Front Cover
 Table of Contents
 Division activities
 Scott Fogler of the University...
 Penn State
 The prospects of population...
 Teaching the basic elements of...
 Book reviews
 A telephone tutorial service
 Take two pills every four hours:...
 The road to hell
 Thermodynamic heresies
 Use and abuse of efficiencies in...
 What does the practicing ChE want...
 Back Cover


Chemical engineering education
http://cee.che.ufl.edu/ ( Journal Site )
Full Citation
Permanent Link: http://ufdc.ufl.edu/AA00000383/00057
 Material Information
Title: Chemical engineering education
Alternate Title: CEE
Abbreviated Title: Chem. eng. educ.
Physical Description: v. : ill. ; 22-28 cm.
Language: English
Creator: American Society for Engineering Education -- Chemical Engineering Division
Publisher: Chemical Engineering Division, American Society for Engineering Education
Place of Publication: Storrs, Conn
Publication Date: Winter 1978
Frequency: quarterly[1962-]
annual[ former 1960-1961]
Subjects / Keywords: Chemical engineering -- Study and teaching -- Periodicals   ( lcsh )
Genre: serial   ( sobekcm )
periodical   ( marcgt )
Citation/Reference: Chemical abstracts
Additional Physical Form: Also issued online.
Dates or Sequential Designation: 1960-June 1964 ; v. 1, no. 1 (Oct. 1965)-
Numbering Peculiarities: Publication suspended briefly: issue designated v. 1, no. 4 (June 1966) published Nov. 1967.
General Note: Title from cover.
General Note: Place of publication varies: Rochester, N.Y., 1965-1967; Gainesville, Fla., 1968-
 Record Information
Source Institution: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
Resource Identifier: oclc - 01151209
lccn - 70013732
issn - 0009-2479
Classification: lcc - TP165 .C18
ddc - 660/.2/071
System ID: AA00000383:00057

Table of Contents
    Front Cover
        Front Cover 1
        Front Cover 2
    Table of Contents
        Page 1
        Page 2
    Division activities
        Page 3
    Scott Fogler of the University of Michigan
        Page 4
        Page 5
        Page 6
        Page 7
    Penn State
        Page 8
        Page 9
        Page 10
        Page 11
        Page 12
        Page 13
    The prospects of population balances
        Page 14
        Page 15
        Page 16
        Page 17
    Teaching the basic elements of process design with a business game
        Page 18
        Page 19
        Page 20
        Page 21
        Page 22
    Book reviews
        Page 23
        Page 24
        Page 25
    A telephone tutorial service
        Page 26
        Page 27
        Page 28
        Page 29
    Take two pills every four hours: Hydrodynamic analog for drug dosage regiments
        Page 30
        Page 31
        Page 32
    The road to hell
        Page 33
    Thermodynamic heresies
        Page 34
        Page 35
        Page 36
        Page 37
    Use and abuse of efficiencies in separation processes
        Page 38
        Page 39
        Page 40
        Page 41
        Page 42
        Page 43
    What does the practicing ChE want in materials education
        Page 44
        Page 45
        Page 46
        Page 47
        Page 48
    Back Cover
        Back Cover 1
        Back Cover 2
Full Text

cemical engineerig eduat



Most oil and natural gas are
burned as fuel. About 4% become
petrochemical products-synthetic
fabrics, paints, plastics, even
medicines. Another product is
jobs. There are 11 million pet-
rochemical-related jobs in the
United States.

Through heat and cold, pressure
and vacuum, we transform petro-
leum molecules into the man-made
resources that will build a better life
for more of the world's people.
Millions of pounds of Union Carbide
ingredients - solvents, resins and
latexes - help modem paints '
protect and beautify just
about everything
under the sun.
And rain. On tm

To feed the world's growing
population, we need to stop
the insects that compete with
us for food. Around the world,
Union Carbide's pesticides
are helping increase yields
of such basic foods as rice,
potatoes, soybeans and

Plastics will increasingly replace
heavier metal parts as auto
makers strive for better gas
mileage. But Union Carbide is
already helping auto makers,
with petrochemicals for every-
thing from light urethane bump-
ers to polyethylene electri-
cal insulation. We even make
Prestone II" anti-freeze.
Your carefree synthetic fabrics
are petrochemicals, too.
Union Carbide makes the
basic ingredient in polyester,
the most popular synthetic
of all.


: mD

Union Carbide Corporation, 270 Park Avenue, NewYork, N.Y. 10017

Department of Chemical Engineering
University of Florida
Gainesville, Florida 32611

Editor: Ray Fahien
Associate Editor: Mack Tyner

Business Manager: R. B. Bennett
Managing Editor: Bonnie Neelands
(904) 392-0861
Publications Board and Regional
Advertising Representatives:
Darsh T. Wasan
Illinois 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
WEST: George F. Meenaghan
Texas Tech University
William H. Corcoran
California Institute of Technology
William B. Krantz
University of Colorado
EAST: 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

26 A Telephone Tutorial Service,
D. Himmelblau
33 The Road to Hell,
K. Zipf

4 The Educator
Scott Fogler of the University of Michigan

8 Departments of Chemical Engineering
Penn State

14 Lecture
The Prospects of Population Balances,
D. Ramkrishna

18 Classroom
Teaching the Basic Elements of Process
Design with a Business Game,
T. Russell and D. Frankel

30 Laboratory
Take Two Pills Every Four Hours: Hydrody-
namic Analog for Drug Dosage Regimens,
S. Jackson and J. Stevenson

34 Views and Opinions
Thermodynamic Heresies, M. Sussman

38 International
Use and Abuse of Efficiencies in Separation
Processes, A. Drinkenburg

44 Curriculum
What Does the Practicing ChE Want in
Materials Education, R. Griskey
3 Division Activities
43, 47 Letters
23, 37, 46 Book Reviews

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 32028. 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 � 1978 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.


"At Du Pont you don't get lost

in a big company atmosphere.

t's very personal"

-George D. Peterson

BS, Chemical Engineering


"Du Pont is a big com-
pany but it's broken down into
satellites. So you don't get lost
in a big-company atmosphere.
It's very personal, and I think the
people are top-notch.
"I started in technical
here at the Belle Plant in West
Virginia. Now I'm a production
supervisor. Production is solv-
ing problems on a day-to-day
basis. I like working under that
kind of pressure. When things

work out, it's very rewarding. So
is working with people. I'm
responsible for helping 22 peo-
ple do their jobs.'
George was recruited by
Du Pont from the Michigan
Technological University
campus in 1973. He interviewed
about 25 companies.
George's story is typical
of many Chemical, Mechanical
and Electrical Engineers who've
chosen careers at Du Pont.

We place no limits on
the progress our engineers can
make. And we place no limits
on the contribution they can
make-to themselves, the
Company or to society.
If this sounds like your
kind of company, do what
George Peterson did. Talk to the
Du Pont representative who
visits your campus. Or write:
Du Pont Company, Room
35972, Wilmington, DE 19898.

At Du Pont...there's a world of things YOU can do something about.

An Equal Opportunity Employer, M/F




University of California
Berkeley, California 94720

T HE PENTENNIAL Summer School for
Chemical Engineering Faculty was held in
Snowmass Colorado-July 31-August 5, 1977.
There were 270 professional attendees. Many
brought their families, so that there were over 700
persons in Snowmass connected with the Summer
Financial support was contributed by thirty
industrial companies and two foundations; donors
are shown in the Table. This covered expenses for
workshop leaders, travel and meal/lodging subsidy
for participants and both a group dinner and a
group barbecue. There were 37 attendees present
from industry. This contributed positively in
many ways.
The program of the Summer School was built
to a large extent around new applications of
chemical engineering. There were sessions on bio-
chemical engineering, food processing, metallurgi-
cal processing, a novel approach to industrial
chemistry, electrochemical engineering, surface
and colloid phenomena, and technology assessment.
Other popular topics included kinetics and reactor
design, the structure of the chemical process in-
dustries, process economics, novel teaching
methods, uses of interactive computing, and
various administrative questions.
Colorado proved to be hospitable in many
ways, including the weather (until the last day!).
Participants got to know Aspen and explored
many scenic hiking trails in the vicinity during
free afternoons.
The Organizing Committee for the 1977
Summer School consisted of Mike Williams and
Jud King (Berkeley) -Co-Chairmen; Peter Clark
(Virginia Poly) ; Stan Barnett (Rhode Island) ;

Alex Bell (Berkeley); Fraser Russell (Dela-
ware) ; Don Woods (McMaster) ; Ernie Henley
(Houston) ; and John Prados (Tennessee). The
next Summer School, probably to be held in 1982,
will be organized by Fraser Russell of the Uni-
versity of Delaware. He will welcome comments
and suggestions. E
Sponsors of 1977 Summer School for Chemical
Engineering Faculty
Union Carbide Corporation
Dow Chemical U.S.A.
E. I. duPont de Nemours & Co.
Stauffer Chemical Company
The Upjohn Company
Diamond Shamrock Corporation
Celanese Corporation
The Procter & Gamble Co.
Shell Development Company
BASF Wyandotte Corp.
Exxon Chemical/Research & Engineering
Fluor Engineers & Constructors, Inc.
General Electric Company
PPG Industries
Weyerhaeuser Company
Standard Oil Company (Ohio)
International Paper Company
Standard Oil Company (California)
Standard Oil Company (Indiana)
Ethyl Corporation
Phillips Petroleum Company
Monsanto Corporation
Texaco, Inc.
Eastman Kodak Company
Rohm & Haas Company
Continental Oil Company
NL Industries
Occidental Research Corporation
Envirotech Corporation
Adolph Coors Company
National Science Foundation
The Camille and Henry Dreyfus Foundation



A Teacher Of Learning


University of Michigan
Ann Arbor, Michigan 48109

SCOTT FOGLER ENJOYS teaching, enjoys
students, enjoys the challenge of arousing
interest in his classes, enjoys the fulfillment of ac-
complishment in his students. In short, he comes
as close to a Teacher of Learning as one is apt to
find as this typical statement from one of his
students shows: "I believe he really cares about
each and everyone of his students; how they are
doing in his courses, in other courses; and in
particular the problems that students have in
understanding course material. He is a top man.
I would like to see more dedicated men in the
teaching profession like him."
Scott remembers his first class as a teacher.
It was during his first summer as a graduate
student at Colorado, and he was asked to fill in

Another important influence
in Scott's teaching career was an
ASEE workshop he attended in 1969. It
was led by A. A. Root, and catalyzed his
interest in finding new approaches to teaching

for a month, teaching a rate operations course for
juniors. Beginning teachers usually experience a
combination of exhilaration and fear: Scott felt
both. He loved the teaching, and the experience
was a major reason why he decided to teach. But
he also had fears.
"What if I teach all my life . . . and do it
ineffectively?" Scott has paid attention to not
doing it ineffectively. His sensitivity to students'
interests, mastery of teaching techniques and
communicable enthusiasm produce classes which
challenge-and entertain-his students. He moves
about the room, gesturing, poking at formulas
on the board. He pauses for effect. He calls
students by their first name, asking questions, and
throwing in one-liners that keep the class alert
and entertained. As one student says: "He's got
to be good to keep a class this awake at 8:00 in
the morning!"
An intensity and deep involvement pervades
most of Scott's activities. He is always a man
in motion striving for perfection-in class, in
research conferences, in faculty meetings-his
intense persistence on goals and achievements
sometimes exhausts the efforts of others to keep
up his pace.



S COTT'S ENTHUSIASM for teaching is ex-
plainable. His father was a professor of
chemistry at Illinois State Normal University, in
Bloomington, Illinois. His father's example and
Scott's own intellectual curiosity proved a decisive
combination: he gave up his interest in competi-
tive swimming after graduating from Morgan
Park High School in Chicago to devote more time
to his studies. At the University of Illinois, where
he received a BS (in 1962) he studied with Max
Peters, one of the influential teachers in Scott's
life. He was so impressed with Peters that he
followed him to Colorado in 1962 when Peters
accepted the Deanship there.
At Colorado, Scott had the fortune of working
with Klaus Timmerhaus, another master teacher.
From Timmerhaus, Scott learned the significance
of maintaining an open, permissive atmosphere
for students. He learned how to let students con-
front problems in their own way, and to learn
from mistakes as well as successes. In this
stimulating environment, Scott was encouraged
to start his own seminar in interfacial phenomena
as a graduate student.
After receiving his PhD in 1965, Scott joined
the Faculty of The University of Michigan.
Beginning the following year, he fulfilled his
ROTC obligation, spending two years at the Jet

The Fogler Tribe.

Propulsion Laboratories. There, he also taught
evening courses in mass transfer through UCLA's
evening extension program.
Another important influence in Scott's teach-
ing career was an ASEE workshop he attended
in 1969. It was led by A. A. Root, and catalyzed
his interest in finding new approaches to teach-

ing. Always a hard-driving perfectionist, Scott
first dug into the literature of learning theory and
developed a comfortable ease with the concepts
and language for the analysis of educational
approaches. "Open-ended, programmed learning,
guided design, computer gaming, simulation, in-
formation dissemination, Keller plan, synthesis,
motor skills," etc. were only some of the con-
cepts that Scott brought to the Chemical Engi-
neering Faculty over the next few years. At first,
these were but abstractions to the rest of the
faculty, but Scott made them real by applying
them to his classroom activities. The results are
remarkable, as students and colleagues attest.
Scott has confronted the problem of individualized
instruction in large classes with success. At least,

Scott uses audio-visual materials in other ways
such as in computer graphics. He currently
has six interactive computer programs,
two of which are played like games.
One game is a murder mystery and
uses knowledge of rate reactions to find
the body and determine the murderer.

the students think so: "I feel that I participate
more actively in Professor Fogler's classes as one
student in 80 than in some other classes where I
am one out of ten."
Scott Fogler's teaching techniques are aimed
at a double goal: to convey basic information, and
also to teach the process of creative problem
solving. His classroom approach reflects this
philosophy. Scott spends class time telling his
students about analysis and synthesis; how he
thinks when he tries to solve a problem. He
constantly asks himself "What intellectual ability
am I teaching?" What he strives for is not just
the factual basis for problem solving, but the
creative ability to choose the best way of finding
solutions. He feels that lab sessions are a time
when the student should use his own intellectual
arsenal for problem solving. Learning factual
material, deriving equations and other "book
work" is for the students' own time, out of class.

S COTT CALLS TEXTBOOK exercises "... con-
vergent: if you work the formulas long


enough, you'll come up with the right answer. The
world isn't like that. In industry, you may not
know even if there is a problem. And if there is a
problem, it may not have an answer or it may have
many answers."
Scott reaches for "divergent" exercises, ones
which challenge the student to use all his abilities
for analysis and the synthesis of a solution. One
of his favorite projects in an open-ended labora-
tory course he developed is a microplant. This is

Scott has confronted the problem
of individualized instruction in large
classes with success. At least, the
students think so: "I feel that I participate
more actively in Professor Fogler's classes
as one student in 80 than in some other classes
where I am one out of ten."

a continuing effort, begun several semesters ago,
which is continued by succeeding classes. The
project is a miniature plant for manufacturing
polystyrene. It has progressed through the design
to the hardware stage. Presently, after three years
of student efforts, it produces small quantities of
polystyrene. Continuing student efforts are
directed to improving the product and increasing
plant efficiency.
A student may be called on for abilities com-
pletely outside chemical engineering to solve
problems in Scott's classes. Another project is to
dramatize some classic material in ChE in a 10-
minute videotape. The effort injects creative
problem solving into the perfunctory experiments
every chemical engineer has to know.
Scott uses audio-visual materials in other ways,
such as in computer graphics. He currently has
six interactive computer programs, two of which
are played like games. One game is a murder
mystery and uses a knowledge of rate reactions
to find the body and determine the murderer. It
must be in the processing vat because its conver-
sion shifted dramatically at about the time of the
murder. Each time the student signs on the com-
puter, there will be a new randomly selected
murderer and victim. The other computer game is
more immediate: the student is told he has just
been infected by a lethal bacteria. He has only a
few minutes to perform a limited number of ex-
periments. The first problem: which experiments

must he choose? The student who becomes too
engrossed in experimentation will be told
abruptly that he has taken too long, and has just
died. As this game demonstrates, Scott feels that
experimentation must be taught as a method of
creative problem solving, and not as an end in
itself. He cautions students to experiment eco-
nomically, to try to reach the best solution with
the fewest possible tests.
Another interactive computer graphics pro-
gram simulates a microplant which has randomly-
selected faults. With this program, each student is
confronted with a unique diagnostic problem. For
example, one of the components, such as a reactor,
may be malfunctioning. Through a series of inter-
active diagnostics the student must find the faulty
unit and suggest corrective measures. This
sophisticated simulation took about three years
to complete.
Scott is very concerned that the student be
allowed to develop at his own speed whenever
possible. He has tried the Keller plan of teaching,
which allows individual rates of progress, but
found that the need for proctors made the plan
One of Scott's techniques for large classes is
straight out of Education School: the Buzz Group.
Scott gives a brief lecture, and the students then
break up into small groups to solve a class
problem. As they work, Scott goes from group
to group, encouraging, answering questions, prob-
ing. With this method, he can, in fact, provide a
personal touch even in classes of 80 students.
Scott's greatest success to date with individual-
ized learning is his Programmed Text in Chemi-
cal Reaction Engineering (PTCRC). In this text,
the student learns incrementally, frame by frame,
pretty much at his own pace. One of the first texts
of its kind in ChE, it is in its second printing in
just three years.

S COTT REALIZES THAT masterful teaching
techniques are not enough to keep a Professor

Now, there are six PhD
students doing research with
Scott, and he has a bibliography of
over 35 publications and over $125,000
per year in research funding.


