he carries out a research program in the area of electrochemical

the number of credit hours, the style and nature
of the ChE department concerned and the rela-
tion among engineering departments through
core programs. This paper outlines one route
which has been found effective.

THE COURSE, "The Chemical Engineering Pro-
fession," is required in the second semester
of the freshman year and has as prerequisite one
semester of college chemistry. The 1-hour course
meets fifteen times during the semester. There is
no required text. Grades are based upon home-
work problems, a field trip report, and a semester
Lecture content, outlined in Table 1, includes
use of slides as well as demonstration experiments
performed by the instructor or his assistant. The
lectures are grouped into three general topics:
a) The characteristics of chemical engineering
which distinguish it from other disciplines.
b) The activities of chemical engineers.
c) The importance of combining common sense,
the scientific method, and economic awareness
in defining engineering problems.


TABLE 2: Demonstration Experiments
Soap is prepared from lye and lard by the assistant following
the instructions on a lye bottle purchased in a grocery store.
Nucleate vs. Film Boiling
A copper tube containing a thermocouple is immersed in liquid
nitrogen and the cooling curve is recorded on a strip-chart. The
tube is then removed and coated with a thin layer of vaseline
and immersed again. The insulated tube cools faster because
nucleate boiling occurs instead of film boiling.

Cooking Hot Dogs
A thermocouple is inserted along the axis of a hot dog which
is plunged into boiling water, and the increase of temperature
at the centerline is recorded and compared with theoretical
unsteady-state heat conduction calculations.
Time Bombs
Cans are prepared according to instructions in the reference
and filled with natural gas. The gas is ignited and the time be-
fore explosion is recorded and compared with theoretical

Polyurethane Foam Demonstration
Ingredients from a commercially available foam kit (Mobay
Chemical Co., Penn Lincoln Parkway West, Pittsburgh, Pa. 15205)
are mixed and the exothermic process occurs. After two minutes
the foamed plastic is rigid.
Nylon Rope Synthesis
6-10 Nylon is synthesized from sebacoyl chloride and hexame-
thylenediamine by interfacial condensation. The nylon skin is
removed from the interface, forming a rope, and is wound
upon a rod.
Additional experiments planned for the near future include demon-
strations of viscoelastic behavior [12], pseudoplastic flow [13] and
a model Solvay tower [14].

The demonstration experiments which accompany
the lectures are outlined in Table 2.
The first lecture emphasizes the economic
need for chemicals and how a ChE background
gives access to many business areas in addition
to the purely technical aspects which are seen
by the students in coursework. An introduction
to the department is always of interest: the lay-
out of the building and labs, the faculty size,
number of students in the curriculum, the nature
of employment and salaries of recent BS gradu-
ates, and the fraction going on to graduate educa-
tion. A list of trade periodicals (CEP, C&E News,
etc.) is provided along with the library location
and procedures. It is also useful to provide in-
formation about applications for scholarships
and loans which might be available.
Lecture Group (a) emphasizes three charac-
teristics of chemical engineering:
* Ch.E.'s understand chemical reactions.

* Ch.E.'s know how to separate chemicals.
* Ch.E.'s know how to carry out processes on a large scale.
Slide presentations are used to show flow sheets
and process equipment. Nitrogen fixation is a
good example since ample material is available
[1] to illustrate all three points. The manufacture
of synthetic rubber is also well-documented [2]
so that a slide presentation can be prepared. As
a change of pace, a discussion on making moon-
shine [3] gives a good opportunity to point out
dilemmas involving materials of construction,
siting the facility, process engineering, produc-
tion problems, quality control, marketing stra-
tegies, and ultimate plant recovery. The produc-
tion of penicillin [4] is always impressive owing
to the conditions under which the process was de-
veloped. The small-scale home preparation of
soap [5] (Expt. #1, performed in class) can be
compared with commercial manufacture of de-

LECTURE GROUP (b) consists of examples rang-
ing from R&D to marketing. The discussion
of research emphasizes the importance of intuition
and the ability to predict and to scale-up. Experi-
ment (2) nucleatee vs. film boiling) usually
tricks the student's intuition and leads nicely to
a discussion of optimum heat exchanger fin de-
sign [7]. Results from Experiment (3) (cooking
hot dogs) can be compared with unsteady-state
heat conduction calculations for a rigid solid [8];
agreement within 10% is usually obtained. Ex-
periment (4) (time bomb) is especially impres-
sive [9] and demonstrates scale-up criteria by

The first lecture emphasizes the
economic need for chemicals and how a ChE
background gives access to many business
areas in addition to the purely technical
aspects which are seen by the students
in coursework. An introduction to the
department is always of interest.

mathematical modeling. It is important to empha-
size the value of graduate education for those in-
terested in R&D endeavors.
Process evaluation and optimum design is
nicely illustrated by the design of an overland sul-
fur transportation system [10]. To stimulate the
imagination, Experiments (5) (polyurethane


foam) and (6) (nylon synthesis) are good
examples for drawing out further discussion.
Problems of designing around hazards [15], and
analysis of plant failures [16] always makes a
sobering impression of the energy contained in
chemical plants.
Plant operation, process engineering and pro-
cess management topics can be brought out
through presentation of slides of process equip-
ment. For example, I obtained from a campus re-
cruiter a detailed sequence of several dozen slides
involving a pipe-still furnace. Of special value
at this stage in the course would be a field trip

The discussion of research emphasizes the
importance of intuition and the ability
to predict and to scale up. Experiment (2)
usually tricks the student's intuition and leads
nicely to a discussion of optimum
heat exchanger fin design. Experiment (3)
(cooking hot dogs) can be compared with unsteady
state heat conduction calculations for a rigid solid.

to a local production facility.
Marketing, sales engineering and higher-level
management are areas where the importance
of communication skill, personal style and busi-
ness acumen can be emphasized. It has been
difficult to obtain ancillary material for this por-
tion of the course, and I rely upon personal ex-
Lecture Group (c) is based primarily upon
materials contained in Ref. [17]. A good starting
point is the discussion of different perceptions of
advantageous routes for carrying out chemical
reactions as viewed by a chemist versus a
chemical engineer (Chpt. 2, Ref. [17]). The
dichotomy emphasizes once again the chemical
engineer's concern about large scale processing
with impure substances under economic and
safety constraints. For example, the evaluation
of five different process routes for phenol pro-
duction provides a good basis for extended dis-
cussion. Economic aspects of choosing different
reaction paths (Chpt. 2, Ref. [17]) is impressive
to students since it demonstrates the narrow profit
margin involved in large-scale production. Relat-
ed aspects include uncertainty of feedstock price,
sudden application of pollution standards on by-
product disposal, development of new processing
technology, the economic nature of the market
for the product, and establishing the optimum
return on investment needed for competitive sur-
vival. Once the best process route is chosen, a

discussion of species allocation and flow sheets
(Chpt. 3, Ref. [17]) demonstrates the importance
of common sense and good engineering intuition,
including an awareness of corrosion and classical
physical chemistry. An introduction to simple ma-
terial balances is always of interest since the
students know that the next ChE course will be-
gin at this point. Once the process flow sheet is
developed, the problem of choosing the best sepa-
ration method provides another basis for a com-
mon sense approach (Chpts. 4 and 5, Ref. [17]).
Lecture Group (c) often motivates students by
demonstrating the importance of learning their
engineering and scientific fundamentals in order
to develop their intuitive prowess. It becomes
abundantly clear that the act of defining technical
problems is central to good engineering, and that
that act requires application of the scientific
method, common sense, and economic awareness.

SEVERAL ADDITIONAL topics can be salted into
the foregoing outline as the mood of the class
dictates. An important topic is graduate educa-
tion; students are usually interested in engineer-
ing, business, medicine and law. I outline the
time-scale for making these decisions, mention
the different financial arrangements involved and,
within engineering, describe the different styles
which departments may have respect to graduate
program, the better students often begin thinking
about their next move at this time. For detailed
examples of research in engineering, I draw upon
my own program and sometimes invite a gradu-
ate student to give a short presentation of his
research topic.
Another topic concerns departmental affairs
in which freshmen can participate such as
A.I.Ch.E. Student Chapter Meetings. We also
have an Engineering Open House for which fresh-
men often prepare demonstration experiments as
a basis for their term paper. Such activities often
create a sense of identity and pride which sus-
tains student interest in ChE in face of challenges
in other coursework.

THE COURSE HAS BEEN presented four times with
class sizes ranging between 23 and 75 students.
There was no difficulty in stimulating class dis-
cussion even with the larger class sizes. Students
from other departments constituted about 14%
of class enrollments.


The letter grading of the course is necessary
because it is a required course. The grade is usual-
ly based on homework (50%), term paper
(25%) and plant trip report (25%). Because
the plant trip is not required for the course, those
students who do not attend are asked to imagine
what they would have seen and submit a brief re-
port of their imagined observations. The average
grade distribution to date has been: A-53%, B-
30%, C-11%, D-3%, E-3%. I suggest that the D
and E students drop ChE, and that the C students
think carefully about their career choice. Grad-
ing by pass-fail would be attractive if it were
Homework problems were chosen so that the
students had the opportunity for extended pur-
suit of the problem if they wished. For example,
instructions were provided for the home-made
production of soap by the batchwise process
demonstrated in class in Experiment (1) ; in
addition, the chemistry for a two-step (hydroly-
sis/neutralization) process was provided. Stu-
dents were asked to evaluate which process makes
it possible to design for continuous, not batch-
wise, operation, to estimate production rates for
one million people, to develop a flow sheet for a
continuous process and discuss the overall en-
gineering design. Three or four homework prob-
lems were usually assigned during the semester.
The response was very conscientious, with the
better quality problems often running ten pages
of discussion.
In defining the term paper, the students were
instructed to choose any appropriate topic which
interested them and pursue it in whatever

A good starting point is the discussion of
different perceptions of advantageous routes
for carrying out chemical reactions as viewed
by a chemist versus a ChE. The dichotomy
emphasizes the ChE's concern about large
scale processing with impure substances
under economic and safety constraints.

manner they saw fit. I offer to help discuss paper
content if the students come to me with a topic
in mind. The papers were surprisingly articulate,
well-poised and conscientiously executed. In many
cases, students performed experiments, did calcu-
lations or literature reviews, and submitted
physical props in support of their work. Pre-
paring the term paper was the most valuable
experience to many because it got their feet wet.

A teaching assistant is essential for preparing
lecture demonstration experiments, grading, and
developing course improvement topics. For the
range of class sizes encountered, a single assistant
was adequate.
The course content, including slides and
demonstration experiments, was developed with-
out excessive effort in a period of about six
months. During this time the ChE trade journals
were scanned regularly, along with the standard
texts on chemical processing. The major difficulty
was in developing demonstration experiments
and obtaining slide sequences of process facili-
A crucial aspect of the course lies in sensing
the mood of the class, and not proceeding too
quickly into detailed discussion if their interest
is not yet aroused. Because the course met only
once a week, each lecture had to be complete in
and of itself.
Although it is difficult to measure success of
freshman courses, one can claim that the reten-
tion of freshmen into the sophomore year is a
useful measure of whether the course succeeds in
developing interest in the curriculum. For the six
years prior to offering the freshman course, the
average retention of second-semester freshmen
into the sophomore year was 57 %. For the period
during which the course has been offered, 86%
of the students who took the course continued
into the next semester in ChE. Although such
data are influenced by any number of other fac-
tors, it seems reasonable to suggest that the
course has contributed to increased retention to
a considerable extent.

