<%BANNER%>
HIDE
 Front Cover
 Table of Contents
 Carol McConica, of Colorado State...
 Letter to the editor
 Colorado School of Mines
 No respect!
 Process control education in the...
 The unstructured student-designed...
 From molecular theory to thermodynamic...
 Stochastic modeling of chemical...
 Book reviews
 Chemical compatibility of polymeric...
 Book reviews
 The use of Lotus 1-2-3 macros in...
 Incorporation of process control...
 Temperature effects in heterogeneous...
 Back Cover


UFCHE



Chemical engineering education
http://cee.che.ufl.edu/ ( Journal Site )
ALL VOLUMES CITATION THUMBNAILS DOWNLOADS PAGE IMAGE ZOOMABLE
Full Citation
STANDARD VIEW MARC VIEW
Permanent Link: http://ufdc.ufl.edu/AA00000383/00106
 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: Spring 1990
Frequency: quarterly[1962-]
annual[ former 1960-1961]
quarterly
regular
 Subjects
Subjects / Keywords: Chemical engineering -- Study and teaching -- Periodicals   ( lcsh )
Genre: periodical   ( marcgt )
serial   ( sobekcm )
 Notes
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: AA00000383:00106

Downloads
Table of Contents
    Front Cover
        Front Cover 1
        Front Cover 2
    Table of Contents
        Page 61
    Carol McConica, of Colorado State University
        Page 62
        Page 63
        Page 64
    Letter to the editor
        Page 65
    Colorado School of Mines
        Page 66
        Page 67
        Page 68
        Page 69
        Page 70
    No respect!
        Page 71
    Process control education in the year 2000: A round table discussion
        Page 72
        Page 73
        Page 74
        Page 75
        Page 76
        Page 77
    The unstructured student-designed research type of laboratory experiment
        Page 78
        Page 79
    From molecular theory to thermodynamic models: Part 2. Mixtures
        Page 80
        Page 81
        Page 82
        Page 83
        Page 84
        Page 85
        Page 86
        Page 87
    Stochastic modeling of chemical process systems: Part 2. The master equation
        Page 88
        Page 89
        Page 90
        Page 91
        Page 92
    Book reviews
        Page 93
    Chemical compatibility of polymeric materials: Some simple guidelines
        Page 94
        Page 95
        Page 96
        Page 97
        Page 98
    Book reviews
        Page 99
    The use of Lotus 1-2-3 macros in engineering calculations
        Page 100
        Page 101
        Page 102
        Page 103
        Page 104
        Page 105
    Incorporation of process control computers in the undergraduate laboratory: A case study
        Page 106
        Page 107
        Page 108
        Page 109
        Page 110
        Page 111
    Temperature effects in heterogeneous catalysis
        Page 112
        Page 113
        Page 114
        Page 115
        Page 116
    Back Cover
        Back Cover 1
        Back Cover 2
Full Text








m 0I education






















NEW FROM WILEY
FOR YOUR UNDERGRADUATE CURRICULUM!


A Contemporary Introduction to all the
Essentials of Dynamic Behavior & Automatic
Control Processes!

PROCESS DYNAMICS & CONTROL
DALE E. SEBORG, U. of California, Santa Barbara
THOMAS F. EDGAR, U. of Texas, Austin &
DUNCAN A. MELLICHAMP, U. of California, Santa Barbara
1989 714 pp.- cloth 86389-0

Striking an appropriate balance between process instrumen-
tation and control methodology, this in-depth examination
includes the latest control strategies...from model-based,
predictive and supervisory control to six full chapters on
digital control. The book emphasizes the advantages of dy-
namic process models, and offers a definitive treatment of
such topics as empirical modeling, controller tuning, control-
loop troubleshooting, CAD techniques, feed-forward control,
and sampling and filtering. Numerous examples and exer-
cises clarify the material, and an appendix on software for
control system design is included.


WILEY


A Comprehensive Study of Chemical
Reaction Engineering...
For Both Graduates & Undergraduates!

CHEMICAL REACTOR ANALYSIS
& DESIGN, Second Edition
G. F. FROMENT, Rijks Universiteit-Gent, Belgium &
KENNETH BISCHOFF, U. of Delaware
1990 733 pp. cloth 51044-0

From basic definitions to practical applications, the Second
Edition of this comprehensive textcompletely covers applied
kinetics and reactor analysis and design. Maintaining thefirst
edition's successful basics approach to industrially-related
problems, this edition reflects contemporary progress in
modeling and the latest developments in computer capabil-
ity. Its two part organization allows readers to study the
detailed kinetics in a given pointer local region first, and then
extend the specific application to overall reactor behavior.
And, the text's insightful coverage of abstract topics and
current literature make it an up-to-date handbook or refer-
ence students can use in their careers.


For more information, please contact your local Wiley representative, or write on your school letterhead
to: Brad Wiley II, Dept. 0-0362, John Wiley & Sons, Inc, 605 Third Avenue, New York, NY 10158. Please
include your name, the course name, enrollment, and the title of the text you currently use.
John Wiley & Sons, Inc. 605 Third Avenue New York, New York '10158 0-0362 rhm/cj












EDITORIAL AND BUSINESS ADDRESS:
Chemical Engineering Education
Department of Chemical Engineering
University of Florida
Gainesville, FL 32611

EDITOR: Ray W. Fahien (904) 392-0857
ASSOCIATE EDITOR: T. J. Anderson
CONSULTING EDITOR: Mack Tyner
MANAGING EDITOR: Carole Yocum (904) 392-0861

PUBLICATIONS BOARD

*CHAIRMAN.
E. Dendy Sloan, Jr.
Colorado School of Mines

*PAST CHAIRMEN.
Gary Poehlein
Georgia Institute of Technology

Lee C. Eagleton
Pennsylvania State University

*MEMBERS.
South
Richard M. Felder
North Carolina State University

Jack R. Hopper
Lamar University

Donald R. Paul
University of Texas

James Fair
University of Texas

Central
J. S. Dranoff
Northwestern University

West
Frederick H. Shair
California Institute of Technology

Alexis T. Bell
University of California, Berkeley

Northeast
Angelo J. Perna
New Jersey Institute of Technology

Stuart W. Churchill
University of Pennsylvania

Raymond Baddour
Massachusetts Institute of Technology
Northwest
Charles Sleicher
University of Washington
Canada
Leslie W. Shemilt
McMaster University

Library Representative
Thomas W. Weber
State University of New York


Chemical Engineering Education
VOLUME XXIV NUMBER 2 SPRING 1990


EDUCATOR

2 Carol McConica, of Colorado State University,
Susan Skog

DEPARTMENT

6 Colorado School of Mines, E. Dendy Sloan, Jr.

CURRICULUM

72 Process Control Education in the Year 2000: A
Round Table Discussion, T. F. Edgar

LABORATORY

78 The Unstructured Student-Designed Research Type of
Laboratory Experiment,
A Macias-Machin, Guotai Zhang, Octave Levenspiel

106 Incorporation of Process Control Computers in the Under-
graduate Laboratory: A Case Study,
Wm. Curtis Conner, Jr.

AWARD LECTURE

80 From Molecular Theory to Thermodynamic Models:
Part 2. Mixtures, Stanley I. Sander

CLASSROOM

8 Stochastic Modeling of Chemical Process Systems:
Part 2. The Master Equation
R.O. Fox, L.T. Fan

100 The Use of Lotus 1-2-3 Macros in Engineering Calculations,
Edward M. Rosen

112 Temperature Effects in Heterogeneous Catalysis,
Charles D. Schaper, C.O. Bennett

MATERIALS

94 Chemical Compatibility of Polymeric Materials: Some
Simple Guidelines,
Kenneth A. Solen, Marvin C. Kuchar

RANDOM THOUGHTS

71 No Respect, Richard M. Felder

65 Letter to the Editor
93,99 Book Reviews


CHEMICAL ENGINEERING EDUCATION (ISSN 0009-2479) is published quarterly by the Chemical Engi-
neering Division, American Society for Engineering Education and is edited at the University of Florida. Cor-
respondence regarding editorial matter, circulation, and changes of address should be sent to CEE, Chemical
Engineering Department. University of Florida, Gainesville, FL 32611. Advertising material may be sent di-
rectly to E.O. Painter Printing Co., PO Box 877, DeLeon Springs, FL 32130. Copyright 1990 by the
Chemical Engineering Division, American Society for Engineering Education. The statements and opinions
expressed in this periodical are those of the writers and not necessarily those of the ChE Division, ASEE,
which body assumes no responsibility for them. Defective copies replaced if notified within 120 days of pub-
lication. Write for information on subscription costs and for back copy costs and availability. POSTMAS-
TER: Send address changes to CEE. Chem. Engineering Dept., University of Florida, Gainesville, FL 32611.


SPRING 1990










educator


CAROL McCONI



SUSAN SKOG
Colorado State University
Fort Collins, CO 80523

THE VIRTUES of solitude have not been los
Carol McConica. In many ways, her life has
shaped by them. In solitude, she has been fre
speculate, to experiment, to innovate-and to
traditional constraints.
At an early age, this Colorado State Unive:
chemical engineer grew to love the feeling of b
alone, of forging a kinship with nature. The daug
of Colorado geologists, Carol and her sister s
many summers living out of a tent in rural sett
throughout the West, isolated from the constr;
and expectations of civilization.
"We had no TV, no media, no Seventeen maga:
We had no running water, no electricity. We had r
ing. We had a natural environment for a playgro
We grew up being in touch with nature, and my
ents couldn't have cared less about societal ro
McConica remembers.
"That was wonderful. I think what happened
that I was molded by nature rather than by man.
become very creative, very independent and
lient."
Today, at 37, McConica has replaced the tei
the wilderness with a research lab, but the isok
from traditional limitations still allows her to se
for knowledge in unconventional areas.
Continuing to relish creativity, McConica is or
only a handful of chemical engineers on the cuti
edge of integrated circuit processing. After secu
funding for the sophisticated, ultra-clean equipr
and facilities necessary for her research, McCc
built one of the nation's pioneering academic progi
in the deposition of tungsten as the conducting ir
connect on silicon computer chips. She believes
tungsten (which, ironically, was mined by her gr
father in the Colorado mountains) may be the ke
denser, faster, more powerful microchips.

0 Copyright ChE Division ASEE 1990


of Colorado State University


CHEMICAL ENGINEERING EDUCATION









"In a lot of ways, I am leading my own solo ascent.
It's like breaking a trail in a howling snowstorm, year
after year. I am drawn to that, but it is overwhelming
at times.
"You are out there breaking a new trail by your-
self, raising money by yourself, being absolutely and
totally isolated. On the other hand, without the con-
straints of a bureaucracy, I have a freedom of motion
that no corporation can offer."
That freedom of motion allows McConica to travel
between the academic world and the corporate envi-
ronment, which she first entered in 1979 as a Hewlett-
Packard Company engineer. A female manager with
HP lured McConica to the computer company just as
she was completing her graduate program at Stan-
ford. McConica was the first American woman to re-
ceive a doctorate in chemical engineering from Stan-
ford.
The integrated circuits industry, McConica soon
discovered, was a good match for her curiosity and
temperament. "I was attracted to it because it is such
a high-paced industry, and I am a real driver-driver.
I like to have an idea, test it out today, and see if it
works tomorrow.
"In the oil industry it may take five years to design
and test an experiment. But in the integrated circuits
industry, processes last only one or two minutes, so
you quickly get a lot of information about your basic
ideas."
While it is rewarding to help advance integrated
circuit technology in the United States, Carol says
her chief goal is to help individual companies boost
their profits. "I love nothing more than to go into a
company and show them how my knowledge can help
them. As long as I think that my contributions are
going to help their bottom line, I feel victorious."
About a year and a half ago, she developed a
theory that explained why companies couldn't get ma-
terial into the holes of the chips the way they desired.
"I developed a rough-cut model that utilizes basic
chemical engineering principles. It showed the right
trends, so the industry could get in the right mode of
operation. It also allowed them to take a major leap
forward in yield."
After demonstrating McConica's ideas, several
companies incorporated them into chip production. "I
captured the essence of the problem, and today it's
helping someone's bottom line. To me, that is satisfy-
ing."
McConica's findings on integrated circuit process-
ing are sought by large manufacturers like AT&T,
small equipment suppliers, and now by a new indus-
try/government consortium (known as Sematech)


. Carol is fulfilling a dream she had when she
left HP for Colorado State in 1982. "I had hoped that
I would be able to have an influence on industry
even after I left. I absolutely and
totally love industry. .."


which is trying to counter the foreign semiconductor
competition. Sandia National Laboratories, which has
funded McConica's research for seven years, asked
Carol to support the Sematech effort.
Although it's still premature to gauge Sematech's
impact, one of its best achievements so far has been
to boost the recognition of equipment suppliers' im-
portance to the integrated circuits industry, McConica
points out. Many of those suppliers now ask Carol to
help them become more successful as they improve
their processes (often for the first time) with in-house
scientists. At times, the advice she offers the
suppliers about their equipment or facilities is met
with disdain.
Becoming a successful company can be painful. "I
reveal information about their equipment which they
would rather not know. They really don't want to
know that their reactor has many nonidealities. It's
like raising children. They don't enjoy discipline, but
you have to do it for their own good."
Whether promoting the integrated circuits indus-
try through companies like IBM, AT&T, or through
small start-up companies, Carol is fulfilling a dream
she had when she left HP for Colorado State in 1982.
"I had hoped that I would be able to have an influence
on industry even after I left. I absolutely and totally
love industry. . I love the pace of industry, I love
the accomplishment of objectives. I thrive on the com-
petition."
And, much like her early enjoyment of the geolog-
ical adventures with her family, Carol thrives on being
free to explore new terrain on her own. Fortunately,
her life as a researcher and a teacher allows her to try
out new research ideas away from the commercial con-
straints of manufacturing.
She explains that in academia she can push the
boundaries of current integrated circuits technology
because she isn't limited to research on equipment and
processes that lead only to production. "I am allowed
to build my own equipment, which is totally unrelated
to someone else's goals. I can try out new ideas and
make contributions that people in industry cannot
make because they are tied to production."
McConica has long known the thrill of testing new
ideas and limits. Her early interest in biology and
math was fueled by the fact that nearly every math


SPRING 1990









and science teacher she had in the ninth through
twelfth grades was a woman. The idea that a woman
could be a scientist was both acceptable and conven-
tional.
She first discovered the irresistable lure of a re-
search lab while growing up in Boulder-home of the
University of Colorado-in the unconventional 60s. At
the time, Boulder was a counterculture cocoon that
sheltered free thinkers and innovators. Wrapped in a
culture that encouraged individual self-realization,
Carol found it natural to spend much of her time in
CU labs, helping neighbors and family friends with


Carol feels that hands-on experience is invaluable, and
many of her classes focus on experiments.

their research. While in high school, she was chosen
to conduct research with CU researchers under a Na-
tional Science Foundation program. "I was able at 17
to do the kind of work that PhD students get to do.
If I hadn't had that hands-on research experience, I
never would have known how much fun it can be."
Later, as an undergraduate at the University of
Denver, Carol's love of learning was further chan-
neled by professors whose primary goal was teaching.
She now feels a strong kinship with her own students,
remembering the guidance offered by her DU profes-
sors, and says, "I felt cared for, I felt nurtured, I felt
mentored, I felt accepted, I felt challenged-every-
thing an undergraduate should feel."
Now, as a Colorado State faculty member,
McConica is determined to provide the same quality
of instruction and commitment to her students. She
feels that excellence in engineering instruction comes
from hands-on knowledge; therefore, many of her
classes focus on experiments.
For instance, if her graduate students are studying
reactor design, she will instruct them to build a


simplified version of a reactor and then study flow and
diffusion theories. Her students have built plexiglass
reactors filled with beads and water in order to study
the flow rates of dye and other substances. She be-
lieves that a hands-on, senses-oriented approach to
teaching is the only way students can really experi-
ence the joy of science-and understand its fundamen-
tals.
"I have seen many students who are capable of
deriving differential equations in the dark without a
pencil. They are brilliant. But they have no concept
of engineering. You ask them how they would design
some very simple experiments, and they have no idea.
I think we are bringing up and importing a whole gen-
eration of students who have never been in a
hardware store. As educators, we need to remember
that profits come from products, not theories."
To counter this lack of practical experience,
McConica challenges her students to do things such as
disassembling a bicycle down to its last nut and bolt
and then putting it back together again. And she is
adamant that they also learn how to ask for help if
they need it. "By the time I am through with my
graduate students, they should have good hands-on
ability and interpersonal skills. They should be able to
say, 'I don't know,' and to admit their mistakes.
Otherwise, they will be impossible to work with in
industry."
To better position her students for career success,
Carol teaches seminars on issues encountered in the
workplace. She addresses, for instance, corporate
politics and risk-taking, time management, personal-
ity styles, negotiation and listening skills, and quality
control. Most of all, she views herself as a conduit
through which well-educated and mature students can
enter the corporate world. "I see myself as trying to
train the best people for industry."
But Carol's loyalty to the corporate arena doesn't
blind her to its faults. She is a staunch critic of the
corporate world that encourages and rewards achieve-
ments at the expense of family stability. She feels that
in the drive for success and materialistic glory, some
workers and employers have forgotten that families
are the ultimate foundation upon which society (and
corporations and universities) rests.
She argues that men and women in their 20s to
40s, for instance, should focus on raising and instilling
values in their children, but they are instead pres-
sured to become corporate superstars or research
wizards. Carol points out that a solution to these
skewed values may lie in the philosophy of Confucius,
who taught that no community could respect a man
who could not lead his own family.