I �

going: "To have any impact on teaching, you need
to have a sound research program before anyone
will listen to you. I had some early ideas about
guided design, but my research program really
wasn't where it is now." Now, there are six PhD
students doing research with Scott, and he has a
bibliography of over 35 publications and over
$125,000 per year in research funding. In the
beginning, Scott's own research interests came
before his interest in teaching. He decided to
pursue a PhD because he found he liked research
after a summer project with John Quinn at the
University of Illinois. It was that summer class
in rate operations at Colorado that convinced him
to teach. Scott started his research career with
Klaus Timmerhaus in the area of ultrasonics. His
interest in ultrasonics expanded at The University
of Michigan to include some pioneering work on
ultrasonic emulsification, and he recently achieved
a breakthrough in predicting liquid-liquid droplet
breakup dynamics in an ultrasonic field based on
fluid mechanical and interfacial considerations.
Scott has become deeply involved in the
kinetics and mechanism of heterogeneous inter-
facial dissolution of minerals, especially as applied

Scott's graduate research group holds a weekly seminar.

to improving oil and gas recovery (acidization)
in porous rock formations. Scott is especially
excited about his recent development of a mathe-
matical model that predicts the movement of re-
action and permeability fronts in porous media.
In related work, he has applied a fundamental
kinetic approach to obtain some very strong leads
on the interrelationship of acid attack on minerals,
based on the crystal structure of the mineral and
the behavior of interfacial reaction systems. One
colleague commented that Scott was the first
person to study the fundamental reaction of
minerals in contact with acids, and his work will

He is proud of the Dow Award
he received in 1972, a recognition
given to outstanding young faculty in
the mid-west. Scott has been honored
by the University of Michigan class of 138 E
as an outstanding young faculty member,
and has also received the U-M Junior Faculty Award.

be of lasting importance to investigators in that
In addition to his research interests, Scott
spends time consulting for Chevron Oil. He agrees
that constant industrial contact is necessary for
one who is training future chemical engineers. He
brings as much non-proprietary data as he can to
his classes.
Scott's enthusiasm for teaching-and doing it
right-has won him recognition as an outstand-
ing educator. He is perhaps most proud of being
a Fulbright Scholar to Norway in 1974-75, at the
Physical Chemical Institute of Bergen. While
there, he studied flow and reaction in porous
media, specifically the North Sea Oil wells. He is
also proud of the Dow Award he received in 1972,
a recognition given to outstanding young faculty
in the mid-west. Scott has been honored by the
University of Michigan Class of '38E as an out-
standing young faculty member, and has also re-
ceived the U-M Junior Faculty Award. Scott also
remembers with pleasure the Annual Canoe Trip
Seminar at the University of Pennsylvania: the
invited guest gives an informal seminar after a
scenic canoe trip.

S COTT'S ENTHUSIASM and intensity per-
vades most of his activities, both inside and
outside the University. He is very much involved
in the activities of his family, and through his
children, has become very active in Little League
and Indian Guides.
Indian Guides teaches the virtues of self-
reliance, honesty, and concern for others through
bi-weekly meetings, and other activities such as
camping and canoeing. It emphasizes participation
by the father-son team; in this case, Scott and his
sons Pete, age 11 and Robby, age 9. Robby also
shares his dad's affinity for scary movies, and
periodically they share an evening of pleasurable
Continued on page 36.


np department .


With Historical Notes by Floyd L. Carnahan
University Park, Pennsylvania 16802

one of the major academic institutions in the
United States. With a total enrollment of about
67,000 in 1976, it ranked 11th nationwide. About
33,000 students are located at the main campus,
University Park, with the remainder distributed
among 20 branch campuses throughout Pennsyl-
vania. Except for the University's College of
Medicine at Hershey, the major graduate pro-
grams are located at the University Park Campus,
as are the approximately 6,000 graduate students.

You may also have noted that Penn State has a
football team.
The University Park Campus is on a 4,786-
acre tract of land, of which 540 acres comprise the
central campus. There are 272 major buildings at
University Park but the many large shade trees
and expanses of lawn give much of the campus a
park-like appearance. The University is associated
with the town of State College, a name dating
back to a time when the University itself was a
college. The permanent town population is some-
what smaller than the University's and no major
industries are based in State College. As a conse-
quence, most of the town's business activity is
directed toward serving the University popula-


tion, offering shops, restaurants, entertainment
and residences for many of the students.
The University, which was originally es-
tablished as the Farmer's High School in 1855,
is located in an almost completely rural section of
the state, very close to its geographical center.
The Appalachian Mountain range and nearby
forested mountains and state parks offer a wide
variety of outdoor activities throughout the year.
These are balanced by the many cultural events
and facilities found on campus. Penn State offers
a quality education in a relaxed, coherent atmos-
phere without the distractions and disadvantages
of the large city locale of many comparable insti-

Chemical Engineering at Penn State had its
roots in Chemistry which separated from General
Science in 1888. Dr. George Gilbert Pond was the
first Professor of Chemistry. He and one in-
structor taught all the chemistry offered in 1888.
The first chemistry graduate in 1890 was William
H. Walker (now generally recognized as "the
Father of Chemical Engineering"). Walker went
on to G6ttingen for M.A. and Ph.D. degrees and
returned to Penn State as an Instructor in
Chemistry (1892-1894). He moved to M.I.T. in
1894 where he established the School of Chemical
Engineering Practice (1917) and collaborated
with W. K. Lewis and W. H. McAdams in writing
the first ChE textbook, the classic "Principles of
Chemical Engineering" (1924).
A curriculum in Industrial Chemistry at Penn
State was first offered in 1902 under Jesse B.
Churchill. The distinctive element of this new
curriculum was its emphasis on integrated chemi-
cal processes with stoichiometry and material
balances serving as powerful practical tools of
analysis. In 1924 with formation of the new School
of Chemistry and Physics, the curriculum was re-
named Chemical Engineering, and the then
modern unit operations approach to chemical

The department established
its early reputation through its
pioneering research in petroleum
processing and lubrication and these
continue to be active
research areas.

process design and analysis was promoted with
the aid of the new Walker, Lewis, and McAdams
Early in 1929 Merrell R. Fenske (Sc.D., MIT,
1928) became associated with the School of
Chemistry and Physics in a research and instruc-
tional capacity. With distillation equipment of
unique design installed in Pond Laboratory, he
began studies on the composition of the lower
boiling fractions of Pennsylvania crude oil. Excit-
ing results came quickly; industrial and govern-
ment support proliferated; and in 1931 additional
laboratory space was obtained in the Old College
Power Plant. These were the humble origins of
the soon to become internationally recognized
Petroleum Refining Laboratory. The laboratory
was strictly a research organization staffed mainly
with chemical engineers and chemists, as many
as 70 during World War II. Techniques developed
in the Petroleum Refining Laboratory helped in-
sure an adequate supply of aviation gasoline,
hydraulic fluids, and a variety of lubricants which

S. .

A view of Mount Nittany from Beaver Stadium.

were essential to the Allied War effort.
The Chemical Engineering and Chemistry De-
partments were separated in 1948 with Donald
S. Cryder (Sc.D., MIT, 1930) as Head of the
former. Vigorous interaction between the Petro-
leum Refining Laboratory and the Department of
Chemical Engineering resulted in a merger in
1959 with Dr. Fenske as Head. Dr. Fenske
reigned until his retirement as Department Head
in 1969. The search for his successor consumed a
year's effort, and in 1970 Lee C. Eagleton,
formerly of the ChE Department at the University
of Pennsylvania, became Head.


reputation through its pioneering research in
petroleum processing and lubrication and these
continue to be active research areas. Professors
McCormick, Jones, Klaus, Tewksbury, Peiffer, and
Barton grew up with the Petroleum Refining
Laboratory and they carry on the fine traditions
of that organization. In the late '50's and early
'60's, ChE research and education experienced a
fairly universal drift toward more fundamental
ChE science. Penn State kept pace with this
current by acquiring Professors Engel, Daubert,
and Kabel whose fields of expertise (optimization,
process dynamics, reaction kinetics, and complex
phase equilibria) were expanding rapidly at that
time. In the late '60's and early '70's, Professors
Danner, Eagleton, Ultman, and Duda strengthened
departmental efforts in phase equilibria and re-
action kinetics while adding new expertise in inter-
facial and transport phenomena, polymer process-
ing, and biomedical engineering. Most recently
(1976), the addition of Professors Vannice and
Tarbell (with their major interests in hetero-
geneous catalysis and applied mathematics) has
rounded out the current faculty.
Although as a group we are most proud of
our technical abilities and accomplishments, there
are those who would argue that the true measure
of a man's worth is the breadth of his interests.
For example, when Dr. Eagleton first arrived on
campus in 1970, he was shocked to find that no
one on the faculty played tennis (Lee was
seventh man on the tennis team at MIT one year,
but never won a match). As a perceptive ad-
ministrator, he quickly recognized this deficiency
and soon convinced Dr. Danner (as Assistant
Professor at the time) that tennis might be an
important component of his professional develop-
ment. Ron was obliging and served admirably as
a partner until he received tenure, at which point
his tennis enthusiasm suddenly waned. This situa-
tion was alarming and an exhaustive search for
new talent was undertaken. Fortunately, Dr. Duda
(whose background in polymer science was sur-
passed only by his twenty years of tennis ex-
perience) was looking for an academic position
at that time. Larry and his wife were conveniently
lured away from Dow Chemical Company to com-
plete a formidable mixed doubles opponent for the
The competitive spirit in the department is
perhaps best exemplified by the infamous Kabel-

Danner squash rivalry. It is now widely accepted
by members of the faculty that our weekly de-
partmental meetings must not be scheduled on
Monday, Wednesday, or Friday at 4:00 p.m. since
these hours are forever reserved for the most
pressing faculty activities. Beyond squash and
tennis, these have often been known to include
graduate student tutorials at the local pubs of
State College.
In addition to his squash exploits, Dr. Kabel
is also noted for his ability as an amateur aviator.
A few years ago when Bob's research activity
suddenly switched from reaction kinetics to air
pollution meteorology, many on the faculty were
baffled. In retrospect, this phenomenon is not
difficult to explain. In what other field is it possible
to include flying time in the budget of a research
Community service is another area in which
our faculty excel. Dr. Engel and Dr. Duda are
active in the local Boy Scout troop. With their
vast knowledge of outdoor life, they are uniquely
qualified to lead twelve year old boys on expedi-

Student performs in a pulmonary gas mixing


Industrial Chemistry
(15 credits)
Chemistry (40 credits)
Engineering (23 credits)
Mathematics (14 credits)
Physics (12 credits)
Other Courses (46 credits)

Total-150 credits

Walker Laboratory.

tions through the fields and streams of Pennsyl-
vania. Recently, Al and Larry were observed re-
turning to State College late one Sunday evening
with a mysterious L-shaped canoe on the roof of
Larry's station wagon. Al was overheard saying,
"Maybe next time we ought to try something a
little less ambitious like a weenie roast in your
back yard, Larry."
Actually, the departmental naturalist is Dr.
Jones. On Mondays at lunch (while others are in-
volved in lively discussions of the latest Penn State
gridiron battle), Jennings sits alone in the corner
offering a dissertation on his latest observations
of the mating habits of the beardless fly catcher.
If modern music turns you on, then you will
surely find the ChE trio (Danner-piano, Vannice
-banjo, Ultman-vocals?) an inspiration. Their
performances, usually reserved for intimate
faculty dinner parties, are among the leading
examples of dissonance available on major uni-
versity campuses.
The list of faculty interests could go on, but
surely at this point it is not difficult to conclude
that ChE at Penn State is a truly catholic depart-

T HE UNDERGRADUATE ChE curriculum at
Penn State has experienced considerable
evolution since the industrial chemistry era. The
table below compares the curriculum as it ap-
peared in the 1923-24 catalog with the current
(1977-78) curriculum.
Although the total credits required for a de-
gree has declined slightly, this has been mainly
in non-technical areas. The major change has been
the shift away from chemistry (55 credits then,

Chemistry (23 credits)
(35 credits)
(15 credits)
Mathematics (18 credits)
Physics (11 credits)
Other Courses (37 credits)
Total-139 credits

23 credits now) toward engineering (23 credits
then, 50 credits now). The component of this
change which pleases us most and which we feel
best serves the interests of our students is the
present 15 credits of engineering electives. This
flexibility allows our seniors to pursue specialized

Two students comprised the
first Penn State graduating class
in ChE Engineering (Industrial Chemistry
1906). This year we expect to graduate
105 students with B.S. degrees in ChE.

courses of their choice in such areas as mathe-
matical modeling, process dynamics, cryogenic
engineering, nuclear chemical engineering, and
polymer processing as well as in advanced offer-
ings in process design, petroleum technology, in-
dustrial chemistry, transport phenomena, mass
transfer operations, thermodynamics, chemical re-
actor design, and a host of courses in other engi-
neering departments.
Also available is the senior research option
which typically involves the student in an on-going
departmental research project wherein he is
exposed to research methodology and obtains
"hands on" experience in a specialized field.
During each of the past four summers, the de-
partment (with support from the National Science
Foundation) has sponsored between 10 and 15
undergraduate students on departmental projects
related to energy-environment problems such as
tertiary oil recovery and catalysis for SO, oxida-
tion. Not only Penn State students, but students
from neighboring departments in the northeast
have participated in this program.
Two students comprised the first Penn State
graduating class in ChE Engineering (Industrial
Chemistry-1906). This year we expect to gradu-
ate 105 students with B.S. degrees in ChE.


During the interim, 2,176 B.S. degrees were
granted by the department.

offers programs leading to the M.S. and Ph.D.
degrees. Over the years we have awarded 310 M.S.
and 104 Ph.D. degrees. However, the number of
graduate degrees awarded has accelerated in
recent years with 20 M.S. and 4 Ph.D. degrees
granted in 1976-77. For the last several years we
have maintained a graduate population of 50 to
60 students and at the present time about 30%
of our graduate students are working toward the
Ph.D. degree. The department supports graduate
students with fellowships, teaching assistantships
and research assistantships. The primary vehicle
for support is the half-time research assistantship
which allows students to get deeply involved in
their thesis projects early in their residence on
The environment of our graduate program
provides a unique opportunity for cultural ex-
change. We currently support students from the
Far East, the Middle East, India, Africa, Western
Europe, Latin America, and, of course, the United
States. We have all been enriched by personal re-
lationships developed with individuals of diverse
backgrounds in both academic and social activi-
Our graduate students carry out most of their
research work in the department's 35 individual
laboratories and four story pilot plant. The ChE
shop is well equipped and is staffed with two full
time technicians who assist students in the design
and construction of experimental apparatus. We
are fortunate to be part of a large university for
this allows us ready access to the facilities, pro-
grams, and expertise of its many fine departments.
Interdisciplinary research projects with the Uni-
versity's Center for Air Environment Studies,
Applied Research Laboratory, Milton S. Hershey
Medical Center, Materials Science Department,
Mineral Engineering Department, Meteorology
Department, and Bioengineering Department have
proliferated in recent years. This trend will surely
continue as the technological problems facing
society demand increasingly sophisticated solu-
Beyond their usual interaction with the Penn
State faculty, graduate students have the oppor-
tunity to listen to and indeed speak to many
visiting academics and industrialists as a part of

the ChE seminar program. During the past year,
26 seminar speakers representing 10 universities,
10 industrial corporations, and several government
agencies spent a day or more as guests of the
Of course, the faculty's research interests have
the greatest influence on the character of the
graduate program.

from the applied to the fundamental in both
classical and modern areas. Many projects
embrace several disciplines, but in what follows
current research is classified under broad and
conventional labels.
* Energy and Environment
A major effort in tertiary oil recovery under
the direction of Professors Klaus, Duda, Danner,
and Jones is aimed at perfecting chemical flood-
ing technology. This requires the development of
surfactant synthesis strategies, and physico-
chemical measurements of the phase equilibria,
interfacial tension, and bulk viscosity of surfac-
tant solutions. The surfactant solutions are non-
Newtonian, viscoelastic fluids and their flow in
porous media characteristics are being studied
with a view toward designing an optimal solution
based on a characterization of the porous media.
Greater understanding of the fundamentals of
lubrication, friction, and wear (tribology) can

Also available is the senior research
option which typically involves the student in
an ongoing departmental research project wherein
he is exposed to research methodology and
obtains "hands on" experience
in a specialized field.

result in improved lubricants which might save
5 to 15 percent of the gasoline consumed by the
U.S. automotive fleet. Elmer Klaus and Elmer
Tewksbury are studying the fundamental adsorp-
tion, chemical reaction, and film removal processes
which underlie boundary lubrication with the goal
of developing improved lubricants.
Al Engel is investigating the catalytic hydro-
genation of algae to form an "oil" product which
may serve as an energy source. An oil of
acceptable quality has been produced and now


the reaction mechanism is being probed in order
to develop a preliminary reactor design for
economic evaluation.
Chuck Peiffer is looking at cocurrent contact-
ing as a means of saving energy in separation
processes by reducing the pressure drop required
for a specified thru-put and separation.
The effect of combustion modifications for the
control of nitric oxide emissions on the fuel
economy of utility boiler systems is being evalu-
ated by John Tarbell. Detailed mathematical
models are used to simulate utility boiler operation
with special emphasis on coal combustion and
fuel nitrogen conversion. In related work, Al
Engel is looking at catalytic processes for the
oxidation of SO2 in stack gases.
Bob Kabel is involved in air pollution meteor-
ology with emphasis on the natural removal of
atmospheric pollutants at the earth's surface.
Mechanisms of removal and the prediction of
mass transfer coefficients for the atmosphere,
large bodies of water, vegetation and soil are
being investigated with the aid of an aircraft
measurements program.
Paul Barton is currently performing a field
evaluation of limestone treatment of industrial
acid waste waters. His other projects include de-
waxing of petroleum oils with crystallization by
direct contact with liquid freons, molecular sieve
separations with dense gas volatility amplification,
and modeling of multi-stage Purex extractions of
nuclear fuels in short residence time contractors.

* Kinetics and Catalysis
The vapor phase oxidation of organic com-
pounds such as hydrocarbons, alcohols and alde-
hydes leads to a host of products depending on the
reaction conditions. Jennings Jones has been
studying the effect of temperature, pressure, and
reactor surface conditions on the yield and selec-
tivity of these complex reactions. In related work,
Tom Daubert has been investigating surface
effects in complex hydrocarbon oxidative dehydro-
genation reactions.
Bob Kabel is attempting to elucidate the most
important parameters in selection, preparation,
and application of non-noble metal catalysts for
the abatement of automotive exhaust pollution. Al
Vannice is studying the effect of preparative
variables such as solution pH, metal salt, and type
of support, on metal dispersion in catalyst prepa-
ration. These projects aim to reduce catalyst
preparation to a science rather than an art.

Al Vannice is also involved in a kinetic study
of a new family of catalysts for CO/H2 reactions
viz., metals supported on carbon molecular sieves.
These sieves can be prepared with different pore
size distributions to alter diffusivity which in turn
affects product distribution. In addition, Al is
using infrared spectroscopy to determine the effect
of metal-support interactions and metal crystallite
size on the adsorbed state of intermediates in
methanation and Fischer-Tropsch reactions.