A ONE-HOUR FRESHMAN course for chemical
engineers has been developed in order to pro-
vide qualitative information upon which career
decisions may be made by students. Discussion
topics, including lecture demonstrations, are
chosen to illustrate the wide scope of ChE activi-
ties. Students have open-ended avenues of re-
sponse through homework and term projects.
Freshman courses could also be built around
the development of quantitative skills through
which insight into engineering methods may be
gained. However, with respect to the goal of
career orientation, the development of quantita-
tive skill to sufficient depth would be difficult to
achieve in a one-hour course. The qualitative
Continued on page 145.




University of Maine
Orono, Maine 04473

A T MANY UNIVERSITIES the once monolithic
common core of studies for beginning students
is crumbling. There is a widespread feeling that
students should not have to wait for as much as
two years to come into close contact with their
department and chosen discipline, and that this
delay is an important contributor to the loss of
students from engineering during the first two
years of study. Once the decision is made to make
available to engineering freshmen a course in
chemical engineering, the obvious next question is

.. during much of their training, students will
not receive or at least will not perceive
an integrated experience. I believe this
lack of ... seeing how all the parts of their
training fit together . is a major factor in
what students perceive as a lack of relevance ...

what this course should be. Perhaps it should
be plant design. Recently in this journal Gordon
Youngquist [1] wrote of his experiences with a
freshman course in plant design at Clarkson Col-
lege. I would like to describe my own experiences
with a similar course at the University of Maine.
Most ChE departments offer a plant or pro-
cess design course as an integrating experience in
the senior year. Its placement in the final year of
study seems reasonable in that the student at
that point has the most knowledge to integrate.
But implicit in that decision is the idea that dur-
ing much of their training, students will not re-
ceive or at least will not perceive an integrated
experience. I believe that this lack of integration
-of seeing how all the parts of their training fit
together and further their career development-
is a major factor in what students sometimes per-

ceive as a lack of relevance in their training.
The students also may not have a clear idea
of the systems aspect of the chemical process,
i.e. that there are interactions between process
elements such as the reactor and the separator,
and that optimal design requires examination of
the system as a whole. Finally, the student may
lack a clear idea of the role of economic con-
siderations in reaching optimal engineering de-
cisions. (They may as a result fail to elect courses
in economics from the smorgasboard of humani-
ties and social studies electives we offer them.)
Plant and process design courses are excellent
vehicles for remedying these problems, but they
come late. I wished to test the idea that by
studying the design of a very simple chemical
process in their freshman year, students could
obtain these important insights at the start of
their studies rather than at the end.
At the University of Maine, ChE freshmen
all take a two-semester course "Introduction to
Chemical Engineering" in which they select and
work on a number of laboratory projects from
among those offered by the department. The
projects are designed to introduce them to the
practice of chemical engineering. Each project
lasts about four weeks, and the students work on
a total of six during the year. As one of the
projects, I offered the design of a chemical plant,
and I taught this to three different groups during
one semester in the Fall of 1975. The groups met
one afternoon each week for four hours. There
was no homework assigned other than the prepa-
ration of a final report by the group. There were
no formal examinations.
There were six to nine students in each group.
We met around a table in a room which did not
have a blackboard. There was about one hand or
desk calculator per two students. I believe that
all of these elements-small groups, calculators,
an informal setting, close contact between in-
structor and students-were important positive
factors. The electronic hand calculator, for


example, is working a quiet revolution in
engineering studies. The number and kinds of
calculations that we could carry out in a short
period of time was very much influenced by the
availability of these instruments. The absence of
a blackboard helped in keeping our sessions from
degenerating into the lecture format. There was a
great deal of "eyeball contact" and it was not
difficult to keep everyone involved. The instruc-
tional method used involved a combination of
questioning and guiding. Calculations were
carried out simultaneously at several places
around the table. Feed-back, the detection and
correction of errors, was immediate.

DURING THE FIRST session with each group we
developed the basic scenario. The process
might best be described as a "let's pretend"
game in which everyone participated. I began
by proposing that we wished to react A and B in
a chemical plant and sell the product. "What do
we need to know to design the plant?" With
some coaxing and guiding the students began
to ask the necessary questions and to provide
the answers. The basic chemical plant developed
in each case consisted of a reactor and a separa-
tor. In the separator the unreacted A and B were
removed from the final product C and recycled
to the reactor. In one project the separator was

Ronald A. Shelden studied chemical engineering at the City
University of New York (B.Ch.-1958) and Princeton University
(Ph.D.-1964). He did post-graduate research at the Milan Polytechnic
in Italy, and Kyoto University in Japan. He has taught at Tufts
University, the University of El Salvador, and, as a UNESCO ad-
viser, at the Catholic University, Santiago, Dominican Republic. Dr.
Shelden is now an associate professor in the chemical engineering
department at the University of Maine at Orono. His present major
research interest is techno-economics.

an evaporator. In the others it was a filter. The
reaction was second order, and irreversible. Did
we need to know the rate of reaction and how it
varied with concentration? We discussed the kind
of experiment we would carry out to obtain this
information and then we imagined the result!

ChE freshmen take a two semester course
... in which they select and work on a
number of laboratory projects ...
designed to introduce them
to the practice of
chemical engineering.

Did we need physical property data? We imagined
that A had the properties of hexane and looked
them up in a handbook. No two projects were
the same, because no two projects developed the
same scenario. We discussed the factors that
might determine how big our plant should be
and then picked a preliminary design capacity.
We discussed the factors that might determine
the optimum conversion in the reactor and then
picked a preliminary design conversion.
With the basic scenario set, we carried out
the necessary calculations together. The students
had all taken differential calculus and high school
chemistry and could readily grasp the idea of a
reaction rate expression in terms of concentration
and its implications for design. For batch re-
action they were able to recognize the integrated
solution to the rate equation, even though they
had not all studied integration. They all under-
stood the concept of the mole, and were able to
participate in the calculation of quantities flow-
ing between process units by material balance.
We were able to calculate the necessary size of
the reactors-both batch and continuous stirred
tank, and estimate their cost. [2] A comparison
of these reactors for the same conversion brought
out the impressive fact that the volume of the
continuous reactor had to be far greater than that
of the batch reactor for the same conversion.
ChE is not simply chemistry in bigger beakers!
By assuming filtration rates (after another
thought-experiment on a laboratory filter) we
could determine the size of the filtration unit, and
estimate its cost. We could see the trade off be-
tween reactor size and filter area. (In one project
we calculated energy costs for the evaporator and
saw the trade off between equipment costs and
energy costs.)




1. Overall, how would you rate the value of your
experience in plant design?
2. How would you rate the project as an introduc-
tion to the role of economics in chemical
3. Do you feel that the project gave you a good
understanding of how your future courses fit
together, and the purpose of each one?
4. How would you rate the project in terms of
helping you to understand the work of the
chemical engineer?
5. What percentage of the work we
covered do you feel you understood?
6. Do you think that a course in plant design
would be a good first course for
chemical engineers?

Using approximate Lang factors [2], we could
estimate the cost of the plant from the cost of
the major pieces of equipment. The students were
then able to compare the relative advantages of
batch and continuous operation, at least in terms
of the higher initial equipment costs for the latter
and the higher estimated labor cost for the form-
er. How should these costs be compared? We dis-
cussed the concepts of depreciation and marginal
return on investment, and carried out the
necessary calculations. The students also examined
the interaction between the demand curve for the

During the first session
with each group we developed
the basic scenario. I began by proposing that
we wished to react A and B in a chemical
plant and sell the product. "What do we
need to know to design the plant?"

final product and the engineering design cal-
culations in determining the optimum size for
the plant. In every project they were able to see
the role of economics in determining what con-
stitutes an optimal design.
Although we did not determine, for example,
the size of pumps, the students understood that
pumping costs could be an important factor in
determining the optimal conversion and hence
the optimal design. I explained that they would






range 75 100

Poor Very Poor

mean 87

learn how to determine the pumping requirements
in their future course work in fluid dynamics.
Similarly, I tried to show how their other future
courses would meet specific needs that suggested
themselves during our design work, but which
we did not have time to treat.

H AD TIME PERMITTED, if this were a full semester
course rather than a 1/3 semester course, we
could perhaps have included a recycle pump, a
recycle heater, or even a distillation column as
the separator. We might have attempted pro-
gramming the calculations and finding the op-
timum design rather than comparing just a few
designs. The possibilities are exciting.
I feel that the course accomplished several
important objectives.

I think the students now have a better understand-
ing of the curriculum they will follow. They saw the
kinds of things one needs to know to design a chemical
They learned that in general we have to consider
the whole system if we are correctly to design any of its
They gained a better understanding of the role of
economics in engineering decision-making, and of what
we mean by an optimal solution.
They obtained a clearer view of the meaning of
chemical engineering as a discipline, and the factors that
set it apart from, for example, chemistry.


This is of course a great deal to claim for
one short course, and one may well ask whether
simply going through the calculations together
with their instructor constituted a significant
learning experience for the students. My own
impression is that we were able to keep together
as a group, and that student comprehension was
good-surprisingly good. The students them-
selves, when surveyed several weeks after the
course was over and the final grades were in,
indicated that they had understood most of what
we covered (see survey results below). On the
basis of the written final reports they prepared
presenting their results, and our close contact

Continued from page 125.
"mathematical." Moreover, originators of the
theory offer no promises of insight into structure
and evolution of living things, of the stability of
societies, or of anything else so grand. Indeed,
their interest in the past few years has been
focused not upon thrusts toward trendy applica-
tions, but rather upon critical and scholarly re-
examination of existing theory.
I appreciate all of this, and that is why I was
predisposed toward Astarita's viewpoint before
the book was sent for review. It is also for this
reason that, upon reading the book, I probably
reacted more sharply to shortcomings than would
someone less interested in its success. Before I
describe the book and point out what I think are
its blemishes, let me state in unequivocal terms
that I think Professor Astarita has made a bold
and important contribution to our literature and,
considering the brevity of the book, has rendered
a surprisingly effective exposition of difficult ma-
terial. He has served us well.
Chapter 1 is devoted to mathematical pre-
liminaries. Readers who have not been exposed
to mathematics required for, say, a graduate
course in fluid mechanics are not likely to find
this chapter adequate; on the other hand, readers
who have had this exposure but little more will
find it helpful. Some of the "preliminaries"
offered orthogonall tensors, covariant and contra-
variant components of vectors and tensors) are
never used in the book and might just as well have
been omitted.
Chapter 2 is similar to the first chapter of
Truesdell's monograph3 insofar as it tentatively
deals with thermodynamics of homogeneous sys-

in class, I feel their evaluation is substantially
I think the experiment was very encouraging,
and that the idea of offering freshmen a course in
chemical plant design well merits considera-
tion. E

1. Youngquist, G. R., Chemical Engineering Education,
Winter 1975.
2. Peters, M. S. and Timmerhaus, K. D., Plant Design
and Economics for Chemical Engineers, McGraw-Hill,

teams, primarily as a vehicle for sketching the
Coleman-Noll methods.
In Chapter 3 the familiar field equations for
balance of mass, momentum, and energy are dis-
cussed, the local form of the Clausius-Duhem in-
equality is placed alongside these as a thermo-
dynamic postulate, and the stage is set for demon-
stration of how that inequality serves to place
restrictions upon constitutive equations.
In Chapter 4, application of the theory is
demonstrated through successive consideration of
ideal fluids, viscous fluids, and elastic solids-all
regarded as heat conductors.
Chapters 5 and 6 are devoted to Coleman's
study of implications the Clausius-Duhem in-
equality has for materials with fading memory.
The development is closer in technical detail to
Day's exposition4 of the same subject then it is
to Coleman's 1964 paper.
In discussing what I regard to be the book's
weaknesses I should point out that these are
more tactical than they are technical. It is im-
portant to make a distinction between, on one
hand, the methods introduced by Coleman and
Noll in 1963 and, on the other hand, Coleman's
application in 1964 of those methods to materials
with fading memory. The first should, I think, be
given clear priority in an introductory work;
fortunately, the methods are brilliant in their
simplicity and can be taught clearly without much
need for advanced mathematics. The second is
likely to interest a more limited audience and
requires such delicate functional analysis that
any brief treatment intended for chemical
engineers must, of necessity, be more suggestive
Continued on page 151.