CHEMICAL ENGINEERING EDUCATION










"It would be good for us to study the teachings of
Confucius. Somehow our society has forgotten that a
prestigious career and a weak family are as useful to
society as a house with no foundation. In Indian
philosophy, life stages (known as ashrama) are ac-
knowledged. A man is responsible first for learning,
and then, in his later years, he must lead his family
as a "householder." As he grows older, he leads his
community and ultimately prepares for death. It is
much more sensible to make our older and wiser work-
ers the vital essence of our institutions while letting
the younger members build solid homes in their early
years."
The workplace needs to accommodate the multiple
roles of men and women and not to penalize those
workers who choose to have children and continue
their careers," says McConica, the mother of 11-year-
old Anna and 14-year-old Ian, who were born while
she worked on her degrees. "The national labs, the
top five companies, and the top education institutions
fail to recognize any existence other than one which
is experienced by a single male with no obligations
beyond the classroom. They hire based upon graduate
GPAs and years elapsed between degrees."
Because of these inequities, McConica sees many
young women choosing not to have children, fearing
that the workplace will not allow them to have both




letters


HEALTH AND SAFETY TEACHING AIDS

To the Editor:

Mr. J.P. Gupta's article in the summer 1989 issue of
Chemical Engineering Education outlines one way to teach
chemical process safety and health for those undergraduate
engineering students who elect this course. The Center for
Chemical Process Safety of the American Institute of Chem-
ical Engineers has chosen a different means teaching
health and safety to virtually all students within the frame-
work of required, traditional engineering courses. Teach-
ing health and safety concepts in several courses is an im-
portant step toward satisfying "minimum" ABET Criteria.
The teaching material, available for the 1990-91 aca-
demic year, consists of 90 problems which illustrate safety,
health, and loss prevention concepts, such as vapor releases,
explosions, and toxic exposure, and which supplement the
teaching of traditional engineering courses, including
thermodynamics, heat transfer, kinetics, process design.
They require mathematical solutions using engineering
principles as well as consideration of safety, health, and
loss prevention safety issues.
The problems were conceived and developed by chemi-
cal engineering faculty of several universities,


children and a career. "In the corporate board rooms
of America, there are three taboo subjects: childbear-
ing, childrearing, and death-events certain to hap-
pen to most of us. It is comical to me that the very
engineers who pretend to understand boundary condi-
tions and initial conditions so well seem to be com-
pletely ignorant of the fact that tomorrow's students
and employees come from women who have agreed to
supply their wombs for the creation of those lives. In
today's society, with dual careers, there is little incen-
tive for a woman to make this sacrifice."
Corporations and society must support women and
men who choose to balance children and careers,
McConica says. She adds that practical solutions could
be found in government-mandated parental leaves (in-
cluding job security), the encouragement of part-time
employment and flexible hours, and significant tax
credits for the work accomplished by homemakers.
As exciting as corporate achievements, travel, and
consulting can be, society must judge itself through
its elderly and its children, she says. "I will consider
myself a success if my children freely understand that
they have choices in their lives and if my students
understand that the human side of engineering is just
as important as the technical side. It is the balanced,
whole person who ultimately builds a strong soci-
ety." E


government officials, and industry professionals working
under the auspices of the Undergraduate Education Com-
mittee of CCPS. To assure realism and ease of use, the mate-
rial has been reviewed by engineers in industry for ac-
curacy and applicability and has been tested and critiqued
by chemical engineering faculty of 40 colleges and univer-
sities.
To encourage widespread use of these problems, the In-
structor's Guide, with problems, student and instructor
notes, and solutions, is available free of charge to faculty
who wish to use the problems with the student's book. The
Student Problem book, good for all years of study and later
reference, will be sold through bookstores at $18. The U.S.
Environmental Protection Agency and National Institute
for Occupational Safety and Health which consider this a
high priority program are, along with CCPS sponsors, subsi-
dizing project costs.
Information about the Instructor's Guide and Student
Problems book is being mailed in February to all chemical
engineering faculty in the U.S. and Canada. Faculty mem-
bers who do not receive this information are urged to contact
the Center for Chemical Process Safety at AIChE's offices,
345 East 47th Street, New York, NY 10017, or by calling (212)
705-7319.

F. Owen Kubias
Undergraduate Education Committee
CCPS/AIChE


SPRING 1990





























Alderson Hall: Home of the Chemical Engineering and Petroleum Refining Department.


department I


COLORADO

SCHOOL OF MINES


E. DENDY SLOAN, JR.
Colorado School of Mines
Golden, CO 80401

THE CHEMICAL ENGINEERING and Petroleum
Refining Department at the Colorado School of
Mines reflects the physical and intellectual community
in which it is situated. Our campus is located in Gold-
en, a suburb of Denver, in the eastern foothills of the
Rocky Mountains. The town of Golden contains two
main institutions: the Colorado School of Mines and
the Coors Brewery. A few years ago a pipeline was
installed linking the two facilities, but the administra-
tion (overriding student protests) insisted that the
pipeline contain only steam, to be used for heating
purposes.
The prevailing westerly wind over the Rockies un-
dergoes adiabatic cooling as it rises on the western
slope, supplying ski areas such as Aspen and Vail with
0 Copyright ChE Division ASEE 1990


A hangglider's perspective of the campus, taken from a
mountain just outside Golden.


CHEMICAL ENGINEERING EDUCATION


mm


cImvF









the powder for which our state is famous. When the
wind descends on Golden it is both warm and dry,
providing a climate with more than 300 sunny days
per year. The Rocky Mountains offer a great variety
of year-round outdoor activities such as skiing, moun-
tain climbing, hiking, mountain-biking, river-rafting,
etc. all in spectacular scenery within easy reach of the
campus. Perhaps less well-known are the cultural ac-
tivities in the mountains, such as the Aspen Institute
for Humanistic Studies or the various classical and
popular music festivals held in the summer. The city
of Denver serves as a western cultural center for the
nation, offering a diversity of opportunities in the
arts, in sports, and in business.
With a population of 14,000, the town of Golden
has a relatively small, college-town atmosphere. How-
ever, Golden's proximity to several other universities
(Denver, Colorado, Metro State, and Colorado State)
and facilities such as the Solar Energy Research Insti-
tute (SERI) and the National Institute for Standards
and Technology (formerly the National Bureau of
Standards) creates an intellectual environment nor-
mally found only in a much larger metropolitan area.

AN UNUSUAL HISTORY
In 1870, after extensive debate on the relative
merits of a school of engineering versus a wagon road
for miners, the Colorado legislature decided in favor


In 1870, after extensive debate on the
relative merits of a school of engineering versus a
wagon road for miners, the Colorado legislature
decided in favor of the former.

of the former. The state built the School of Mines to
co-exist with a divinity school, called the "University
Schools at Golden." The official starting date was
listed as 1874, with the initiation of the annual state
appropriation. In 1878 the divinity school was de-
stroyed by fire, leaving only the School of Mines plant-
ed in the small town twelve miles from the center of
Denver.
The school has a long history of concern for the
quality of student-faculty interactions, beginning with
the first meeting between the student body and the
Board of Trustees in 1883. Nontraditional students
have always been commonplace in the school; the 1880
president's report to the Board of Trustees lists the
average age of the students as thirty-one, with many
of them coming from the "rough-and-ready" silver
mining communities in Colorado. Before the turn of
the century, one of the first (1890) football teams of
these miners/students (see photograph) humiliated
the fuzzy-cheeked fellows from the University of Col-
orado by a score of 103 to 0!
As the school grew, emphasis shifted from strictly
mining. Currently the Colorado School of Mines (like


Binary Choice

This photo is:

a) The CSM
state
champion
football team,
circa 1890


or -


b) the CSM
chemical
engineering
faculty,
circa 1990


SPRING 1990










the schools of mines in London or Paris) graduates
only a few mining engineers, yet many of its traditions
(e.g., the silver diploma for graduate degrees) are still
associated with the mining industry. The school cur-
rently has a student body of about 2500 (one-third of
which is composed of graduate students) with about
20% women. Entering freshmen are highly qualified,
with an average SAT combined score of 1200. An edu-
cation at CSM is highly prized, as indicated by the
fact that both the entering students' SAT score and
the undergraduate tuition are among the highest for
any state-assisted school in the nation.
The Colorado School of Mines has developed a
unique reputation as a world-class institution for edu-
cation and research in the mineral, energy, and mate-
rial fields. As a special-purpose university for science
and engineering, today's school offers degree pro-
grams in twelve technical disciplines which are related
to its mission. For one hundred and fifteen years the
school has been committed to providing the education
needed by future business and research leaders in the
industrial areas it serves.

THE DEPARTMENT

The 1912 catalog lists a degree in chemical en-
gineering which grew out of the applied chemistry de-
partment, but the degree was abandoned in 1926 be-
cause of financial considerations. Then, in 1946 a pe-
troleum refining degree was offered as an option stem-
ming from the petroleum department. It came to be
called the Chemical Engineering and Petroleum Re-
fining degree, in direct contrast to most other chemi-
cal engineering departments which originated in
chemistry departments. James 0. Ball was the first
department head-a post which he held for fourteen
years until James O. Gary joined the school as head
of the department in 1960. With Dr. Gary's promotion
to Dean of Faculty in 1972, Phillip F. Dickson became
head and remained until an untimely illness forced him
to step down. Since 1984, Arthur J. Kidnay has ably
led the department.
The department is large enough to provide the di-
versity in research and teaching which is necessary
for a sound educational experience, but it is not so
large that personal contact between students and fac-
ulty is lost. We have consciously determined to keep
the ratio of graduate students-to-faculty at about five
to one, with about one-fourth of those enrolled study-
ing for their PhD degree. Our undergraduate program
is one of the largest in the country and ranks about
twelfth in the number of bachelor degrees granted.
The large size of our department makes it possible
for students to construct a program best suited to


TABLE 1
Faculty Research Interests
R.M. Baldwin DSc, Colorado School of Mines
Fuel Science Coal Liquefaction
A.L. Bunge PhD, University of California, Berkeley
Membrane Transport and Separations Mass Transfer in Porous
Media Ion Exchange and Adsorption Chromatography
J.H. Gary PhD, University of Florida
Petroleum Refinery Processing Heavy Oil Processing Thermal
Cracking Visbreaking Solvent Extraction
J.O. Golden PhD, Iowa State University
Phase Change Phenomena Solvent Extraction Processing of
Polymers Fluid Mechanics
M.S. Graboski PhD, Pennsylvania State (Research Faculty)
Fuels Development Emissions Alternate Fuels (Coal, Biomass,
Heavy Crude)
A.J. Kidnay DSc, Colorado School of Mines
Thermodynamic Properties of Gases and Liquids Vapor-Liquid
Equilibria Cryogenic Engineering
R.L. Miller PhD, Colorado School of Mines
Liquefaction Coprocessing of Coal and Heavy Oil Particulate Re-
moval Multiphase Fluid Mechanics Educational Methods
T.B. Reed PhD, University of Minnesota (Research Faculty)
Biomass Conversion by Combustion and Gasification Methanol
Production from Wood and Municpal Waste Diesel Fuels from
Cooking Oils Alternative Fuels
M.S. Selim PhD, Iowa State University
Heat and Mass Transfer at Moving Boundaries Sedimentation and
Diffusion of Colloidal Suspensions Heat Effects in Gas Absorption
with Chemical Reaction Entrance Region Row and Heat Transfer *
Surface Phenomena
E.D. Sloan PhD, Clemson University
Natural Gas Hydrates Thermodynamic and Transport Properties of
Fluids Adsorption Educational Methods
V.F. Yesavage PhD, University of Michigan
Thermodynamics of Polar-Associating Fluids Properties of Coal
Derived Liquids Equations-of-State for Highly Nonideal Systems *
Flow Calorimetry Surface Phenomena Treatment of Mixed
Wastes Photochemical Wastewater Treatment

their individual needs. Conversely, the small size of
our campus enables a new student to quickly become
familiar with the campus and the valuable offerings in
other departments. Our department has eight full-
time faculty members, all actively engaged in teaching
and research, and two research faculty. The research
interests of the faculty are listed in Table 1.
The challenges facing the chemical engineering
community have changed considerably. Easily
exploited resources and reserves of the past are now
largely gone, and technologies appropriate thirty
years ago are no longer economically feasible or en-
vironmentally acceptable. A committee report, "Fron-
tiers in Chemical Engineering: Research Needs and
Opportunities," sponsored by the National Research
Council, identified eight high-priority areas of national
need in chemical engineering. At CSM we have active
research in five of those eight areas: (1) liquid fuels
(shale, coal, biomass) for the future; (2) responsible
management of hazardous substances; (3) surface and
interfacial engineering; (4) advanced computational
methods and process control; (5) in-situ processing of
resources.


CHEMICAL ENGINEERING EDUCATION










In addition, we continue to maintain active pro-
grams in all the traditional areas of chemical engineer-
ing, such as applied thermodynamics, kinetics,
catalysis, and heat and mass transfer. Interdiscipli-
nary research is taking place in fields as diverse as
materials science, hazardous waste treatment, and
transport across human skin. Table 2 lists some of the
research projects in our department.
Most graduate research is carried out in the de-
partment's modern and well-equipped laboratories
which occupy one-half of the third and fourth floors of


TABLE 2
Typical Major Research Areas
Center for High Altitude Fuels and Engine Research The
department is establishing a new research laboratory, dedicated to re-
search on fuels and emissions from internal combustion engines. This
lab will contain both stationary gasoline and diesel research engines
with sophisticated real-time analytical monitoring capabilities for both
engine performance and emissions data. The primary focus of the labo-
ratory will be research on the effect of fuels on emissions for conventional
and novel fuels. The laboratory is scheduled for dedication during the
spring of 1990 and will be the only facility of its type in the US that is ca-
pable of measuring and correlating fuels properties with engine perfor-
mance and emissions at high altitude.
Applied Thermodynamics CSM is known internationally for re-
search in this area. Thermophysical properties research is included
along with phase equilibria of nonideal systems, heat of mixing, and flow
calorimetry. Recent work has incorporated supercritical fluid technol-
ogy, equation-of-state development, advanced computational thermody-
namics, and a program to evaluate the impact of thermodynamic property
research on the natural gas industry.
Natural Gas Hydrates Very large deposits of low-molecular weight
hydrocarbons are present around the world in solid hydrated form,. Our
studies in hydrate thermodynamics, physical properties, and processing
are aimed at both recovery and prevention in various portions of the gas
production and processing industry. Our laboratory is the largest in the
nation in this area and includes an interdisciplinary effort with several
other departments, namely chemistry and geochemistry, geology,
physics, and petroleum engineering.
In-Place Remediation of Contaminated Soils Of the options for
cleaning contaminated soils, methods which do not require soil excava-
tion prior to treatment offer obvious advantages. The objective of this pro-
gram is to develop a comprehensive research effort studying in-place
methods for remediation in zones above the water table. Present projects
include soil flushing with chemically enhanced aqueous solutions, en-
hanced evaporation by forced aeration, and bioremediation. Centered in
chemical engineering, this multidisciplinary program involves faculty
from chemistry and geochemistry, geological engineering, civil engi-
neering, environmental science, and petroleum engineering.
Coal Liquefaction A number of fundamental and applied studies in
coal liquefaction science and engineering are in progress, aimed at coal
reactivity correlation and low-severity liquefaction processes. The re-
activity research investigates the relationship between coal chemical
structure and the rate and extent of conversion to liquids by direct hy-
droliquefaction. The low-severity program incorporates reactivity en-
hancement by mild chemical pretreatment, catalysis by basic nitrogen
compounds, and low severity coprocessing studies.
Further Research Areas Other innovative research is being carried
out in such areas as:
Biomass Conversion Catalytic Hydroprocessing of Lignin De-
activation of Zeolite-Based Isomerization Catalysis Development of
Novel HDO and Naphtha Isomerization Catalysts Emulsion Liquid
Membrane Studies Extraction of Brewery Products with Supercriti-
cal Fluids Fuels Testing Center for Pollution Control Mineral
Extraction with Supercritical Water Moving Boundary Problems *
Pedagogical Methods of Integration of Humanities in Engineering *
Sedimentation Theory Suspension Rheology Solute Transport
Across Human Skin Surface and Interfacial Flows Photochemi-
cal Wastewater Treatment


Alderson Hall. In 1991 a new wing of Alderson Hall
will be constructed which will effectively double the
available research space. Graduate students are nor-
mally assigned office space separate from research
laboratories. Some graduate research is done in con-
junction with local industrial and government re-
search laboratories, such as the National Institute for
Standards and Technology, the Solar Energy Re-
search Institute, Coors, and IBM. Our goal is to main-
tain strength in areas critical to existing industries
while creating research programs in areas vital to new
and emerging technologies.