During the past year, 26
seminar speakers representing
10 universities, 10 industrial corpo-
rations, and several government agencies
spent a day or more as guests of the department.

* Transport Phenomena and Thermodynamics
Larry Duda has been investigating diffusion
in polymer solutions. Recent work has led to a
new sorption technique for determining the con-
centration dependence of diffusion coefficients,
and a new theory for the prediction of concentra-
tion, temperature, and molecular weight depend-
ency of diffusion coefficients in concentrated
polymer solutions. Related efforts are concerned
with the thermodynamics and statistical me-
chanics of polymer solutions and the coupling of
relaxation and diffusion in polymer systems.
Jim Ultman is studying the mechanism of gas
mixing in lung airways and its role in pulmonary
function testing. Tracer impulse-response tech-
niques are used to measure the residence time
distribution of the bronchial tree. Further work
along these lines involves the development of a
continuous monitor of lung compliance and blood
oxygen concentration to aid the physician attend-
ing an infant suffering from hyaline membrane
John Tarbell is determining the radial trans-
port characteristics of periodic flows with second-
ary motion. These flows arise naturally in the
human circulatory system when blood travels
through curved arteries and branching vessels and
may play an important role in the pathogenesis of
The prediction and correlation of thermo-
dynamic and transport properties for materials
Continued on page 47.


Sl lecture

EDITOR'S NOTE: This paper continues a feature begun by CEE in the
Summer 1976 issue. If you have a paper to submit, please send it to the editor.


Purdue University
West Lafayette, Indiana 47907

THE DISPERSION OF one phase into another
has been the crux of the chemical engineer's
craft for carrying out a host of transfer opera-
tions. Thus, numerous separation processes based
on direct phase-contacting such as liquid-liquid
extraction, distillation, absorption etc. are con-
ducted in dispersed phase systems. There are
others that are essentially particulate in nature
such as crystallization, fluidization, communition,
microbial growth, etc. The behavior of such sys-
tems is a complex combination of processes oc-
curring at the single particle level. Thus, each in-
dividual particle may participate in rate processes
(such as by its neighborhood in the continuous
phase being under non-equilibrium conditions)
and in processes such as breakage and agglomera-
tion with other particles, that continually destroy
the identity of existing particles.
The method of population balances falls some-
what naturally into the mathematical treatment
of dispersed phase systems but for a variety of
reasons, the methodology has not been adequately
exploited. A notable exception is, perhaps the area
of crystallization, mainly due to the efforts of
Randolph and Larson [1]. Chiefly among the
reasons for the unpopularity of population bal-
ances are (1) the complexity of the integro-
differential equations, which result from them, and
(2) the lack of suitable experimentation to evalu-
ate the models. It is the objective of this communi-
cation to provide an overview of progress in the
application of population balances and to point to
their lucrative credentials for further work.

T HE CENTRAL IDEA of population balances
is to formulate a number balance equation for
particles of each "type". Particles are identified
by "types" that are quantified as discrete vari-
ables or more discreetly, as continuous variables.
Any given type may be destroyed into, or formed
from, other types. In writing a number balance
for each type one is concerned with the "source"
and "sink" terms for that type.
Population balances are essential for the de-
scription of systems in which not only are par-
ticles present but where the identity of individual
particles is modified or destroyed by processes

Doraiswami Ramkrishna received his B(Chem)Eng. degree (1960)
from the Bombay University Department of Chemical Technology and
his Ph.D. (1965) from the University of Minnesota. After teaching for
two years at Minnesota, he returned to India in 1967 and taught at
the Indian Institute of Technology, Kanpur until 1974. He was a
Visiting Professor at Wisconsin (1974-75) and at Minnesota (1975-76)
and is now Professor of Chemical Engineering at Purdue University.
He is a consultant to General Mills, Inc., Minneapolis. His research
includes dispersed phase systems, stochastic modeling and applications,
bioengineering and problems of general applied math interests.
Normally quite gentle, he reacts rather violently to criticism of cricket.


such as breakage or agglomeration. The frame-
work becomes somewhat redundant in situations
where the identity is preserved permanently for
all particles.
The description of rate processes of course
proceeds through the formulation of the equations
of transport phenomena. Thus, for example, to
describe mass transfer in a single drop in a liquid-
liquid extraction process, the required apparatus
is furnished by the methodology of transport phe-
nomena. However, this is true only insofar as the
identity of the drop is preserved without disap-
pearing into another type. Clearly, therefore in
dispersed phase systems the population balance
framework is essential. More detailed considera-
tions have been presented elsewhere [2, 3].

T HE PARTICLE "TYPE" is described by one
or more state variables* generally regarded as
continuous. If a single variable is used then we
refer to it as a scalar state variable as against a
vector state variable for types described by more
than one variable. The number of particles in the
system is assumed to be sufficiently large that a
continuous variable may be used to denote the
total number of particles in the system. The choice
of the state variables depends much on the system
of interest. Generally, one must select all particle
properties which determine completely the be-
havior of single particles.
Let the particle state be denoted by a vector
x -- (x1,x2,...,Xs), which is a set of s physical quan-
tities, whose numerical values will identify a given
particle (Particles of identical states are assumed
to be indistinguishable). The fundamental quan-
tity describing the population is the number
density function, n (x,t), which is regarded as a
smooth function of x and t. It is the number of
particles per unit volume of the state space. The
total number of particles, N(t) in the system is
given by
N(t) = n(x,t)dV
where dV is an infinitesimal volume in the state
space of dimension, s. Limits on the volume in-
tegral have been excluded by design to indicate
that the integration extends to the entire state

*Examples of state variables are particle size, age,
temperature, concentration of some dissolved solute etc.;
physical space variables may also be included.

The state of any given particle may change
due to one reason or another. We are here refer-
ring to continuous changes in particle state in
which the identity of the particle is preserved.
Thus a change in particle size by "growth" such
as in a growing crystal or a microorganism comes
under the present context, whereas a size change
due to, say particle breakage does not. Such
changes in state can be frequently modeled on a
physical basis, e.g. conservation principles. We
denote the rate of change of a particle of state x

There are other processes that
are essentially particulate in nature
such as crystallization, fluidization, communication
microbial growth, etc. The behavior of such systems
is a complex combination of processes
occurring at the single particle level.

by a vector function X, which may depend on x
and variables associated with the continuous
For the purpose of deriving the population
balance equation in the number density function,
it is useful to regard the particles as embedded in
a continuum which deforms in accordance with
the kinematic field represented by the vector X (x).
(For the present we exclude variables connected
with the continuous phase). By embedding the
particles on this deforming continuum we imply
that a particle at a point x moves with the local
velocity X(x). Alternatively, no relative velocity
can exist between the continuum and the particle.
This viewpoint makes the derivation of equations
particularly convenient. Besides in dealing with
situations where particle state changes randomly
about a mean rate, we may look upon the particles
as diffusing in the continuum deforming with the
mean velocity field.
Let h (x,t)dV be the rate of increase in the
number of particles in a volume dV about x in the
state space. Similarly we may define a sink func-
tion h-(x,t) so that the net generation rate h(x,t)
is given by
h(x,t) = h+(x,t) -h-(x,t) (1)
The population balance equation can now be
readily written by invoking the continuity op-
erator in the particle state space.


--n(x,t) + V. in(x,t) = h(x,t) (2)

Equation (2) has been derived by Hulburt and
Katz [4]. It must be coupled with mass balance
equations for continuous phase variables (see for
example [5]).
At this point, it must be pointed out that what
we have accomplished is only the mathematical
formulation of a rather obvious accounting prin-
ciple for particle numbers. Equation (2) by itself
is therefore not to be construed as a population
balance model. The modeling lies in identifying the
nature of the functions X and h (x,t) for a given
As observed earlier, X may often be modeled
by physical conservation principles and transfer
coefficients. The function h (x,t) depends on the
process by which particle-types appear and dis-
appear. For example, communition operations in-
volve particle splitting. For such processes, one
identifies a specific rate of splitting of particles
of state x' ( a transition probability function),
say r (x'), a function v (x') representing the mean
number of particles formed by splitting of a par-
ent particle of size x', and a conditional probability
distribution p (x,x') for the sizes of particles
formed from breakage. Thus for the present case
we have
h+(x,t) = v(x') F(x') p(x,x') n(x',t) dx' (3)
h-(x,t) = F(x) n(x,t) (4)
When Equations (1), (3) and (4) are sub-
stituted into (2), the population balance model is
completely identified. Of course boundary and
initial conditions must also be appended. The im-
portant point to note is that the functions, F(x'),
v(x), p(x,x') are actually unknown and must be
obtained by more detailed modelling of the split-
ting process, or must be inferred from suitable
Similar problems arise also in the modelling of
agglomerating populations. Thus, consider a pop-
ulation of particles distributed according to their
volumes, in which any two particles of volumes v
and v' agglomerate in the time interval t to t+dt
with probability q (v,v') dt. Then it is readily
shown that
h(v,t) =- q (v-v',v') n (v',t) n (v-v',t) dv'

Again, the transition probability of agglomera-
tion, q(v,v') requires identification by more de-
tailed modelling and experimentation.
As pointed out earlier, the significant diffi-
culties in the application of population balances
are in the solution of the integro-differential equa-
tions, and in the identification of the probability
functions which describe particle behavior. Some
past work is reviewed here in regard to either of
these aspects.

SINCE, FREQUENTLY the leading moments
of the number density function is a satisfac-
tory description of the population, it has been
suggested [4, 6, 7] that moment equations be di-
rectly obtained from the balance equation. Fre-
quently, this leads to trouble either in the form
of unclosed moment equations, equations with
fractional moments, or those that simply do not
directly yield moments. To overcome these diffi-
culties, a Laguerre function expansion of the
number density function, has been suggested [4].
These methods can be readily shown [8] to be a
special (and therefore restricted) application of
the method of weighted residuals. Thus,
Subramanian and Ramkrishna [9] have solved
population balance equations for a microbial pop-
ulation distributed according to their mass, in
which individual cells grew by assimilating nutri-
ent material from the environment and repro-
duced by binary division. Solutions for the popu-
lation balance equation, which was coupled to the
mass balance equation for the substrate concentra-
tion, were obtained using Laguerre functions as
trial functions and orthogonalizing the residual
with various choices of weighting functions.
The choice of the trial function is a vital aspect
of success with weighted residual techniques.
Thus, "standard" choices such as Laguerre poly-
nomials can often be significantly improved upon.
For example, one may generate "problem-specific
polynomials" [10] from the set (x") by Gram-
Schmidt orthogonalization using suitably weighted
inner products. A desirable weight function for
the inner product should essentially have a shape
and trend similar to that of the solution. The
advantage of generating such polynomials as trial
functions for solving population balance equations
- n (v,t) f q (v,v') n (v',t) dv' (5)


by the method of weighted residuals has been
demonstrated by Singh and Ramkrishna [11, 12].
Thus transient solutions have been obtained in
which specifically generated time-dependent trial
functions assure rapid convergence of the solu-
tion at all times[12].
When the particle state variable is a vector, the
resulting multivariate number density functions
are likely to be much harder to solve for. This
problem requires further investigation. An al-
ternative route to obtaining solutions, however
lies in simulation techniques [13-17]. Although
simulation techniques often involve arbitrarily
discretizing the time interval, a recent method due
to Shah et al [17], handles the artificial evolution
of the system in an elegant manner by generating
random numbers representing "intervals of
quiescence". Each interval of quiescence is a
period, in which every member of population re-
tains its identity, and has an exactly calculable
probability distribution. Thus no tests for the
adequacy of the fineness of discretization would
be necessary in such a simulation procedure.

izing random particle behavior must be identi-
fied before population balance equations can be
quantitatively applied to real systems. As an ex-
ample, consider the particle-splitting process re-

The central idea
of population balances is to
formulate a number balance for
particles of each "type." Particles are
identified by "types" that are discrete variables
or more discreetly, as continuous variables.
Any given type may be destroyed into,
or formed from, other types.

ferred to earlier, for which the model was defined
by the functions, F(x'), v(x'), p(x,x'). A direct
experimental determination of such probability
functions is a very difficult task. With suitable ad-
ditional modelling, however the problem may at
times be tractable. In a liquid-liquid dispersion,
with a low dispersed phase fraction coalescence
between droplets is likely to be negligible during
the temporal evolution of the dropsize distribution
which primarily occurs by drop breakage. By pro-
posing that the breakage probability function for

a drop of volume v is given by r (v) = kvn, it can
be shown [18] that the cumulative-volume distri-
bution of drop-volume denoted F(v,t) has an ex-
plicit similarity solution in the variable vnt, i.e.,
F (v,t) = g(e), where e = vnt. In order to test
this hypothesis, if experimental data on dropsize
distributions are available at various times in a
batch vessel, then a plot of lnv versus /nt for any
fixed value of F should produce a straight of
slope - n. Besides, parallel straightlines should
be obtained if the plots are made for different
fixed values of F. From the experimental data of
Madden and McCoy [19], such tests have in fact
shown [18] that a power law breakage model may
be a good representation of F(v). The similarity
plot using the calculated value of n, can then be
used to determine the size distribution of the drop-
lets formed from the broken drop [18]. The data
of Madden and McCoy yield approximately a value
of 2 for the power n. Based on modelling drop
breakage as a result of relative velocity fluctua-
tions across the droplet surface, arising from the
continuous phase turbulence, the application of
Kolmogorov's theory of local isotropy appears to
vindicate the power law expression with n having
a value of about 2.67 [20].
As another example, one may consider denser
liquid-liquid dispersions with high dispersed
phase fraction. Since breakage and coalescence are
both important in this situation the breakage and
coalescence probabilities must be known. Follow-
ing an earlier visualization by Curl [21] of the
coalescence-redispersion process as a single-step
process, Bajpai et al [22] proposed that droplets in
a dispersion coalesce and immediately redisperse
into two new droplets in a perfectly random man-
ner. They solved the population balance analyt-
ically to obtain an exponential drop-volume dis-
tribution at equilibrium, which showed good agree-
ment with experimental data from diverse sources.
The implication of the two preceding para-
graphs is that there seems to be sufficient evidence
pointing to the tractability of population balance
models from an experimental viewpoint.
P OPULATION balance equations are essentially
sentially for describing the behavior of large
particle populations in which random behavior of
individual particles is averaged out. The number
density function n (x,t) is the expected population
density. Although most systems of interest in
Continued on page 43.


I classroom



University of Delaware
Newark, Delaware 19711

In this paper we describe an educational tool
which effectively illustrates how basic chemical
engineering skills in reactor design and process
analysis are combined with economic consideration
to design a processing plant whose performance
is tested by its ability to compete profitably in
the market place.
Since it is not possible to actually build and
test proposed designs, we have developed a busi-
ness game to provide evaluation of the process
designs in a more realistic fashion than by the
usual procedure of grading a design report. The
game also deals with the important aspects of
competition and uncertainty in projected market,
factors which are almost impossible to incorpo-
rate into most design teaching.
The game described in this paper requires
the very simplest reactor, process and economic
analysis. It was deliberately designed this way
after some early experimentation so that the
student would clearly see the interaction between
the basic engineering skills, economic considera-
tions and the need to have a profitable operation.
Class and student time required to complete
the game varies with the sophistication of the
students from 15 to 25 hours. More complicated
forms of the game are under development which
will take longer and require much more analysis.

ALL PARTICIPANTS are given a copy of
Figure 1 which shows expected sales of
product "D" and expected selling price at various
sales levels. In addition the following information
is given in memo form.

(i) Chemical Equation A --> D
(ii) Constitutive Relation for Reaction Rate
rA = kCA
k = 0.005 min-1
The simplest possible chemistry is chosen so
that process design can be developed with a mini-
mum of mathematical manipulation.
(iii) The design equations for a continuous flow
stirred-tank reactor
a) Component mass balance for A (1)
0 = q [CA - CA] - kCAV
b) Component mass balance for D (2)
0 = -qCD - kCAV

V = volume of fluid in the CFSTR, liters
q - volumetric flow rate of fluid, into and from
the CFSTR, liters/min
k = specific reaction rate constant = 0.005 min-'
CAP - concentration of reactant A in the inlet
stream, gm-mole/liter
CA - concentration of reactant A in the CFSTR
and in the exit stream from the CFSTR,
CD, concentration of product D in the CFSTR
and in the exit stream from the CFSTR, gm-

The simple reactor is chosen so that those
new to process design thinking are not over-

0 I 2 3 4
FIGURE 1. Sales Demand and Selling Price.


T. W. F. Russell is a Professor of ChE and Associate Dean of the
College of Engineering at the University of Delaware. He obtained his
bachelors and masters degree from the University of Alberta and after
working as a design engineer with Union Carbide, Canada for three
years, he obtained his Ph.D. from the University of Delaware. Pro-
fessor Russell is a coauthor of "Introduction to Chemical Engineer-
ing Analysis" (J. Wiley 1972) and Structure of the Chemical Process
Industries-Function and Economics" (McGraw Hill, in press).
Dave Frankel will receive his Ph.D. from the University of Dela-
ware in May 1978. He will be working for Exxon Production in
Houston, Texas.

whelmed by mathematical computation. It is a
simple matter to modify the memo to let more
experienced students develop their own design
(iv) The concentration of raw materials A,
"CA 0.2 liter

(v) A simplified process flow diagram as shown in
Figure 2
(vi) Cost of reactant A, $0.20/g-mole
(vii) Depreciated capital cost, maintenance costs and
operating costs of the process unit are assumed
proportional to the reactor volume V, and ap-
proximated as Sv = $45/liter-year
This is another simplification introduced to
keep the algebra simple. The economics can be
made more realistic by basing the separation
column capital cost on unit throughput, q, and re-
lating all operating costs to the unit throughput,
q. This complicates the algebra but, because of the
nature of the process, makes very little numerical
difference from the simple expression given above.
(viii) Inventory charges will be $ .10 per gm mole
per year.
(ix) Operations which develop a debt of $2,000,000
will be assumed bankrupt and not permitted to
With the above information a process unit can
be designed and then operated to produce product
D for a simulated market with four companies.
Each of the four companies must decide upon the
reactor size that they will have in their process
unit and how to operate it each year to produce a
maximum profit. The game begins when each
company has made its decisions and submitted to
control the reactor size and the process unit out-
put for year one. A typical set of such inputs is
shown in Table I.
Once the size of the reactor has been specified
the company cannot change it by adding addi-

tional capacity during the simulated five year
operation of the game. Each company is of course
free to manipulate feed rate, and hence conver-
sion, to the reactor for each of the five periods.
Input data from each group is processed by
control using the program shown on the Logic
Flow charts presented in Appendix A. The pro-
gram operates in the following manner.
* Input is checked for accuracy and internal consistency;
i.e., a company could not call for a rate of production
which would necessitate a larger volume of CFSTR
than they had designed and built.
* The true total market demand is generated randomly
within limits about the projection supplied to the
players in Figure 1. Selling prices are computed con-
* Sales are allocated to the companies by a simple
algorithm based on previous market share and the
projected sales which the company specifies on its input
* Profits, cumulative profits and inventories are computed.
The output is presented to each company in
the following format:

Total Market
Selling Price
Company Sales
Market Share
Profit for the Period
Cumulative Profit.