A Freshman Course



University of Arizona
Tucson, Arizona 85721

equations is being used as the thread from
which to weave the fabric of an introductory
course in chemical engineering for freshmen at
the University of Arizona. The basic philosophy
of the course is to introduce students to as many
elements of ChE as possible, but in a unified way
in order to preserve coherency. In a series of
demonstration experiments, students exercise the
process of analysis by applying a mathematical
model to experimental data obtained. Experiments
have been chosen which follow first order mathe-
matics for simplicity since most of the students
are concurrently enrolled in calculus. The use of
experiments which follow a single mathematical
algorithm, in an approach similar to those of
Shair [1] and Gerrard ]2[, also has the advantage
of demonstrating analogies which exist among
quite different phenomena. Concepts illustrated
include dimensional analysis, scaleup, energy con-
servation, heat transfer, mass conservation,
mixing, and chemical reaction, though many
other equally good experiments could be used.
Other concepts which are introduced are the
difference between empirical and semi-theoretical
modeling, shell balances, the distinction between
lumped and distributed parameter systems, the
distinction between steady state, unsteady state,

The basic philosophy ... is to introduce
students to as many elements of ChE
philosophy as possible, but in a unified way in order
to preserve coherency. In a series of demon-
stration experiments, students exercise the
process of analysis by applying a
mathematical model to
experimental data obtained.

and equilibrium, and the use of various items of
equipment to obtain process data. The choice of
experiments was also influenced by the desire
to utilize most of the elements of analysis demon-
strated in the first part of the course in the
synthesis of part of a process design as the last
course assignment. This last assignment involves
some computer programming which is a rein-
forcement of the FORTRAN studied in the pre-
vious semester.

T HE SEMESTER IS BEGUN by introducing some
tools which are useful later in the course. These
include the correct use of units and dimensions
and graphing on various kinds of graph paper
(cartesian, log-log, and semi-log). While in the
area of dimensions, dimensional analysis is cover-
ed. The goal in this exercise is to illustrate a sys-
tematic method for empirical modeling in an
efficient manner. In one homework assignment,
students determine the dimensionless groups
necessary to predict what will happen in mixing
a liquid in a large unbaffled tank by doing experi-
ments in a smaller one. How this works in prac-
tice is then demonstrated in class by using the
Reynolds and Froude Numbers to predict at what
mixing speed air entrainment will occur in a large
unbaffied vessel using data from a smaller one.
For this purpose a sugar solution is mixed in two
different sized glass beakers agitated with mag-
netic stirring bars. Mixing speed is measured with
a strobe light. This is related to practicality by
mentioning that air entrainment often results in
frothing. As an aside, it is also effective to show
what happens when the vessels are baffled.

F FOLLOWING THIS VENTURE in pure empiricism,
the notion of mechanistic modeling is intro-
duced. The mathematics used is simply the first


order ordinary differential equation of the form
dx -- a (y + b) (1)
y (x = xo) =yo
This is very carefully introduced and related to
their calculus background. The solution is then
derived in the logarithmic form.

in + a (x xo) (2)

Students who are taking pre-calculus math or
who are otherwise uneasy about this material are
assured that it is correct and if they want, all they
need do is memorize it at this point since it will
be used several times in the excerises to come.
The utility of semi-log graph paper in determining
the coefficient (a) becomes evident at this point.
The first semi-theoretical modeling experience
involves the use of a material balance on a tracer
to determine if a continuous flow, stirred tank is
perfectly mixed. The unsteady state material
balance is derived by the finite element approach.
The analogy of this equation to the mathematical
form given by equation 1 is demonstrated and the
solution to the equation is written. Experimental-
ly a red dye is injected into a small glass, mag-
netically stirred tank and the effluent concentra-
tion is monitored by use of a Bausch and Lomb
spectrophotometer fitted with a continuous flow
cell [3]. Students are assigned the task of deter-
mining from the data whether the tank is per-
fectly mixed or not.
Next in the sequence comes the analysis of
heat transfer from a hot fluid flowing through a
circular tube. Again the finite element method is
used, this time using the principle of conservation
of energy. The concepts of heat transfer, heat
transfer coefficient, and plug flow are discussed.
The resulting differential equation is compared to
equation (1) and the solution is written. Ex-
perimentally, hot air is blown down an aluminum
tube which contains several thermocouples placed
along its axis. At steady state the axial tempera-
ture profile is determined by a multipoint digital
temperature indicator and the students are asked
to determine the heat transfer coefficient.
The last demonstration experiment is to de-
termine the reaction rate constants for a pseudo
first order chemical reaction in a batch reactor.
The glass vessel used in the mixing experiment is
now used as the reactor since we have determined

that it is well mixed. The reaction employed is
the alkaline fading of phenolphthalein (4). Since
there is a color change associated with the re-
action, the Bausch and Lomb spectrophotometer is
used to monitor the reaction progress. This reac-
tion is reversible so that the color never completely
disappears as equilibrium is approached. Using

The first semi-theoretical modeling experience
involves the use of a material balance on a tracer
to determine if a continuous flow, stirred tank is
perfectly mixed. The unsteady state material balance
is derived by the finite element approach.

the data generated, students are asked to deter-
mine the forward and reverse reaction rate co-
efficients in a graphical manner analogous to the
way previous experiments were handled.

B Y THIS TIME the semester is nearing the end.
After a discussion of process synthesis, a
specific process design case is presented. To date,
the case used has been the manufacture of deter-
gent by an exothermic benzene alkylation reaction
in a continuous, stirred tank reactor. This situa-
tion is a little different from any previously
covered, and combines the elements of heat trans-
fer to a coil, material conservation, and chemical
reaction in order to determine the annual cost
as a function of such variables as reactor tempera-
ture, conversion, and exit cooling water tempera-
ture. This study effectively summarizes the se-
mester and introduces the method of synthesis
for process design. In doing this the students
write FORTRAN subroutines for the reactor
analysis and coil analysis which must conform
to a specified format so as to interface with an
executive program given to them. This allows
them to see some of the advantages of pro-
gramming with subroutines which include versa-
tility (use of a subroutine over and over again),
ease of debugging, and allowing several persons
to be involved simultaneously in solving a problem
by computer by working on different but com-
patible parts.

THIS COURSE has been presented in this manner
for two successive years. Student reception
Continued on page 145.


A Freshman Course



Clarkson College of Technology
Potsdam, New York 13676
than a publicity ornament or marketing aid.
It is used in all phases of project engineering from
concept evaluation through design and construc-
tion. Other applications include maintenance and
personnel training. Nearly all engineering en-
deavors involve some model effort. In fact, many
engineering accomplishments survive only as
models-long after the full-scale version has
passed into oblivion.
In the chemical industry the engineering
process model has become an essential part of
engineering design [1-7], as well as being useful
in construction[8], maintenance [9,10], and process
analysis [11,12]. The model-building itself can
be a critical path activity in project engineering
[6]. Even the computer design of piping systems
can be based on model measurements [7].
Numerous illustrations of such chemical [13] and
nuclear [14] plant models can be found in the
This study suggests that the design and con-
struction of process models can serve as an effec-
tive introduction to complex design for engineer-
ing freshmen.

FOR SEVERAL YEARS the engineering cur-
riculum at Clarkson College of Technology has
included a two-course freshman engineering se-
quence. The principal objective of this sequence
is to provide an introduction to computer pro-
gramming and engineering design. The general
organization and history of the sequence have
been discussed earlier [15,16]. In particular, the
second course, entitled "Introduction to Complex
Design," extends throughout an entire fifteen-

week semester. During this period, the student
is primarily involved in a group design project.
Faculty members from all engineering depart-
ments are assigned to this design course as project
supervisors. In addition to the faculty instructor,
several undergraduate students are usually se-
lected as student tutors for a project and are
given an honorarium for this activity. Each in-
structor for this design course prepares a short
project description for distribution to prospective
students and from 30 to 70 freshmen are then
assigned to a project on a preference-ranked basis.
As a result, a chemical engineering project will
usually involve students from other engineering
There is no fixed format or content for this
freshman design course. The only expressed goal
is the involvement of the student in some phase
of engineering design, preferably through a
first-hand experience. As a result, the nature of
the course has varied widely [17]. The most
effective chemical engineering activities for these
large project groups can be classified as design
synthesis or design execution.
In the design synthesis approach [18], a
loosely-defined process engineering problem is
posed. The students, in three-man design teams,
are gently guided through the steps of problem
definition, flow charting, material and energy
balance calculations, equipment selection, and
economic analysis as needed to complete a pre-
liminary design feasibility report. Typical projects
have involved wet combustion of sewage, conver-
sion of waste to oil, coal gasification, and heat
exchanger parameter optimization. This ap-
proach is relatively effective for the large student
groups involved and is economical to operate. It
can easily be guided to completion so as to pro-
vide the students with a sense of accomplishment.
The design execution approach has emphasized
the planning, construction, and testing of a de-


sign. The student, again as part of a three-man
group, actually constructs a prototype design.
Typical projects of this type have involved a fuel-
cell parameter optimization, fuel-cell power sys-
tem for a minibike, a hydrogen combustion
engine, and a fermentation reactor optimization.
Since a freshman engineering student at Clarkson
College is not required to take any laboratory
courses, this second approach offers the appeal of
"gadgeteering" and hardware involvement that
many engineering students seek. However, it is
more costly and involves an extensive faculty
effort to achieve enough hardware development
for student satisfaction.
A third approach-process model-building-
has now been developed to introduce engineering
freshmen to complex design and project engineer-

motivated by student responses on a survey
questionnaire during the first class meeting in
Spring 1974. The thirty-four students who had
selected the project topic "Nuclear Power" ex-
pressed a surprisingly strong preference for build-
ing scale models of nuclear power plants over a
variety of other analytical and laboratory choices.
Two independent model-building sections of
seventeen students each were rather hurriedly
established without much prior planning. Two
student tutors were assigned to one section and
one to the other. Both sections were under the
supervision of a single faculty member. At the
second meeting of the class, the guidelines of
Table I were developed after some amount of
During the next four class meetings, sixty-
minute lectures were scheduled on the following
Nuclear Power History
Nuclear Power Industry-Today
Reactor Plant Descriptions (PWR, BWR, HTGR)
Project Engineering (Organization, Schedule, De-
sign and Construction)
Textbook and journal references were provided
to stimulate a literature search, reading, and dis-
cussion. In addition, the multi-volumed "Pre-
liminary Safety Analysis Review" (PSAR) and
"Supplement to the Safety Evaluation Report"
(SSER) of both the Diablo Canyon I and Nine-
Mile Point I reactor plants were made available.
Reasonably thorough system descriptions of the