FACULTY AS PEOPLE

The research interests listed in Table 2 invigorate
our faculty's activities. However, members of the fac-
ulty are vital people in other ways as well. They are
professors in the fullest meaning of the word-their
intellectual activity and availability extends beyond
the time and space boundaries of the classroom/labora-
tory.
On the wall of Bob Baldwin's office there is a cer-
tificate of musical accomplishment from Iowa State-
implying that there was a difficult career choice dur-
ing his student days. Bob teaches in the school's Hon-
ors Humanities program and has won several teaching
excellence awards. Last year he served as Associate
Dean for Undergraduate Studies. When he can man-
age time away from the Mines campus and the Golden
area, Bob is an inveterate globetrotter.
The fact that Annette Bunge is the best athlete in
the department does damage to our "Rambo" image.
Annette coaches the school's mens/women Alpine and
Nordic ski teams and participates in all training
events with the team. Last year when the team ran a
two-mile training run, she had to wait over 1.5 mi-
nutes for the second-place finisher. She is an avid out-
doorswoman and participates in rock climbing, river-
rafting, hiking, crosscountry racing, and diving. She
is the recipient of the Dow Outstanding Young Fac-
ulty Award from the American Society for Engineer-
ing Education (ASEE).
Jim Gary is perhaps our best known faculty
member because of his long academic tenure and his
classic book in the field of petroleum refining. He came
to the school in 1960 and served as Department Head
and as Vice President for Academic Affairs and Dean
of Faculty (each for about a decade) before resuming
an active career in teaching classes and industrial
short courses in petroleum processing throughout the
world. As the department's only septuagenarian
(2.9%) and one of its most active computer users,
he frequently teaches his junior colleagues the newest


SPRING 1990









in computer hard/software. Jim has received the
George R. Brown Medal of Achievement from the
school and is a Fellow of both AIChE and AAAS.
John Golden returns to the department after hav-
ing been led astray into academic administration for
the past fifteen years. He has served the School of
Mines as Director of Research Development, Dean of
Graduate Studies and Research, and Vice President
for Academic Affairs and Dean of Faculty. For the
1990-91 academic year he will take a well-deserved
administrative leave to relearn some chemical en-
gineering that he forgot during his years of academic
administrative combat service.
Mike Graboski returns to the school as research
professor after managing his own business in biomass
gasification for three years. Mike continues those per-
sonal interests he began as a graduate student at Penn


An Ore Cart race on Engineer's Day (the traditional
"Spring craziness day" on campus).

state, where he was president of Trout Unlimited.
His current hobbies include cross-country skiing, hik-
ing, hunting, and fishing.
Art Kidnay is the department's fearless leader,
ranking weightlifter, and intrepid long-distance run-
ner. His colleagues appreciate his magnanimous at-
titude as well as his limitless capacity for new in-
terests-such as biofeedback tapes to improve run-
ning. Art is a Fellow of the AIChE and has won the
school's outstanding teaching award.
Ron Miller is the youngest, and by far the most
irreverent, faculty member. Students closely identify
with Ron-some claiming him as a good friend even
after he has taught them! Along with Ron's technical
research, he has recently begun pedagogical research
to integrate humanities into the initial chemical en-
gineering course. Ron has won school-wide awards for
teaching excellence at the University of Wyoming and
at the School of Mines.


Tom Reed is a research professor who came to us
in 1986 after fifteen years at MIT and nine years at
the Solar Energy Research Institute. His initial tech-
nical interests were in crystallography and material/
energy science, but for the last seventeen years his
interests have been in alternative fuels such as
methanol and biomass. He has recently started a pri-
vate company to convert waste cooking oils to diesel
fuels.
Sami Selim, the department's mathematical
wizard, has a graduate degree in mathematics as well
as three degrees in chemical engineering. He
specializes in making difficult analytical problems dis-
solve into thin air, while exhibiting an international
flavor of kindness. Sami serves as both the depart-
ment's opera aficionado and its culinary Epicurean.
He has been presented with school-wide teaching ex-
cellence awards at three universities, including CSM.
Recently, the only trace of Dendy Sloan has been
his voice on an answering machine in his office. He
was sequestered in the school library until he emerged
with the manuscript for Clathrate Hydrates of Natu-
ral Gases, published in the winter of 1990. His hobbies
include attempts at music on the banjo and guitar.
Dendy balances a two-career family with his wife, who
is an attorney. He is the fifth departmental faculty to
be the recipient of a school-wide teaching award.
Vic Yesavage is a displaced New Yorker who
rapidly took to the great outdoors. He enjoys family-
oriented activities such as camping trips to national
parks in the west. Within the department he enjoys
the role of graduate advisor to students. In recent
years he has become a student of Eastern European
history, and he follows the recent developments in
that part of the world with great interest.
The faculty feel a collegiality for each other and
join in parties, cross-country ski trips, and campouts.
These events are filled with appropriate amounts of
good cheer, exercise, and comraderie to subsequently
remind us of our mortality. While we each maintain
independence of thought, our faculty is small enough
(and friendly enough) to arrive at a consensus on most
issues of departmental concern.
Another outgrowth of this collegiality is a coopera-
tive spirit in which most faculty members have en-
gaged in joint research projects. Cooperation between
faculty members is but one indication that our depart-
ment research activities are continuing to evolve. The
intellectual abilities of the faculty, along with fresh
input from graduate students, are recognized as the
best resources of the department. These resources
will carry us into new adventures and new ideas in the
coming years. D


CHEMICAL ENGINEERING EDUCATION










Random Thoughts...





NO RESPECT!


RICHARD M. FIELDER
North Carolina State University
Raleigh, NC 27695

The problem is, there's no glamour in being a
professor. People don't think of us as powerful and
important, like politicians and corporate executives; or
as practicing a noble and beneficial profession, like
doctors; or as pulling down a bundle for a few minutes
work, like doctors, lawyers, and corporate executives; or
as romantically unprincipled and somewhat sinister, like
politicians, lawyers, and televangelists. In fact, people
don't think of us at all. We get no crowds pointing us out
and whispering to one another as we walk by; no fathers
telling their children that some day they may grow up to
be like us; no groupies.
Trying to figure out the reason for this sad state of
affairs, I've concluded that we just don't know how to
handle ourselves on the job and those other folks do. The
solution is clearly for us to copy them. "But how?" I hear
you cry. "I am a scholar, at home and happy in the
realm of virial gases, canonical ensembles, and stress
tensors. What do I know of these worldly things?"
Well, you're in luck-as usual, I have the answers.
Here, then, is Professor Power: Becoming Rich and Fa-
mous in a One-Hour Work Week.



M.D. MODEL-GENERAL PRACTITIONER
Teach five classes each semester. Schedule them all
at 9:00 on Tuesday in separate classrooms. To keep the
students from getting restless while they're waiting for
you, leave some stimulating reading lying around, like a
few three-year-old issues of Centrifugal Pump Digest.
At 10:00 make an appearance in the first classroom,
spend about ten minutes teaching something, give an
assignment, and dismiss the class, telling them to pay
their hourly tuition in the department office before they
leave. Do the same thing in your other classes. After the
last one, take the rest of the week off to avoid burnout.
DENTIST VARIANT
Same as the G.P., except instead of making the stu-
dents wait for over an hour before the class starts, make
them wait only 45 minutes and then have a teaching as-
sistant give them some drill before you show up for
your ten minutes.


MEDICAL SCHOOL FACULTY VARIANT
Put your graduate student advises on an 80-hour
work week. Two weeks before a proposal or paper
deadline comes up, make them work 20-hour days,
providing them with a cot in the laboratory to get some
sleep during the remaining four hours. If anyone in the
administration complains, remind them that you could
be earning a great deal more in private industry. They
won't give you any more trouble.

LAWYER MODEL
Invite the students to call on you any time they have
difficulty with the course material. When they come to
your office or phone you, keep track of the time you
spend and charge $2.50 a minute for it. If any of them
are ever caught cheating, go before the judicial review
panel and make tearful references to their previously
unblemished record, the hardships they endured as
children, and their devotion to their aged parents and
half-blind dog. Then make disparaging and unprovable
suggestions about the integrity, ulterior motives, and an-
cestry of the professor who caught them. Apply the
usual charges.

POLITICIAN MODEL
On Day 1 of your course, promise that you will 1)
teach the students everything they will ever need to
know, 2) give all A's, and 3) provide free beer in class.
Spend the semester telling them how valuable the
course is and how hard you're working to meet their
needs, but never actually teach them anything. Cancel
about a third of the classes to attend conferences in
places like Hawaii and the south of France, calling the
trips "fact-finding missions." The day before the
students fill out course evaluations, pass out the beer.
Then give a comprehensive final, fail most of the class
for not learning the material, and explain that it was all
the administration's fault. Assure them that next
semester things will be different-they'll get A's, free
beer, and pizza. Most of them will believe you.

TELEVANGELIST VARIANT
Same as the politician, only 1) promise the students

Continued on page 92.


SPRING 1990










curriculum


PROCESS CONTROL EDUCATION IN

THE YEAR 2000


A Round Table Discussion


T. F. EDGAR
The University of Texas at Austin
Austin, TX 78712

THIS AUTHOR RECENTLY presented a paper on
process control education at a joint India-U.S.
symposium in Bangalore, India [1]. The paper [2] re-
viewed the current practices and philosophy of teach-
ing undergraduate process control in a typical chemi-
cal engineering department and presented an outline
for a course to be taught in the year 2000. This future
course would cover the forecasted advances in
hardware and software which should take place in the
next ten to fifteen years.
A main difficulty with the one-semester process
control course at most schools is that its starting point
is still the same as it was when the landmark textbook
by Coughanowr and Koppel [3] was first published in
1965. In order to incorporate all the advances in con-
trol engineering that have taken place in the past
twenty-five years (as well as the projected develop-
ments) considerable streamlining of the curriculum
material must be carried out. The problem faced by
most educators is that we tend to adjust courses in a
slow feedback mode. We do not adapt a course in a
feedforward fashion so that it will match the technol-
ogy encountered by BS graduates in a modern chem-
ical plant.
In an effort to promote some thought and discus-
sion within the process control community and to
begin making curriculum changes now, an outline of a
Thomas F. Edgar is professor and
chairman of the Department of Chemical Engi-
nearing at The University of Texas, Austin. He
earned his BS in chemical engineering from
the University of Kansas and his PhD from
Princeton University. He has published over
100 papers in the fields of process control,
optimization, and mathematical modeling of
processes such as separations and combus-
tion. He is coauthor of Optimization of Chemi-
cal Processes and Process Dynamics and
Control, and author of Coal Processing and
Pollution Control Technology.
SCopyright ChE Division ASEE 1990


TABLE 1
Course Outline for Process Control (ca. 1988)

1. Introduct. concepts: feedback vs. feedforward control (1 week)
2. Mathematical modeling of physical systems (1 week)
3. Linear system analysis: Laplace transforms (2 weeks)
4. Response characteristics of typical process systems (1 week)
5. Controller hardware, instrumentation (1 week)
& Closed-loop analysis, stability calculations (1 week)
7. Tuning of PID controllers (2 weeks)
& Frequency response analysis (1-2 weeks)
9. Advanced control methods: feedforward, cascade, multivariable,
adaptive, supervisory, etc (3-4 weeks)
10. Plant control strategies, case studies (1 week)
11. Miscellaneous topics
The above outline excludes time spent in an associated process control laboratory.


future course (discussed later in this paper) was circu-
lated to a cross-section of educators and industrial
practitioners for their comments, criticisms, and sug-
gestions. Many of the responses were quite detailed
and most interesting, and edited comments are pre-
sented in the Appendix to this paper. There is a sur-
prising amount of agreement on the directions in
which the field is moving, although there is no clear
consensus on how a one-semester course can ac-
complish the stated objectives. Perhaps a two-semes-
ter sequence (such as is practiced in many schools
abroad) is the only answer.

GOALS OF AN UNDERGRADUATE PROCESS
CONTROL COURSE (1988)
A one-semester or one-quarter undergraduate pro-
cess control course is required in virtually all US de-
partments of chemical engineering. In some cases a
two-quarter or, more rarely, a two-semester course is
taught. The content of a typical undergraduate pro-
cess control course is not intended to train process
control specialists. Rather it presents the key con-
cepts in dynamics and control and attempts to incul-
cate in BS engineers an understanding of transient
operations and the influence of feedback control on
responses.


CHEMICAL ENGINEERING EDUCATION










A typical course has the following learning objec-
tives:

Understanding the difference between dynamic and steady
state behavior courses in chemical engineering generally
deal with steady state analysis only. This fact sets apart the
subject matter in process control from other courses in the
curriculum. Mathematical modeling is a key ingredient.
Becoming proficient in analysis of dynamic systems the
principal tool employed in Laplace transforms. As long as
the course focus is on linear continuous systems, Laplace
transforms will always be the starting point, unless this is
covered in a prior course in mathematics. The amount of
emphasis on Laplace transform operations is an important
issue, as discussed below.
Learning the effect of feedback control and several
industrially-accepted methods of tuning PID controllers -
this leads to the issues of stability and performance in de-
signing feedback controllers. Computer simulation with
interactive graphics is a key pedagogical tool.
Appreciating the benefits of advanced methods such as
feedforward and cascade control students should know
under what conditions various methods should be imple-
mented.
Exposure to modern instrumentation and controller hard-
ware as practiced in industry in particular, a digital control
system interfaced to an actual process. A laboratory experi-
ence should be included in the control course or as part of a
unit operations laboratory.

Table 1 shows the typical course content for a 15-
week process control course based on 1980s textbooks
such as Stephanopoulos [4], Smith and Corripio [5], or
the new book by Seborg, Edgar, and Mellichamp [6].
There is wide disagreement on the amount of time
that should be dedicated to mathematical modeling,
since every additional hour spent there must be taken
away from other material. Exemplary systems can be
studied, such as the stirred tank heater which is de-
scribed by a first-order linear differential equation.
However, systems of industrial relevance are quite
complex, and developing models for these systems in
a few weeks of a process control course is clearly
beyond the capabilities (from a fundamental point of
view) of a typical undergraduate student. Neverthe-
less, such models can be presented to the student by
employing simulators with rich graphics capabilities.
The objective of such a simulator is to give the student
a "feel" for dynamic behavior. However, it is unrealis-
tic to expect the student to become even marginally
competent in simulation or associated numerical
analysis issues in this course.
Laplace transforms are the basic mathematical tool
in process control, and the teaching of this subject
(along with frequency response) has historically been
viewed as a major part of a process control course.


The basic ideas in stability and PID controller
tuning are important, but interactive software can be
employed to solve realistic problems after a few
tutorial examples. Root locus should
only be briefly mentioned.

However, given the emergence of mainframe and per-
sonal computer software for linear systems analysis
and simulation, does the current heavy emphasis on
Laplace transform manipulations need to be re-
evaluated? The early dependence on Laplace trans-
forms arose out of necessity because computational
and graphical tools were not available. Rigorous
analysis was necessary to obtain transient responses.
As a tool for complex systems, Laplace transform
analysis to obtain time-domain responses is of margi-
nal utility, especially when time delays exist in the
process. The key to reducing the current course effort
on linear systems analysis is the good interactive
software which is available today [1]. It also would be
helpful to modernize and focus the differential equa-
tion course which is taught by our colleagues in the
mathematics department.
Controller hardware and instrumentation is a sub-
ject which requires continual updating as new prod-
ucts are introduced. While there is a lot of material
here, most of it is descriptive in nature and tends to
be vendor-specific. It should be mandatory that some
background on the digital version of the PID control-
ler be provided here since all controllers sold today
are digital units (that appear to be analog). Program-
med logic controllers (PLC) should also be covered.
The basic ideas in stability and PID controller tun-
ing are important, but interactive software can be em-
ployed to solve realistic problems after a few tutorial
examples. Root locus should only be briefly men-
tioned.
There are many ways to tune a PID controller [6].
Methods based on stability considerations alone are
generally not satisfactory; performance-based meth-
ods are both stable and predictable with respect to
the design criteria. For simple systems, most tuning
methods give approximately the same results. The ef-
fect on model errors should also be addressed, leading
to a robust PID controller. In controller design the
quality of the results depends directly on the level of
computational effort. The Ziegler-Nichols algebraic
correlations based on the process reaction curve and
the quarter-decay ratio give inconsistent perform-
ance. Improved performance can be achieved by fre-
quency response. While application of this technique
can be tedious, especially when undertaken manually,


SPRING 1990










interactive computer graphics permits the design of a
PID controller to be completed very quickly. Unfortu-
nately, many engineers who are responsible for con-
troller tuning were subjected to the manual trial and
error approach while they were students and have
never since looked at this option. The fact that fre-
quency response is rarely used in industry needs to
be addressed (and corrected) by the educational sec-
tor.
The understanding of modern control systems pro-
vided by vendors or design firms requires considera-
tion of a number of advanced control strategies. In
the early 1970s, there were only a handful of plants
using feedforward control. This algorithm is now con-
sidered to be the standard approach when combined
with feedback control. Just as significant, cascade con-
trol is routinely used in computer control systems.
Multivariable and adaptive control are of lesser impor-
tance, although industrial activity in these areas is
growing rapidly. Industry is especially interested in
self-tuning (adaptive) controllers because of reduced
manpower requirements and improved performance
with a negligible cost difference.
Plant control strategy is a topic properly em-
phasized throughout the text by Stephanopoulos [4].
While it may be arguable that the average under-
graduate student is not intellectually mature enough
to absorb this type of material on top of everything
else, case studies which analyze a group of intercon-
nected unit operations rather than a single process
unit have merit as the "capstone" component of a
course in process control. Safety issues also should be
covered here.
Table 1 has omitted many specific topics that could
be covered in an up-to-date control course; see Table
2. Many of these topics will increase in importance in
the future.