The companies make their decisions for the
next period based on these results. The game is

A Typical Set


of Input Data


to Process Design

Process Unit
9.25 x 106
6.30 x 106
6.20 x 106
6.05 x 106

run for five periods and performance is evaluated
by comparing cumulative profits.


TO PROPERLY DEVELOP a game it must be
played a number of times and modified as a
result of the experience gained. To date this game
has been played about ten times with most of the
modifications carried out in the first three to five
sessions. A listing of the course using the game is
given in Appendix B.


In the first two games the companies were
allowed to set the selling price as if the product
were new on the market. Market share was
partially based on this selling price in the control
program and this gave the participants an extra
degree of freedom to manipulate for market share.
The scheme worked reasonably well for upper
level students (seniors and first year graduate
students in a technical management course) but
turned out to be too complicated for the freshman-
sophomore level student for which we were de-
signing the game. We modified our procedure to
the more realistic situation where price is deter-
mined by total market demand. The function-
ability is shown in Figure 1.
We next modified the game to add an inventory
charge. This also is a more realistic simulation of
what actually occurs in the real world. It is a

Typical Set of Results for Process Design Game.

Projected Market
Actual Market
Selling Price

(Figure 1) 25.2 x 106
(Program) 26.2 x 106

Market sion
Company Share CA/CAF
A 31.6% 0.40
B 23.1% 0.407
C 22.8% 0.191
D 22.4% 0.23%


Projected Market
Actual Market
Selling Price



(Figure 1) 27.2 x 106
(Program) 26.8 x 106
0.439 1.59
0.407 0.41
0.19 0.69
0.238 0.62


Projected Market
Actual- Market
Selling Price


(Figure 1) 37.8 x 106
(Program) 37.5 x 106
0.439 0.82
0.511 0.95
0.518 1.86


tive Profit
of $





necessary element of the game which helps to
prevent companies from "flooding" the market to
gain a large market share.
A bankruptcy limit also was imposed after
our initial experiences to make the game more
true to life and to prevent companies from un-
realistic operation in the initial periods to build
up market share. We have found that a bank-
ruptcy occurs about every second or third game.
Sometimes this is because of deliberatively ag-
gressive action and sometimes because of error.
When a bankruptcy occurs, the structure of the
game changes markedly since the total demand
must be met by three instead of four companies
and companies who have designed a small reactor
may find themselves at a considerable disad-
A typical set of results is shown in Table II
for the companies whose input data for period 1
are shown in Table I. In this particular game,
Company D went bankrupt and Company C almost
went bankrupt. The large reactors were unprofit-
able with four companies competing for the
market and only became profitable when one
company was forced out.
Some basic process analysis can be easily per-
formed for this game since the simplest possible
chemistry, and reactor type have been specified.
It is also quite easy for students familiar with
basic calculus to compute an optimum value for
the conversion, CA/CAF. One can then compute the
optimal volume for a given production rate as

Yearly Profit
= Income from - Cost of - Capital-Operating
Sales A costs
= SDqCDY - 0.20qCAFY - 45V (3)
This yearly profit can be expressed in terms
of the variable CA
= SeqCDY - 0.20qCDCAFY - 45qCD (4)
CAP - CA 0.005CA
SD = selling price of D, $/g-mole
Y = 504,000 min/year
This yearly profit can be differentiated with
respect to CA to yield a quadratic equation in the
variable, CA/CAr, which can be solved to yield

CA optimal = 0.4015 (5)

The relationship between reactor volume and
the throughput q is




FIGURE 2. Process Flow Diagram.

V = 2490 qC, (6)
The simple analysis is a necessary step in the
problem solution but it is far from sufficient to
assure that one will have a good profit or in fact
even a profitable operation. Two factors, competi-
tion and a growing market need to be considered.
There is no theoretical analysis, sophisticated or
simple, which can be carried out to deal with
these two factors.
Most groups design their reactor to supply
some share of the market (usually 30-40%) in
years three or four. In the game shown in Tables
I and II, Companies C and D felt they could cap-
ture a large share of the market so they con-
structed larger reactors than Companies A and B.
Unfortunately, they did not operate them close
enough to the optimal in the early years; they did
not achieve large shares of the market and
Company ID went bankrupt. Had Companies C
and D been more aggressive and operated with a
higher throughput in years 1 and 2, they might
well have forced Company B with the small re-
actor into bankruptcy. In this particular game,
Company C had the best position with only three
companies supplying the market. Unfortunately,
they did not do the simple optimal analysis and
as a result, operated with values of CA/CAF which
were too low.
It is necessary for the students to draw upon
learning experiences from several disciplines in
order to make design decisions. We feel that the
engineering game exercise was much more re-
warding for introductory students than a dry
optimization problem using only principles of the
calculus. The game impressed upon the players
that engineering is more than finding equations
and plugging in numbers: it is more of an art in
which the engineer, and not a textbook, must
make decisions. Hopefully, this experience will
enable the students to keep their coursework in
its proper prospective, and discourage the point

of view that macroscopic balances and differential
equations are all that is necessary to pinpoint an
answer to any engineering problem.
The game captivated student interest in engi-
neering, since the groups were always eager to
receive and evaluate their output, and make de-
cisions for the next selling period. The added
feature of near instantaneous feedback makes the
game approach valuable from an educational psy-
chology standpoint.
The game also has worked surprisingly well
with engineers and chemists with some consider-
able industrial experience. Some of our most en-
thusiastic players have come from this group of
mature persons. We feel that this is partly at-
tributable to the insights that are obtained with
regard to the process analysis and partly attribut-
able to the simple insights that are obtained into
the economics of the chemical process industries.

Since it is not possible to actually build and test
proposed designs, we have developed a busi-
ness game to provide evaluation of the
process designs in a more realistic
fashion than by the usual pro-
cedure of grading a design report.

We would like to thank all those who have
helped us develop this educational tool by play-
ing the game in its initial stages and providing
us with feedback. Dr. R. L. McCullough of the
Chemical Engineering Department of the Uni-
versity of Delaware and Mr. P. H. Bailey of the
Engineering Department of the E. I. du Pont
Company were kind enough to spend time on dis-
cussion and comment. We appreciate their efforts
very much. The Dean's Office in the College of
Engineering provided both funds and encourage-
ment and we are grateful for this support. Mr. R.
Pratt, Engineering Computation Specialist in the
College of Engineering has been most helpful in
setting up the necessary computer programs. One
of us (TWFR) developed the initial idea while
on sabbatical leave at the Swiss Federal Institute
of Technology (ETH) in Zurich and I am ap-
preciative of discussions with colleagues at that




I = Company Index
N = Number of Companies
T = Selling Period Index
CAF = Feed Concentration of "A" = 0.20 gm-mole-liter-1
CUPROFI,T = Cumulative Profit, $
INVI,T = Inventory, gm-mol
k = Specific Reaction Rate Constant, min-1
P = Selling Price, $ - (gm-mole)-1
PROFIT = Profit, $
PTS, = Projected Total Sales, gm-mole
PUO1 = Process Unit Output, gm-mole-min-1
q, = Volumetric Flow Rate, liter-min-1
QT = True Total Demand, gm-mole-min-1
SI,T = Normalized Market Share
SI,T = Non-Normalized Market Share
Sy = Volume Cost Parameter = 45 $ -(liter-year)-1
VI = Reactor Volume, liter
x = [1-Conversion of A] = CA/CAF
R = Random Number O QI = Sales Volume, gm-mole
NOTE: 350-day operating period -> 5.04 x 108 min



1=1N I
Profits are computed

PROFIT = P1-SvV-qCAF[0.20$-(gm-mole A) ] [5.04X1min]

Cumulative profits are computed




1) ChE 690
Technical Project

2) EG 125
Introduction to
3) ChE 530
Engineering Analysis
for Non-Majors

4) ChE 667
Special Topics
5) Engineering Analysis
for Chemists

6) Introduction to

7) Engineering Analysis
for Chemists

Fall 1973; Fall 1974
Seniors and graduate
students in chemical
Fall 1973
Freshmen students in
chemical engineering
Spring 1974
Junior and senior
students in chemistry
life science, mathematics
and electrical engineering
Winter 1974 Session
A group of senior students
in chemical engineering
Summer 1974
A course for industrial
chemists-a group from
the Swiss chemical and
pharmaceutical industry
Spring 1975
A course to introduce
high school juniors to
Spring 1975
A course for industrial
chemists-a group from
the Organic Chemicals
Department of the E. I.
DuPont Company

book reviews

5th Symposium of Biotechnology and
Plenum, New York. (f25.00)
Reviewed by Charles Walter, University of

The 5th Symposium of Biotechnology and
Bioengineering was about "Cellulose as a Chemi-
cal and Energy Resource." The organization of
the topics includes contributions about "The Sub-
strate," "The Enzyme System," "The Process,"
and "The Product."
"The Substrate" is cellulose. In this section
there is a weak chapter about cellulose economics
which reflects confusion about scientific matters
and relies heavily on meaningless figures (for
example, the figures about cellulose conversion

into protein or ethanol, or alcohol conversion into
adenesine triphosphate).
The remainder of the section about "The Sub-
strate" is highly recommended. An excellent intro-
ductory statement establishes that the greatest
portion of what we call waste cellulose is not
really "waste" at all, and that processes utilizing
the substrate must be economically viable. This
theme is continued in a later chapter dealing
principally with agricultural "wastes." Other
chapters in this section contain excellent discus-
sions of the relationship between energy input and
energy yield for cropping systems and a specific
cost analysis for producing plant biomass on a
hypothetical plantation. This analysis leads to an
optimistic estimate of about $10/ton of dry bio-
mass, or $ .65/106 Btu. The important chapter by
Diaz puts into prospective however, that even if
cellulose were obtained from "waste" sources that
were "free," the substrates used as chemical or
energy resources would be considerably more ex-
pensive due to the high processing costs involved.
Bassham's chapter provides an excellent sketch
of the overall energetic of cellulose production
in green plants, including a discussion of the
merits of C-4 plants versus plants without this
extra CO2 - fixing pathway, and an estimate of
the photosynthetic efficiency expected for this
process. The number Bassham arrives at is 5%
which is about half the often-quoted maximum
theoretical efficiency for photosynthetic processes.
"The Enzyme System" is cellulase but the
worthwhile contribution to this section of the
volume is about the action of H,02/Fe(II) on
cellulose-a process which obviously could lead
to significantly lower costs for commercial cellu-
lose digestion. This, together with the fact that
many cellulolytic organisms apparently secrete
little or no cellulase, is a compelling argument for
more research on the HsO2/Fe(II) system and
brown-rot fungi and less emphasis on isolated
and reconstituted enzyme systems. The deep-
seated prejudice that compels many biochemists
to isolate biomolecules from their three-dimen-
sional, functional environment and study their
properties in an irrelevant setting dominates most
of the other papers in this section. Judging from
comments made in other sections of the volume
(for example, "Too much of our existing
knowledge about cellulose hydrolysis has been
derived from studies with purified raw materials"
by E. L. Gaden on page 161) many of the sym-
Continued on page 47.


ff �00




Chemistry of Catalytic
Bruce C. Gates, G.C.A. Schvit, both of the
University of Delaware, and James R. Katzer,
Stanford University
The interrelationship of catalytic chemistry and en-
gineering requirements is fully illustrated in this
applications-oriented guide. The authors provide a
much-needed overview of real world practices
while covering the complexity of industrial
catalysts. Each of the five chapters deals with an
industrial process or class of processes. Quantita-
tive examples are featured to illustrate design
methods, and problems are included with each
chapter, making the book an excellent graduate
level text for courses in catalytic kinetics and reac-
tion engineering.
1978, 512 pages (tent.), $28.50 (tent.)
The Structure of the Chemical
Processing Industries:
Function and Economics
J. Wei, Massachusetts Institute of Technology,
T.W.F. Russel, University of Delaware, and M.W.
Swartzlander, Union Carbide Corporation
This vital new text broadens the scope of chemical
engineering students and practitioners by examin-
ing the organization and use of resources in chem-
ical manufacturing; the economic and socio-
political forces that affect the chemical process in-
dustry (CPI), and the need of the industry to adapt
to these influences in order to survive. In exploring
the complex role of the CPI in society, the book
uses a variety of analytical tools, including
microeconomics, production functions, game
theory, financial analysis, basic accounting prac-
tice, theory of the firm, and input and output analysis.
1978, 640 pages (tent.), $21.50 (tent.)
Solutions Manual and Instructor's Manual available
Biochemistry Engineering
James E. Bailey, University of Houston, and David
F. Ollis, Princeton University
This volume deals broadly with engineering fun-
damentals and applications of biochemical pro-
cesses. In addition, the necessary biochemistry and
microbiological principles are included, with spe-
cial attention devoted to such topics as enzyme
kinetics, bioenergetics, metabolic pathways, and
molecular genetics. The volume stresses special
engineering considerations, the mathematics
needed by the biochemical engineer, environmen-
tal engineering, and the involvement of biochemi-
cal engineering practices in modern industry.
1977, 576 pages, $25.50

Chemistry For Environmental
Engineering, Third Edition
ClairIm. Sawyer, formerly of the Massachusetts
Institute of Technology, and Perry L. McCarty,
Stanford University
Here is a text that focuses on those aspects of
chemistry particularly valuable to the practice of
environmental engineering. It also builds a solid
foundation for understanding the area of
specialized quantitative analysis-the basics for all
common phases of environmental engineering.
Requiring only a one-year college chemistry
course, this book is suitable for advanced under-
graduate and graduate level students of engineer-
ing and applied science. The presentation of the
most current analytical procedures and latest con-
cepts also makes it a valuable source of informa-
tion for the professional engineer. Practice-oriented
problems and worked examples help increase the
reader's understanding of basic principles.
1978, 544 pages (tent.), $19.50 (tent.)
Solutions Manual available

Introduction to Polymer
Stanley Middleman, University of Massachusetts
Up-to-date and complete, this text offers a basic in-
troduction to the methods of analysis of the major
polymer flow and fabrication processes. The mate-
rial is arranged to offer easier understanding by first
developing the fundamental equations of heat and
mass transfer, fluid dynamics, and rheology; then
applying these equations to the development of
models in a wide variety of polymer processes.
End-of-chapter problems were selected to provide
the experience of building, comparing, and evaluat-
ing models of varying complexity.
1977, 544 pages, $25.00 Solutions Manual available

Introduction to Chemical
Edward V. Thompson and William H. Ceckler,
both of the University of Maine, Orono
This text introduces the student to the chemical
process industry and its overall breadth while also
developing strength in the analysis of material and
energy balancing. The material is arranged around
a series of analytical topics selected from important
sectors of the chemical industry. Each topic is dis-
cussed by offering an introductory descriptive
chapter followed by the necessary techniques and
skills. Chemical principles, material balances, and
energy balances are treated and developed simul-
taneously, with an early introduction to heat and
1977,576 pages, $19.50

Chemical and Catalytic
Reaction Engineering
James John Carberry, University oTNotre Dame
Dr. Carberry's presentation embraces a diversity of
heterogeneous reaction engineering phenomena.
The text includes a discussion of homogeneous
chemical reaction kinetics, followed by generaliza-
tions pertaining to ideal reactor types and their
limiting environments. Following a treatment of
real reactor equations and their parameters,
heterogeneous reaction-reactor networks are
1976, 704 pages, $22.50

Unit Operations of Chemical
Engineering, Third Edition
Warren L. McCabe,Emeritus, North Carolina State
University, and Julian C. Smith, Cornell University
Continuing in the tradition of the earlier, interna-
tionally acclaimed editions of this text, the third edi-
tion is a carefully integrated and balanced discus-
sion of theory and practice. The revision now offers
a thorough discussion of the three unit systems:
FPS, CGS, and SI units; introduces fugacity and ac-
tivity coefficients in the study of phase equilibria;
and contains a completely new chapter on multi-
component distillation. Other significant changes
in the text include the extension of the Kwauk
method for counting the number of independent
variables in complicated separated operations; a
thorough revision of the crystallization chapter to
include recent work on contact nucleation; and ad-
ditional material on mixing.
1976,980 pages, $24.00

Mass Transfer
Thomas K. Sherwood, Robert L. Pigford, and
Charles R. Wilke, all of the University of California
at Berkeley
Providing broad coverage of mass transfer, this text
emphasizes the practical aspects and real prob-
lems that demand an understanding of theory. Yet,
theoretical derivations are minimized by explicit ci-
tation of over 1,100 contemporary references.
1975, 704 pages, $22.50
prices subject to change

1221 Avenue of the Americas if
New York, N.Y. 10020 * I HI


The University of Texas at Austin
Austin, Texas 78712

the Chemical Engineering Department at The
University of Texas is now in its twelfth year.
It is possible to cite many individual cases of
undergraduate students who have been helped
through difficult periods in various courses with
the aid of this service, and who have gone on to
achieve an enviable record in their college work.
Our tutorial activity supplies individual tutoring
in the afternoons as well as a telephone tutoring
service both in the afternoons and in the evenings.
I will first describe some of the reasons why
the program was established and then explain the
details of the program itself. For those interested
in initiating a similar program I have included
an explanation of how the tutors are chosen, how
the work is handled by the tutors, and a descrip-
tion of the facilities and equipment. Some ad-
vantages and difficulties with the program will
be discussed as well as the costs.