FIGURE 1. Diablo Canyon 1 Nuclear Power Plant
BWR and PWR plants (by General Electric and
Westinghouse) were also provided.
The remaining time during the first five weeks
was largely spent in student discussions on what
to build, where to get suitable information, and
how to proceed. The projects were identified as
the "Diablo Canyon I Power Plant" and the
"Oconee I Reactor Building." These choices ap-
pear to have been based on the large amount of
PSAR information in the first case and on the
availability of a good journal feature story in the
second case. The first project quickly named a
manager and started to develop as a project
team. The other project never selected a manager
and tended to operate as independent sub-system
groups. At the beginning of the sixth week, the
student tutors were encouraged to take a more
active role in helping the students develop better
project organizations.
From this point on, the Diablo Canyon section
quickly evolved into a coherent project group.
These students made effective of the many en-
gineering drawings in the Diablo Canyon PSAR.
They were able to analyze and interpret the
drawings, even to the point of finding two incon-
sistencies in the drawings. However, the actual
model construction was very slow. This can be
attributed to the lack of experience characteristic
of these students. During the entire semester the
students maintained a high level of interest and
activity. This produced the Diablo Canyon plant
model shown in Figure 1. This section also pre-
pared a well-written report and made an effective
oral presentation.
The Oconee section never really managed to
develop an overall project organization. However,


the various sub-groups proved to be quite com-
petent at developing drawings and constructing
models. This section required considerable direct
help from the student tutor. A final crash effort
produced the Oconee Reactor Building model
shown in Figure 2.
The overall effort, interest, and accomplish-
ment of the two sections were better than had
been anticipated. The quality of the models was
high enough to utilize them as instructional aids
in upper-level engineering courses and as displays.
On the negative side, a few students were
bothered by the amount of shop or craft work,
which they felt was a waste of time. Several
students were never really able to adapt to the
demands of a group effort and, as a result, lost
the sense of participation in the overall project.
However, the most severe problem was the lack
of prior planning for this venture by the faculty
supervisor. This, coupled with a lack of experience
for the activity, led to an excessive emphasis on
"fire-fighting" activities instead of planned

was repeated with a group of 37 freshmen
in Spring 1976. Four project teams were organized
and an undergraduate tutor was assigned to each.
A number of significant changes were made in
order to accelerate the initial effort and to intro-
duce the students to project engineering.
The first change was the addition of three
more guidelines. The project schedule mentioned
in Item 2 was a typical manhours schedule for
the entire project. Scheduled manhours for future
activities were shown for the appropriate dates
and actual manrours for past activities were listed
where expended.
At the first class meeting the students were
asked to organize themselves into four inde-
pendent project groups. Source material from re-
actor plant vendors, utilities, and government
agencies were made available and other literature
sources were listed. The students were asked to
select a project and define the model scope by the
end of the second week. This definitely improved
the student effort during the first part of the
The lectures given to the class in 1974 were
repeated, but were spread out in short segments
over the first six weeks of the course. In addition,
specialized mini-lectures were given in response

FIGURE 2. Oconee Reactor Building Model.
to requests from the individual project groups.
This permitted the groups to schedule a faculty
lecture at their convenience and to request
specialized topics relating to their particular
The four projects of this second effort were
(A) Pickering Reactor Building, (B) Fulton
Generating Station, (C) Diablo Canyon Reactor
Building, and (D) Gentilly II Generating Station.
The results, represent a significantly higher level
of accomplishment than before. This improved
performance probably can be attributed to better
planning and organization of the course. The
significant factors were (a) better development
of the tutors as project consultants, (b) accelera-
tion of the initial project phases, and (c) the re-
quirement of weekly progress reports.

THE DEVELOPMENT OF additional project
management techniques for this model-build-
ing effort might be effective in generating student
interest and providing an introduction to such
methodology. Computer programs could be pre-
pared to provide the printouts and graphs


characteristic of the methods used in project
management practice. Using these, the students
could prepare schedules, control costs, allocate
effort, and develop a better sense of ongoing proj-
ect management. This would help to illustrate the
use of the computer as a managerial tool. It
would add realism to the project management
task and provide a meaningful management as-
signment for the students who dislike the shop
construction activities.
A freshman-level textbook could be developed
for model-building courses. While model-build-
ing references exist (19,20) and specialized
supply sources are available (21), a need exists
for a student textbook covering (a) the specialized
techniques of engineering model-building, (b)
descriptions of chemical process equipment and
their function, and (c) an introduction to project
management techniques. This should include
numerous illustrations and examples, as well as
sample management programs.

AS NOTED ABOVE, the preliminary planning
for this course is particularly important. A
set of project guidelines should be formulated be-
fore the course begins. Those given in Tables I
and II evolved from the problems encountered
in the initial effort. Other items that should be
considered include:
Adequately documented reference materials, par-
ticularly in the form of drawings and photographs,
should be assembled for several different projects so as to
simplify the design choice, minimize literature searching,
and help give the sections an early sense of direction.
Laboratory areas with sufficient space, work tables,
storage cabinets, and tools should be set up for this
activity. It is important that each project have a separate
defined area. This can be achieved if a "model-table"
and related space are assigned to each project group.
Additional nearby space should be available for project
conferences, writing, drawing, and minilectures.
A clear definition of the role of the student tutor
should be developed. Without this, it is possible for the
tutor to assume such conflicting roles as instructor,
faculty assistant, consultant, project manager, or fresh-
man colleague. A proper balance must be established
between guidance and assistance in both faculty-tutor and
tutor-freshmen relationships.
Project conferences and mini-lectures should be
planned to introduce the unit operations and chemical
processes associated with the prototype. This helps to
focus attention on the fullscale prototype as a functional
Some instructional effort should be devoted to the
concept that model-detailing is the art of creating an
illusion of reality, rather than true prototype miniaturiza-

tion. When student effort seems to be misguided, it is
particularly effective to offer one possible solution and
challenge the project team to seek other solutions.

A S AN INTRODUCTION to complex engineer-
ing design, this model-building approach
provides an outlet for the creativity, curiosity,
and ingenuity that characterize many engineer-
ing freshmen. Even though miniaturized, it tends
to focus upon the total art of engineering design
[22] through practice in a real-world environ-
The student is not involved in analytical de-
sign or actual equipment operation, as he would
be in the other types of chemical engineering
projects mentioned earlier. However, he is intro-
duced to the techniques and needs of project
engineering, as well as learning to function as
part of a large project team. It is also possible to
use this model-building project to acquaint the
student with the appearance, purpose, and func-
tion of process equipment used in the prototype.
The faculty supervisor can utilize the modeled
process as a vehicle around which to develop
problems in upper-level engineering courses. One
possibility is to have the freshmen model a project
that is being studied concurrently by a senior de-
sign group. Another approach is to utilize area
industry as prototypes and include plant tours as
part of the course. Incidentally, a faculty member
can even generate interest in his research specialty
by developing a model project that relates in some
way to his research.
From an administrative point of view, this
model-building approach should be of interest
because (a) it can be made appealing to a wide
variety of engineering students of all disciplines,
(b) a reasonably large number of students can
be accommodated effectively and economically,
and (c) it involves the freshman student with a
real design experience that can be satisfactorily
completed in a fixed time schedule. This type of
course could even be offered to non-engineering
freshman as an introduction to engineering.
The student tutors, who usually are juniors
and seniors, can gain an invaluable educational
experience by working with a process model-build-
ing group. This is particularly true if they are
given considerable responsibility for helping the
freshmen develop an effective project organiza-
tion and complete the project on schedule.
Continued on page 151.



University of Wisconsin-Milwaukee
Milwaukee, Wisconsin 53201

T HIRTY YEARS AGO it was a relatively simple
task for those in industry, government, and
education to rank or rate chemical engineering
graduate programs. At that time, programs were
few in number and could be easily evaluated by
knowledgeable observers. The trends of the in-
tervening years, namely, the rapid proliferation
of graduate programs and the general rise in
quality have clouded the situation. In the complexi-
ties of today's academic world, the simplistic in-
sights of the past no longer work. It is essential,
therefore, to have realistic, objective techniques
for graduate program evaluation.
Others have grappled with this problem [1],
[2], [5]. For example, in 1966 the American
Council on Education (ACE) published the

The ACE Studies ... depended to a large extent
on opinion. As such there was always the
question of personal subjectivity or in some
cases the danger of lack of knowledgeability.
... lesser known departments could be ignored
because they do not have the national
exposure of better known units.

Cartter Report "An Assessment of Quality in
Graduate Education" [1]. Again, in 1969 the same
organization completed a follow-up study "A
Rating of Graduate Programs" by Roose and
Andersen [2]. Basically these studies consisted
of polling selected faculty members in universi-
ties and asking them to rank departments both
on "quality of Graduate Faculty" and "Effective-
ness of Doctoral Program." The initial study by
Cartter found a high degree of correlation be-
tween these rankings. This was in essence repli-
cated in the 1970 study. The results of these
studies for chemical engineering departments are
given in Table I.

American Council of Education Ratings

1966 1970 School

1 1 Wisconsin
4 2 Minnesota
4 3 Cal., Berkeley
1 4 M.I.T.
10 4 Stanford
8 6 Illinois
3 6 Princeton
6 8 Michigan
9 9 Cal. Tech.
6 10 Delaware
10 11 Northwestern
14 11 Rice
12 13 Carnegie-Mellon
12 14 Texas
15 Pennsylvania
15 16 Wash. (Seattle)
17 Purdue
2.5 2.9 range:
Brooklyn Polytech. Louisiana State
Cal., Davis Maryland
Case Western Res. N. Y. U.
Colorado Notre Dame
Columbia Ohio State
Cornell Oregon State
Florida Penn. State
Houston Rensselaer
Ill. Inst. of Tech. Tennessee
Iowa State (Ames) Washington (St.L.)
2.0 2.4 range:
Buffalo Oklahoma State
Cal., L.A. Pittsburgh
Cincinnati Rochester
Georgia Tech. Syracuse
Kansas Texas A & M
Kansas State Tulane
Michigan State Utah
Missouri Virginia
N. C. State Va. Polytech.
Oklahoma Yale

The ACE studies, while valuable, depended to
a large extent on opinion. As such, there was al-
ways the question of personal subjectivity or in
some cases the danger of lack of knowledgeability.


For example, lesser known departments, although
capable, could be ignored because they do not have
the national exposure of better known units. The
present paper develops a system whereby ob-
jectivity can be maximized and the potential prob-
lems of the earlier studies can be avoided.