PROCESS CONTROL IN THE YEAR 2000
What will the state of affairs be in the year 2000?
While most educators believe the undergraduate stu-
dents of that era will be more facile with the use of
computers, it is unlikely that there will be a quantum
jump in the mathematical preparation of those stu-
dents. So the starting point of a typical course will be
about the same. However, the industrial environment
where process control is carried out will probably be
quite different than it is today. Because of greater
integration of the plant equipment, tighter quality
specification, and more emphasis on maximum profit-
ability while maintaining safe operating conditions,
the importance of process control will be increased.
Very sophisticated computer-based tools will be at the


disposal of plant personnel, who will at least need to
understand the functional logic of such devices. Con-
trollers will be self-tuning, operating conditions will
be optimized frequently, total plant control will be im-
plemented using a hierarchical (distributed) multivar-
iable strategy, and expert systems will help the plant
engineer make intelligent decisions (those he or she
can be trusted to make). Plant data will be analyzed
continuously, reconciled using material and energy
balances with optimization, and unmeasured variables
will be reconstructed using parameter estimation
techniques.
How much emphasis needs to be placed on ad-
vanced techniques in the year 2000 course? Should we
abandon analog (continuous) analysis methods in favor
of digital ones such as z-transforms? What about the
PID controller? Will it be replaced by a more general
approach based on nonlinear programming? The an-
swers to these questions are complicated by the fact
that advancements in undergraduate education do not
really cause a new industrial environment. There is
probably much more influence at the graduate level.
The second problem is that there is a great lack of
uniformity in the modernization of chemical plants
with respect to process control.
By the year 2000, the analog systems currently in
use will have been replaced by digital systems. There
will probably be sufficient computing capability avail-
able in each process plant (via distributed control) to
implement any or all advanced techniques. There will
still be single-loop panel-based controllers and control
systems utilizing personal computers; while these can
communicate with higher level computers, they will
employ many different algorithms and functions than
those offered in the standard PID controller today. So
this may be the time when the standard under-
graduate control course can be largely converted to
digital control. Laplace transforms could be eschewed
in favor of discrete time analysis (difference equa-
tions) and z-transforms.
Table 3 shows a 15-week lecture course for the


TABLE 2
Additional Topics for Undergraduate Process Control


* Alarms
* Computer control systems, data
acquisition
* Predictive control
* Simulation
* Distributed control
* Unit operations control appli-
cations
* Batch sequence control
* Process control languages


* Statistical process control
* Process control data base
management
* Real-time computing,
architecture
* Expert systems, AI
* Digital control algorithms
* State space analysis
* Supervisory control
* Model identification


CHEMICAL ENGINEERING EDUCATION










year 2000 and indicates the emphasis of various topics.
The selection of topics can be justifiably criticized be-
cause it presupposes a reasonable level of training in
fields such as optimization. It also demands that Lap-
lace transforms and linear dynamic systems be (ap-
propriately) taught in the mathematics department.
However, fifteen years from now we could use non-
linear programming tools in the same way as we em-
ploy numerical analysis for simulation today. The stu-
dent does not need a deep understanding of the num-
erical details involved in order to have confidence in
the answers. Even today linear and nonlinear prog-
ramming tools have matured to the point that they
are used routinely in commercial operations and serve
as the basis for management and operating decisions
[7]. Optimization can also provide a unified approach
for model identification and parameter estimation.
The course in Table 3 would emphasize developing
familiarity with the techniques of process control,
with a distinct unit operations flavor. A one-semester


TABLE 3
Course Outline for Process Control (ca. 2000)


Topics


Comments


Dynamic Simulation Concept of time constants for various
(2 weeks) physical systems, nonlinear behavior,
commercial simulation packages
Response characteristics First, second, and higher order; unusual
(1 week) response characteristics (with examples)
Development of discrete- Fitting of discrete-time equations to data,
time models (1 week) use of convolution models


Analysis of discrete-time
systems (2 weeks)
Conventional and pre-
dictive controller
structures (2 weeks)
Optimization methods for
controller design
(2 weeks)

Tuning of controllers/
robustness (1 week)

Feedforward, adaptive,
and multivariable
control (2 weeks)

Digital hardwareAmple-
mentation (1 week)
Expert systems (1 week)


z-transforms, transfer functions, stability
analysis
Conventional digital feedback vs. predict-
ive control, supervisory control, cascade
implementation ofcontrol trajectories
Optimal tuning ofPID controllers, non-
linear programming formulation of de-
sign problem (e.g., dynamic matrix con-
trol or DMC), constraint handling
Effect of tuning parameters for
PID/predictive controllers, treatment of
model errors
Extension of optimization methods to
cover disturbance rejection, model
parameter changes, and multivariable
interactions
Equipment features and configurations,
sampling, filtering
Structure and purpose of expert systems,
alarm analysis, selectors


NOTE: Laboratory experiments employing a modern digital control
system are recommended to supplement the lectures described above.


course would be insufficient to train specialists in pro-
cess control, more so than it is in 1988. However, the
ability of an engineer to creatively solve process con-
trol problems can be enhanced by continuing educa-
tion and experience.
Obviously the content of the undergraduate pro-
cess control will not exhibit a step change near the
year 2000 but will evolve more or less continuously.
This will require the interim development of educa-
tional materials to supplement existing courses. Prob-
ably the biggest discontinuity will arise in the conver-
sion from continous-time analysis (e.g., Laplace trans-
forms) to discrete-time, but this transition may never
occur completely.

SUMMARY

Process control is a rapidly changing field, and its
high technology nature demands continual updating
of process control courses and laboratories. Perhaps
the major issue to be addressed for the future is the
role of continuous time analysis (vs. discrete-time)
and increased use of simulation. A larger role for op-
timization in process modeling and controller design
is envisioned.

REFERENCES
1. Ramkrishna, D., P. B. Deshpande, R. Kumar, and M. M.
Sharma, eds., "Chemical Engineering Education: Cur-
ricula for the Future," Proceedings of the Indo-U.S. Sem-
inar, Bangalore, India; January 1988
2. Edgar, T. F., "Process Control Education: Past, Present,
and Future," p. 117 in ref. 1., January 1988
3. Coughanowr, D. A., and L. B. Koppel, Process Systems
Analysis and Control, McGraw-Hill, New York (1965)
4. Stephanopoulos, G., Chemical Process Control, Prentice-
Hall, Englewood Cliffs, NJ (1984)
5. Smith, C. A., and A. B. Corripio, Principles and Practice
of Automatic Process Control, Wiley, New York (1985)
6. Seborg, D. E., T. F. Edgar, and D. A. Mellichamp, Pro-
cess Dynamics and Control, Wiley, New York (1989)
7. Edgar, T. F., and D. M. Himmelblau, Optimization of
Chemical Processes, McGraw-Hill, New York (1988)

APPENDIX
Manfred Morari: Caltech
If you consider Laplace transforms simply as a tool for solving
differential equations, then this aspect of Laplace transforms is obviously
obsolete, and the use of Laplace transforms for obtaining system
responses should be totally de-emphasized in the future curriculum, I.
however, look at Laplace transforms and frequency response analysis more
as a means of understanding the issues of stability, performance and
robustness. There is simply no replacement in sight which conveys these
issues with the same clarity.
a. The effect of a time delay variation, for example, on the stability and
performance of a control system can be easily explained and nicely under-
stood from a Nyquist curve analysis. Any other method would involve
only trial and error via simulation and would not transmit the same degree
of insight.
b. With the proper training, an undergraduate can learn to look at a Bode
plot (obviously generated by CAD software) and determine from one curve
the speed of response, the likelihood of overshoot,


SPRING 1990











steady state offset, the behavior of the system for a range of different
disturbances, the possible sensitivity of the closed loop system to
modeling errors, if non-minimum phase characteristics are present, etc. To
obtain the same information and insight from either an analysis of
difference equations or extensive simulations would be essentially
impossible, or, to say the least, rather involved.
"Will the PID controller he replaced by a more general approach
based on nonlinear programming?" Largely not. The one important issue
absent from your paper is modeling. The PID controller provides
reasonably good control with a minimum of modeling effort. The
information required to set up a nonlinear program for online control is
much larger and in most cases the effort is not justifiable. This is also the
reason why fewer model predictive control schemes have been
implemented than the public has been led to believe.

Irv Rinard: CUNY
One concern is that process control has traditionally been taught from
the bottom up. Now that is okay if we are training our students to be
process control engineers. But if the plant control engineers are going to
he chemical engineers who occasionally have to worry about process
control along with a lot of other things, bottom up is probably not
appropriate. They spend a semester getting to the point where they can
analyze and design a SISO feedback controller, then they go out into a
chemical plant only to find out that PID controller tuning is not the
plant's critical control problem.
Along the lines of what you have suggested, perhaps there should be
two undergraduate control courses: one an overview course which everyone
would take, and a second course for those who intend to go into the
systems engineering side of the business.
Another concern is that the focus of process control has been too nar-
row. Algorithms and their implementation have received most of the
attention. Students go forth only to learn that measurements can be bi-
ased, or noisy, or fail altogether; that control valves stick; and that other
critical items are either messed up or maxed out. Tuning a loop is more
than just determining P, I, & D: it is also zeroing and spanning, fixing
and adjusting, and sometimes even rewiring. Ninety percent of a proper
computer control algorithm is data checking. While the topics of data
reconciliation and fault diagnosis are on your agenda for the year 2000,
they belong properly and prominently in the very first undergraduate
course.
Along the same lines, students go forth thinking that the regulatory
control system is it. They are almost totally unaware that the most
important control system in the plant is not the regulatory control sys-
tem, but the safety system. The former affects the size of your paycheck:
the latter, whether or not you'll be around to collect it. Only Rijnsdorp
has given this subject any coverage in a control textbook, at least as far as
I can recall offhand.
What I would like to see is a revision of the entire curriculum to make
it more model-based. Students should connect the basic idea of dynamic
simulation to the solution of differential equations early on. Then, in the
various courses, the appropriate models would be developed as a
pedagogical tool. For instance, in thermodynamics, instead of learning
about flash calculations in the abstract, the students could develop a
dynamic model of a flash drum: in unit operations, dynamic models of
heat exchangers and distillation columns. Then, when they get to the
process control course, they already have the basic background in process
modeling. I have found in teaching process control that modeling is what
the students are weakest in. Emphasizing it throughout the curriculum
might help. Perhaps this is an issue that CACHE should take up.

Jim Doss: Tennessee Eastman
In order to streamline the curriculum, a first step would be to put
Laplace transforms into the mathematics courses. However, students tend
not to retain the mathematical theory but to remember the experiences
from control laboratory experiments and simulations. It is also important
to emphasize the use of computation, especially with computer graphics.
Students need to learn more about modeling and identification of process
models. More digital control needs to be presented, and a parallel presen-
tation of s and z transforms (such as in Saucedo and Schiring's textbook)
might be necessary in the future. However, other digital devices such as


PLCs and their use in interlocks are important, combined with discussion
on alarms and process safety. Finally, students need to understand the
concept of total plant control.

Wayne Bequette: Rensselaer Polytechnic Inst.
It is interesting that ChEs handle process control so well, despite the
fact that we are trained (at the BS level, where 90% of the control
engineers come from) on black box or linear system models. Our
knowledge of "real" processes comes from our background in steady state
modeling and design. Rarely in a typical BS curriculum are we teaching
students using complex, nonlinear dynamic models. Our ideas, when we
get into industry, about what effect certain manipulated variables have on
certain output variables are based solely on our steady state background. I
guess that one of the most important experience that an undergraduate
control student can have is controlling laboratory equipment. A good
dynamic process simulator can provide almost as good of an educational
experience.
Sometimes it is amazing how well ChEs control processes in the real
world, with such a poor theoretical background. It is well known, of
course, that it takes a year or two of experience before a BS candidate can
make a real contribution-but this is true of most industrial positions, not
just process control engineering. In addition, most problems will be
solved by the simplest method available, so the lack of theory is not a
major hindrance.
I believe that for the vast majority of control loops, there will be no
issue of digital vs. analog control. The lowest level of control
(constituting > 80% of the loops) will continue to be a simple Pl flow
controller. The sampling rate is high at this level, so there is not a vast
difference between digital and analog control. The main advantage of
digital at this level is the ease of maintenance issue. That will be the main
advantage of most loops for a period of time, because, if a particular
control strategy is ineffective, digital technology allows a quick retrofit.

Brad Holt: University of Washington
Some of the key questions really must be dealt with. Should we be
teaching continuous or discrete control theory? Can we teach the course
using discrete theory completely and yet convey to the students the feel for
dynamics and modeling that we do with continuous theory? How does
modeling fit into such a course? Do we teach them difference equations or
discrete approximations to ordinary differential equations? There simply is
not time in such a course to teach both continuous and discrete theory,
but almost all of the discrete texts that I have seen really assume a contin-
uous background. Although I feel that teaching the course from the
discrete standpoint would be very valuable, I haven't figured out how to do
it and convey all of the ideas and information that we do now.
One important area which I feel that you could have said more is in
how to actually design controllers. Most of the control books present P,
PI, and PID as "the" controllers. You select one of these and then follow
some rules to tune it. The books do not do a good job of suggesting when
they will work well, when they don't and why there are problems. This
year I taught the seniors an IMC based control philosophy as the first
step. We started with feedforward controllers and how to design them, pro-
gressed to IMC as a technique to handle disturbances and uncertainty, and
finally introduced the standard control configuration as the normal imple-
mentation method. This led to PI and PID controllers, how to tune them,
and when they are likely to work. The students really feel that they know
how to "design" controllers. They understand the role of uncertainty, the
importance of models, and why systems with non-minimum phase ele-
ments are difficult to control. Although I will do some things differently
next year, the experiment worked rwell.

Daniel Rivera: Shell Development
The course should begin by reflecting on fundamental system proper-
ties that establish chemical process control as afield in its own right. The
effect of deadtime, inverse response, constraints, uncertainty, and operating
requirements on achievable closed-loop performance should be emphasized.
Discussing these issues can be done at the beginning of the course because
these represent inherent limitations independent of control design. All of
the course material should revolve upon technologies to meet these re-
quirements.


CHEMICAL ENGINEERING EDUCATION











The benefits of Laplace and frequency--domain methods should not be
rejected because of implementation considerations. Frequency-domain
analysis is useful even when controller design is performed in the time do-
main. The recent theory on robustness of control systems is one such ex-
ample. What is probably more reasonable is to replace such exercises as
inverting Laplace transforms and the like with instruction on the use of
fr-equency-domain techniques for performance and robustness analysis.
Why should the undergraduate curriculum have to wait until the year
2000 to include a treatment of model uncertainty and constrained control?
While a thorough treatment of these topics is probably most suited for
graduate level courses, there is enough existing theory to justify, at the
very least, a conceptual introduction to these subjects.


Lin Tung: Fisher Controls
ChE's should understand the process as well as control and should
have some background in control strategies for various unit operations.
Increased use of the concepts should not be at the expense of process
understanding. PID control will still be a key control concept in 2000 (and
probably not be replaced by nonlinear programming), although as part of
distributed control systems (DCS). DCS system concepts should be
presented and students should be exposed to such equipment (most vendor
systems employ the same basic ideas although the equipment may look
different). We need to upgrade the operator's educational level; in Europe
BS engineers are used (why use a high school graduate to control a multi-
million dollar process?).


Ed Bristol: Foxboro
Teaching of PID tuning should have a strong root locus component
(the closed-loop response is shaped by the dominant three poles). We need
to get students to think more in the frequency domain and to develop a
practical feel for dynamics and control. An experienced tuner is like an
experienced car driver. Theory should be used to gain insight, not just to
implement a tool. Control engineers should not restrict themselves to
facts that can be proven mathematically. We want methods that work even
when the theory does not. Model uncertainty (such as nonlinearity, model
order, or noise) should in practice lead one to use a simpler approach,
while many theories tend to give more complex answers.

Christos Georgakis: Lehigh University
Regarding the observation that we might abandon the continuous time
domain for the discrete time one, you are right that the widespread use of
digital control computers is pushing us in this direction. However, many
chemical processes are slow, and if slow composition measurements are
not used, then the sampled character of the digital control computer has no
effect on the performance of the controller. In this case, continuous time
might be sufficient. I, however, agree with you that the sampled data con-
cerns should start being incorporated in the first process control course.
The extent will depend on what is the philosophy of the most popular
texts between now and the year 2000.
I expect that "expert systems" will have an impact on process control
education much earlier than the year 2000 and to a larger extent than you
estimate in your paper. In my definition of "expert systems" I include sys-
tems that are not necessarily "expert" but complement the numerical
calculations, of, say, a PID algorithm with symbolic calculations (or
logic, if you wish) to design the overall control system. A selector is the
simplest example. While in practice we use override controls and PLCs,
we do not teach our students about them in a systematic way.

Joel Hougen: Consultant (U. of Texas, retired)
We need to strongly emphasize accurate instrumentation and the im-
portance of obtaining good data. Many existing plants are instrumented
without much thought about needed performance characteristics. Students
need to appreciate the importance (and lack) offield instrument calibration
and the difficulty of obtaining fundamental plant models (hard to predict
steady state or dynamic characteristics in advance). Undergraduates should
have the experience of successfully verifying simple dynamic models in
the laboratory. A reasonable goal is 2% accuracy in material balances.
For most processes, simple dynamic models are adequate and PID
controllers are satisfactory. However, Ziegler-Nichols tuning is not


appropriate for today's controllers to achieve high performance. A great
amount of process understanding is necessary to develop process control
strategies; algorithms are secondary. In the course, theory should connect
to reality (and not just be a mathematical exposition).