IN ChE A STUDENT must understand a sub-
stantial number of basic concepts in the cur-
riculum if he or she expects to progress satis-
factorily. Any concept not fully understood at the
time he or she first encounters it may continue to
cause the student trouble as subsequent material
is encountered. One way a student can get almost
instant help is via an ongoing tutoring program.
Freshmen and sophomores particularly feel
isolated from professors and other students at
large universities, and they experience difficulty
in obtaining help quickly when they flounder on a
problem. Such a student is then likely not to learn
what he or she should when he should. The
Chemical Engineering tutoring program was es-
tablished at The University of Texas to give

students who had to work alone, or found it con-
venient to work alone, or found it inconvenient to
work with others, a chance to interact with an-
other more advanced student on a problem of
personal interest.
There were some additional reasons for es-
tablishing the tutorial program that are not so
obvious. First, it is convincing evidence to our
undergraduate students that we are sincerely
interested in their difficulties. A student who has
a difficulty in a course might first go to see the
professor in charge of the course. On the other
hand, the student may be slightly embarrassed to
bother the professor but would not hesitate to see
a tutor. Second, we have to admit with all due
candor, that professors are busy individuals and

Professor Himmelblau received his B.S. degree from M.I.T. in
1947 and thereafter worked for the International Harvester Company
of Chicago, the Simpson Logging Company in Washington, and the
Excel Battery Company in Washington. He returned to school and
received his Ph.D. from the University of Washington in 1957. Ever
since then, he has been teaching at the University of Texas where
he is now a Professor and Chairman of the Department of Chemical
Engineering. He is a member of a large number of professional and
honorary societies, has been a consultant for several companies, and
has been quite active in the AIChE. He was a Director of the AIChE
from 1973-76. He was on the Executive Committee of the Chemical
Engineering Division of the ASEE from 1970-71, and on the Editorial
Board of "Industrial and Engineering Chemistry Process Design" from


that students sometimes do not have the incentive,
perseverance, or time to locate a professor at the
time the question arises. Therefore, the fact that
he knows a tutor is available four days a week
and is available by telephone as well, makes the
tutorial program a definite convenience.
It is interesting to note that some of the better
students also take advantage of consulting a tutor
in order to resolve questions and probe more
deeply into the subject material.


LET ME NEXT EXPLAIN how the tutoring
program is carried out. Every Monday,
Wednesday, and Thursday afternoon from 3:00
to 5:00 p.m., and for variety, Tuesdays from

monthly or semester assignment sheets from those
professors who hand out such sheets so that the
tutors can prepare themselves for questions when-
ever they are momentarily unoccupied.
Some tutors prefer to help in certain courses,
but all are sufficiently competent to tutor in any
course. For increased efficiency often each tutor
will answer all questions concerning one or two
classes on a given day. However, the tutors con-
tinually change the classes they tutor to gain
additional experience. Sometimes it takes all three
tutors to answer a particularly difficult question.
If a student demonstrates that he or she has
not seriously attempted to start the homework
assignment or read the required material, the
student is asked to return after doing so. This is
done to prevent the tutoring program from be-

A professor who wishes can use the tutoring program as a current
and informal tool of teaching evaluation by finding the types and degree of
difficulties students have with his classes. Also, an instructor if he goofs on an assignment,
can leave a message concerning last minute changes in the homework assignments
for the tutors to place on the tape.

12:00-2:00 p.m., three tutors are available to help
undergraduate chemical engineering students.
Due to scheduling problems and lack of demand
by students, the Friday session we used to have
has been terminated. During these afternoon
tutoring sessions, an average of twelve students
are helped by calls or visits. The length of each
student's visit varies from about a minute for
a brief question to over an hour if he or she is
thoroughly confused and does not even understand
how to start the homework assignment. Most
students find personal visits more effective than
telephone inquiries for complicated problems so
that our experience during the day is that only
about ten percent of the tutoring contacts are via
the telephone.
Tutoring takes place in a four hundred square
foot seminar room. A large table is placed in the
center around which are seats for up to fifteen
students. An additional table at one side of the
room holds the telephone and Code-a-phone. A
large blackboard on one wall is used for explana-
tions when four or more students from a particu-
lar class have the same questions. The tutors have
access to a copy of the textbooks currently being
used in all the required courses in the ChE
curriculum. Every attempt is made to obtain

coming a problem work session, with the tutors
assisting in working the homework assignments.
We have recitation sections in many classes for
such activities.
Any tutor who is free at the moment or closest
to the telephone answers it. To provide help over
the telephone is often difficult because the tutor
often does not have the particular problem or text
available at hand to read as does the student.
Consequently, the tutor has difficulty in under-
standing what the student is asking. Even when
the tutor understands the problem, he finds it more
difficult to explain equations over the phone than it
is to write them ,down and show them to the
student directly. As a result, most students with
long, involved questions visit the tutors in person,
and the phone is used for brief questions.

U SUALLY FIVE individuals work in the
tutorial program, but not all on the same day.
One graduate student is placed in charge of the
entire operation. He finds suitable tutors, co-
ordinates tutoring activities, and sees that daily
tapes are made. Explanations and hints to prob-
lems prepared one day by one group of tutors do
not have to be redetermined on a succeeding day


because the head tutor is present every day. The
remaining tutors each work only one or two days
a week.
A good tutor needs to be patient, speak English
well, be technically competent, and be relatively
familiar with the assignments of the undergradu-
ate courses. To meet the latter requirement it is
best (but not essential) that the tutor have gone
to undergraduate school where he tutors so that
he has been in the classes of most of the pro-
fessors. An academically qualified senior student
best meets the requirements but may not have the
maturity of a graduate student. Because many of
the questions of ChE students relate to homework
problems, we found it helpful to employ as tutors
individuals who were graders in the sophomore
and junior classes. These are the primary classes
that cause students to come for help. The head
tutor can also easily work with the class grader
to give appropriate information to the students.
Although the tutors are available to answer
questions concerning any of the undergraduate
ChE courses, the bulk of the questions come from
4 or 5 sophomore and junior courses, particularly
material and energy balances, transport pheno-
mena, and unit operations. Hence, after one semes-
ter the tutors become fairly familiar with those
classes that cause students the most problems,
which increases the effectiveness of the tutoring.

IN ADDITION TO tutors answering telephone
calls in the day, we have an automatic telephone

Our tutorial activity supplies
individual tutoring in the afternoon
as well as a telephone tutoring service both
in the afternoon and in the evening.

response in the evening. A Model 200-A "Code-a-
phone" by Ford Industries, Inc. is connected to
the tutorial telephone line. This machine can re-
cord up to six minutes of taped messages. It
permits a student to listen to the recorded message
but does not enable him to leave a message on the
What bothers one student about an assign-
ment usually bothers others. Consequently,
students ask identical or related questions about
ChE homework assignments due in the next day

or two. Because several students are likely to en-
counter the same difficulties, but for various
reasons might not contact the tutors during the
day session, a recorded message is prepared by
the tutors at the end of each tutoring period. An
extract of a typical message about one and one-
half minutes in length is in the Appendix. This
tape contains suggested approaches to homework
assignments and discussions of difficulties that
had caused the most questions during the tutoring
proceedings of the day. Also included on the tapes
are changes, corrections, or additions to home-
work assignments called in by the ChE instruc-
tors, and announcements by ChE organizations.
An average of one hundred fifty calls are re-
ceived by the tape machine per night. (We get
this information from a digital counter attached
to the machine.)

O NE OF THE PROBLEMS a student faces in
getting a message from the Code-a-phone is
he must go through all of the message up to the
point of interest. We examined different ways of
having the student dial directly to his class
number, but have not yet found any inexpensive
equipment that would be suitable. In principle the
introduction of such equipment would save a
student the boring wait until his pertinent mes-
sage came up on the tape.
At one time we though we might make a tape
available on which a student could leave a
message to which a tutor could reply at some
hour in the evening, but the demand for such a
service was low. No one wished to stay home
waiting for the reply. Several years ago we not
only had the telephone service but also broadcast
the tape over the student radio at 10:30' p.m.
each day. Eventually the broadcast was stopped.

M ANPOWER COSTS comprise the bulk of the
operating costs of the tutoring program. One
teaching assistant supervises the program and
assists in the tutoring at a cost of $2,200 per
semester or about $500 per month. In addition,
about 4 seniors or graduate students are employed
each for about 5 hours per week at a rate of $4 to
$5 per hour, or another roughly $2,000 per
semester. The telephone rental is only $16 per
month or about $200 per year, and the cost of
the recorder has been written off long ago. In
terms of the student visits, the cost is about $3.50


per visit. However, in terms of visits plus tele-
phone calls, the cost is less than $1 per contact.
Our tutoring program has the usual
benefits you might deem pertinent. It helps a
student understand the class assignments as he
goes along so that future material will be less
difficult. This prevents a slow learner from
getting too far behind his or her classmates. Some
students at large universities are afraid to or are
actively discouraged from asking their professors
outside class about those small troubling ques-
tions that bother them. The tutoring program
allows these students the satisfaction of getting
their questions answered. The tutors also answer
questions concerning the teaching style of a pro-
fessor and what he stresses on exams. A professor
who wishes can use the tutoring program as a
current and informal tool of teaching evaluation
by finding the types and degree of difficulties
students have with his classes. Also, an instruc-
tor if he goofs on an assignment, can leave a
message concerning last minute changes in the
homework assignments for the tutors to place on
the tape.
In addition to the primary benefits, some
additional advantages exist because of the tutor-
ing program. Undergraduates gain contact with
upperclassmen, contact that they would not other-
wise have. From this interaction they obtain in-
formal advice concerning course scheduling,
future job interviews, and graduate school. The
tutoring program gives students an additional
opportunity to meet each other outside of their
classes. By getting to know other students they
begin to help each other directly. We find seniors
rarely use the tutoring service largely because by
the time they become seniors they know many
students in their classes and are therefore able
to study with each other.

F THE STUDENTS who use the tutoring
service are required to be prepared the best
they can by themselves before they ask for help,
the tutoring program does not make addicts of
students. Such difficulties as exist tend to be oper-
Some students cannot find a spot in their
schedules for a visit to the tutors because of time
conflicts with other courses or outside work. Often
the tutors are flooded with visits and frequently
interrupted by telephone calls. On such days the
tutors may not be as effective as they should be.

In addition to tutors answering
telephone calls in the day, we have
an automatic telephone response in the evening.

They often give quick answers rather than help
the student get to the answer by indirect question-
ing. On other days, the tutors are not called on to
help as many students as they could efficiently
handle. Sometimes the tutors run into a question
or problem that they cannot immediately answer
because they do not have the proper background.
In such cases the student is asked to return the
next day in order to give the tutor time to check
into the matter. A student is encouraged to see
his professor in such circumstances.
But on the whole the program has been favor-
ably accepted and widely used by an ever chang-
ing student population, and strongly supported by
the faculty. O
Example of Recorded Message Heard by Students
During Non Tutoring Hours
Tonight the Chemical Engineering Tutoring Service
will discuss ChE 317 problems 4.69 and 5.9, and Dr.
Smith's section of ChE 322 problem number two. First, I
would like to announce that there will be an AIChE
meeting this Friday the thirteenth in the Geology Build-
ing, room number 100 at 4:00 p.m. The program will
consist of a panel discussion with the Chemical Engi-
neering Department Visiting Committee.
ChE 317 Problem 4.69: This is a review problem. Don't
forget that you are supposed to work part b only. This
problem is worked in a similar manner as example 4.33.
Use equation 4.51 on page 301. Note that equation 4.51
is actually a special case of the general energy balance
you used throughout chapter four when working heat of
reaction problems.
ChE 317 Problem 5.9: For this problem use the enthalpy
concentration chart for the sulfuric acid water system
on page 463. Use the chart as shown in example 5.09 for
the sodium hydroxide water system. This problem is of
the mass and energy balance type you have had many
times before and is used merely to illustrate use of en-
thalpy concentration charts.
ChE 322: This is a multistage adiabatic compressor
problem. There is intercooling between each stage and a
5 psi pressure drop in each intercooler. Equation 78 on
page 674 should be used since the gas temperature enter-
ing each stage is the same and each stage may be
assumed to have the same compression ratio. For a given
number of stages, calculate the total work required. Then
guess a different number of stages and again calculate the
total work required. A plot of total work required as a
function of compressor stages is used to determine the
desired number of stages and hence the operating costs
of the system.


i $ laboratory


A Hydrodynamic Analog

For Drug Dosage Regimens

Cornell University
Ithaca, NY 14853

drug orally at prescribed time intervals is the
basis for the mathematical analysis and experi-
mental demonstration described here. A two-
compartment stirred-tank model is used as a
lumped-parameter model for the human body.
This mathematical model was presented in a
junior-level course at Cornell titled "Engineering
Analysis of Physiological Systems" and the demon-
stration was used with student participation
during open houses. The preparation of a video-
tape recording of the mathematical analysis and
the experiment is currently being planned for a
sophomore-level mathematics course.

compartment hydrodynamic model is
shown in Figure 1. The first tank with uniform
concentration C, stands for the gastrointestinal
tract from which the drug is absorbed into the
rest of the body (blood, muscles, tissues, etc)
represented by the second tank. Oral ingestion of
the drug is represented by pouring specified
amounts of the drug analog into the first tank at
prescribed time intervals. The rate of absorption
from the gastrointestinal tract is linearly related
through the proportionality constant k, to the
time-dependent drug concentration in the tract
C1 (t). The hydrodynamic analog of absorption is
the volumetric flow rate q between the first and
second tanks. The drug is eliminated from the rest

of the body through the kidneys at a rate k2C2 (t)
where C2 (t), the concentration in the second tank,
stands for the drug concentration circulating in
the body. Elimination is represented by the exit
stream from the second tank.
In order for the drug to be safe and effective,
the concentration level in the body C, must be
maintained above the minimum effective concen-
tration C2min but below the toxic concentration,
Czmax. By specifying the initial and subsequent
maintenance doses, mi and mm, and the time in-
tervals following the initial and maintenance
doses, Ti and Tm, a concentration plateau can be
achieved in which the concentration CQ (t) never
drops below the minimum effective concentration
C2min after the initial time interval and never
exceeds the toxic concentration C2max. Although
this model is a relatively simple representation of

q- k, meter
r^^ [~- ''-�� i-- , f _ _ _

FIGURE 1. Schematic drawing of the two compartment
model and a reluctant "dosee."


, w 'W Awr
Scott C. Jackson received his BSChE from Cornell University (1977)
and is currently a graduate student in the Chemical Engineering De-
partment at the University of Delaware. Scott is an avid photographer,
bicyclist and humorist with a fine sense of the absurd. (L)
James F. Stevenson received his BSChE from Rensselaer Poly-
technic Institute and his MS and PhD degrees from the University
of Wisconsin. He is currently an associate professor in the School
of Chemical Engineering at Cornell University. His research interests
include polymer rheology and processing and mass transport in
membranes. (R)

a complex process, it does illustrate the general
features of drug distribution kinetics.

T HE ANALYSIS GIVEN below has been
adapted from a paper by Buell et al. [1]. Mass
balance on the two stirred tanks give the follow-
ing governing equations:

d = -kC1 (1)
W, = kC, - kC. (2)
where for convenience we have specified that the
volumes of well-stirred liquid in the tanks are
equal, V, = V2 = V, so that k, = k, = K = q/V.
Prior to time t = 0, the stirred tanks contain no
drug and at t = 0 the initial dose mi is ad-
ministered to the first stirred tank. An instant
later at t = 0+, the initial concentrations are
Ci(0+) = mif/V
C2(0+) = 0. (3)
A periodic condition C, is that the concentration
of drug in the first stirred tank just prior to a
maintenance dose C, (Ti + nTm-) plus the increase

in concentration due to the maintenance dose
mm/V is equal to the concentration in the first
stirred tank just after the maintenance dose
Ci(Ti + nTm+) or
Ci(Ti + nTm-) + mm/V = Ci(Ti + nTm+) (4)
n = 0, 1, 2, 3, . . . N.
To achieve the plateau effect mentioned previously
the concentration at the end of the initial time in-
terval C,(Ti) must be equal to the concentration
at the end of all of the maintenance time intervals
C2(Ti + nTm) or
C2(T) = C.(Ti + nTm) n = 1, 2 ... N.
A similar condition also applies to the first tank
(1) :
C (Ti) = Ci(Ti + nTm-) n = 1, 2 . . . N.
General solutions to the above system of equa-
tions have been given by Buell et al. (1). The solu-

In order for the drug to be
safe and effective the concentration
level in the body C2 must be maintained
above the minimum effective concentration
C2min but below the toxic concentration C2max.

tions for the special case considered here are as
For the initial time interval, 0 < t < Ti-,
C,(t) = (mi/V) exp[-kt] (7)
C,(t) = (mi/V) kt exp[-kt] . (8)
For the maintenance time intervals,
Ti + nTm+ < t < Ti + (n + 1)Tm-,
C, (t) = [C1 (Ti + nTm-) + (mm/V]
exp[-k (t - Ti - nTm)] (9)
C2(t) C(T, + nTm) exp[-k(t-Ti-nTm)]
+ [C,(T, + nTm-) + mm/V] [k(t-Ti-nTm)]
exp[-k(t - T, - nTm)]. (10)
The results given above can be used to obtain
the following relations among the parameters Ti,
Tm, mi, mm, Czmin and C2max:


T_ 1
Tm 1 - exp[-kTm] ,
mi _ exp [kT1] ,
mm exp[kTm] - 1

mi _ exp[kTi]
VC2min kTi '
C2max _ exp[kTi - 1]
C2min kTi






It can be shown that, in general, the maximum
concentration in the second tank during the
initial time interval is equal the maximum con-
centration during the maintenance intervals.
Eqs. (11) - (14) place four restrictions on
the six parameters Ti, Tm, mi, mim, C2min and C2max.
At most, two of these parameters can be specified
at will. For example, if Tm and C2min are specified,
then Ti is calculated using Eq. (11), mi and mm
are determined from Eqs. (13) and (12) in that
order. C2max is given by Eq. (14).