T HE METHODOLOGY USED in this study is simple,
direct, and effective since it is based on
published statistical data. Fundamentally, rank-
ings on four indices of performance are used to
generate an overall index of performance that
ranks chemical engineering departments by
effectiveness or productivity. Unlike the earlier




0 .2 .4 .6 .8 1.0 1.2 1.4 1.6 1 2.0 22
FIGURE 1: Frequency Distribution for M.S. Degrees per
Faculty Member per Year.

studies, this ranking reflects overall graduate
and research productivity and not just doctoral
program effectiveness. The four indices of per-
formance are: Master's Degrees Awarded per
Faculty Member per Year, Doctoral Degrees
Awarded per Faculty Member per Year, Thou-
sands of Dollars of Extramural Research Funds
Expended per Faculty Member per Year and
Refereed Publications per Faculty Member per

The development of indices based on units of
performance per faculty member was purposeful.
First, it was felt that gross data such as numbers
of M.S., Doctorates, or publications for a given
department could be quite misleading. For
example, a small department (of say five faculty)
could turn out five doctorates and appear not as
productive as a large department (of say twenty
faculty) that turned out ten doctorates. Yet, if
these data were reduced to the basis of per facul-
ty member, the smaller department would have
an index of 1.0 while the larger department would
an index of 1.0 while the larger department would





1.0 1.1

0 .1 .2 .3 / .5 .6 .7 .8 .9

FIGURE 2: Frequency Distribution for Doctorates per
Faculty Member per Year.

be only 0.5. Thus, a clearer, more objective pic-
ture could be obtained.
Two sources of information were used for the
statistical data to compute the indices. The first
was the annual supplement of Engineering Edu-
cation titled, Engineering College Research and
Graduate Study [3]. This volume gave the numbers
of Master's and Doctor's degrees awarded and the
amount of extramural funds expended. The
American Chemical Society publication [4], Di-
rectory of Graduate Research, furnished listings
of refereed publications. The former source [3]
gives annual data while the latter is on a biennial

Richard G. Griskey received his B.S. in Chemical Engineering from
Carnegie-Mellon University in 1951. From 1951 to 1953 he was a First
Lieutenant in the Combat Engineers of the U. S. Army Corps of En-
gineers. In 1953 he entered Carnegie-Mellon where he was awarded
an M.S. (1955) and Ph.D. (1958).
The National Academy of Science appointed him as Senior Visiting
Scientist to Poland in 1971. In the same year he was appointed Dean
of the College of Engineering and Applied Science of the University
of Wisconsin-Milwaukee as well as Professor of Energetics.
He has had industrial and consulting experience with DuPont,
Celanese Fibers, Celanese Research, Phillips Petroleum, Thermo Tech
Inc., Hewlett-Packard, Litton Industries and the U. S. Veterans Ad-
ministration. He is a member of AIChE, Cryogenic Society, Society of
Plastics Engineers, ASEE, and the Society of Rheology.


.. in this study . rankings on four indices
of performance are used to generate
an overall index of performance
that ranks chemical engineering departments
by effectiveness or productivity. Unlike earlier
studies, this ranking reflects overall graduate
and research productivity and not just
doctoral program effectiveness.

Frequency distribution plots of index values
for all four categories are given in Figures 1, 2, 3,
and 4. These data give a valuable insight into the
performance of chemical engineering depart-
ments. If the most frequent index is taken for
all four areas, the performance of an "average"
department could be computed regardless of size
of faculty. For example, such a ten member de-
partment would generate 7 M.S. degrees per year,
3 doctorates per year, $170,000 in total extra-
mural research funds per year and 14 total re-
fereed publications per year. On the other hand,
a twenty member department would double those
figures for "average" performance.


A LTHOUGH SUCH DATA as Figures 1-4 are useful,
they do not answer the question of overall
effectiveness or productivity. In order to satisfy
the need, a different approach was taken. This ap-
proach involved the reduction of the indices in
each area to a decimal scale. For example, con-
sider the situation for Master's degrees per facul-
ty member per year. The top value determined



z) 6 -
LL 4-


0 I I I I I 1 I I I I
0 8 16 24 32 40 48 56 64
FIGURE 3: Frequency Distribution for Thousands of
Dollars of Extramural Funds per Faculty Member per

for any institution was 2.08. This figure was then
divided into each index value to give a reduced
2.08 1.04 etc.)
decimal score (i.e. 20 = 1.00; 2.08 = 0.5, etc.).

The same process was repeated for the other
three areas (of course, using the appropriate top
index value). The result was that each area now
could be described on a decimal scale ranging
from low values to unity. The top index values
for all four areas are given in Table II.
Next, the reduced decimal scores for the four
areas (i.e. Master's Degrees per Faculty Mem-
ber per Year, etc.) were summed for each


S i I L I I I I I I It I I I L
0 .4 .8 1.2 1.6 2.0 2.4 2.8 3.2 3.6
FIGURE 4: Frequency Distribution for Publications per
Faculty Member per Year.

chemical engineering department for which all
four categories were available. Theoretically, the
top score would be 4.00. Actually, this value was
found to be 2.75. This figure was then used to
reduce all the data to a decimal score (i.e. 2.75
1.0). These decimal scores were designated as
a Graduate and Research Productivity Index
(GRPI). The final ranking of the institutions by
means of GRPI is given in Table III.
Institutions that were used in the various
phases but not in the final compilation (because
of lack of certain data) are given in Table IV. Be-
fore commenting on the data of Table III, it is
worthwhile to cite the fact that one of the insti-
tutions of Table IV had the top index in the area
of publication. However, none of the others were
at the top of the remaining categories.
Now, in regard to Table III, the rankings were
listed as shown to match the system used by


Top Index Values for Categories


M. S. Degrees Awarded/Faculty Member/Year 2.08
Doctorates Awarded/Faculty Member/Year 1.14
Thousands of Dollars in Extramural Funds
/Faculty Member/Year 122.2
Refereed Publications/Faculty Member/Year 3.62

Cartter [1] and Roose and Andersen [2] in their
earlier studies. In essence, first a ranking of
schools by order in the higher category and second
an alphabetical listing of the other institutions
that ranked lower. As a first step, it was decided
that correlation between each of the earlier
studies and the present should be checked. It was
found that the respective correlation coefficients
between the present work and the earlier studies
were 0.5 for the Cartter Report and 0.73 for the
later study by Roose and Andersen. The probabili-
ty levels for correlation were about 0.10 for the
Cartter Report and between 0.01 and 0.001 for
the later study. The greatly improved correlation
with the Roose-Andersen study most likely reflects
changes in departmental effectiveness with time.
The interesting result of the correlation is that
there is a strong relation between the perceptions
of the faculty raters and the objective rating
system used in this work for the top rated institu-
As was indicated, the earlier studies only
ranked numerically the top rated institutions. The
groups following these were cited only alpha-

Institution by Ranking of
Graduate and Research Program Effectiveness*

1. Stanford 12. Notre Dame
2. Rice 13. Carnegie-Mellon
3. M. I. T. 13. West Virginia
4. Illinois 15. Minnesota
5. Oklahoma 16. PINY
6. Pennsylvania 16. Stevens Institute
7. Illinois Institute 16. SUNY (Buffalo)
of Technology 19. UCLA
8. Columbia 20. Purdue
9. University 21. Texas (Austin)
of Southern California 22. Clarkson
10. Lehigh 23. Iowa State
11. Northwestern 23. Ohio State

= 100-

w 80-


? 40-
0 20-
S o0 .2 .4 .6 .8 1.0
FIGURE 5: Ranking Versus Graduate and Research
Productivity Index (GRPI).

betically. This, of course, prevented a direct cor-
relation study being made of all listed schools.
However, it was possible to make an indirect
check. This was done in the following manner:
the names of the first 37 institutions in the present
study were compared to those named in Cartter's
work [1] (i.e. Cartter listed 39 departments, two
of which no longer exist) and the names of the
first 55 institutions in the present work were
compared to the 55 listed by Roose-Andersen [2].
The number in common was then divided by either
39 or 55 as the case dictated. The result was about
a 60% ratio. Furthermore, if the departments not
included in the present study because of lack of
complete data were dropped, the ratio ran up to
the 90% level.
As a result of the direct correlation and the
indirect approach it can be seen that the results
from the faculty panels used earlier compare quite
favorably with the present objective technique.
This shows that the perceptions of knowledgeable
faculty are a good guide to qualitatively ranking
departmental effectiveness. However, it should
also be apparent that the objective technique set
forth in this paper gives a one to one quantitative
ranking of departmental productivity or effective-
ness which should be more meaningful.
It is interesting also to consider the findings
of Bernier, Gill and Hunt [5]. These authors
correlated a number of factors (citations, re-
search expenditures, publications, etc.) for 21
ChE departments named in the Roose-Anderson
study [2]. They found good correlation between
various factors dealing with citations and re-
search expenditures and the Roose-Anderson
work [2].


Institutions Not Rated But Used To Supply
Certain Data

A. The following institutions were used to supply data
for the evaluation of M. S. doctorate and extramural

Arizona State
Cal. Tech.
Case Western Reserve
Catholic U.
Cooper Union
Georgia Tech.
U. of Iowa
Kansas State
Louisiana State

Michigan Tech.
Mississippi State
New Hampshire
New Mexico State
Ohio U.
South Dakota Mines
Texas Tech.
Washington State
Washington (Seattle)

B. The following institutions were used to supply data
on doctorates and publications.

California (Berkeley)

Texas A & M*

*Also involved in M. S. Evaluation

The question that naturally arises is what
about those institutions in Table IV or others
for which no data were available? This can be
handled by first pointing out what was cited
earlier, namely, that all available data were used
to compile the decimal scores that were summed
to get the GRPI. In fact, as was mentioned
earlier, the 1.0 decimal score for publications was
attained by one of the departments in Table IV.
Actually there is no problem in any department
finding where it ranks by this method. In Figure
5, the ranking is plotted as a function of GRPI.
Hence, if a department can compute its GRPI, it
can determine its rank. Consider an example to
see how this can be done. Suppose a department
had 1.04 M.S. degrees per faculty member per
year, 0.57 doctorates granted per faculty member
per year, 61.1 in thousands of dollars of extra-
mural research funds per faculty member per
year and 1.81 refereed publications per faculty
member per year. By taking the top index values
of Table II the decimal score for each category

could be computed. In this example these decimal
104 0.57 61.1
scores would be: *.04 0.5, 0. 0.5; 61.1
2.08 1.14 122.2

0.5; and 1 = 0.5. The sum of the decimal
scores is found to be 2.00 and the resultant GRPI,
2.0= 0.73. From Figure 5, the ranking cor-
2.75 -
responding to this GRPI shows that the institu-
tion ranks above 88% of the institutions or that
only 12% of the institutions rank above it.

T IS FELT THAT the method outlined in this paper
offers an objective realistic way of evaluating
chemical engineering department graduate and
research productivity and effectiveness. In light
of the excellent correlation between "Quality of
Graduate Faculty" and "Effectiveness of Gradu-
ate Programs" found by both the Cartter and
Roose-Andersen studies, it would also appear that
the scale developed in this paper also is a strong
indicator of quality of graduate faculty in
chemical engineering departments. Beyond the ap-
parent impact on rank, there is another important
ancillary benefit. This is to provide chemical en-
gineering departments a way of comparing their
annual performance on a year by year basis. In
other words, is the department standing still, de-
clining or improving? In today's tight academic
budget situation, the method presented in this
paper could be extremely useful in showing re-
luctant university administrations that a given
program is either worthwhile or on the upgrade.
Regardless, however, of the ultimate use to which
the present method is directed, it cannot but help
to bring a more reasoned approach to an im-
portant area of consideration. El

1. Cartter, A. M. "An Assessment of Quality in Gradu-
ate Education," American Council on Education,
Washington, D.C. (1966).
2. Roose, K. D. and C. J. Andersen, American Council
on Education, Washington, D.S. (1970).
3. "Engineering College Research and Graduate Study,"
Engineering Education 64 No. 6 (Supplement)
4. Directory of Graduate Research, American Chemical
Society (1974).
5. Bernier, C. L., Gill, W. N. and Hunt, R. G. Chem.
Eng. Ed., 9, 194 (1975) "Measures of Excellence of
Science and Engineering Departments: A Chemical
Engineering Example."