George Stephanopoulos: M.I.T.
Prerequisites for the design of good controllers are: the in-depth un-
derstanding of open-loop process dynamics and closed-loop behavior under
various control modes (proportional/integral/der-ivative). A good coverage
of these two subjects gives a strong imprint of analytical attitude, which
completely characterizes the educational experience in the course.
But within such an environment the following issues are hardly ever
raised: What are the operational objectives in the plant? How does one
convert informal operating requirements (e.g., minimize operational cost)
to formal and explicit control objectives?
Even for the design of single loops, some important considerations are
only lightly touched upon. For example: How does one systematically
develop the process model needed for a particular control task? What is the
effect of model inaccuracies on the stability and performance robustness of
a control loop? How does one design a control loop in the presence of
input and output constraints?
While the above questions are asked by practicing engineers on a daily
basis, it is not true that e they are difficult to answer or require an extensive
expansion of lecture hours.
The continuing preoccupation with the analytical leg of process
control is partly due to our inability to deal with non-analytic, factual,
poorly articulated, often contradictory and qualitative knowledge. We do
not know how to handle conflicting facts, or we downplay the importance
of qualitative knowledge. Our ability to harvest the added opportunities
offered by knowledge-based systems depends on our awareness of the new
computing technology. Object-oriented programming is indispensable in
capturing structured knowledge around processing units, controllers,
control design tasks, order-of-magnitude reasoning, etc.

Yaman Arkun: Georgia Tech
Dynamic modeling should be covered throughout the ChE curriculum.
The control course should focus on the utilization of dynamic models for
control purposes rather than setting them up from first principles which
can he best accomplished in other core ChE courses. It is better to spend
the time on relevant control issues like the extent of required modeling so-
phistication, e.g., nonlinear vs. linear approximations, effects of
parameter uncertainties, neglecting secondary physical phenomena, etc.
I personally do not devote more than two lectures to Laplace trans-
forms. I believe the home for detailed treatment of Laplace transforms is
in a math course. However, the topic is important as it naturally bridges
linear dynamic models with continuous transfer functions and frequency
response analysis. The emphasis on frequency response should remain
since practical and fundamental problems such as stability, performance,
and robustness with uncertainty can be nicely interpreted using Bode,
Nyquist plots, and M-circles without resorting to trial and error dynamic
simulations.
In the very near future, I believe we will see more coverage of dis-
crete-time systems and model predictive control in the undergraduate
control courses. The reason for this is the industrial success of MPC and
the fact that it does provide a framework within which a wider scope of
realistic control problems can be conveniently couched and conveyed to
the students. The issues of process economics, operational constraints,
changing objectives with time, and the utilization of process models on-
line are difficult if not impossible to illustrate using PID or other more
classical controllers. Any undergraduate textbook in this area will have to
be supplemented with simulation software which implements MPC. De-
velopment of case studies mimicking the exercise a control engineer goes
through in practice will be invaluable. Such projects would be assigned at
the beginning of the course very much like a senior design project and
solved in parallel with the lectures covering areas such as problem
formulation, model development and discrimination, control structure
selection, and finally, tuning and performance assessment. We have done
this using PID, feedforward, and cascade controllers, and I can envision
doing it in the near future using MPC and more challenging industrial
problems. 0


SPRING 1990










laboratory


THE UNSTRUCTURED STUDENT-DESIGNED


RESEARCH TYPE OF LABORATORY EXPERIMENT


A. MACIAS-MACHIN,' GUOTAI ZHANG,2
and OCTAVE LEVENSPIEL
Oregon State University
Corvallis, OR 97331-2702

THE STANDARD LABORATORY experiment in
chemical engineering centers around a fixed piece
of equipment, so the whole exercise is pretty much
unchanged from year to year. But in these times when
use of the personal computer is widespread, student
reports of these experiments can easily be saved,
merged, and passed on year after year, in ever-im-
proved form-sometimes with little thought on the
part of the preparer.
We would like to encourage the increased use of a
different kind of exercise: the research type of labora-
tory experiment. Here, instead of showing the stu-
dents the equipment to be used, and telling them what
to do and how to write it up (eight sections in the
report, starting with introduction, theory, etc.), tell
them what you want to discover and let them choose
their own way of doing it.
In this paper, this type of experiment is discussed
and illustrated with one example. The main idea is as
follows:
1. Tell the team of students the question you want
answered. Choose a question which can be
answered in more than one way-something
which is not in their textbooks and which will
require that they develop their own analysis;

Agustin Maclas-Machin, assistant pro-
fessor at the Polytechnic University of Canary
Islands (Spain) is presently at Oregon State
University on a two-year visiting faculty ap-
pointment. He is doing research on various
projects, all focusing on solar energy storage
in phase change materials, which is a critical
problem for the Canary Islands.



'On leave from Polytechnic University of Canary Islands, Spain
'On leave from East China University of Chemical Technology,
Shanghai


something which was not asked last year or the
year before.

2. The students should consider the alternatives
and decide among themselves, after discus-
sion, how to go about answering the question.

3. Once a decision is made, the students should
present their plan to the instructor in order to
see if equipment is available. At this point, they
might be asked (gently, of course) if they woula
like to reconsider part of their plan.

4. The students are then to proceed with the ex-
periment, to compare their results with the liter-
ature, and to write up their findings-not a big
report, but one which is to the point.
EXAMPLE OF THE MINI-RESEARCH EXPERIMENT
The Question
Tell the student team that you want them to find
h for melting ice, maybe because you have been asked
to look into the feasibility of capturing antarctic
icebergs for towing to parched lands for fresh water
(make up a good story). More precisely, tell them to

Guotai Zhang is an associate professor at
the East China University of Chemical Tech-
nology (Shanghai) and is director of the
hydrocarbon processing laboratory there. He
is presently a visiting researcher at Oregon
State University studying ways of fluidizing ex-
tremely fine particles which do not want to flu-
idize.



Octave Levenspiel is professor of -
chemical engineering at Oregon State Univer-
sity and is particularly interested in chemical
reactors. He has written a number of books
and was one of the earliest recipients of
ASEE's Lectureship Award. He recently re-
ceived an honorary doctorate from France for
his "internationally outstanding scientific repu-
tation."


0 Copyright ChE Dwivsion ASEE 1990


CHEMICAL ENGINEERING EDUCATION


EcIB










We would like to encourage the increased use of a different kind of exercise: the research type of laboratory
experiment. Here, instead of showing the students the equipment to be used and telling them what
to do ... tell them what you want to discover and let them choose their own way of doing it.


develop an expression for h for downfacing ice sur-
faces in quiescent water at different temperatures, to
compare this with what's available in literature, and
to recommend an expression for use.
Tell them that there is no experimental set-up for
this purpose. However, say that the laboratory has
vats, thermometers, scales, and calipers available,
and that Professor X has a refrigerator with a freezer
section in his office which he may allow them to use if
asked nicely.
Tell the team to report back to you when they are
ready and to tell you what they plan to do, what equip-
ment they've assembled, and what they found in the
literature. We suggest reserving about one-third of
the marks for this presentation, to see if they really
have thought the problem through. The whole exper-
iment should take two laboratory periods.

One Way to Answer the Question
1. Take half of a fast-food hamburger styrofoam
container, fill it with water, and freeze it.

2. Place it face down in a vat of water, remove
any air bubbles that are present, and then
measure the thickness of the slab of ice with
calipers at various times. That is all there is to
the experiment itself.

3. The analysis needed to find h should not be
difficult, but since it will not be found in any
book they will have to develop it themselves.
They should be able to do it. Don't help them.
They should find that the slope of the thick-
ness-time curve is all they need. Figure 1


Thermometer


% *V -
S\ T= 5C
74-
,2

r T IOC




S1 T= 15C

TI I I

0 10 20 30 40
Time (min)
FIGURE 2. Typical findings for the thickness of ice layer
vs. time for horizontal downfacing slabs of ice in water
at various temperatures.

shows the procedure, and Figure 2 shows
what we found when we did this experiment.

4. In the analysis and discussion of their results,
you may want to look for the following points:
Were the students able to find a literature correlation for
h for cold downfacing plates in water? Did they check
Perry?
Did it occur to them that h for melting ice may differ from
h for ordinary flat surfaces, and did they search for this h
value in the literature? Did they even consider this whole
matter? (Extra points!)
Did they compare their values with the literature values
and discuss the differences?
If they found a lower initial slope in Figure 2, as we did,
did they try to explain why this was so? Or did they just
least-square the whole set of data? (Poor.)
Did they at least plot the data and look at it? Or did they
just generate a computer program which calculated h
without human intervention orjudgement? (Terrible!)
5. As for the experimental procedure:

Did they try to insulate the top and sides of their block
of ice, somewhat as we did, or did they plunge the whole
Continued on page 116.


SPRING 1990


FIGURE 1. Experimental set-up.










Award Lecture



FROM MOLECULAR THEORY

TO THERMODYNAMIC MODELS

Part 2: Mixtures


STANLEY I. SANDLER
University of Delaware
Newark, DE 19716

N THE PREVIOUS paper we showed how one could
establish a theoretical basis for both understanding
and testing the molecular level assumptions contained
in common pure fluid equations of state and for de-
veloping new ones. We now extend this analysis to
mixtures and will consider activity coefficient models
and equation of state mixing rules.

THE GENERALIZED VAN DER WAALS
PARTITION FUNCTION FOR MIXTURES
The starting point is again the canonical partition
function, here for N1 molecules of species 1, N2
molecules of species 2, etc., contained in a volume V
at temperature T

Q(N,,N2,...,V,T)= e-Ei(N,N2...,VT)/kT (1)
states
where Ei is the energy of the ith quantum state. From
this partition function all other thermodynamic prop-
erties can be computed (Eqs. (1-2 to 4) of [1]). (We
will refer to equations from [1] using the designation
1.)
Following the same analysis as in [1] of separating
the translational, rotational, vibrational, electronic,
and interaction energy states, we obtain the following
expression for the generalized van der Waals partition

Using the terminology of (1), this term
is referred to as the configurational contribution to
the free energy. The second term is the residual term;
it arises from the soft repulsive and attractive
forces among the molecules-that is,
from the molecular interactions.


function for a mixture of simple molecules

Q= N1 Y(qttqrqvqe)Ni

V N(T.V,NVN2....)exp (T ,VNN,,...)
where
-2kT ECON(NI,N2,...,V,T) dT
(N2,.... VT)= kT (3)


f Et Ecow(N,,N,.... V,T)d T
N i/T=0 4,T)
with
ECONF(NI,N2,...,V,T)= EjO N(N1,N2,....V,T) (4)

and N = INi. Once the mixture free volume Vf and
the average configurational energy for each species i
interacting with species j molecules, ENF, is known,
Eq. (2) can be used to obtain the equation of state and
other thermodynamic properties of a mixture.
Alternatively, instead of using the mixture parti-
tion function directly, we can consider the difference
between the partition function of the mixture and
those of the pure components to obtain the change in
properties on forming a mixture from the pure fluids.
In particular, to obtain an excess Helmholtz free
energy change on mixing that is equal to the excess
Gibbs free energy at constant temperature and pres-
sure from which we can obtain activity coefficients,
the mixing process must be one in which we start with
the pure components at temperature T and pressure
P, where their molar volumes are Vi, and then adjust
the pressure of the mixture so that there is no volume
change on mixing; that is, that [2]

Vm = xi i

In this case we have


0 Copyright ChE Division ASEE 1990


CHEMICAL ENGINEERING EDUCATION









A = GT,

= Ami(T,V, N,N2,...)- 7 A(T, Vi,Ni)- kT Y Nitn xi



= -kTn Vf(N,N2 .. V.)N 1

S[L fi. (Ni, Vi)(N..]
i I



kT n Vf (N, N2,... Vmix)N
S[N r,(TV (Ni,N,,.) -N,(TV,,N,




T [yZ.E ONF(T,V,N,.... )- I:EONF(T,Vi,Ni)]dT
-kT kT2

=AEX +AX (5
= AONF + ARES (5


The first term on the right-hand side of the equation,
which arises from the difference in free volume terms,
is the excess Helmholtz free energy of mixing that
persists at very high temperatures; it depends upon
the hard-core size and shape differences between the
molecules. Using the terminology of [1], this term is
referred to as the configurational contribution to the
free energy. The second term is the residual term; it
arises from the soft repulsive and attractive forces
among the molecules-that is, from the molecular in-
teractions.
There are two different ways to proceed in ther-
modynamic modeling. One, for high pressure mixtures
(especially of hydrocarbons and inorganic gases), is to
use an equation of state to describe both the vapor
and liquid phases. The other, for mixtures at low pres-
sure and with more complicated molecules, is to use
an equation of state only for the vapor phase and an
excess Gibbs free energy (activity coefficient) model
to describe the liquid phase. While it is common to
think of these two methods of thermodynamic model-
ing as being completely distinct, we see from Eq. (2)
(the derivative of which leads to the equation of state)
and from Eq. (5) (the composition derivative of which
leads to activity coefficients) that both have the same
origin: the statistical mechanical partition function.
Consequently, any assumptions made about the mix-
ture free volume and configurational energy will lead
to an equation of state and its mixing rule as well as
to an activity coefficient model. As we will soon see,


the assumptions which lead to the usual equations of
state produce only the simplest excess Gibbs free
energy models, while the assumptions which lead to
the most commonly used free energy models result in
equation of state mixing rules which do not satisfy an
important theoretical boundary condition.

LOCAL COMPOSITIONS AND
THERMODYNAMIC MODELS
For demonstration purposes we will consider a
mixture of square-well molecules (see [1] for a defini-
tion of this potential). Following the analysis in [1] we
obtain
E ONF N Nij"ij
2 (6)
where Nj is the average number of i molecules in-
teracting with a central j molecule at the temperature
and density of interest. Thus, Ni may be thought of
as a species-species coordination number. In order to
proceed further we need to have information about
) the free volume in the mixture and the species coordi-
nation numbers Nij as a function of temperature, com-
position, and density. We will now consider each of
these terms separately.
For mixtures of hard spheres (or the hard-core
part of square-well fluids) the free volume can be ap-
proximately estimated using the van der Waals ex-
pression
Vf= V-(.Ni)b with b= yxixjbu
[Further using bj = (bii + bjj)/2, which is correct for
hard spheres, we have b = xibi.] Using this result
in Eqs. (1 and 1-3) gives the usual van der Waals con-
figurational or free volume part of the equation of
state


pCONF = kr a n V,
V av N


=NkW (aT Vr = Vb (7)
aV N, V Nb


Similarly using this expression for the free volume in
the configurational contribution to excess Helmholz
free energy, Eq. (5), gives
AEN = -kT(N n Vt,mix Ni in nVf + +Nin xi)

S (V I Nibi )N xNi f i
n -Nb, N =kTXNin (8)
l(vi Nibi)Ni Xi
where
Of,i = (Vi Nibi) / (V Nibi,)
is the free volume of pure species i divided by the
total free volume in the mixture.
If we assume that the free volume fraction of
species i is equal to its volume fraction, Eq. (8) be-
comes the well-known Flory expression for the config-
urational free energy term [3]. Clearly other assump-


SPRING 1990









tions can be made; for example, we can also use the
Carnahan-Starling free volume expression (Eq. (1-15))
and its analogue for mixtures, though at the cost of
greater mathematical complexity.
The simplest species-species coordination number
model is that the mixture is random, that is

N.LC
V
where C is the same constant for all species-species
interactions. This is the generalization of the van der
Waals assumption that the coordination number is a
linear function of density that we used in [1]. Using
this in Eq. (2 to 4, and 1-3) we obtain
N2 C 1
Pm= V-.- Xx'xiej=j Xxixjaui (9)
where
ai = -CN2 ei / 2
in analogy with [1].
Combining the configurational (Eq. 7) and residual
(Eq. 9) contributions gives the van der Waals equation
of state (Eq. 1-14b) with the following mixing rules
a= Y xixjaij (lOa)
and


b= xixjbij


(10b)


Eqs. (10 a,b) are known as the van der Waals one-fluid
mixing rules. The first part of the name refers to its
originator, and the second to the fact that they lead
to mixture being described by the same equation of
state as the pure fluid, but with composition-averaged
parameters.
It is known from statistical mechanics [4] that the
mixture second virial coefficient, that is, the coeffi-
cient Bix in the expansion for a mixture

PV B (T)
PV=+ )+.. (11)
RT V
has a quadratic composition dependence. Since the low
density expansion of any cubic equation of state re-
sults in the second virial being a linear function of the
equation of state parameters a and b (for example,
Bmix(T) = b (a/RT) for the van der Waals equation),
the known quadratic composition dependence of B(T)
requires that Eqs. (10 a,b) be satisfied at low density.
This is an important theoretical low-density boundary
condition. In fact, in chemical engineering the mixing
rules of Eqs. (10 a,b) are generally used at all densi-
ties. One present area of equation of state research is
density-dependent mixing rules which have a more
complicated composition dependence at high density
but reduce to Eqs (10 a,b) at low density.
Using the random mixing assumption in Eq. (5)
with the further approximation that the molar volume


of each species is approximately the same leads, for a
binary mixture, to

AEx = GEx = 1N2
ARES= R= NES -Niji =-C --'x2(E11 +F22 -2E12)
(12)
which is the one-constant Margules expression [5], or
the two-constant Margules expression if we do not
assume that the molar volumes are equal. Thus, from
the analysis so far we see that the Margules equation
with a Flory-Huggins correction (or without it if we
neglect the contribution of Eq. 8) for the excess free
energy and activity coefficients, and the van der
Waals one-fluid mixing rules have the same origin in
molecular theory, the random mixture.
From statistical mechanics we can easily show that
the exact low density result for the species-species