A S SHOWN IN FIGURE 1, the experimental
apparatus consists of two stirred tanks hold-
ing equal volumes and connected in series with
a short piece of large diameter tubing. At the
appropriate times the prescribed amounts of drug
analog, sodium chloride, are poured rapidly into
the first tank through the funnel. To achieve
rapid, uniform mixing, the tube carrying the in-
flow stream for each tank ends in a region ad-
jacent to the magnetic stirrer. The entrance of
the outflow tube is located as far away as possible
from the magnetic stirer. The concentration in the
second tank is measured continuously using a con-
ductivity meter.
A convenient method for setting the pa-
rameters is outlined below. During the initial dose
interval, the maximum concentration in the second
tank C2max occurs at the time Tmax = 1/k (1).
Using the value for k determined by this method,
one can specify Tm to be
Tm = 1/k (15)
and from Eq. (11) obtain the result
Ti = 1.5812 Tm . (16)
Next C0min can be specified and Eq. (13) used to
mi/V = 3.074 Cmin . (17)
From Eq. (12)
mi = 2.829 mm . (18)
Finally C0max during the maintenance and initial
intervals is determined from Eq. (14) to be
C2max = 1.131 Cmin . (19)
An experimentally measured trace C,(t) is
shown in Figure 2. For this experiment q =
11.6 ml/sec and V = 310 ml not including the
small volumes in the connecting tubing. The ex-
perimentally measured value of k = 1/Tmax =

0.0370 sec-1 is in close agreement with the pre-
dicted value k = V/q = 0.0374 sec-1. Setting
Tm = 1/k = 27 sec and C2min = 0.0379 moles/I,
we obtain Ti = 43 sec, mi = 0.0361 moles, mm =
0.0128 moles and C2max = 0.0429 moles/1 using
Eqs. (15) - (19). These parameters were used
to obtain the experimental results shown in Figure
2 except mm was increased to 0.0138 moles. This
adjustment in mm was necessary to obtain the
nearly uniform minimum values for C2 (t) shown
in Figure 2. The increase in mm and the fact that

FIGURE 2. Graph of C2 vs. time. Arrows along the time
axis indicate the intervals and relative amounts for the
drug doses. The last peak represents the response when
the dose mm is injected directly into the second tank.
the measured C0 (t) values fall slightly below their
predicted maximum and minimum values are
probably caused by less-than-perfect mixing in
the tanks and the unmixed volumes in the con-
decting tubing. Note that these effects also cause
a 3-4 second lag time between the administration
of the maintenance dose and the minimum in the
C0 (t) curve. The last peak in the C2 (t) trace in
Figure 2 represents the response of the system
to a direct injection of mm into the second tank.
Some precautions necessary to insure good
results in this experiment are accurate measure-
ments of mi, mm, T1 and Tm and care in construct-
ing the hydrodynamic analog so that it will
correspond as closely as possible to the idealized
two-compartment model. O
The authors wish to acknowledge Professor K. B.
Bischoff, Neal Zislin and Charles Baker for their contri-
butions to this project.
Buell, J., R. Jelliffe, R. Kalaba, and R. Sridhar, Math.
Biosci., 5, 285 (1969).



Carnegie-Mellon University
Pittsburgh, Pennsylvania 15213

In the course of their education, chemical
engineers probably work enough homework
problems to pave the road. The following ques-
tion was assigned by S. L. Rosen to the New
Alternative students this past summer.
Prove that Hell is isothermal.
This proof requires two assumptions, both
probably pretty good:
a) There are some capable engineers among
the inhabitants.
b) They are suffering as much as the other
lost souls.
The expected answer involved the concept
that a heat engine can always be run between
two reservoirs at different temperatures. There-
fore, if Hell were not isothermal, the engineers
could build engines to run air conditioners, shovel
coal into the fires, etc.
However, Karl Zipf's answer showed a good
deal more originality. It follows here:

G 0O TO HELL. Yes, this is probably the easiest
way to prove whether Hell is isothermal or
not. All one has to do is record some meaningful
data. However, I shall try to prove or disprove it
without undertaking the journey.
PV = nRT (1)
One can use the above equation for the basis
of the proof, but first the theological problem of
how many moles to a soul must be solved. If the
soul is a physically real item* then it will have a
molar mass. Thus over a period of time there
should be an increase in the souls in Hell, and
therefore, an increase in the number of moles in
Hell. This assumption can be readily proven by
the fact that the population has been increasing.

*There are indications that the soul is physically real
and is a vapor.

A further assumption is that the ratio of good:
bad has remained constant. However, some
denominations believe that if one does not sub-
scribe to their doctrine then one is going to Hell.
These sects often mutually exclude each other
and there could be the possibility that everyone
is going to Hell. Regardless of the exact numbers
involved it is apparent that the overall number
of souls in Hell is on an increase. Since the popu-
lation of Hell is parallel to the population of
Earth, then the general trend in Hell can be seen
as a rapidly increasing exponential population.
Lastly, it can be concluded that the volume
of Hell has remained constant, since Hell has not
manifested itself upon the Earth, contrary to
popular belief.
Now let us review the two assumptions.
1) There is an increase in the number of the
moles of souls in Hell.
2) The volume of Hell is constant.
Upon rewriting Eq. (1) :
/ P AnR
T - V (2)
As one can see that as the moles of souls increase
the AP increases or AT decreases. If the pressure
increased, then there could eventually be an ex-
plosion, and then all Hell would break loose. Be-
cause this has not happened it can be assumed
that the pressure is constant and that the tempera-
ture must decrease. Thus, Hell is not isothermal.
Furthermore, the decrease in temperature sup-
ports Dante's observations, for according to his
data the center of Hell is a frozen lake. E
Karl Zipf
MCMLXXVI Anno Domini

Karl Zipf is a single, male student in the Department of Chemical
Engineering at CMU. He is finishing an M.S. thesis on Soil Stabiliza-
tion with Professor Rosen this semester. He is 24. Karl has a B.S.
in Biology from Lehigh University and is one of our second year
New Alternative graduates.


views and opinions


Tufts University,
Medford, Mass. 02155

oae &t: 4 1ahe anSd Mileadi#
_% ac4iUe SJkae'uk'we oj 4ccepled


where, for: a) a definition of energy; b) the
significance of AG>O; c) the process limitations
dU = TdS - PdV, and with unfailing regularity
the three lead statements will be forthcoming.
Usually the more reticent the class, the stronger
their conviction, that these at least are truths
they have mastered.

Should there be some
among the multitudinous readership
who feel that stronger remedies of a
more metaphysical nature, are needed to
dispel the doctrines here condemned, I have
in my files a copy of the exorcism formula,
pronounced prior to hanging, against the
murderers of the Archbishop of Dublin . . .
adapted for use on thermoheretics.

Yet the lead statements are at best misleading,
and at worst, false. They are thermodynamic
heresies that are universally held. It is time to
banish these misleading ideas from the company
and discourse of the elevated and learned, by

FIG. 1. Energy Flow in Power Plant.

which I of course mean chemical engineers. In
lieu of Bell, Book and Candle, I will attempt to
exorcise them by examining each so closely that
its inherent misrepresentation stands revealed.

"Energy is the Ability to do Work"
If only it were. The operation of a modern
plant would then be radically changed. Instead
of having energy flows such as those shown in
Figure (1) where most of the incoming energy
leaves with the condenser waste water and only
35% is converted into electricity (work), we
would have the electric energy (work) output of
the power plant equal to that of the fuel energy
input. But not only does most of the energy
escape in the condenser cooling waters, these
torrents of energy usually have negative work
ability because work must be done to dispose of
them properly.
Were statement I true there could never be an
"energy shortage" because energy is always con-
served. The air, sea, and earth are full of energy.
No matter how many power plants, automobiles,
air conditioners, steel mills, etc. we build, the



I Ch :_`

energy stores are not reduced because energy is
never destroyed.
"The ability to do work," however, is easily
destroyed and terribly fragile. It is easily con-
sumed, and frequently is destroyed without ever
fulfilling its work potential. The proper appelation
for this fragile property is "availability," or avail-
able energy." Availability, not energy, is the
measure of the "ability to do work." The "avail-
ability shortage" and not "energy shortage" is
and will be a permanent and growing problem of
industrial society.
The question of the definition of energy raised
in the opening paragraph is perhaps an unfair
one to spring on an unprepared class because
energy is a difficult and subtle concept whose
adequate definition goes well beyond the purpose
of this paper. Suffice it to say that Energy is: that
which is always conserved in all processes; that
which manifests itself as heat or work when
crossing the boundaries of a closed system; and
that whose accumulation within a system is altered
to an extent exactly equal to the net mass, heat,
and work interchanges that the system has with
its surroundings. The "ability to do work" it is

"If AGreaction is Positive, the Reaction Does Not Go"
T HIS IS THE MOST prevalent, misleading, and
insidious heresy on our list. It is taught as
catechism in chemistry courses the world over yet
it is at best a half truth. If it were true, major
parts of the chemical industry would not operate.
There would be no cracking or reforming plants.
Methanol would not be synthesizable from CO and


oS, "


aA -bB
AGR > 0

-------------- B (PURE)

- -- -- --------- A- A (PURE)
.. . , - - O E- IBRIM
I I 0

E. . lat.

FIG. 2. Path for Reaction Free Energy Change.

M. V. Sussman of Tufts University was a reasonable facsimile
of the above photo, in an earlier edition. His thermodynamic thoughts
have graced this journal previously ("Seeing Entropy, or the In-
complete Thermodynamics of the Maxwell Demon Bottle", p. 149-156,
Summer 1974; "Approaches to Statistical Thermodynamics", p. 40, 49,
Summer 1968 and may be found in full measure in "Elementary
General Thermodynamics", Addison-Wesley, a book featuring full
page photos of Thermodynamic's "AII-Time'AII-Stars" and a method
for out-maneuvering Maxwell's Relations."

What then, is significance of AGr>O? The
AGr is the free energy change that accompanies
the conversion of pure reactants to pure products
at a specified temperature and total pressure.
For example for the gaseous reaction:
A (pure, at T and P) -> B (pure, at T and P)
the computation path for the free energy change
of reaction may be represented as in Figure 2,
where the total pressure is taken to be 1 atmos-
phere. To evaluate AG, we sum the free energy
changes along path A-pA-pB-B. A free energy
loss occurs as A expands to its partial pressure
pAe in an equilibrium reaction mixture of A+B.
No free energy expenditure is needed to convert
A at PAe to B at its equilibrium concentration
(Pee). But the free energy of B must be increased
to concentrate it from pie to P.
The total change for the process is the sum of
the JVdP from A to PAe, PAe to Peo to B, and is
equal to AGOreaction. When we sum these integrals
we obtain the familiar result
AGer = - RT In- -
AGO =- RT In K
for any reaction.
Now AGOr is shown as positive in Figure 2.
Does this mean, "The reaction does not go"?
Clearly it does not. The positive value of AG�r
simply indicates that the concentration of product
in the equilibrium mixture is less that of reactant,


or that K in equation (2) is less than 1. Were we
to use this reaction to produce B, the equilibrium
mixture leaving the reactor would contain less B
than A, and consequently would need to be
separated into its components, with the unreacted
A being recycled to the reactor. Notice that the
free energy change in moving pure reactant to
the equilibrium state is negative even when the
overall AG�r is positive. Therefore the reaction
always goes to its equilibrium state. If AGOr is posi-
tive the concentration of product in the equi-
librium reaction mixture is low and insufficient to
make K>l. Of course if K< tion may be so low as to be insignificant, as for
example in the decomposition of water to hydro-
gen and oxygen at room temperature. On the
other hand as K- l, for valuable or easily isolated
products, the product concentration may be large
enough to make cleaning up the equilibrium mix-
ture worthwhile.

"dU = TdS - RdV For A Reversible Process
(in a simple system)"
The statement is indisputable but only be-
cause it is a tautology. You can say with equal
dU = TdS - PdV, in Paris in the Spring;
or, on Tuesdays or Fridays;
or, for an irreversible process
I consider it heresy because it implies to too many
students that dU, a differential of a property, is
dependent on process or path, and is otherwise
defined for an irreversible process.
Statement III should never stand alone,
though it does all too frequently in many respected
texts. Better still to avoid it completely or replace
it with the following:
For any process, reversible or irreversible,
that moves a simple system from one equilibrium
state to another, the internal energy change may
be evaluated by integrating:
dU = TdS - PdV
along any reversible path that interconnects the
terminal states of the process.
I have discoursed briefly on some old, treasured
and well rooted thermodynamic prejudices.
Should there be some among the multitudinous
readership who feel that stronger remedies of a
more metaphysical nature, are needed to dispel
the doctrines here condemned, I have in my files a
copy of the exorcism formula, pronounced prior
to hanging, against the murderers of the Arch-

bishop of Dublin, in 1534, and adapted for use on
thermoheretics. This I will be glad to send to the
initiated in unmarked brown envelopes upon re-
quest. O

ChE EDUCATOR: Scott Fogler
Continued from page 7.
Scott's daughter, Kristin, age 6, was quick to
feel left out from the Indian Guides activities.
Scott realized that there wasn't a similar activity
for young girls in Ann Arbor. At Kristin's urging,
he organized a council of "Indian Princesses" in
Ann Arbor. Scott was the first Nation Chief of
the Indian Princesses. He's been a successful
Chief: In the first year there were five tribes with
a total of about 50 fathers and daughters.
Peter, age 11, got Scott involved in another
after-hours effort: Little League. When Peter's
5th grade class couldn't find a willing coach, Scott
stepped in to lead the team to a 1 and 9 record
for the season, which doesn't speak too well for
the ability of the team (or coach?). But, imagine
keeping eighteen 10-year-olds interested enough
to keep playing ball even though they were losing
all the time! That takes real dedication and under-
Jan, Scott's wife, is also involved in teaching
as she has 25 piano students and currently serves
as president of the Ann Arbor Area Teachers'
In his few leisure moments, Scott spends some
time gardening. He finds Michigan a frustrating
place to raise plants because of its hard clay soil.
He plants three trees for each one that lives.
The whole Fogler family shares an enthusiasm
for travel, and Scott has lectured in Scandanavia,
Italy, South America, and Mexico City. Whenever
he travels, he takes along his programmed-
learning text. He has a file of slides which show
him reading the text in front of landmarks such
as the Tower of Pisa. He uses the slides as visual
one-liners during his lectures.
Scott Fogler loves teaching, loves research
and approaches them both with unbounded energy.
He is perhaps his own best example of creative
synthesis. He has developed his teaching skills
and mixed them with humor to produce memor-
able classes for his students. He has used some
bit of educational theory and his own creativity
to gain recognition as an outstanding educator.
As he says: "A little theory is very practical!" 0


N Jbook reviews

By Robert M. Bethea, Benjamin S. Duran and
Thomas L. Boullion
Marcel Dekker, Inc., 1975. 583 pages.
Reviewed by Richard W. Mensing,
Iowa State University

Anyone writing a book on statistical methods
for engineers is confronted with a decision about
what statistical topics to include in the book.
There are many areas of engineering and the
most applicable statistical methods are not the
same for all groups. For example, industrial,
traffic and electrical engineers frequently use
probability modeling as a tool in analysis. Thus,
the most applicable statistical methods for these
engineers includes estimation, tests of goodness of
fit, regression analysis, and statistical analysis
of data taken over time. Reliability is a topic of
principle concern to nuclear and mechanical
engineers so life test data, statistical analysis of
exponential, Weibull and lognormal data and pro-
pagation of errors are of utmost importance to
this group. On the other hand, chemical, sanitary
and materials engineers are often concerned with
experimental data and thus make heavy use of re-
gression analysis and the analysis of variance.
The authors of this book address themselves to
the latter group of engineers and as such cover
most of the usual topics which would be introduced
in a first course in statistical methods for these
After a brief introduction, Chapter 2 intro-
duces the basic concepts of probability. This is
followed by a chapter on distributions. Included
in this chapter are both experimental distributions
(as usually derived from sample data) and theo-
retical or probability distributions. The notion of
the mean and variance of a probability distribu-
tion is also introduced in this chapter. Expected
values and moments are again covered in Chapter
5 along with joint probability distributions and the
independence of random variables. These chapters
represent the introductory background material
on probability. Chapter 4 covers descriptive statis-
tics. Basic statistical inference is the topic of
Chapters 6 and 7. Estimation is covered in
Chapter 6. Also introduced in this chapter are

three sampling distributions, the t, X2 and F dis-
tributions. Chapter 7 covers the usual tests of hy-
potheses about means, variances and proportions.
The method of the analysis of variance is intro-
duced in Chapter 8 as a method of comparing
several normal populations. One, two and three
way analyses of variance are covered. Also,
Bartlett's test for comparing several variances is
discussed in Chapter 8. Regression analysis, in-
cluding simple linear, multiple linear, polynomial
and nonlinear regression is the topic of Chapter
9. A separate chapter, Chapter 10, is devoted to
orthogonal polynomials. The final chapter is on
experimental design and covers the analysis of
variance associated with completely randomized,
randomized complete block, latin square and split
plot designs. Factorial experiments are also dis-
cussed in this chapter.
In considering this book as a textbook for an
introductory course in statistical methods for
engineers and scientists, I believe it has several
drawbacks. For one, there are several places
where I think the book is too terse, particularly
in introductory sections and sections on defini-
tions. For example, in Chapter 3 on distributions,
a random variable is defined as "a function from
a sample space to the real line" with no further
discussion. I do not believe this brief definition
is enough for someone encountering this concept
for the first time to really understand what a
random variable is and what its importance is in
statistics. Also, populations and a sample (defined
as "part of a population") are only defined, but,
although it is used throughout the book, there
is no discussion of a random sample. In Chapter
11, much of the terminology surrounding experi-
mental design (e.g. treatments, experimental
units, experimental error, factors, etc.) are only
briefly defined with only a minimal amount of
discussion. This certainly would have to be
supplemented by the instructor for a student to
gain an understanding of these terms. On the
other hand, for a methods book, I believe the
authors go into too much theory on some topics.
This is particularly true in Chapter 5 on expected
values where there are several derivations which
are unnecessary.
The authors mention that the book is intended
for undergraduate students in engineering and
the physical sciences. I believe the students should
be upper level undergraduate or beginning
graduate students. A two-quarter course which
Continued on page 46.


M international



University of Groningen,
Groningen, the Netherlands

In two phase separation processes often confusion
arises about the meaning and definition of stage-
contact-efficiencies. The efficiency, sometimes
erratically, is considered to be a measure of the
purification obtained in the process under study
or in part of it. Moreover, there are many ways
to define an efficiency e.g. the Murphree plate
efficiency based on the vapor feed or on the liquid
feed, a Hausen efficiency and a point efficiency.
In this paper we will look shortly into the differ-
ence between degree of purification and efficiency
and elaborate somewhat further upon the physical
meaning of the efficiencies, as normally used in
Most separation processes can be shown to be
built-up from units in which two flows make
physical contact and thereby exchange part of
their components, or heat. For simplicity's sake
let us first suppose that one feed, F, is introduced
and that two flows, L and V, leave the unit. A
component, called A, has to be separated in puri-
fied form. All other components are taken to-
gether, as B. The composition of the flows is then
XA resp. XB. xA, XB and F, V and L must be taken
in consistent units, e.g. concentrations in mole
fractions and flows in mol/s. Or flows in kg/s
and concentrations in weight fractions.



vA >
A' B

FIGURE 1. Process with one inlet and two outlets.