DOUGLAS: ChE Educator
Continued from page 113.
university research administrators. He prepared
a proposal for submission to NSF without the
usual overhead funds in the budget. The document
managed to clear all but the Treasurer's Office.
When news of the attempt filtered back like a
water hammer, there were an awful lot of red
faces, but not Jim's.


O NE ROLE AN ENGINEER often plays is that of
an entrepreneur. An outgrowth of Douglas's
interest in sailing brought him into partnership
with two other engineers from U. Mass., seeking
to develop new metal forming procedures useful
in forming hulls. His avocation energized an
interest in Engineering Entrepreneurship and
developed course material for both undergraduate
and graduate courses.
We began this article with a clear exposition
that James M. Douglas is an uncommon man. This
we have shown as true in all his pursuits of
scholarship and of leisure. His intensity fires the
interest of students and of some colleagues, and
the passions of others. "L'dminence grise" (for
the gray hair) continues to be a major con-
tributor to the growth of this department and
the chemical engineering profession. El

ALKIRE: The ChE Profession
Continued from page 129.
course described here achieves its purpose in an
efficient manner. FD

1. Scientific American, September, 1970.
2. Synthetic Rubber, Inter. Inst. Synth. Rubber Pro-
ducers, New York.
3. The Foxfire Book, ed. E. Wigginton, Anchor Press/
Doubleday, Garden City, N.Y., 1972, p. 308.
4. Pencillin Production, A. L. Elder, ed., CEP Symp.
Ser. 100:66 (1970).
5. The Foxfire Book, ed. E. Wigginton, Anchor Press/
Doubleday, Garden City, N.Y., 1972, p. 150.
6. C. W. Cowley, W. J. Timson and J. A. Sawdye,
I&EC Proc. Des. and Dev., 1:12, 81 (1962).
7. C.-C. Shih and J. W. Westwater, Int. J. Heat Mass
Transfer, 15, 1965 (1972).
8. R. B. Bird, W. E. Stewart, E. N. Lightfoot, Transport
Phenomena, Wiley, New York, 1960, p. 357.
9. N. DeNevers, Chem. Eng. Educ., 98, Spring (1974).
10. Samuel W. Bodman, The Industrial Practice of
Chemical Process Engineering, MIT Press, Cam-
bridge, Mass., 1968.

11. P. W. Morgan and S. L. Kwolek, J. Chem. Educ., 36,
182 (1959); P. W. Morgan, J. Chem. Educ., 42, 12
(1965); anon., J. Chem. Educ., 46, A755 (1969).
12. A. A. Collyer, Phys. Educ., 8:2, 111 (1973).
13. C. B. Weinberger, Chem. Engr. Educ., 80, Spring
14. M. Page and F. H. Hooper, The School Science Re-
view, 45, 155 (1964).
15. D. F. Rudd and C. C. Watson, Strategy of Process
Engineering, John Wiley, New York, 1968, Chpt. 13.
16. CEP, 67, June issue (1971).
17. D. F. Rudd, G. J. Powers, J. J. Siirola, Process
Synthesis, Prentice-Hall, Englewood Cliffs, N.J., 1973.

WILLIAMS & COSART: Freshman Analysis
Continued from page 135.
has been enthusiastic. We feel that they have a
much better understanding of chemical engineer-
ing and are certainly much better equipped to
handle a rigorous stoichiometry course in the
next semester as a result. H

1. Shair, F. H., "Chemical Engineering Concepts and
Laboratory for Freshmen," presented at the Work-
shop on Undergraduate Chemical Engineeiing
Laboratories, ASEE Summer School for Chemical
Engineering Faculty, Boulder, Colorado, August, 1972.
2. Gerrard, A.M. "Some Simple Experiments for First
Year Students," Chemical Engineering Education,
9 (1), Winter 1975.
3. Hile, L. R. and Williams, R. D., "Flow-Through De-
vice for Colorimetric Analysis," Chemical Engineer-
ing, 82 (14), July 7, 1975.
4. Hile, L. R. and Andres, R. P., "Alkaline Fading of
Organic Dyes: An Ideal Reaction for Homogeneous
Reactor Experiments," Chemical Engineering Educa-
tion, 9 (1) Winter 1976.

14 oMnews

WORCESTER, Mass.-Dr. Imre Zwiebel has been ap-
pointed head of the Worcester Polytechnic Institute
chemical engineering department, effective Sept. 1.
He has been a member of the WPI faculty since
January, 1964, when he came to Worcester after three
and a half years as a research and development engineer
with Esso Research and Engineering Co., Linden, N.J.
A native of Budapest, Hungary, he came to this
country in 1948 and was educated in New York City.
Following graduation from University of Michigan with
a bachelor of science degree in chemical engineering, he
was employed for three years by E.I. DuPont Demours &
Co. in Wilmington, Delaware.
He held four fellowships at Yale University where
he received both Master of Science and Doctor of
Philosophy degrees.




Georgia Institute of Technology
Atlanta, Georgia 30332

sciences, involves many quantitative relation-
ships and operations. Hence, education in this
field includes many, hopefully realistic, exercises
using these relationships. These exercises general-
ly take the form of problems intended to illustrate
or reinforce a given concept, and are used as
homework assignments, lecture demonstrations
and examination topics. There are many areas in
chemical engineering, including reaction engineer-
ing, in which quantitative problems are employed
more or less extensively in the educational pro-
The instructor of ChE, particularly one who
specializes in a given field such as reaction
engineering and who regularly teaches in this
field, rapidly accumulates a copious set of quantita-
tive problems for the purposes mentioned above.
After some time, the organization and manage-
ment of these resources can become an unwieldy
and frustrating task. In particular, the operation
of information retrieval, as it applies to the act
of selecting a problem for the purpose of illus-
trating a given concept, often requires more than
just a good memory (especially if some variety
is hoped for in course offerings). Thus, the pur-
pose of this article is to describe an efficient,
manual method for organizing reaction engineer-
ing problems, based upon the key concept method
of information retrieval.
As its name suggests, the key concept method
requires, firstly, the identification of a number
of terms pertaining to various concepts of in-
terest. In a large general field such as ChE,
hundreds of such terms would be necessary for
an efficient information retrieval system, and
computer methods, rather than manual, would
be almost essential. For a relatively specialized
application, however, such as the organization

... the operation of information
retrieval, as it applies to the act of
selecting a problem for the purpose of
illustrating a given concept, often requires
more than just a good memory (especially if some
variety is hoped for in course offerings).
Thus, the purpose of this article is to
describe an efficient manual method
for organizing reaction engineering problems.

of reaction engineering problems, the list of
identifying concepts can be kept to a size easily
manageable by manual methods. As an aside, the
very act of organizing the subject matter of a
given field into such key concepts is, by itself, a
very valuable aid in the structuring of a course
into modular units.
The usage of the key concept method for in-
formation retrieval has been described by
numerous authors (1-4). After the key concept
words for a given application have been selected,
a table form, typically an index card, is set up
for each such key concept. Items to be accessed
via this system are then assigned code numbers
which are essentially arbitrary; the only re-
striction is that there be a one-to-one cor-
respondence between each item and each number.
The code number for a given item is then record-
ed on the table forms for each of the key con-
cepts associated with or imputed to this item.
For a manual system the code numbers are
generally arranged in an ascending order for
each key concept; typically, larger numbers are
assigned as the system grows. A separate
reference file is maintained which relates each
code number to its item. When the items being
organized are literature articles in some scientific
field, for example, the reference file might consist
of another set of index cards, arranged in as-
cending numerical order with one code number
per card, with such pertinent information as
authorss, affiliation, source, abstract and the


key concepts themselves. One could also have a
file of the articles themselves, also arranged in
ascending order of the code numbers.

T HE SYSTEM THEN operates as follows for the
retrieval of specific items. The table forms or
index cards for each key concept of interest in
a given search are scanned and all code numbers
which appear on all such table forms are stored
or recorded. The code numbers resulting from
this scanning operation are then used to locate
the corresponding items (journal articles, ab-
stracts, etc) in the reference file. In very sophis-
ticated systems, additional letter or numerical
codes may be assigned to each key concept. The
purpose of these additional codes is to denote the
role of each key concept. Thus, these codes may
be used to denote whether the key concept serves
as an input, output, environmental factor, active
concept, passive concept, means, etc. These role
codes can then be linked to establish a very
specific search of a large system. In this case, a
given key concept may require a number of
separate table forms, one for each role code as-
signed to that word. In a relatively simple system
such as the one described in this article, such
sophistication is not necessary and was not em-
The list of key concepts selected for this re-
action engineering application is given in Table
1. It is not pretended that this list would serve
as an all-inclusive one for the entire reaction
engineering field. Within an educational environ-
ment, however, it is felt that this list is quite
representative of the key concepts covered in a
typical undergraduate course in chemical reaction
engineering. The reference file for this problem
organization system would relate each code
number to a specific problem or the source
thereof. In the search operation, code numbers
would, as before, be obtained by scanning and re-
cording the matches. A specific example of this
search procedure will be given later.
The selection of the key concepts themselves
is naturally somewhat subjective. A given person
may attach various subtle interpretations to cer-
tain key concepts. Hence, amplification of some
of the entries in Table 1 would perhaps be useful.
For example, numerical integration is intended
to refer to problems in which analytical integra-
tion of the governing differential equations is not
possible, and would thus also embrace graphical

and other manual methods of integration. The
nonisothermal entry is intended to also include
series of reactors operated at different but per-
haps constant temperatures. A key concept such
as activation energy, half-life, residence time or
selectivity is associated with a given problem only
when that concept is felt to be an integral part
of the solution procedure to that problem.
The items to be organized in this system are
problems in the area of reaction engineering from
various sources such as textbooks, manuals and
journal articles. The problems from textbooks
can be either solved example problems or un-
solved ones such as appear at the ends of various
chapters. For brevity of presentation purposes
in this article, the number of organized problems
has been restricted to several hundred, but the
extension of this system to any number of entries
should be readily apparent.
Copies of the table forms for this system are
shown in Table 2. This particular type of form,
with a vertical arrangement into ten columns
headed by the digits 0-9, is a very popular one.
The code number for a given item is listed in one
of these columns, depending upon its last digit.
Within a given column, the code numbers are list-
ed vertically in ascending order. This particular
arrangement of the code numbers on a table form

List of Key Concepts
of Reaction
Activation Energy
Batch Reactor
Fractional Order
Half Life

in the System for Organization
Engineering Problems.
Multiple Reactors
Numerical Integration
Residence Time
Semi-Batch Reactor
Tubular Reactor
Unknown Order

greatly facilitates the search procedure. The code
numbers for individual reaction engineering prob-
lems beginning with unity, are assigned in as-
cending order as the number of entries increases
and are recorded manually on the appropriate
table forms.
The reference file for this system is presented
in Table 3. A shortcut, mnemonic method for
identifying sources has been employed here. This
method, although somewhat arbitrary, has proven


2Io9 EC. lN 1S 1S24

00 20'5' 2 43 9. 3 44 4s 7 12.