TABLE 1
Local Coordination Number Models
and Equations Which Result
Local Coordination Equation of State Free Energy
Number Model Mixing Rule (Activity Coefficient)
Model

N.
N0 =--C vdW 1-fluid Margules

Ni
N,=-C vdW 1-fluid Margules

N = e'kT vdW 1-fluid Margules
V

Ni i vi nonquadratic, Van Laar and
Nj Njvj density independent regular
with = xixjviaij solution [6] if
No +N = Nj xvi co = 0
Nu+Na=Ni Xxlvi
and if or Flory-Huggins
8i independent N if Flory term
of T and V N VCj used for AxC


Nij = Ni i e(ij-jij)'k
ij Nj Vj
Wilson [7]
with as above
equation
Ni +N ii= Nd

nonquadratic, UNIQUAC [8]
Surface area density equation when
fractions independent Guggenheim-
Staverman
expression used for
AEXc
"CONF


CHEMICAL ENGINEERING EDUCATION









coordination number in a mixture of square-well
molecules is

Lim N,(N1,N,,...,V,T)=Ni 4 (R? -l1) eeU (13)

This is an interesting result since it requires that the
local composition of i molecules around a j molecule is
proportional not only to the mole fraction of species i,
but also terms that depend on the sizes and energies
of interaction of the i and j molecules. Thus, in gen-
eral, the mole fraction of i and j molecules around a
central molecule will be different than their bulk mole
fractions. That is, the random mixing model is incor-
rect, unless all species have the same size (aii = -jj
= a), well width (Ri = Rjj = Rij), and energy of
interaction (eii = Ejj = Sij). We refer to departures
from random mixing as a local composition effect.
Assuming that Eq. (13) is valid at all densities, we
obtain for the residual part of the equation of state

pRES N 2 2 -T Y kT
V 3 xj o(R)(e -1)
N2
--Z xixXjaU (14)
where

a kT2iR, 3 R -1)(eiJ/kT-1)

Thus, again the van der Waals one-fluid mixing rules
and the Margules expansion for the activity coefficient
(which we leave as a proof for the reader) are ob-
tained, though this time from a non-random, local
composition model. In fact we can generalize the
analysis to show that any assumption in which the
local composition Ni is a linear function of the density
of species i (regardless of its temperature dependence)
results in the van der Waals one-fluid mixing rules
and the Margules Gibbs free energy or activity coeffi-
cient model. Table 1 contains a number of local compo-
sition models and the equation of state mixing rules
and activity coefficient models which result.
A different class of thermodynamic models results
from starting instead from assumptions about the
ratio of local compositions, which we will write as
Nij N
Ni, Na
For example, from Eq. (13), we have

LjG?-N. oa (R?-l) (%_..)/k
Lim N! Ni U- e(-)/T
p-o Njj Nj o!, (R3-1)
so that

Lim j = (15)
p-o40 (R-1))


However, to proceed with generalized van der Waals
theory, each of the Nij are needed, not merely their
ratio. A common (implicit or explicit) additional as-
sumption contained in many activity coefficient mod-
els is that the total coordination number for each
species
Nj = Y Nij

while it may be a function of temperature and density,
is independent of composition. That is,


This assumption has its origin in lattice-based models
of liquids which generally require that the lattice on
which molecules are placed is fixed, so that the coordi-
nation number of each lattice site is unchanged with
composition. This assumption is correct if the random
mixing assumption, Ni = CNi/V, is valid, but is incor-
rect otherwise.
For a binary mixture using Eq. (16) to solve for
Nij in terms of ij leads to


Xj N
Ni + j
xiBij+xj X


Xieii
and Nij= x +
J xi,9+Xj


Table 1 also contains the activity coefficient models
which result from the combination of Eqs. (5 and 17)
with various choices for ij. Note that we have not
shown the corresponding equation of state mixing
rules in this table. This is because the mixing rules
which result from using Eq. (17) do not satisfy the low
density boundary conditions of Eqs. (10 a,b). For
example, the combination of Eqs. (2, 17, 1-13) with
the assumption that the total coordination number is
a linear function of density yields the van der Waals
equation of state residual term (Eq. 9) with

a=-ZX xixj aij (18)
xi9ij + Xj

if 9ij is independent of temperature and a somewhat
more complicated expression if it is not. The impor-
tant observation is that this mixing rule is not quadra-
tic in composition because of the denominator (unless
ij = 1). However, using this local composition model
also leads to a residual contribution for the free energy
(or activity coefficient) of the widely used regular so-
lution or van Laar form if ij is taken to be the ratio
of some measure of the molecular sizes. Further, com-
bining this residual term with the Flory expression
for the configurational term, Eq. (8), gives the Flory-
Huggins model [9].


SPRING 1990


Nj Nj (Xi,X2,...XN)










In Table 2 we display a collection of recently pro-
posed density dependent local composition models
which lead to density dependent equation of state mix-
ing rules that are quadratic only at low density, and
to one new activity model to be discussed shortly.


COMPARISON WITH COMPUTER SIMULATION

Given the collection of local composition models in
Tables 1 and 2, we can now ask two questions. First,
is the local composition effect real? That is, do local
compositions exist in the vicinity of a molecule that
are different from the bulk compositions? Second, if
the answer to the first question is yes, which of the
local composition models in these tables is correct, if
any? To answer these questions we again turn to the
Monte Carlo computer simulation method used in [1],
but now for binary mixtures of square-well molecules.
For each species we use the potential of Eq. (1-8) with
the following combining rules to obtain the paramet-
ers for the interactions between the unlike molecules
-l 1
E,12= ;Fi-2 and a12 =- (a +a)22
2

(In our simulations we also chose R11 = R22 = R12 =



TABLE 2
Local Coordination Number Models Which
Result in Density-Dependent Equation of State
Mixing Rules


Local Coordination
Number Model


Equation of Stale
Mixing Rule


Whiting & Prausnitz [12] complicated,
see ref. 12 None given
Nij = Ni e(ij-eii)N/kT
Nj Nj quadratic only at
Ni +Nij = Nq = Cjp low density

Hu, et al. [13] complicated,
see ref. 13
-4t R g. 1- 3 Ni e aij
N 4 13 1 l)a exp kT None given
3 XV 4 \k
quadratic
at low
/ l 3 ,s1 density
a= 0.60-0.58(pxo) density



Nu= xiNV.i eeu/2kT Eq (22)
V + e I quadratic at
low density


1.0


0.8
e12


0.6


0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
REDUCED DENSITY po3
FIGURE 1. The local composition ratios 02, and 012 as a
function of reduced density po-3 for the square-well fluid
with 2e,,/kT = E22/kT = 1.2 and o,, = -22. The points
were obtained using Monte Carlo simulation [10]. The
arrows (-) are the theoretical low density limits, --- is
the Whiting-Prausnitz model [12], --- is the Wilson
model, --- is the model of Hu et al. [13], and ---
results from the model of Eqn. (20) for different mole
fractions.


1.5.) The results obtained in [10] for the species-
species combination numbers Ni for mixtures of
square-well molecules of equal size, but different well-
depths, are shown in Figure 1, and in [11] for mixtures
of molecules of equal well-depths, but unequal size, in
Figure 2. In the first of these figures we have plotted
the ratio

Ni Nj
N. Ni

which would be unity if there were no local composi-
tion effects (that is, if Nij/Njj = Ni/Nj), while in Figure
2, based on Eq. (13), we have plotted the ratios

03
aoj N Ni oaj

In this case if the local compositions were proportional
to the covolume fractions, the ratios would be unity,
while if the mixtures were random the ratios would
be equal to the constant crj/uj independent of temper-
ature, density, and composition.
The first important observation from Figures 1
and 2 is that the local composition or nonrandom mix-
ing effect is real; the local composition ratio is not


CHEMICAL ENGINEERING EDUCATION


/
= xi =0.25
o=x= 0.50 /
+ =Xl0.75


-


S---- -- -- ---'-




0 0









equal to the bulk composition ratio (i.e., ij is not equal
to unity in Figure 1, or -/cr4j in Figure 2). Further,
the local composition ratios are a strong function of
density, but only a weak function of mole fraction.
Also, for mixtures of equal size molecules (Figure 1),
where local compositions result only from attractive
forces, the local composition or nonrandomness effect
is strongest at low densities and weakens as the den-
sity increases. There is a simple physical explanation
for this. At low densities the molecules are, on the
average, widely separated, and while few molecules
approach each other, when they do the effect of the
attractive potential well is strong. On the other hand,
at high density the spacing between molecules is small
so that each molecule is constantly in the attractive
well of several of its neighbors. In this case the attrac-
tive potential provides an almost uniform background
in which the molecules move, and the hard cores,
which exclude a molecule from certain regions, play a
dominant role. It is for this reason that for the case
of equal size, unequal attractive energy mixtures the
local composition effect is large at low density (where
the difference in the attractive wells is important) and
small at high density (where the effect of the equal-
size hard cores predominates).
For the case of unequal size molecules, the size
difference plays an important role at all densities, as
may be surmised from Eq. (15). Consequently, by
using covolume fraction ratios, the remaining local
composition effects are small in magnitude and rela-
tively simply dependent on both density and composi-
tion. Figure 1 also contains the predictions of various
thermodynamic models when their parameters are
identified with those in the intermolecular potential.
In Figure 2 we show only the predictions of our local


composition model since those of most other models
are so seriously in error as to be off the scale of the
figure! The second observation, then, is that only our
recently proposed local composition model (to be dis-
cussed in the next section) is in even approximate
agreement with simulation results.
Another observation is that the local composition
ratios obtained from simulation are only very slightly
dependent on composition; indeed, to the accuracy of
the simulations they may be independent of composi-
tion. Thus, in agreement with the assumptions in a
number of thermodynamic models, ij may not be a
function of mole fraction. This implies that the simple
quadratic equation of state mixing rules of Eq. (11)
may be adequate at all densities-at least for
molecules that can be modeled by the square-well po-
tential.
In fact, in our studies of the high pressure phase
behavior of light hydrocarbons and inorganic gases
[14], we found that the simplest and most accurate
cubic equation of state correlation was obtained using
Eqs. (10 a,b) with the combining rules

aij =,[i(1- ki) (19a)
and


(19b)


where kij and dij are fitted to experimental data. We
can understand the success of this simple procedure
from the fact that the simulation results establish that
the composition dependence which underlies the van
der Waals one-fluid mixture rules is approximately
correct, so that the adjustable parameters in the com-
bining rules (Eqs. 19 a,b) can be made to compensate
for any remaining small errors.


1.0




0.9

0.8


0.1 0.3 0.5 0.7 0.1 0.3 0.5 0.7 0.1 0.3 0.5 0.7

p33 p63 p33


FIGURE 2. The local composition
ratios 021,or13/ro2 and 0,120223/
-r123 obtained from Monte Carlo
simulation [ 1] as a function of re-
duced density par = p. xo;ii3 for
the square-well fluid with = e22/
kT = 0.4 for various values of the
diameter ratio o22/or, The points
[, A, and 0 are for the mole frac-
tions x, = 0.25, 0.50, and 0.75,
respectively, and the lines ---,
-, and --- are the predictions
of Eqn. (20) at the same composi-
tions. Other local composition
models would not appear on the
scale of this figure. The exact low
density result for both these local
composition ratios is unity.


SPRING 1990


bij = 1 (bii+b) (1- di)









To test the assumption of the independence of the
total coordination number on composition, Nei ob-
tained from simulation is plotted as a function of com-
position for various different densities, temperatures,
and molecular size ratios in Figure 3. There we see
that it is only in the case of molecules of nearly equal
diameters that the total coordination number is ap-
proximately independent of composition, as assumed
in Eq. (16). In general, this lattice-based assumption
is incorrect; a more nearly correct assumption is that
the total coordination number is a linear function of
composition. This observation calls into question one
of the assumptions underlying the van Laar, Wilson,
UNIQUAC, and some other activity coefficient mod-
els.
Consequently, the effectiveness of these models
may be more a result of the limited density range in
which they are used, their flexible mathematical form,
and the adjustable parameters they contain, than
their theoretical correctness. Indeed, we find that we
can choose a set of parameters in any local composition
model which leads to reasonable agreement with our
simulation data over a limited range of density,
though these parameters are not related to the
parameters in the interaction potential model.

A NEW LOCAL COMPOSITION MODEL
One local composition model that we have found
[15] to be in approximate agreement with simulation
data over a large range of density, temperature, and
molecular size and energy differences, is


Sxi Nm Vij eij2kT0
"V + VoJ(e (20)


D0
0.00 0.25


where
V,,ij=Na|/V2 and Nm
is the coordination number at close-packing (18 if
Rij = 1.5).
This model is an empirical extension of Eq. (1-18)
for a pure fluid. Example results from Eq. (20) are
given in Figures 1 and 2; though not perfect, it is
clearly more accurate than other local composition
models.
Using Eq. (20) in Eqs. (2 to 4 and 1-3) results in
the mixture form of Eq. (1-19) which we write as
PV (PV Nus (21)
v a (21)
RT RT) V+a
with the following density-dependent mixing rule
SYxixjaij
V+ai.
a xixj (22)
Sv+a
where

aj = V,, (e -i1) and (-
is the mixture hard-sphere compressibility factor from
the van der Waals or other free volume models.
There are two features of Eq. (22) to be noted.
First, that at low density (V co), Eq. (22) reduces to
Eq. (10a), as it should. Second, that the number of
terms in the summations, and therefore the order of
Eq. (21) with respect to volume, increases with in-
creasing number of components; thus, Eq. (22) is not
a one-fluid mixing rule. From our comparisons with
experimental data [14], we find that if one does not
use correlative binary parameters (i.e., kij = di = 0
in Eqs. 19 a,b) the mixing rule of Eq. (22) leads to a
slightly better prediction of high pressure phase be-


FIGURE 3. The total coordi-
22 22 nation numbers N,, and Nc
1.2 = 1.5 2.0 for the same square-well
l l mixture considered in Fig. 2
obtained from Monte Carlo
** simulation [ 1]. The unfilled
0 and filled points are N I and
0 o No2, respectively, corres-
So 0 ponding to following densi-
o o 6 6 ties: (0,E) pd- = 0. 1, (A,A)
A A A 2 o p5" = 0.3; (0,0) p#- = 0.5;
a oA and (0, ) pd3 = 0.7. The im-
A a p portant observation is that the
3 03 13 1 a total coordination number for
..I I each species is a function of
0.50 0.75 1.00 0.25 0.50 0.75 1.0 0.5 0.50 0.75 1.00 mole fraction.
X Xi Xi


CHEMICAL ENGINEERING EDUCATION










TABLE 3
Correlation of Low Pressure Binary
Aqueous-Organic Mixtures
Using Two-Parameter Activity Coefficient Models
Vacation of
Average error Average error parameters over
In pressure In vapor temperature
mm Hg mole fraction range (%)
Two-Constant 13.56 0.0162 11.4
Margules

van Laar 8.52 0.0107 9.4
Wilson 8.95 0.0088 40.3
UNIQUAC 9.20 0.0101 206.7
Equation 23 6.73 0.0060 9.0

second components were acetaldehyde, acetone, 1-butanol, 2-butanone,
butyl acetate, cyclohexanone, diethylamine, diethyl ether, 1,4-dioxane,
ethanol, methanol, methyl acetate, methyl diethylamine, 3-methyl
pyridine, 1-propanol, 2-propanol, pyridine, tetrahydrofuran, and thiazole

havior (especially in the critical region) than do the
van der Waals one-fluid mixing rules. However, when
binary parameters are used (kij = 0), Eq. (22) and its
analog for other equations of state is not significantly
better than the simpler Eq. (10).
The excess free energy or activity coefficient
model that results from the combination of Eqs. (5)
and (20) is


G=pCEX GExT OiN b.
GEx = Gp co NmRT 7 xixj In bl
T,P TP I b-tu
1 bU


where

bij =1+ V., (eeUi/2kT- and
I


bi= (e 2kT-1)
2\


As shown in Table 3, this new activity coefficient
model correlates data for aqueous-organic mixtures
better than other two-parameter activity coefficient
models [16]. However, we have found that for other
mixtures the ability of this new equation to correlate
experimental data is approximately equal to that of
other activity coefficients now in use.

CONCLUSIONS

In this paper we have presented the generalized
van der Waals partition function for mixtures and
have shown both how it can be used to understand the
models we use in thermodynamics in terms of species-
species and total coordination numbers, and how to
develop new models. Using computer simulation, we
have shown that the local composition effect is real.