Now the degree of purification can be defined

Lx Lx
Fx Fx

F F (1)
Fx F Fx F
Note that this expression has the advantage that
the degree of purification remains the same, ir-
respective 1) which outlet stream (L or V) is
taken into consideration and 2) whether com-

FIGURE 2. Two phase separation process.

ponent A or the sum of all other components, B,
is considered.
Also important is that P will always have a
value between 0 and 1, zero if the flows L and V
have the same composition as flow F, thus when
no separation has actually taken place and one
if the two components A and B are completely
The expression for P was originally introduced
for cyclones [1]. In many cases the feed entering
the separation unit is in itself split up into two
flows, for example when a stage of a counter-
current separation process is considered. Now the
incoming flows may be taken as those leaving an
imaginary process (drawn on the left in figure 2,
marked with the number 1), which is fed by F.
This means that the incoming flows in the actual


Bart Drinkenburg received his engineers degree and Ph.D. from
the Technological University of Eindhoven, the Netherlands. He
spent one academic course teaching at the University of London and
thereafter joined the University of Groningen, the Netherlands, to
become an associate professor in chemical engineering. His main
field of interest in research is two-phase flow and mass transfer in
packed columns, including trickle bed reactors.

piece of equipment on the right 2, already have a
degree of purification:

Vi x Ai

V x Ai

Vi x Bi

Vi x Bi
SAi Li x Bi +Vi x Bi

The flows leaving the actual equipment, 2, have a
degree of purification
Vo x V Vo x Bo
Pout BAoo
Ai Ai Bi +V i

We expect, as a result of the contacting process,
that the degree of purification will increase,
Pout > Pin. Its difference, AP, is the working of
the piece of equipment under study:
V.x V - V, Vox V Vx V
P Ao Ai Bo Bi
L V x L V
Lix Ai + Vix Ai Bi +Vx Bi
Ai AIi ^ BiBi
It is this number, AP, in which the process engi-
neer will be interested when he compares alter-

natives for separation.
Note that, until now, nothing has to be known
about the contacting process itself. The only tool
used a mass balance over the equipment, or part
of it.

IN MANY CONTACTING processes the equip-
ment not necessarily has to be considered to be
a black box. Contacting stages are so devised that
the 'flows leaving the stages are more or less in
physical equilibrium. This means that besides the
mass balance an equilibrium relationship comes
into the picture. A theoretical stage (theoretical
plate) is a part of the equipment where the out-
going flows are in physical equilibrium. Its
efficiency is taken to be 100%. However, the out-
going flows from practical stages are seldomly in
equilibrium and then a problem arises. The
efficiency of the stage then has to be expressed
into flows and concentrations. The definition of
the efficiency is often ambiguous as we will see.
For only one definition, the efficiency can be
shown to be consistent with the defined degree
of purification.
The relation between the effects of a theo-
retical stage and a practical stage is elucidated by
means of a graphical representation, figure 3.
Point C represents the compositions of the
flows L and V entering the contacting stage. We
took it that L and V do not change during the
contacting process, a condition that is appropri-
ate in many practical circumstances and in many
other circumstances can be made appropriate by

operating line in
/case of 1000/0 eff.
/operating line in
case of eff.< 100%/o

X� Xo Xi -- L X
FIGURE 3. Composition diagram. Action of a
contacting stage.


choosing suitable units to express L and V.
Line CB then represents the mass balance for
component A, since

L.xL + V.x A
Ai Ai
and therefore

= L.x + V.x

V V L [ L L
In the following the subscript A will be omitted
since everywhere x will represent the concentra-
tion of A in the flow under study.
For a 100% efficiency, point B on the equili-
brium line gives the compositions of the two flows
leaving a theoretical contacting stage. Point F
and E, as is well known, then represent the con-
centrations of A in the flows that pass each other
in between the contacting stages in a multiple-
stage-counter-current contacting process and are
points of the so called operating line. The slope
of the operating line has the opposite sign as the
slope of the above mentioned mass balance plot:
V ,the flow ratio of the two contacting phases.
In case the state of equilibrium is not reached,
the concentrations of the flows leaving the
practical stage are not given by B, but the
process stops somewhere on the line CB, e.g. B'
and consequently the operating line will shift
to E'F'.
When we wish to compare the performance
of the practical contacting stage to that of a
theoretical one it is logical to relate its degree of
purification to that of a theoretical stage and
therefore we now express its efficiency as:

E = APpractical stage - Ppractical out--Pin
E=APtheoretical stage Ptheor. out-Pin
If L/V is constant then:

V (xov' - xv)
Lx1L +V V
V(xY + xjV)
L XiL + V xiV

V (1-xov - 1 + xiv)
L(1-xi-) + V(1-xi)
V(1-XoV- 1 + xv)
L( - xiL) + V(1 - xiV)

or: E = xv-- x = EH

which is known as the Hausen efficiency [2] and
represents in fig. 3 the fractional cut-off BE"E
or F or BC

This definition of efficiency is the best one
available in terms of a mathematical and physical

description of a contacting stage.
If L/V does not remain constant during the
process of exchange the original equation (4)
has to be inserted for both the theoretical as well
as the actual contacting stage; then, however,
the expression will be very complicated and does
not reduce to simpler terms.
Standart [3] has tried to use a simplified equa-
tion for this situation, but although his definition
of the efficiency comes down to an equal value
irrespective whether it is related to gas phase
parameters or to liquid phase parameters, the
physical meaning of the numerical values which
he obtained cannot be directly related to a degree
of purification. Nevertheless in the limiting case,
if L/V remains constant, Standart's definition
also reduces to the Hausen efficiency.
However, The Hausen efficiency is seldom used
in the profession, partly due to historical reasons,
partly because the line CB, although it describes
in mathematical terms the mass balance of the
contacting stage, does seldom represent composi-
tions of the two phases which are in near physical
contact at certain points in the system.

W E MAY TRY TO represent in the concentra-
tion diagram sets of concentrations in the two
phases that are in close contact with each other.
For actual stages often the two phases are con-
tacted in cross flow, e.g. gas bubbling through
holes in a plate while liquid traverses the plate
from one side to the other.
If the liquid on the plate is well mixed, as will
be the case for even relatively large plate di-
ameters, then it has everywhere the composition
Xo' and line a (E'B') in Fig. 4 describes the con-
centrations in the gas phase which will occur
along the height.
If the gas flows in plug fashion through the
liquid all points of line a represent actual
occurring pairs of concentrations; if the gas is
mixed to some extent, the line will not start at
point E' but somewhat higher. In the case that the
gas also would be completely mixed, point B'
would represent the concentration pairs on all
points of the plate.
In the same way it can be shown, that line b
(F'B') represents processes in which the gas
phase is well mixed and the liquid phase flows in
more or less plug fashion through the stage. This
may be true in a shallow spray-tower. Here line b
shrinks in the direction of B' when also mixing


equilibrium Line

operating Line

FIGURE 4. Composition diagram. Possible
process paths.

of the liquid phase occurs.
Line c, (CB') represents actual concentration
sets if cocurrent flow exists without any extent
of mixing in gas or liquid phase. All other types
of contacting must be represented by other curved
trajectories in the concentrations diagram. For
all these systems except the case where the liquid
is well mixed, the concentrations of the gas
leaving the plate will differ for each local point.
If we assume that the liquid on a plate is well
mixed vertically, although not necessarily so in
the horizontal direction, then for each local point
on the plate we may define a driving force for
mass transfer between vapor and liquid. When
the vapor below the plate is well mixed, its com-
position upon entering will be everywhere x7.
Then, depending upon the local point considered
on the plate, the driving force for mass transfer
will be in Fig. 4 the vertical distance from a
point on line CE' to IG. If the vapour comes into
equilibrium with the liquid, the driving force of
the vapour upon leaving the plate will be zero.
In practical circumstances this will not happen.
Therefore the degree into which the driving
force is reduced locally during passage through
the liquid layer is called the point efficiency, Ep.
The point efficiency is very difficult to measure,
since both local concentrations of the leaving gas
and liquid must be known. Moreover, as will be
shown, the term efficiency is not appropriate.
If the liquid on the plate is well mixed
horizontally too, then the point efficiency will be
the same anywhere on the plate, and consequently
the vapour leaving the plate will have the same

composition everywhere. This means that in this
case the point efficiency is given by GE' . Since
this ratio for any practical stage is called the
Murphree vapour efficiency, Emv, this means that
for plates with well mixed vapour entering and
with perfectly mixed liquid on the plate, there
is an equality between the point efficiency and
the Murphree vapour efficiency. Now it can be
seen that the Murphree efficiency is in fact not an
efficiency, since a Murphree efficiency of 100%
defined in the same terms, thus with point E' on
the same point in the diagram, would correspond
with point M for the mass balance, which is con-
tradictory to the definition of a contacting stage.
Of course, if the Murphree efficiency would rise,
point E' also would shift to the left, until ulti-
mately point E would be reached. This implies
that the Murphree efficiency must not be con-
sidered as an efficiency in the pure meaning of
the word, but as a qualitative measure for the
contacting process that can be sensible in some
circumstances viz. in those circumstances where
on basis of a physical model the Murphree
efficiency can be expected to remain constant with
varying flow. In the same way a Murphree
efficiency can be defined for the liquid phase:
_ B'F'
ML - H F'

It has equal drawbacks as those mentioned
about for EMv. Since the Murphree efficiency has
shot so many roots in the field of distillation, it is
not logical to eradicate its use. However, it
should be realized that the Murphree efficiency
does not provide a quantitative grip upon the
number of steps which are actually needed in a
distillation column. Then recourse has to be
taken to the Hausen efficiency or what amounts
to the same, to the equations describing mass
balance and equilibrium themselves.

ALTHOUGH IT HAS BEEN shown in the fore-
going, that a given Murphree plate efficiency
cannot be translated directly into a purification
grade, there do exist cases where a constancy of
one of the Murphree efficiencies may be predicted
on physical grounds.
For example, consider a distillation process in
* the liquid on the plate is completely mixed, while
* the gas moves in plug flow through the liquid


--x X

* Suppose that the gas flow is constant, while the liquid
flow rate is varied, but
* the liquid height on the plate remains the same.
Now the real local liquid flow velocity will be
made up by phenomena: a) the velocity induced
by the overall liquid flow on the plate, and b) the
statistical flow variations (mixing) caused by
the action of the gas bubbles. It will be clear,
that in most cases phenomena b) will be the one
largely responsible for local fluid movement.
Therefore we may suppose, that a variation of
the liquid flow rate on the plate will not influence
directly the number of gas bubbles nor its dimen-
sions, if the physical properties of the liquid on
the plate remain the same (surface tension, vis-
cosity, density). The physical properties are kept
constant if the composition of the liquid on the
plate is kept equal for different liquid flow rates,
L, by adjusting the liquid feed composition. (from
xIL1 to XiL2).
In this case a gas bubble rising in the liquid
will not observe any change in its surroundings
and therefore will transfer the same amount of
mass regardless of the magnitude of L and hence
EMV is predicted to be constant. From Fig. 5 it is
obvious, however, that only EMV will be constant,
En and EML will change with L. Experimental con-
firmation is given elsewhere [4].
In the same way it can be shown, that if
* the gas "on the plate" is well mixed
* the liquid moves in plug flow through the gas
* the liquid flow rate is constant
* the length of the liquid trajectory is constant, that the
Murphree liquid efficiency, EML will be constant for
different vapour velocities, but not so Emy or EH.
This type of exchange will be expected in a
shallow spray tower (Fig. 6) Cases in which EH
is constant are very difficult to be thought of. But,

FIGURE 5. Constant EMV as a function of L.
xL plate and V are constant.



0 xii
Xo xi - X
FIGURE 6. Constant EML as a function of V.
xv plate and L are constant.
then, the use of the Hausen efficiency, being con-
sistent to a degree of purification, does not need
further justification.

There needs to be made a distinction between the de-
gree of purification and the efficiency of a process. The
degree of purification is derived on the basis of a mass
balance, the efficiency must combine a mass balance with
equilibrium relationship. The Hausen efficiency is based
on a mass balance and an equilibrium relation and can
readily be translated into a degree of purification.
Numerical data on the Murphree vapour efficiency or the
Murphree liquid efficiency, in general, do not provide
complete quantitative information about the separation
process. In certain circumstances the constancy of the
Murphree vapour efficiency or the Murphree liquid
efficiency may be expected on model considerations. []

1. van Ebbenhorst Tengbergen, H. J. and Rietema, K.
in Rietema, K. and Verver, C. C., "Cyclones in In-
dustry," Elsevier Publishing Cy, Amsterdam (1961).
2. Hausen, H. Chemie Ing. Techn. 25 (1953) 595.
3. Standart, G. Chem. Eng. Sc. 20 (1965) 611.
4. Moens, E. P. Drinkenburg, A. A. H. and van der
Veen, A. J. Trans. Inst. Chem. Engrs. 52 (1974) 228.

x concentration, consistent with the unit of flow
L flow rate phase 1
V flow rate phase 2 consistent with x
P degree of purification
E efficiency
El : Hausen efficiency
EM : Murphree efficiency, based on the vapour
EML:, Murphree efficiency, based on the liquid.


Continued from page 17.

ChE involve large populations, there are also
situations in which small particle populations may
be encountered. Thus bubble populations arising
in a gas phase fluidized bed, continually ag-
glomerate as they ascend through the bed, to form
small populations. Such situations cannot always
be described by population balance equations.
Ramkrishna and Borwanker [23-25] have shown
that the framework of population balances derives
as a special case of the theory of point processes.
Thus the population balance equation is shown to
be the first of an infinite hierarchy of equations
in what have been called as product densities all
of which are required for the analysis of small
populations in which random fluctuations may be
important. Further, they have shown [25] that the
model (5) normally used for agglomerating pop-
ulations would be incorrect, when particle states
are correlated. In such a case, additional members
of the hierarchy of product density equations must
be accounted for. Substantial particle size corre-
lations have been predicted for some agglomera-
tion probabilities, These have far-reaching prac-
tical implications. Thus in a fluidized bed reactor,
one may raise the question as to whether or not
randomly behaving bubble populations would give
rise to fluctuations in reactor conversion.
Indeed, there are many engaging problems in
the analysis of dispersed phase systems. Un-
doubtedly, considerably more detailed experi-
mentation is required for further quantitative
application of population balances. In view of the
large variety of applications, the method of popu-
lation balances deserves more vigorous pursuit. El

1. A. D. Randolph and M. A. Larson, "Theory of Par-
ticulate Processes", Academic Press, New York, 1971.
2. Bayens, C. A. and R. A. Laurence, I.&.E.C. Fundls.,
1969, 8, 71.
3. Shah, B. H. and D. Ramkrishna, Chem. Eng. Sci., 1973,
28, 389.
4. Hulburt, H. M. and S. L. Katz, Chem. Eng. Sci. 1964,
19, 555.
5. Eakman, J. M., A. G. Fredrickson and H. M. Tsuchiya,
Chem. Eng. Prog. Symp. Series, No. 69, 1966, 62, 37.
6. Hulburt, H. M. and T. Akiyama, I.&.E.C. Fundss,
1969, 8, 319.
7. Argyriou, D. T., H. L. List and R. Shinnar, A.I.Ch.E.
JL, 1971, 17, 122.
8. Ramkrishna, D., Chem. Eng. Sci., 1971, 26, 1134.

9. Subramanian, G. and D. Ramkrishna, MIath. Biosci.,
1971, 10, 1.
10. Ramkrishna, D., Chem. Eng. Sci., 1973, 28, 1362.
11. Singh, P. N. and D. Ramkrishna, Computers and
Chem. Eng., 1977, 1, 23.
12. Singh, P. N. and D. Ramkrishna, J. Colloid Interface
Sci., 1975, 53, 214.
13. Spielman, L. A. and 0. Levenspiel, Chem. Eng. Sci.,
1965, 20, 247.
14. Rao, D. P. and I. J. Dunn, Chem. Eng. Sci., 1970, 25,
15. Collins, S. B. and J. G. Knudsen, A.I.Ch.E.J., 1970, 16,
16. Zeitlin, M. A. and L. L. Tavlarides, Can. J. Chem.
Eng., 1972, 50, 207.
17. Shah, B. H., J. D. Borwanker and D. Ramkrishna,
Math. Biosci., 1976, 31, 1.
18. Ramkrishna, D., Chem. Eng. Sci., 1974, 29, 987.
19. Madden, A. J. and B. J. McCoy, Chem. Eng. Sci., 1969,
24, 416.
20. Narsimhan, G. and D. Ramkrishna, Unpublished re-
21. Curl, R. L., A.I.Ch.E.J., 1963, 9, 175.
22. Bajpai, R. K., D. Ramkrishna and A. Prokop, Chem.
Eng. Sci., 1976, 31, 913.
23. Ramkrishna, D. and J. D. Borwanker, Chem. Eng. Sci.,
1973, 28, 1423.
24. Ramkrishna, D. and J. D. Borwanker, Chem. Eng. Sci.,
25. Ramkrishna, D., B. H. Shah and J. D. Borwanker,
Chem. Eng. Sci., 1976, 31, 435.

For advertising rates contact Ms. Carole Yocum, CEE
c/o Chemical Engineering Dept., University of Florida,
Gainesville, FL. 32611

Applications are invited for appointment as As-
sistant Professor in Chemical Engineering. (As-
sociate rank may be considered for an outstanding
candidate). Qualifications required are a Ph.D. (or
equivalent) in Chemical Engineering with research
or industrial experience in fluidized reactor engi-
neering. The successful applicant will be required
to teach graduate and undergraduate courses in
chemical engineering, including undergraduate core
courses; and to conduct research and supervise
graduate students in fluidized reactor engineering.
The appointment is effective July 1, 1978. Closing
date for applications is April 15, 1978. Applications
including curriculum vitae and names of three
referees may be sent to:
G. F. Chess, P. Eng.
Acting Dean
Faculty of Engineering Science
The University of Western Ontario
London, Ontario, Canada.
N6A 5B9


arlcurriculum .