45s _a2-3i. i 224 n S __ __ a.
____ ___ 5.L L 3 a 4 __ __ __ __


0_ -.. .. . 1 _2-104 7 7 0 _1
13 1 1--__ 13 4 a IS 14 17 08 19

al-- : 4 7o 1 21_, _ai"
S') '45l 1.420 17 48_2-
Al ._4 .155 7lI- l2 117!2 a_ aI
-3I __ 141. ___ 47...7

F- Th _"81 i 1 __ - = t I38 .7

to a 4a 83 41as 42 24 -- -8 29
70 _7 252 *3 4 85 _>0 __87 138 7 9

_ _.- __ __ __ 2 4 S 4_ I 4 7 ~

S70. 71 8

C(. FTA. L -rI C

3 Y14 L_ 70
4 5 274 .

4=8 4.9
i 89


B8o 9110 93 9 95 G G71 ~i 9.
0 7 _53 1i4. 17S 9 'I -P S
_iso 3- S- iaa 3 _~ 4 s & "' *
l 414E173 1 '9

^30" ~ 18 BCr';< *aa ;&- :-. ..i .23-
zr*^. ~ 47 45G~ l.'0' z ," .96'^-!t^


90 91 a -7 .:14.9
4=1 2 4: .- -8 Q 1 9
8L70 1 -a I : 4 ? 9
"o l71 1-
_2A3-_ _a a a _~. G -a ga-_ :;T i ij < < -* 1
-1a 4 C I I

7 4. AZT .258
83 al. 25 S

9j r0 A1 242! 9:.4 7 "S '~ -la -^ 49
SO II*, I *a. -'= 44 11 94. .I.. 1 6 17 78 .59-
440O I* Ga*:., 3 *' 193101. 1* 3 -- 8 9.
4.S 7 44 14 ..- - -9

1a00 9 -J -:** 15 S S S 7_Q 1
_a58o 194.. A 42' 6 259
Sol 4 2a 7

Q30 91
4O 141
4-00 91
4I10 4010


4 I 3 a G 44 7 '5 11 107 18 259
192ia 93 194 1915 194 197 9 18 ,99
,1 "I 3 414 a45 a44 a47 198 279
a3 4...7 .... .77 78 -._
I -= ]-Z .. I" --7_7 2 -'

I- _-___ CO SEC U^TIV E

3o | 1 41 a 13 14' \35 ~ T78 19
|100 | l -- 33 .._45 [191C 77 98 59
S0 911, 3 1 575 908 99
s80 2l- 113 2 a238094
21 11 9


__ I4 0 3 4 IS a3 =37 7I
_40 10 34 9 g 3 _14- 35 445 _771 78 19
l .~ 10 _a 3 _34- 5 _9 C s74 971 8 39
7 7 142 l83 -4 96 17 08 79
*s> 18 1_74. 193 1454 r .14 157 .128 9911
** ,', 19 203 G14 --SG 1 77 148 109
0 [ all la 3 a Q36j 741 43 ,7r 87 178 1-' 1
24 404 184. 25a 1S0 197 _198 1a 9
-- 41_4a 20_ a4 445 4a50 407 a08 513
--G 414. 237 a48 "19
442a 334. -s 2.7 a G 97.
244 989.


13 44,44 7 38 49.
140 71 74 75 257 4.8- I
371 --- -37: 8 249. .

go 1 10 104. 4.7 1 I-9.
11ii0; 81 __ ., 1 05 I__ __- ____


* 0; 113 ao;^ ~ 4 '. s ^GI~ I ^T \_3
S G71 lB 3I
-4 o 1 7- T 3 -14- 759 7 57 4 _4
90O 141 _72 \ 73 4e4. 92- -7e 1>0 7 4_8 _79
'o 18 1 Il3 114 1175 a 19. 2 0 7 18 _1 1
170 191 92, _153 154 lB S l a l _a8 l99
270 ao 1' 04 1 1 3 18-4 19 740 4- 8 2G9
all a41a i73 234 -a7S 7
-__7aa_~3 7 ___--- -- ==; --- ---
_ _ a 7A -_2 o a _ -- --
28 _A33


.41. 792 7 35 14 _A7 138 G14
7131 B 4 147 IA9 9


G.o 1-i I .. ."1-3 7 1.S 4i ,17_ 9 -- 9]
4. I 83 !a 47 1 -,7

20 41 34 3 7 = -7-- 8 ,09
10 .. 1 4 20 R-- 8--

14 141 41343. 4-33 _14 44 1. 4 13723 40- "- 1
.50 31 4422373 134 272 414C 17 248 229.1
19O 14 51 243 194 23 18 2S8 439e6-*- 11

2 100 151 7, .102 848 I20
470 -81 4 - 7 78

I 71 R 1 ,

12 50 191 2 a 133 1! 4n 7 29 G
t,'o 35 _- L .53 __ . _ .
44 1 4 1 0Z23 a

|| H1b.LF'- LIVE-

l '1 z I I .- 8 --

1*0 ^ -. : ae 9'3 7 F^' r 6f-a s A: ^ I

o. lo- A, 84 -5 SG-2- 7 I- 8 I-
1 0.- 8 a23.

to be very useful and is based in part upon authors'
initials or the first letters of multiple authors'
last names. Thus, for example SMW refers to the
text by S.M. Walas, JMS2 refers to the second
edition of the text by J.M. Smith, and C&J refers
to the text by A. R. Cooper and G. V. Jeffreys.
The numbers following the author letter codes
denote the location within a given text. Again, for

example, 3-4 refers to problem 4 at the end of
Chapter 3, while 157X refers to an example prob-
lem which appears on page 157. A complete di-
rectory of the mnemonic codes is provided in
Table 4.
T HE USAGE OF this system for locating problems
involving specific concepts will be illustrated by
two examples. Suppose one is interested in re-

TABLE 3. Reference File Code Numbers and Sources of Reaction Engineering Problems.

Code Problem Code Problem Code Problem Code Problem Code Problem Code Problem
No. Source No. Source No. Source No. Source No. Source No. Source

1 MB
2 MB
3 MB
4 MB
5 MB
6 MB
10 SWC
11 SWC
12 SWC
13 SWC
14 SWC
15 SWC
16 SWC
17 SWC
18 SWC
19 SWC
20 SWC
21 C&J
22 C&J
23 C&J
24 C&J
25 C&J
26 C&J
27 C&J
28 C&J
29 C&J
30 C&J
31 C&J
32 C&J
33 C&J
34 C&J
35 C&J
36 C&J
37 C&J
38 C&J
39 C&J
40 C&J
41 C&J
42 C&J
43 JMS2
44 JMS2
45 JMS2
46 JMS2
47 JMS2



48 JMS2
49 JMS2
50 JMS2
51 JMS2
52 JMS2
53 JMS2
54 JMS2
55 JMS2
56 JMS2
57 JMS2
58 JMS2
59 JMS2
60 JMS2
61 JMS2
62 JMS2
63 JMS2
64 JMS2
65 JMS2
66 JMS2
67 JMS2
68 JMS2
69 JMS2
70 JMS2
71 JMS2
72 JMS2
73 JMS2
74 JMS2
75 JMS2
76 JMS2
77 JMS2
78 JMS2
79 JMS2
80 JMS2
81 JMS2
82 JMS2
83 JMS2
84 JMS2
85 JMS2
86 JMS2
87 JMS2
88 JMS2
89 JMS2
90 JMS2
91 JMS2
92 JMS2
93 JMS2
94 JMS2


95 JMS2
96 JMS2
97 JMS2
98 JMS2
99 JMS2
100 JMS2
101 JMS2
102 JMS2
103 JMS2
104 JMS2
105 JMS2
106 JMS2
107 JMS2
108 JMS2
109 JMS2
110 JMS2
111 JMS2
112 JMS2
113 JMS2
114 JMS2
115 JMS2
116 JMS2
117 JMS2
118 JMS2
119 JMS2
120 OL2
121 OL2
122 OL2
123 OL2
124 OL2
125 OL2
126 OL2
127 OL2
128 OL2
129 OL2
130 OL2
131 OL2
132 OL2
133 OL2
134 OL2
135 OL2
136 OL2
137 OL2
138 OL2
139 OL2
140 OL2
141 OL2



189 OL2
190 OL2
191 OL2
192 OL2
193 OL2
194 OL2
195 OL2
196 OL2
197 OL2
198 OL2
199 OL2
200 OL2
201 OL2
202 OL3
203 OL2
204 OL2
205 OL2
206 OL2
207 OL2
208 OL2
209 OL2
210 OL2
211 OL2
212 OL2
213 OL2
214 OL2
215 OL2
216 OL2
217 OL2
218 SMW
219 SMW
220 SMW
221 SMW
222 SMW
223 SMW
224 SMW
225 SMW
226 SMW
227 SMW
228 SMW
229 SMW
230 SMW
231 SMW
232 SMW
233 SMW
234 HSF
25 SWB

1 --.-

236 WSL 2-12
237 MS&R2 3-4
238 HBP 2-20
239 CL&W 3-21
240 P&L 22X
241 AIChE 1K_
242 AIChE 4K
243 AIChE 6K
244 AIChE 7K
245 AIChE 24K
246 AIChE 26K
247 AIChE 27K
248 AIChE 31K
249 SMW 46X
250 SMW 2-18
251 SMW 2-19
252 HSF 265X
253 SWB 50X
254 KJL1 84X
255 SMW 86X
256 SMW 92X
257 SMW 4-7
258 HSF 111X
259 SMW 120X
260 SMW 5-17
261 D&T 4-2
262 D&T 4-8
263 D&T 4-9
264 HSF 209X
265 MS&R2 3-7
266 SMW 105X
267 SMW 5-13
268 SMW 5-14
269 D&T 3-7
270 HSF 115X
271 HSF 4-8
272 WSL 2-9
273 AIChE 33K
274 AIChE 34K
275 CEE 116X
276 SMW 7-12
277 CACHE 1X
278 F&P 160X
279 SWB 45X
280 SMW 49X
281 SMW 2-23
282 SMW 7-2

action engineering problems having to do with
consecutive, competitive, second-order reactions
occurring in a CSTR. A scanning search of the
table forms for each of the four key concepts
associated with this class of problems discloses
that the following code numbers appear on each
of these forms: 93, 193, 195, 196, 98, 99. Similar-
ly, a search for problems involving reaction
mechanisms leading to fractional reaction orders
yields the following entries common to each of the
two pertinent table forms: 251, 252, 253, 47, 249.
Some suggestions regarding the usage of these
forms are presented below.
Large numbers of organized items (problems)

necessarily appear on the table forms for the
more general key concepts, such as first-order,
second-order, batch, tubular and CSTR. In a given
search involving several key concepts then, one
is well advised to first scan the table forms for
the more specialized pertinent concepts, e.g.,
autocatalytic, half-mile, multiple reactors, and
then to proceed to the more general concepts. This
sequence prevents the initial accumulation of a
large number of item code numbers which would
later have to be discarded.
This article has described the usage of the
key concept method of information organization
and retrieval for setting up and organizing a



CACHE "Computer Programs for Chemical Engineering Education," Vol. II (Kinetics), Edited by M. J. Reilly, Aztec
Publishing Co., Austin, Texas (1972).
CEE Briggs, D. E., Carnahan, B. and Williams, G. B., "The Use of Computers in Chemical Engineering Educa-
tion," The University of Michigan. Ann Arbor, Mich. (1963).
CL&W Carnahan, B., Luther, H. A. and Wilkes, J. 0., "Applied Numerical Methods," Wiley, New York (1969).
C&J Cooper, A. R. and Jeffreys, G. V., "Chemical Kinetics and Reactor Design," Prentice-Hall, Englewood Cliffs,
N.J. (1973).
D&T Denbigh, F., and Turner, J.C.R., "Chemical Reactor Theory," 2nd Edition, University Press, Cambridge
F&P Frost, A. A. and Pearson, R. G., "Kinetics and Mechanism," Wiley, New York (1953).
HBP Phillips, H. B., "Differential Equations," 3rd Edition, Wiley, New York (1934).