That is, that the local mole fractions in the vicinity of
a molecule in a fluid mixture are different than the
bulk mole fractions. Based on these simulations, we
conclude that some of the thermodynamic models we
commonly use contain assumptions which are not sup-
ported by the results of computer simulations for mix-
tures of square-well (and other) molecules. Thus, the
success of current mixture equations of state and ac-
tivity coefficient models may be more a result of the
limited ranges to which they are applied and the ad-
justable parameters used than their underlying
theoretical basis.
The overall conclusion of this (and the previous)
paper that I would like the reader to come away with
is, that while thermodynamic modeling is a mature
subject, there is still a need for much additional,
theoretically based research. Unlike the past, when
models were developed by insight, intuition, and/or
empiricism, we now have tools such as statistical
mechanical theory, computer simulation, and (though
not discussed here) a variety of experimental tech-
niques for determining local composition effects and
developing models, as well as the generalized van der
Waals partition function presented here, to go from
such microscopic models to macroscopic equations. Re-
search based on these tools should lead to better mod-
els of broader applicability. In particular, since we see
from the equations presented here that both activity
coefficient models and equations of state have their
roots in the partition function, a reasonable goal would
be to develop equations of state and mixing rules to
describe all mixtures, no matter how complex, and to
dispense with activity coefficient models completely.

ACKNOWLEDGEMENTS
This work was supported by Grant No. DE-FG-
85ER13436 from the United States Department of
Energy to the University of Delaware. The work of
two of my recent students, Drs. Kun-Hong Lee and
Lawrence Dodd, contributed greatly to the under-
standing of thermodynamic models presented here.

REFERENCES

1. Sandler, S.I., "From Molecular Theory to Thermody-
namic Models: Part 1. Pure Fluids," Chem. Eng. Ed.,
24,1(1990)
2. Sandler, S.I., J. Fischer, and F. Reschke, Fluid Phase
Eq., 45,251(1989)
3. Flory, P.J., Chem. Phys., 9, 660 (1941); Also Huggins,
M.L., J. Phys. Chem., 9, 440 (1941)
4. Hill, T., Introduction to Statistical Mechanics, Addi-
son-Wesley, Reading, MA, p. 275 (1960)
5. See, for example, S.I. Sander, Chemical and Engi-
Continued on page 116.


SPRING 1990









classroom


STOCHASTIC MODELING

OF CHEMICAL PROCESS SYSTEMS

Part 2: The Master Equation


R. 0. FOX and L. T. FAN
Kansas State University
Manhattan, KS 66506

THE GENERAL PHILOSOPHY of stochastic modeling
was discussed in the first part of this series on
stochastic modeling of chemical process systems.
Moreover, a particular class of stochastic models was
outlined, based on the master equation. In Part 2, the
master equation will be discussed and an approximate
solution technique known as the System Size Expan-
sion will be presented. The formal apparatus de-
veloped here will be utilized in the third part of the
series to model a chemically-reacting system.
In developing stochastic models based on the mas-
ter equation, it is assumed: (1) that a population of
discrete entities exists and evolves through interac-
tion between the entities; (2) that the entities possess
certain characteristics such as size, temperature, and
chemical makeup, which distinguish groups of entities
from other groups; and (3) that the entities exist in
Euclidian space of zero or higher order. A stochastic
model for this population can be derived based on the
concepts of probability theory. The resultant expres-
sion for the joint probability of the random variables
designating the distinct groups of entities in the pop-
ulation is known as the master equation [1,2]. The
master equation arises directly from the assumption
that the interactions between entities possess the
Markov property; changes in the system depend solely
on the present state of the population and not on its
past states.
In what follows, the random variable N denotes
the number of entities in a specific group in the popu-
lation. Subscript j signifies the number of entities pos-
sessing feature j; each feature is assigned a positive
integer. Similarly, multiple subscripts will designate
distinct groups of characteristics, e.g.,

{Ni,j:j E {1,2,3,...},ie {- ,...,-2,-1,0,1,2,...,+o}}
can denote the number of entities with feature j, lo-
cated at point i on a discretized number line. The joint


probability of the random variables {N} will be de-
noted as P({n},t) or simply P, when {{n}: n E
(0,1,2,3,...)}, i.e., when the state space of N consists
of the positive integers. However, for convenience of
mathematical manipulation it will be desirable to ap-
proximate n as a positive real number i.e., {{n}: n E
(0, + o)}, when performing the System Size Expansion
introduced in the following section; the joint probabil-
ity p becomes a joint probability density function de-
noted as p({n},t), or simply p. In both expressions, t
refers to time since the model describes a process
evolving in time. P({n},t) is interpreted as
P({N = nl,N2 =n2,...},t)

which is the joint probability that the random variable
N1 has a value of n1, the random variable N2 a value
of n2, and so on at time t. It is also necessary to define
a conditional probability, P({n}1, tl I {n}o,to), which is
the probability that the random variable N1 has a
value of n11, the random variable N2 a value of n21,
and so on at time t1, given that the random variable
N1 has a value of nio, and so on at time to.

THE MASTER EQUATION
Letting to = t and t, = t + 7, where 7 is a small time
interval tending toward zero, the conditional probabil-
ity P({n}1,t+7 I {n}o,t) can be expanded in a Taylor
series

P({n}i,t+Tr {n}o,t)= 1-Trwi({no,{n})1 ak({n} 1- .)

+ TWt({nlo, {n} )+o(2) (1)

The quantity Wt({n}o,{n}1) is the transition probability
per unit time that the population changes from state
{n}o to state {n}1 in the time interval between t and
t + The quantity
C Copyright ChE Division ASEE 1990


CHEMICAL ENGINEERING EDUCATION










A stochastic model for this population can be derived.... The resultant expression for the joint probability of
the random variables designating the distinct groups of entities in the population is known
as the master equation . [which] arises directly from the assumption that the
interactions between entities possess the Markov property ...
II


ir Wt({n}o,{n})-TWt({n}o,{n}o)
{n}
is the total probability of transition from state {n}o to
any other state during the time interval between t
and t+T. Thus, 7 Wt({n}o,{n}l) is the probability of a
transition from {n}o to {n}i during the time interval
between t and t + and

1- r Wt({n}o,{n}) ak(n {n}0) + TWt({n}o,{n},)
{n}
is the probability that no transitions occur during the
time interval between t and t + T.
Assuming that the states of the population possess
the Markov property, P({n}l,t + T) can be expressed as

P({n}l,t+r)= P({n}l,t+Trl {n}o,t)P({n}o,t) (2)
{n}o
Taking the limit of this expression as 7 0 yields the
master equation:
dP({n}lt) Wt({n}{n}l)P({nlt) (3)
dt

where Wt({n}l,{n}i) is defined as

Wt({n}l,{n}l) = Wt({n}{n})
{n}4)

MASTER EQUATION EXPANSION
The master equation, as given in Eq. (3), is in the
form of an ordinary differential equation. Since P({n},t)
appears only to the first power, the equation is linear.
However, if the state space is large, Eq. (3) is a large
system of coupled equations-one for each possible
state. For example, for the set of two random vari-
ables
{n}i= {nl,n2}i:nj E {O,1},ie1,2,3,4},je{1,2}}
there are four possible events

{n}1 = {,O},{n} = {1,},{n}3 = {,1},{n}4 = {1,1
Note that the state space of either of the two random
variables, N1 and N2, consists of two events, i.e., {0,1}.
The resultant system of differential equations could
comprise four coupled equations. In general, if k(j) is
the number of events in the state space of random


variable N, then the number of coupled differential
equations could be equal to

nlk(j)

Even ifj is equal to 1, this could still result in a very
large system of equations. For example, if the state
space of random variable 1 consists of all the integers
[k(1) equal to + co], the number of equations will be
infinite. It is necessary, therefore, to develop an ap-
proximation procedure for the solution of such equa-
tions.
The use of the System Size Expansion is predi-
cated upon the fact that often, for a system involving
interactions between entities in the population, the
magnitude of the change in the number of entities in
the system following a transition is an extensive vari-
able, e.g., the number of molecules, but the depen-
dence of the rate of transition on the number of en-
tities is expressed as an intensive variable, i.e., the
concentration of molecules. As an example, consider
a system consisting of two populations A and B, un-
dergoing second order interactions between them in a
volume f. Suppose that q members are in population
A and r members are in population B, and that a tran-
sition takes place when a member of population A
meets a member of population B. In most cases, the
rate of such a transition will not only be proportional
to q times r, but also inversely proportional to the
volume squared. This follows intuitively from the
image of the entities moving freely in the volume fl.
Decreasing f will increase the number of collisions
between members of populations A and B. The rate
of transition is thus dependent on the density or con-
centration of entities in the system.
Under the assumption that the System Size Ex-
pansion is valid, the term representing the rate of
transition Wt({n},{n}l) in the master equation, Eq. (3),
is first rewritten as Wt({n};{n}l {n}), where {n}i {n}
is the magnitude of the change in the random variables
{N} during a transition. Letting {~} = {n}I {n}, the
rate of transition can be expressed as Wt({n};{(}). It
can further be rewritten as
({n}; })(5)
if it is assumed to be a homogeneous function of the
random variable. The rate of transition is now a func-
tion of the intensive random variables {N/f}, and the


SPRING 1990









System Size Expansion can be introduced.
Making a change of variables and introducing the
new random variables {Z} and the deterministic vari-
ables {4} such that
1
{N} = { +(t)} + 2 {Z} (6)
the rate of transition is rewritten as

Wt({n}})= t (t)+z ;{} (7)

It will be seen later that the deterministic variables
{(} correspond to the macroscopic behavior of the sys-
tem. The master equation, Eq. (3), is then of the form

dP (t) + f ,t

dt
= ~ t (t) + 2z;{} P R (t) +1 z ,t (8)

To proceed with the expansion, it is useful to define
the first and second jump moments, Ai and Bij, re-
spectively, and Ai and Bij as follows:

Ai({n})= f (n-i -ni) Wt({n},{n)l)
nil

= ti wt({n}; i)=n 1T (t)+a k ; i (9)
i i J


Ai (t)+ 2z = -' Ai({n})


ap({Z-t) dli ap({z},t)
at t dt azi

=- A fi({t)+ z}1p({z},t)1


+ I I fli, (t)+ iz21p({z},t) +0 (
2 azi azj
(13)
where p({z},t) is the probability density function of
the new random variables {Z}, and O(fn-1') represents
terms of order -112 and smaller.
To proceed further, the expansions of Xi and Bij
in powers of f must be performed; they yield

Ai 0(t)+n 2z =Ai({0(t)})+Q 2zj Ai,({t(t)})+O(a-1)
(14)

fij o(t)+n 2 z = fli,({(t)})+o (15)

These expressions define the expansion coefficients
Ai, ij, and Bij. The expanded master equation, Eq.
(13), thus becomes

t i i I i pj 1
ap (1

S ziaz + ) a (16)

The terms of order h'12 on both sides of this expression
cancel if (i obeys


dti 4 i (_(t)0)


and


Bij ({n})= (nil ni)(njl nj)Wt ({},{n}, )
nil njl

= i x jWt ({n};Wi,,j)
ti tj

= };Sj] t (t)+n ;j (11)



Bij (t)+n 2z= Bi(n}) (12)

The expression Wt({n};iQj) denotes the dependence of
the rate of transition on both ni and nj. If no such
dependency exists, either ki or j is identically zero.
The master equation, Eq. (8), can then be expanded
in powers of f to yield


Letting 1f approach infinity thermodynamicc limit),
the last term on the right-hand side of Eq. (16) van-
ishes, thereby yielding


3p rz 1+ -- a2p
at -Zp' rJP 2. ziZj
S i j azi 2 i j


where Ai, Aij, and Bij are given by Eqs. (14) and
(15). quations (17) and (18) are the expressions result-
ing from the System Size Expansion.
Even in the form given by Eq. (18), the master
equation for the system may still involve a large
number of variables {Z}, since the number of random
variables is equal to the number of distinct populations
in the system, which may be large. Nevertheless, Eq.
(18) is a linear Fokker-Planck equation whose solution
yields a multivariate, normal distribution; the linear-


CHEMICAL ENGINEERING EDUCATION









ity is in reference to the coefficients Aij and Bi,j. In
general, a Fokker-Planck equation is said to be linear
if it can be written in the form of Eq. (18) and the
coefficients do not depend on the random variables
{Z}. Although the coefficients, Aij and Bij, are linear,
they are time-dependent through the dependence on
{(}, obeying the system of coupled, possibly non-
linear, differential equations given by Eq. (17). To
solve the Fokker-Planck equation, Eq. (18), it is
necessary to first solve Eq. (17) for {()}.
Solving Eq. (17) for {(} can itself be a highly ardu-
ous task, especially if the equations are non-linear.
Methods for solving the Fokker-Planck equations with
the constant coefficient matrices, Aij and ij, are
available, but the addition of a time-dependence
quickly increases the complexity of the problem. Such
difficulties can be circumvented in cases where a com-
plete expression for p({z},t) can be substituted by ex-
pressions for its moments in general, and for its
means, , and the cross-moments in par-
ticular. This is accomplished by multiplying both sides
of Eq. (18) by zi or zizj, and integrating over all vari-
ables from to + m; this yields


-(Zi)= Ai,&(Zj) (19)
and

d(Z, Z)= ,(k )+ Ak (Zk Zi)]+ ~i,j (20)
k
These expressions give rise to the governing differen-
tial equation for the covariances of {Z} as
d ov[ZiZj]= ikCov [Z,Zl +j,k Cov[Zk,Zi ij
k (21)
Returning to the original random variables {N} and
using their definitions in terms of {t} and {z}, the ex-
pressions for their means and covariances can be ob-
tained from Eqs. (19) and (21), respectively, as

d(Ni)= +n d(Zi)= iZ =QA, +n Aij (Zj) (22)
and
d dr
SCov[Ni,Ns]= dACov[Zi,Z]

= k{Ai,k COV[Nk,Nj]+j,k Cov[Nk,Ni]} + ij
(23)

Note that Eq. (19) is identical to the linear equa-
tion resulting from linear stability analysis of Eq. (22).
Consequently, the real parts of the eigenvalues of the
coefficient matrix, Aij, will be negative if the macro-
scopic behavior of the system is stable with respect


to fluctuations. Since is equal to zero,
will be zero as long as the system is macro-
scopically stable. When this is not the case, the Sys-
tem Size Expansion is no longer valid and must be
replaced by an alternate technique. Macroscopically,
such behavior may correspond to a bifurcation point
where two or more solutions branch from the original
stable state. Probabilistically, the density function for
the system would then no longer be unimodal; it is
this property which invalidates the System Size Ex-
pansion at such points.

DERIVATION OF CORRELATION FUNCTIONS
The foregoing derivations of the expressions for
the means and covariances of the random variables
have yielded little information about the dynamic
characteristics of the fluctuations. The auto- and
cross-correlation functions, however, can provide this
information. These functions yield measures of the in-
fluence of the value of a random variable at time t on
the values of the random variables at time t + T. Two
processes with equal means and variances but differ-
ent auto-correlation functions can behave differently.
For a Markov process, the auto- and cross-correlation
functions can be easily derived [1]; the governing
equations for them are the same as that for ,
Eq. (19). Defining the correlation matrix as

Ki,j () = (Zi (0) Z ()) (24)

the following set of differential equations can be de-
rived by relating K(t) to Cov[Zi,Zj];

dK,j (T)= A j' Ki, (); Ki(0)=Cov[Zi,Z (25)
k

where
"=Aj'k = jk )
{' = steady-state values of {0(t)}
Cov[Zi,Zj]l = steady-state covariance of Zi and Zj
Equation (25) is a direct result of the linear nature of
Eq. (19) and of the fact that the process is Markovian.
It also follows from Eqs. (24) and (25) and the relation-
ship between the random variables {Z} and the origi-
nal random variables {N} that the correlation functions
for the random variables {N} can be found by solving
Eq. (25) subject to the initial conditions

Kij (0)= Cov[Ni,Njr
where
Cov[N,,Nj] = steady -state covariance of Ni and Nj


SPRING 1990









In Part 3, the final part of this series, the master
equation and the System Size Expansion are applied
to modeling of a chemically-reacting system.

ACKNOWLEDGEMENTS

This material is mainly based upon work supported
under a National Science Foundation Graduate Fel-
lowship awarded to the first author.

NOTATION


Cov
Cov


I
P(i{n},t



Wt((n}


Greek








P t


Ai first jump moment
Ai Ai/9
Aij coefficient in expansion of Ai
Bij second jump moment
Bj Bij /
N,,Nj] (NiNj) (N XNj), covariance of Ni and Nj
[Zi,Z] (ZiZj) (i)(Zj), covariance of Zi and Zj
Kij (c) correlation matrix defined as (Zi(0)Zj(r))
for Zi and Zj, or as
(Ni (0)Nj (z))- (Ni(0))(Nj ()) for Ni and Nj
Nj number of entities possessing feature j
Nij number of entities possessing feature i and
feature j
(Ni) expected value of random variable Ni
p((n},t) joint density function of continuous random
variables (N)
?({n),t) joint probability of random variables (N}
I{n}o,to) conditional probability of random variables
(N 1 at time t given the value of random
variables {No0 at time to
o, n} i) rate of transition from state {n}o to state (n) 1
Zi fluctuating component of random variable
Ni
expected value of random variable Zi
expected value of product of random
variables Zi and Zj

Letters
8k (x) Kronecker delta where Sk(0) = 1
and 5k(x) = 0 for x 0
ti magnitude of change in random variable
Ni
S small time interval tending toward zero
*i deterministic variable corresponding to
macroscopic behavior of Ni
- ,;{}} homogeneous intensity of transition function
0 system volume


REFERENCES
1. Gardiner, C.W., Handbook of Stochastic Methods,
Springer, New York (1983)
2. van Kampen, N.G., Stochastic Processes in Physics and
Chemistry, North-Holland, New York (1981) 0


RANDOM THOUGHTS
Continued from page 71.

straight A's for the rest of eternity; 2) pocket their tuition;
and 3) don't give them the beer.