University of Wisconsin-Milwaukee
Milwaukee, Wisconsin 53201

ONE OF THE QUESTIONS that continually
perplexes ChE departments (as indeed all
academic units) is how relevant are their course
offerings. The Materials Engineering Science
Division of A.I.Ch.E. recently undertook a survey
that questioned their membership with respect
to materials courses offered in ChE departments.
The questionnaire (which also covered aspects
of continuing education) is shown in Table 1.
Responses were obtained mainly from ChE's
employed in industry (75% of all responses)
and included Du Pont, Amoco, Monsanto, Dow,
Shell, Owens-Corning, Allied, Continental Can,
Dow Corning, Ray-O-Vac, Pitney-Bowes, Baxter
Laboratories, Union Carbide and Hooker.
The interests (question 2) of the respondents
was most heavily directed toward polymers
(55%) and then toward metals (30%) and
ceramics (14%). Some scattered interest was
also indicated for inks, finishes, elastomers, com-
posites, wood and cement.

T HE RESPONDENTS developed the following
ranking as to what the most important ma-
terials courses in the undergraduate ChE course
should be:
* Basic Materials Science (1.93)
* Materials Science (2.74)
* Polymer Engineering (3.80)
* Polymer Science (4.15)
* Physical Metallurgy (4.60)
* Process Metallurgy (5.20)
* Ceramics Engineering (6.20)
* Ceramics Science (6.25)
Figures in the parenthesis indicate the average of
rank values given by respondents for each

MESD Education Questionnaire
1. Area where employed a) Industry b) Government
(circle one) c) Higher Education
2. Materials areas of interest a) Metals b) Polymers
c) Ceramics d) Other
3. What materials courses are most important in the
undergraduate chemical engineering curriculum?
(rank 1 to 8 with 1 most important)
a) Basic Materials Science
b) Materials Science
c) Process Metallurgy
d) Physical Metallurgy
e) Polymer Science
f) Polymer Engineering
g) Ceramics Science
h) Ceramics Engineering
4. What other undergraduate level materials courses
would be most appropriate for chemical engineers.
5. What graduate level materials courses would be most
appropriate for chemical engineers?
6. What short course continuing education materials
courses would you like to see offered?
7. Please nominate potential instructors for these courses.
8. Would you like to have a materials oriented presenta-
tion(s) for your local section? yes no
__9. If yes, what topics would appeal to you?
10. Please feel free to offer other comments, suggestions,
etc. relating to Materials Education( use additional
sheets if needed).

category. Additionally, there were a number of
other types of undergraduate materials courses
(question 4 of Table 1) that were indicated as
being most appropriate for ChE students. These
included relation of materials and design, plastics
and elastomers, corrosion, joining of dissimilar
materials, fiber science, composites, materials
selection, production processes, electrochemistry,
worldwide materials resources, fracture analysis,


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.

materials testing, environmental and stress be-
havior, economics of materials, surface chemistry
and inter-relationship of energy, materials and
ecology. The most frequently reported of these
listed courses included corrosion, composites and
materials selection.
Appropriate graduate level courses that were
cited included composites, thermosets, mechanical
behavior, (vibration, fatigue, fracture, etc.), cor-
rosion, materials selection and design, adhesion,
fiber science, plastics processing, ceramics, cellular
materials, materials economics, polymer alloying
and basic metallurgy. The most frequently named
were composites, corrosion, plastics processing,
ceramics, mechanical behavior and material selec-
From both the undergraduate and graduate
course suggestions it becomes apparent that a
real need is felt for formal course work on corro-
sion, composites, plastics processing and materials
Recommended continuing education short
courses (question 6) included thermosets, corro-
sion, materials selection, instrumentation ma-
terials for chemical processes, high temperature
materials, advances in engineering materials, ma-

trials economics, electrochemical techniques,
plastics process engineering, fracture analysis,
coatings, polymer alloying and compounding and
polymer engineering.
In a similar vein suggested presented for local
sections included applications of new materials,
plastics for corrosion and erosion service, com-
posites, chlorine stress corrosion, polymer engi-
neering, epoxy resins for environmental protec-
tive coatings, and materials economics. Presenta-
tions named frequently included composites, corro-
sion, polymer engineering and materials eco-
Interestingly, some sixty per cent of the re-
spondents favored a materials oriented presenta-
tion for their local section (twelve per cent nega-
tive with the rest undecided).
One of the most enlightening sections of the
questionnaire was item 10 for comments, sugges-
tions, etc. A few extracted comments are given
"There is very little that A.I.Ch.E. seems
to do for the engineer that works for a small
"Writing of specifications for materials
purchases can be very critical. Help along this
line could be helpful to all engineers."
"Students should have some laboratory
corrosion testing experience."
"A systematic format for applying per-
formance criteria to assist materials selection
for non-structural process materials in critical
usage needs to be developed."
"Wood should not be neglected as an engi-
neering material."
"Materials courses appear to be too theo-
retical-more emphasis needed on applica-

* Practicing chemical engineers whose primary activity
is in the materials field regard Materials Science and
Polymer Engineering as the most important materials
courses for the undergraduate curriculum.
* Courses that respondents felt should be added to the
undergraduate curriculum would deal with the areas of
composites, corrosion and materials selection.
* Graduate courses in the areas of (2) as well as plastics
processing were also felt to be needed.
* A majority of respondents desired some materials
oriented presentations for their local section programs.
* Topics most frequently named to be of interest for local
section presentation included composites, polymer engi-
neering, corrosion and materials economics.
* A tabulation of potential continuing education short
courses was developed from the study. O-


BOOK REVIEW: Statistical Methods
Continued from page 37.
follows the outline of this text is taught at Iowa
State University for advanced undergraduate and
graduate level engineers. This sequence has a
laboratory associated with it in which the
students can apply the statistical methods to prob-
lems in their particular area of engineering. For
these problems, the students have access to a
computer to perform most of the routine compu-
tations. This is particularly true for regression
analysis and analysis of variance computations.
This, I believe, is another shortcoming of this
book; namely, very little mention is mode of the
availability of a computer to do much of the
calculations. Most of the methods of regression
analysis and analysis of variance are based on
hand or desk calculator computations. These
methods should be discussed with the use of a
computer in mind.
Finally, as an introductory book for engineers, the im-
portant topics of (i) goodness of fit tests, (ii) propagation
of errors and (iii) nonparametric methods are ignored or
only treated briefly. The latter two topics are not covered
while the chi-square goodness of fit test is used to test
the parameter p of a binomial distribution and then it is
mentioned that it can also be used for continuous distribu-
The authors do an excellent job of using examples to
illustrate the statistical methods discussed. Most of the
examples are related to chemical engineering. Also, each
chapter contains many problems which should be interest-
ing to the students (answers for selected problems are
In summary, the authors point out in the In-
troduction that "There are no statistical pro-
cedures which are applicable only to specific
fields of study. Instead, there are general sta-
tistical procedures which are applicable to any
branch of knowledge in which observations are
made." This book introduces a subset of these
procedures which are illustrated by examples
taken from engineering. As such, there are several
texts in this area which anyone considering a
book for adoption might look at along with this
book. El
Edited by R. J. Ceresa
John Wiley and Sons, 1976.
Reviewed by R. E. Cohen,
Massachusetts Institute of Technology
The title of this book is misleading. Only about
75 of the more than 365 pages deal directly with

block and graft copolymerization (polymer syn-
thesis). The remainder focuses on interesting and
rather informative material regarding properties
and engineering applications of certain block and
graft copolymers. This particular volume
(evidently the second of a series, although neither
the contents of volume 1 nor of forthcoming
volumes could be found) treats only two varieties
of copolymers . . . Chapters 1 and 2 on Block
Copolymer Polyol Surfactants ... Chapters 3 and
4 on Block and Graft Copolymers of Poly (vinyl
The two chapters on polyol surfactants (by
L.G. Lundsted and I.R. Schmolka) suffer from
the shopping-list approach for presenting proper-
ties and potential applications. There is little at-
tempt to provide any basic connection between
copolymer synthesis, resulting molecular struc-
ture, and the properties observed. The excessive
use of (bold face, capitalized) trade name
acronyms tends to detract the reader. However,
it should be noted that the authors and editor have
organized the physical properties data into easily
used tables and data-grids.
Chapter 3 on PVC blocks and grafts (by R. J.
Ceresa) is without question the most satisfying
in terms of technical content and adherence to
the title of the book. In brief fashion (30 pages)
the many possible synthesis techniques are re-
viewed and the resulting copolymer structures
described. Chapter 4 (by D. Hardt) on proper-
ties and applications of PVC copolymers follows
logically from the synthesis material presented
earlier. There is better balance between structure-
property relations and applications in this chapter
than in the first two chapters of the book.
In addition to his work in Chapter 3, the editor
is to be congratulated for a fine organizational
job with the overall volume. Tables and figures
are conveniently located in the text, the table
of contents and appendices are very complete and
detailed, and there is a novel "addendum" section
put together just prior to publication in order to
bring the reader up to date in a fast-moving area
of polymer technology. In summary, this is a well
organized book which should be of great value to
readers with very specific interests in the two
classes of polymers described; however, the level
of general interest among polymer scientists and
technologists will no doubt be minimal. D


Continued from page 13.

of importance in petroleum refining has been an
active area for Ron Danner and Tom Daubert.
Three editions of the American Petroleum Insti-
tute's Technical Data Book-Petroleum Refining
have been produced in the department since the
project was originated by Merrill Fenske and
Walter Braun in the early '60's. Further activity
includes the very difficult problem of identifying
readily measurable parameters for the characteri-
zation of petroleum fractions which are very
complex and poorly defined mixtures. Ron and
Tom have also been working on the development
of generalized corresponding states methods for
polar fluids and the measurement and correlation
of gas mixture adsorption on solid surfaces.

* Dynamics
Bob Kabel, after developing a thorough under-
standing of the kinetics of certain acid ion ex-
change catalyzed reactions, has been using these
reactions as a vehicle for understanding reactor
dynamics. In particular, he has experimentally
demonstrated the potential of forced periodic re-
actor operation to improve catalyst selectivity. Al
Engel has experimentally demonstrated the use
of forced cyclical operation of stirred tank reactors

Lettr "letters i

Oak Ridge Associated Universities will present four
energy-related institutes for college faculty this summer.
The institutes sponsored by the U. S. Department of
Energy, DOE, are designed for faculty who teach or plan
to teach energy-related courses. A limited number of
stipends are available. The deadline for applying is March
31, 1978. The institutes to be presented are:
June 19-July 7, 1978
July 10-21, 1978
July 10-28, 1978
July 31-August 11, 1978
Full information about the summer institutes and
application material may be obtained from the Profes-
sional Training Programs, Manpower Education, Research
and Training Division, Oak Ridge Associated Universities,
P .0. Box 117, Oak Ridge, Tennessee 37830.
Roger J. Cloutier

to maintain transients in a neighborhood of an un-
stable steady state. Al's recent simulation work
has shown that cyclical operation of a distillation
column may produce energy savings approaching
fifty percent of steady state operation for the same
John Tarbell has been working on non-linear
stability theory for reaction and reaction-diffusion
processes. Liapunov's direct method provides the
theoretical framework and irreversible thermo-
dynamics provides an untapped source of Liapu-
nov functions. Bifurcation phenomena, es-
pecially bifurcation to periodic and chaotic orbits
are also being investigated.
In conclusion, we must emphasize that the
success of our research programs has been and
will continue to be a direct consequence of the
dedication and perseverance of our graduate
students. Ol

BOOK REVIEW: Cellulose
Continued from page 23.

posium participants were aware of the short-
comings of the enzyme studies. The results pre-
sented in these papers lack the raison d'etre of
the H202/Fe(II) studies, and it is not evident
that they can be justified on the basis of Good
Science. The chapter about lignin-degrading re-
actions is interesting, but very speculative. The
conclusions that more data are needed and that
they should relate to whole organisms rather than
isolated organisms, are certainly valid. The
summary statement about cellulase enzymes at the
beginning of this section is well done, but it is
"The Process" is the conversion of cellulose
and lignocellulosic materials into glucose (or
some other, equally useful product). The excellent
chapter about physical and chemical features of
cellulose and lignocellulosic materials would be
better placed in the section about the substrate.
This chapter is informative, and with its emphasis
on susceptibility for the process, certainly not
out of place where it is. The chapter that follows,
also intended to be about the relationship between
structure and process susceptibility, is a classic
example of the ridiculous following the sublime.
To be convinced of the former, one needs only to
refer to the last figure and the claim that the
different shapes of the curves drawn therein are
significant. The chapter on pre-treatment and its


discussion are not only excellent, but they also
are concerned with an economically important
aspect of the process. The chapter about enzymic
saccharification of woody wastes is useful, but
since it deals with only the T. viride cellulase,
prospects for its ultimate commercial applicability
are limited. Individuals with experience using
enzyme kinetics will find the chapter about the
kinetics of cellulose hydrolysis harmless, but
others might not be so fortunate. Even if, as
commonly happens in studies of homogeneous
solutions of single enzymes, the assumptions
(some unlisted, none justified) used to derive
the well known equation for the reaction rate
and its integral do not cause serious problems,
the methods of data analysis (see Figures 2 and
3) used in this chapter probably will. The chapter
about the economics of the enzymic conversion of
cellulose to glucose is of pedagogical value. How-
ever, the very optimistic parameters used in the
model (for example, raw material costs are
estimated to be nil, and the recovery figure for
active catalyst to be at least 3 times what one
would expect on the basis of most experimental
findings) not only strain the imagination, but
probably invalidate even the order of magnitude
of the cost estimate.
"The Product" is . ... .? The important point
of the summary statement is that a diversity of
products will strengthen the market for cellulose.
The chapter about potentially useful products
develops this idea in considerable detail. The
products discussed include fuels, food and organic
chemicals. There is also an interwoven discussion
of product and process feasibility which includes
the questionable suggestion that the old Fischer-
Tropsch synthesis might be commercially useful
now or in the near future. The excellent chapter
on fuel gas production includes a survey of solid
waste disposal technology followed by a descrip-
tion of a bioconversion process for the production
of methane from waste cellulose. The discussion
includes results obtained from a computer model
and process optimization. These results indicate
a 3-fold energy return in the form of $2/106 Btu
methane in a $22 million plant capable of
processing 1000 tons/day of solid waste. As in
some of the previous cost estimates discussed at
the symposium, these figures seem optimistic, in
part because they do not include adequate research
and development costs that would be necessary to
iron the kinks out of a new process. The other
chapters in this section are also highly recom-
mended. The chapter about the acid-catalyzed

hydrolysis of waste illustrates that the conversion
of pre-heated material to glucose can be modeled
as an isothermal plug flow reactor with a resi-
dence time in the range of 20 to 30 seconds. This
chapter, as well as the interesting ones by Miller
and Finn discuss the bioconversion of cellulose-
derived glucose into ethanol.
As mentioned above, two of the shortcomings
of the cost estimates appearing in this volume are
that they tend to be based on optimistic
parameters, and that they seldom reflect sufficient
R & D costs to achieve a smooth-running industrial
process. Another shortcoming of these estimates
is that they do not take into account the interactive
economic forces that make these models so highly
nonlinear. For example, ethylene and ethanol are
interconvertable, but at present ethanol is made
from ethylene because the cost of ethylene plus
processing to ethanol is less than the price of
ethanol available by other means. But what if
ethanol could be made from cellulose at a price
that was sufficiently below the current price of
ethylene? The price of cellulose would probably
increase, and that would cause the price of ethanol
to go up. Furthermore, artificially-set oil prices
would probably be decreased, and that would
cause the price of ethylene to go down. Both
factors would tend to favor the production of
ethanol from ethylene even when conditions were
reached which in present cost analyses would
seem to favor the production of ethylene from
ethanol. Thus, it would seem that the models used
in some of the cost projections are incomplete.
But perhaps the models are nevertheless as
good as they need to be. Although the editor is
to be complimented for the speedy assimilation
of the manuscripts, even a year renders many of
the relevant cost analysis parameters hopelessly
obsolete. One wonders, for example, if Miller's
projected doubling of ethylene costs by 1975
occurred, and if so, what has happened to the
cost of this important chemical now in 1978, three
years later. Furthermore, there is considerable
variation in the numerical values of parameters
that don't depend on time. For example, if in-
dividuals at the same symposium disagree by
20% about the cellulose content of "most wood,"
refining the mathematical model might not im-
prove the modeling result.
It seems to me that most of the cost predictions in this
volume should be treated as a very rough, first approxima-
tion. Since large financial investments usually require
more reliable forecasts, it is doubtful that much action will
(or should) be taken on the basis of these analyses, at
least in the near future. M


Give Them A

Strong Preparation

Tomorrow's chemical engineers must acquire
a strong foundation of knowledge. These
new Wiley texts help you give it to them...

Charles G. Hill, Jr., University of Wisconsin
Here's a balanced discussion of chemical kinetics
and chemical reactor design at an introductory
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reactions in liquid solution. The illustrative exam-
ples and problems throughout the text emphasize
the analysis of representative data from the kinetics
literature and the use of such data in preliminary
reactor design calculations.
(0 471 39609-5) approx. 608 pp.
1977 $21.95 (tent.)
Richard M. Felder, & Ronald W. Rousseau,
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A comprehensive and up-to-date introduction to
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such related fields as environmental science,
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(0 471 74330-5) approx. 576 pp.
1978 $19.95 (tent.)
Stanley I. Sandier, University of Delaware
This modern thermodynamics book-emphasiz-
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- is an ideal text for giving undergraduate stu-
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(0 471 01774-4) approx. 592 pp.
1977 $21.00
To be considered for complimentary
examination copies, write to Art Beck, Dept.
A8150-12. Please include course name, en-
rollment, and title of present text.

Vol. 1: Fluid Mechanics, Byron R. Bird, University
of Wisconsin, Robert C. Armstrong, Massachu-
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Instituttet for Kemiteknik
Vol 2: Kinetic Theory, Byron R. Bird, Ole Has-
sager, Robert C. Armstrong, & Charles F. Curtiss,
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Vol. 1 describes the experimental and theoretical
fluid mechanical methods of characterizing and
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Volume 2 presents kinetic theory methods for
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thorough discussion of the classical Rouse-Zimm
molecular theories of dilute macromolecular so-
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network theory of polymer melts.
Vol. 1: (0 471 07375-X) 576 pp.
1977 $29.95
Vol. 2: (0471 01596-2) 304 pp.
1977 $26.95
James R. Welty, Charles E. Wicks, & Robert E.
Wilson, all of Oregon State University
Revises and updates with current technology the
unified treatment of transport processes. More de-
tails have been added, and areas where students
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(0 471 93354-6) 789 pp.
1976 $23.95
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Prices subject to change without notice. A81 50-1 '


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