Fogler, H. S., "The Elements of Chemical Kinetics and Reactor Calculations," Prentice-Hall, Englewood
Cliffs, N.J. (1974).

JMS2 Smith, J. M., "Chemical Engineering Kinetics," 2nd Edition, McGraw-Hall, New York (1970).
KJL1 Laidler, K. J., "Chemical Kinetics," 1st Edition, McGraw-Hill, New York (1950).
MB Boudart, M., "Kinetics of Chemical Processes," Prentice-Hall Inc., Englewood Cliffs, N.J. (1968).
MS&R2 Mickley, H. S., Sherwood, T. K. and Reed, C. E., "Applied Mathematics in Chemical Engineering," 2nd
Edition, McGraw-Hill, New York (1957).


Levenspiel, 0., "Chemical Reaction Engineering," 2nd Edition, Wiley, New York (1972).
Panchenkov, G. M. and Lebedev, V. P., "Khimicheskaya Kinetika i Kataliz," University of Moscow Press,
Moscow (1961).

SMW Walas, S. M., "Reaction Kinetics for Chemical Engineers," McGraw-Hill, New York (1959).
SWB Benson, S. W., "The Foundations of Chemical Kinetics," McGraw-Hill, New York (1960).
SWC Churchill, S. W., "The Interpretation and Use of Rate Data: The Rate Concept," McGraw-Hill, New York
WSL LaLonde, W. S., "Professional Engineer's Examination Questions and Answers," 2nd Edition, McGraw-Hill,
New York (1960).


Directory of Mnemonic Codes for Identifying Sources
of Reaction Engineering Problems.

"Chemical Engineering Problems," American Institute of Chemical Engineers," New York (1956) (K
suffixed to associated numerical codes refers to the problem set on reaction kinetics).

file of reaction engineering problems. This file,
which has been organized and maintained by
manual methods with no great effort, has been
found to be very useful in an educational environ-
ment. It should be obvious, moreover, that these
same methods should be amenable to other in-
structional areas of chemical engineering. Thus,
one should be easily able to construct similar files,
if one is interested, for such areas as thermody-
namics, unit operations and process control, to
name a few. E-

1. Abramson, H. I., Chem. Engrg. Progress, 60, No. 8,
88 (1964).
2. Cushing, R., Chem. Engrg., 73, Jan. 7, 1963.
3. Holm, B. E., Chem. Engrg. Progress, 57, No. 6, 73
4. Morse, R. and Wall, E., Petroleum Refiner, 263, May,

Continued from page 133.
than precise. Professor Astarita attempts to ex-
plain the methods in a setting which anticipates
the heavy technical needs of the final chapters
on fading memory, a strategy which I think
taints his exposition of fundamentals with a
vagueness impossible to avoid in such an ambi-
tious undertaking.
For example, I believe Chapter 4 is seriously
flawed by its opening section which, in anticipa-
tion of Chapter 5, deals with differentiability of
functionals with respect to present values of
temperature. This discussion is too vague to be of
much use, plays no real role in the balance of
the chapter, and is likely to detract from the
effectiveness of the pedagogically critical sections
immediately following. I wish Professor Astarita
had chosen to divorce his exposition of method-
ology from his skillful, but necessarily sketchy,
description of Coleman's work on fading memory.
I wish also that literature citations had been
heavier so that readers could more readily make
contact with the original literature-indeed, the
crucial Coleman-Noll paper of 1963 is not cited
at all.
Despite these remarks, let me state once again
that the book is an important one for academic
chemical engineers and might substantially in-
fluence the way we think about thermodynamics.
It deserves reading, as do the source papers and
the monographs by Truesdell and Day. Professor

Astarita has reached beyond our own literature
and brought to it something of value.

1. Coleman, B. D. and Walter Noll, The thermodynamics
of elastic materials with heat conduction and viscosity,
Archive for Rational Mechanics and Analysis, 13, 167-
178 (1963).
2. Coleman, Bernard D., Thermodynamics of materials
with memory, Archive for Rational Mechanics and
Analysis, 17, 1-46, (1964).
3. Truesdell, Clifford, Rational Thermodynamics, McGraw-
Hill, New York, 1969.
4. Day, William Alan, The Thermodynamics of Simple
Materials with Fading Memory, Springer-Verlag, New
York, 1972.

WARD: Process Model-Building
Continued from page 139.
Financial assistance from Combustion Engineering
helped make these projects more effective than they
might otherwise have been.

1. Shukis, S. P., and Green, R. C., "Reduce Costs With
Scale Models," Chem. Eng., 64, 6, 235, (1957).
2. Myers, L. A., "How duPont Saves Money With
Models," Petroleum Refiner, 38, 7, 121, (1959).
3. Hammar, W., and Duncan, L. Jr., "Union Carbide
Builds Scale Models First," Petro/Chem. Eng., 87,
11, 56, (1965).
4. Klima, B. B., and Youngblood, E. L., "Inexpensive
Plant Models Easily Made," Chem. Eng., 6, 4, 128,
5. Miller, R. E., "Scale Modeling of Large and Small
Plant Projects," Chem. Eng., 78, 27, 69, (1971).
6. Babcock, J. A., "How To Get The Most Out of
Engineering Models," Chem. Eng., 80, 4, 112, (1973).
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Nine ChE's Receive Awards at ASEE Meeting
ASEE president George Burnet has pointed
out that at the recent ASEE Annual Conference
at Knoxville a number of chemical engineers re-
ceived special recognition. Following is a list of

Lamme Award
Curtis W. McGraw Award
3M Lectureship Award
Western Electric Fund Award
(Illinois-Indiana Section)
Western Electric Fund Award
(Middle Atlantic Section)
Western Electric Fund Award
(New England Section
Western Electric Fund Award
(North Central Section)
Western Electric Fund Award
(Pacific Southwestern Section)
Western Electric Fund Award
(St. Lawrence Section)

John J. McKetta
John H. Seinfeld
Abraham E. Dukler
Ralph E. Peck

Angelo J. Perna

James R. Kittrell

Alan J. Brainard

Fred H. Shair

Joseph Estrin

Dr. Burnet also requested that it be reported that
the editor of CEE received a special award from
the Chemical Division which was accepted on be-
half of the staff of CEE.

LETTERS: Carberry
Continued from page 107.
How, for example, in the name of God, Zeus or what-
ever diety prevails in Buffalo, is Yale* placed in the tail
end "of the class" relative to Buffalo? How is it that Yale
University is ranked with Judas in the Gill report when, in
fact, an even casual survey of their research endeavors
would prompt even a Big-8 anti-Ivy league-type to con-
clude that the graduate research-study program at Yale
is vastly more fundamentally significant than that of
one-half of those departments blessed with top 20 cate-
gorization by Gill et al.? How is it that perhaps several
of the departments assigned a rank in the top twenty by
Gill et al. (including, oddly I contend, his university)
would, on survey, be totally innocent of the nature of
Yale's labors and the Journals within which the Yale
Chemical Engineering people deposit their findings?
I leave it as an exercise to Gill enthusiasts to seek out
those non-AIChE Journals in which Yale Chemical
Engineering people choose to publish their research find-
ings, which areas they choose to pursue as ultimately
relevant to the science of chemical engineering.
We, in chemical engineering, have gone well beyond
the usual pedestrian levels of research inquiry. Survey
your colleagues, dear reader: where do they publish?
Perhaps in an AIChE publication; perhaps elsewhere.
Our noble calling has become, happily, diffuse insofar as
borderlines between chemical engineering and chemical
physics are no longer clear and well defined interfaces.
This I welcome. Provost Gill's survey respects not this
Yale has been and is and will always be a great
university, a summation of innovative departments of dis-
tinct, unique insight whether in the area of literature
or chemical engineering. Having had a distinguished de-
partment of traditional chemical engineering for enough
decades to even inspire a Buffalo, they now choose to
pursue a program of education and research in the
chemical engineering sciences, which enterprise might ul-
timately enlighten over-inflated Buffalo.
As this comment is quite personal, permit me to fashion
the "Carberry Report"-an evaluation of graduate
chemical engineering departments in two categories:
general (catholic-note, please, the lower case c) and special-
ized (I leave it to reformation theologians to fashion a more
definitive category) :

1. Minnesota
2. Delaware
3. Berkeley
4. Carnegie-Mellon
5. Illinois
6. Northwestern

1. Stanford
2. Yale
3. Princeton
4. Pennsylvania
5. Wisconsin
6. Everyman's School

Beyond that, my friends and enemies, its "to each
his own." As for the unmentioned, do your own grand
thing. The "Carberry Report" respects all who labor
in the vineyard, even Gill's Buffalo.
U. of Notre Dame
J. J. Carberry
*of which I am proud to be an alumnus.



Is the leg mightier than the atom?

Before you say no, keep in mind
that we know very little about many
forms of energy available to us.
Including good old muscle
For too long a time we've relied
on oil and gas to serve our needs,
and failed to take full advantage of
other sources of power.
Including the atom.
But recent events make it clear
we must learn about all the options,
and how best to apply them.
At Union Carbide we're study-
ing a wide range of energy tech-
nologies and resources for the

Energy Research and Development
From something as basic as bi-
cycling to the complexity of con-
trolling nuclear fusion.
For instance, we are learning
how to turn coal into oil and gas in
a way that is practical economically.
We're deeply involved in nuclear
research, particularly in finding
ways to make this important source
of energy safer and more efficient.
Our work in fusion power, at
Oak Ridge, Tennessee, offers the
most exciting possibility for the
future: the ultimate source of in-

exhaustible energy.
If we succeed, there will never
be another energy crisis.
But for the present, the answer
to our energy dilemma is not likely
to come from one source, but many.
All the way from the leg to the atom.

Today, something we do
will touch yourlife.
An Equal Opportunity Employer M/F



We're looking for people who are looking for the good life.
The good life involves a lot of the things we've always taken for granted. Like the availability
of enough food to feed an ever-growing population. A cure for disease. Thick forests. A
clean environment. And the time to relax and enjoy it all. Except now we're going to have
to stop looking at life through a tunnel and find ways to protect all forms of it-from our
homes to the farthest corner of the earth. Because life is fragile. And its protection is a
major concern at Dow. So we're looking for people with scientific, engineering, manufac-
turing and marketing backgrounds who'll direct their precious talents, enthusiasm and ideas
to the development of Dow products and systems for the good life. And we'll provide a
dignified, motivational environment to work and grow. If you or someone you know loves
life and wants to live it wisely, get in touch with us. Recruiting and College Relations, P.O.
Box 1713, Midland, Michigan 48640.

*Trademark of The Dow Chemical Company



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