CORPORATE EXECUTIVE MODEL

Demand a high six-figure salary when offered the
position of chancellor. When you get it, use the interest
on your university's $200 million endowment to buy
your way into financial control of a small but productive
college in another state. Fire all their deans and
department heads and put your own people in those
positions. Move their best professors to your university,
fire the others who don't have tenure, take any of their
laboratory equipment you can use and sell the rest. Then
fold the college and use the losses to offset the profits
from the equipment sale, leaving yourself with a net
annual corporate tax liability of $3.27. Keep doing this.
When you've ruined enough small productive colleges
to get your salary up to seven figures, announce that it is
in the university's best interests to teach all classes in
Japanese. Sell controlling interest in the university to the
Kyoto Institute of Technology, participate in the dedica-
tion of the sushi bar where the Burger & Brew used to
be, and retire just in time to miss the cafeteria riot and
the disgusting things those ungrateful student hooligans
do with all that raw fish.




And that's all there is to it. With these few
simple techniques we can easily transform our images
and start to enjoy the good life.
On the other hand, there may be something to say
for the status quo. As things stand now, most of us do
our jobs without exploiting anyone's vulnerability or
innocence, enriching ourselves at their expense, or
trampling on their dignity. We may have to forego the
Swiss bank accounts this way, but it still seems like a
good bargain. We just have to be sure that our success is
measured by the quality of our teaching and research
and by nothing else...but then we're educators and
scholars by profession, so there's no problem.
And now if you'll excuse me, I've got to get my
notes together for the meeting at 10:00 where we review
Greg Furze and Roger Snavely for promotion and
tenure. Furze gets great teaching reviews and he's
written a couple of research papers that people think
very highly of, but there's not much by way of grants.
Snavely is another story. He brings in a mint in funding,
but his teaching evaluations are grim and his graduate
students complain that they hardly ever see him, even
though he keeps them here for as long as seven years.
Should be an interesting meeting. O


CHEMICAL ENGINEERING EDUCATION




























Book reviews

HEAT TRANSFER EQUIPMENT DESIGN
by R.K. Shah, E.C. Subbarao and R.A. Mashelkar
Hemisphere Publishing Corporation,
79 Madison Avenue, New York 10016-7892,
804 pages, $159.50 (1989)

Reviewed by
C.M. Hackenberg
Universidade Federal do Rio de Janeiro

This book is a very well-arranged collection of lec-
tures, the majority of which were presented by invited
authors at an Advanced Study Institute on Heat Trans-
fer Equipment, held in Poona, India, in June of 1986.
The Institute was organized to provide an international
forum for the dissemination of information on the
thermal hydraulic fundamentals and design of heat
transfer equipment. A keynote lecture on energy
conservation and waste energy recovery in industry
was presented in order to give an estimate of the
amount of energy used in industry in the form of heat as
well as to allow for a discussion of the most adequate
energy efficient technology.
The book contains nine chapters, and all the topics
are well-referenced. One will not find a very extended
analysis of the heat transfer fundamentals, but the given
information is sufficient to refresh the latent knowledge
of practicing engineers, and it also encourages the ex-
pert to pose new research questions to the applications
of more advanced studies.
The opening chapter is a general review of the clas-
sification of heat transfer equipment, heat exchanger
design methodology, and basic thermal design methods.
Uncertainties on the design and operation of systems of
heat exchangers and of the problems related to the heat
transfer modeling in heat exchange equipment from
laboratory work to industrial design are also taken into
consideration.


The second chapter briefly treats the codes and
standards of the mechanical design of exchangers, in-
cluding an appraisal of the state-of-the-art for tubular
units. The "meat" of the book begins in chapter three,
which presents the convection fundamentals and their
application to the single phase heat exchangers. The
usual correlations utilized for the evaluation of the heat
transfer coefficients are briefly discussed. It is nice to
find, in this chapter, a concise presentation of computa-
tional fluid dynamics applied to the prediction of the
heat transfer, mechanical, and thermal-stress behavior.
A general notion of the nature and capabilities of the
PHOENIX program, which first emerged in 1981, is
also presented.
Chapter four concerns the procedures of the ther-
mal design of single-phase exchangers. Here one finds
an overall design methodology for shell and tube ex-
changers which offers an approximate sizing technique
for preliminary design. This can be handy for checking
the results of computer-based design methods, as we all
know.
The brief lectures presented in this chapter include
computational applications to several types of heat ex-
changers going through air-cooled equipment and the
syntheses of optimal heat exchanger networks. Going
further, one finds a short analysis of the plate heat
exchangers and their design theory, followed by the
plate-fin and tube-fin design procedures. Furthermore,
other lectures discuss the design of electronic equipment
based on the thermal analysis, nuclear and fluidized bed
heat exchangers, direct fire heaters, and high tempera-
ture waste-heat recovery. There is also a nice discussion
on mechanically-aided heat exchanger design.
In chapter five there is a brief discussion of the fun-
damentals of two-phase flow heat transfer for boiling in
tubes and tube bundles. Then the Nusselt classical the-
ory for laminar film condensation on a vertical plate, a
horizontal tube, and a bank of horizontal tubes is re-
viewed. The condensation on enhanced surfaces is also
Continued on page 99.


SPRING 1990


Request for Fall Issue Papers *

Each year Chemical Engineering Education publishes a special fall Issue
devoted to graduate education. It consists of 1) articles on graduate courses and
research, written by professors at various universities, and 2) ads placed
by chemical engineering departments describing their graduate programs.
Anyone Interested In contributing to the editorial content of the 1990 fall Issue
should write to the editor, Indicating the subject of the contribution
and the tentative date It will be submitted.
Deadline is June 1st.
\_____________________________











materials


CHEMICAL COMPATIBILITY OF


POLYMERIC MATERIALS

Some Simple Guidelines


KENNETH A. SOLEN, MARVIN C. KUCHAR
Brigham Young University
Provo, UT 84602

THE AUTHORS PRESENT here some principles for
specifying general classes of polymers to be used
in contact with acids, bases, oxidants, certain other
common antagonists, and specific solvents. These
principles are appropriate for an undergraduate chem-
ical engineering general course in materials, where
extensive detail and discussion about a myriad of
chemical reactions and polymer variations cannot be
treated.
Many chemical engineers face the problem of
selecting equipment made from or lined with poly-
mers, and the compatibility of the equipment surface
with the chemical to be handled is a significant consid-
eration. It is obviously important to know whether
chemical reactions will occur between the chemical
and the polymer walls and whether solvent effects will
cause polymer swelling, dissolution, or alterations in
mechanical properties. Yet, our chemical engineering
department, like many others, can afford only one re-

Kenneth A. Solen received his BS from
the University of California, Berkeley, in 1968,
and his PhD from the University of Wisconsin, *
Madison, in 1974, both in chemical engineer-
ing. He also earned an MS in physiology from
the University of Wisconsin, Madison, in 1972.
After post-doctoral research fellowships at the
University of Iowa Medical School and the Uni-
versity of Oregon Health Sciences Center, he
joined the faculty at Brigham Young University
in 1976. He is currently a professor of chemical
engineering.
Marvin C. Kuchar received his BS and
his PhD degrees from Brigham Young Univer-
sity in 1958 and 1963, respectively, in organic
chemistry. After working as a Senior Research
Chemist for E.I. DuPont de Nemours he joined
the faculty at Brigham Young University in
1979. He is currently an associate professor of
chemistry and is Chairman of the Department
of Textiles.


H H- S H
Acetals --O--C-O-C-- 0- --C-
H H H


Esters


0 00
-C-O-R- -C-O-R
e


0 o0
Amides -C-N -C-N
C H \H

Urethanes -O-C-N -O-C-N
\H H

0 0o
Carbonates -0C-O- 0- -0--C-O-

e
Cyanides -C=N --- -C N


H H H H
Olefins --C C- C -C--C-

FIGURE 1. Dipole resonant forms in some common
classes of polymers.

quired undergraduate course in engineering mate-
rials. The course is based on one of the popular general
textbooks on engineering materials which covers a
wide spectrum of topics including metallurgy,
ceramics, semiconductor materials, and polymers.
However, the polymer treatment is limited and fo-
cuses largely on forming and molding the polymers
(i.e., mechanisms and kinetics of polymer formation
and rheology of polymer melts) and on physical prop-
erties. Thus, we felt that supplementary coverage was
necessary.
Our goal is to explain polymer-chemical compatibil-
ity, as much as possible, in terms of unifying princi-
ples. The alternative would be to memorize extensive
information about the very large number of specific
reactions encountered between nearly-infinite combi-
nations of polymers and chemicals. Even with the ap-
plication of some central principles, the number of ex-
ceptions and variations would require significant dis-
cussion and tabulation. Such a treatment is attempted
in a few books dedicated to the description of polymers
Copyright ChE Division ASEE 1990


CHEMICAL ENGINEERING EDUCATION


h E










(see references 1-3 for example), but general
textbooks about engineering materials can hardly
begin such coverage. Further, while the vendors of
polymer equipment provide "technical specifications"
about chemical compatibility, those specifications are
typically tables of chemicals matched against their
products with empirical recommendations such as
"good," "fair," and "not recommended." Other tables
specify the maximum usable temperature recom-
mended for each chemical-polymer pair, but do so also
in an empirical fashion. A further complication is that
each manufacturer adds specific agents to its polymer
formulations to modify the properties of the final prod-
uct, thereby adding even greater uncertainty to the
application of general principles. However, chemical
engineers, with their background in organic and phys-
ical chemistry, should know some basic rules which
will allow at least preliminary selection of polymer
types and evaluation of vendor claims for a particular
application.
This paper summarizes some basic principles for
predicting relative chemical attack from acids, bases,
oxidants, and certain other common antagonists and
also for predicting relative solvent effects in polymers.
This material is presented in two or three lectures in
our chemical engineering materials course after re-
viewing with the students the structures and names
of common polymers, discussing structural charac-
teristics (density, crystallinity, etc.), and comparing
the properties of thermoplastic and thermosetting
polymers. The brief treatment described below pro-
vides some understanding (as opposed to memoriza-
tion) which will allow preliminary evaluation of
polymer equipment for handling chemicals and which

Aceals H- H He

Acetals -0_ -C-OH + -C-X
HX- X-orH2 -C-OH + -C-OH

(Do, OH 0
Esters R-C--O-R -- R-C--O-R R-C-OH + R-OH
H20


H
0o- OH
Amides -N'/ -N
H t 'H
H20


O
C-OH +


Cyanides -CN C-OH + -NH2


The paper summarizes some basic
principles for predicting relative chemical
attack from acids, bases, oxidants, and certain other
common antagonists, and also for predicting
relative solvent effects in polymers.


will also serve as a framework upon which information
about specific reactions and cases can later be added.

UNDESIRABLE CHEMICAL REACTIONS

Acid-Base Attack

The susceptibility of many polymers to attack by
surrounding acids and bases is related to the degree
of"charged dipole formation within the polymer struc-
ture. A review of atomic structure will convince the
student that the relative electronegativities of C, N,
and 0 are in the order O> N > C. This helps to ex-
plain that the combination of these elements in a
polymer structure results in the distortion of electron
clouds away from carbon atoms, with a resultant di-
pole as one resonant form (Figure 1). The student
should also be aware, however, that even olefinic dou-
ble bonds have resonant dipole forms. Non-oxidizing
acids generally attack by attraction of the H+ ion to
the negative side of the dipole resonant structure and
formation of a complex. The unstable complex then
further reacts with the negative ion of the acid or with
water (in the case of aqueous solutions) to split the
polymer chain at that point (Figure 2). The attack of
a polymer by a base proceeds in a similar fashion,
with the initial attraction of the OH- and complex for-
mation at the positive site of the resonant dipole and
then subsequent resolution of the unstable complex
(Figure 3).

G0 H, H,
Acetals R- -0- R-o0 =C-O- -- R-OH + C-0-
H OH OH
OH- H20


0o
Esters ,C-O-R -
X OH


O X+
-C-O-R --
OH


O OX+
Amides 5C-N. -C-N
XOH OH H


O
-C-O X + R-OH


0
- - II +
C-O~X +


H H H H
Olefins -C- -C-C-
o H HO H
-kH 0


H H
-. C
- -C--C
OH H


FIGURE 2. Examples of the attack of dipolar resonance
forms of polymers by acids.


H H
Olefins -C C
x,,o,


SPRING 1990


H H
X O-c-cH
- X -C-C-OH
X OH


FIGURE 3. Examples of the attack of dipolar resonance
forms of polymers by bases.










In our materials course, the emphasis is not so
much on the reaction mechanisms as on the principle
that more polar resonant forms will cause greater at-
tack in general. Hence, polyamides (e.g., nylon), ole-
fins (e.g., natural rubber and styrene butadiene), and
polyesters (e.g., polymethylmethacrylate, PMMA)
will be relatively susceptible to acid-base attack.
Examples include the partial hydrolysis of
poly(methylacrylamide) in base to the free acid form,
the conversion of acetals by alkali and acid to produce
alcohols, the cleavage of polyester chains by hot alkali
treatment, etc. Polyurethanes are not quite as suscep-
tible, because the urethane nitrogen atom stabilizes
the resonant form and reduces the polarity. At the
other extreme, polyethylene (PE), with no polar reso-
nance, will generally not be attacked by acids and
bases (which explains why acids and bases can be
stored in polyethylene containers).
Of course, very strong acids and bases especiallyy
oxidizing acids) can attack even polyethylene or poly-
propylene (PP) by directly attacking the C-H bonds,
especially the weaker bonds on the methyl side groups
of the PP. Where these very strong reagents are to


TABLE 1
Relative Rates of Oxidation Versus Structure [4]


Relative Rate
of Oxidation


Structure


CH3
(--CH2-C=CH-CH2--)
t t

CH3
(--CH2--CH---0-)


CH3)
(-CH2--CH--)
T

CH3
0



CH3-CH2--0
C=0
-----CH-


be encountered, the PE chain is used with fluorine
substituted for both of the hydrogens on every other
carbon atom (polyvinylidine fluoride, PVDF) or on
every carbon atom polytetrafluoroethylenee, PTFE)
to reduce such attack. The electron-rich fluorine acts
by stabilizing the polar resonant forms.
Chlorine is also used for a replacement for hydro-
gen on every other carbon, either substituted for one
of the hydrogen atoms on that carbon (polyvinyl-
chloride, PVC) or for both hydrogen atoms of that
carbon (polyvinylidine chloride, PVDC). However,
the larger chlorine atom creates some steric stress
because of its size and has a greater tendency to be
removed. Hence, its resistance to acid-base attack is
limited.

Oxidation
Synthetic polymers are oxidized by oxygen in the
atmosphere, particularly in the presence of light (in
the absence of light the reaction is relatively slow)
and by liquid oxidants, such as permanganate,
peroxides, epoxides, oxidizing acids (e.g., nitric, sul-
furic, and chromic), and even water. The resulting
changes in polymer chemistry yield a more brittle
polymer with corresponding loss of strength.
Oxidation of polymers can be generalized into the
following reactions (4):

Initiation:
Production of Re or RO2a
(where R is some portion of the hydrocarbon chain)
Propagation:
R* + 02 -4 RO2*
RO02 + RH -* ROOH + Re
Termination:
2R* R R
RO2* + Re ROOR
2RO2* -* Nonradical products

Particularly susceptible locations include carbon
atoms which are 1) adjacent to double-bond carbon
atoms (polymers such as polyisoprene or
polybutadiene that contain unsaturated linkage are
susceptible to attack by ozone as well as oxygen), 2)
connected to ether oxygen atoms, and 3) tertiary car-
bons (Table 1, poly(vinylchloride) is very susceptible
to oxidation, and, of the major polymer systems,
polypropylene is more susceptible than polyethylene).
Oxidation can be reduced by adding inhibitors or
by altering polymer structure. UV screeners are


CHEMICAL ENGINEERING EDUCATION


I










added to all polymer formulations for equipment use.
The substitution of fluorine in place of hydrogen
(PVDF, PTFE, etc.) significantly reduces susceptibil-
ity to oxidation, because the electronegative fluorine
causes charge repulsion of the oxidant. Also, poly-
styrene, with its electron-rich aromatic ring to protect
potential oxidation sites, is less susceptible to oxida-
tion than is polyethylene.

Special Addition/Substitution Reactions

Several chemical agents add to the double bonds
of unsaturated polymers, and some may even attack
saturated compounds. The most common of these are:

CHLORINATION: Chlorine gas, hydrochloric acid, chloro-
sulfonic acid, and phosphorus-containing chlorides are
among the agents which will cause chlorine attack of
polymers. Not only will chlorine be added to unsat-
urated bonds (e.g., conversion of PVC to a dichloride),
but polyethylene can also be chlorinated. Chlorination
of natural rubber involves a complex series of addition,
substitution, crosslinking, and cyclization reactions.

HYDROGENATION: Polymers with unsaturated bonds may
be subject to hydrogenation, particularly at high tem-
peratures in the presence of high-pressure hydrogen
gas. For example, polyisoprene can be hydrogenated
to yield poly-isopentane, and polystyrene can be con-
verted to poly-vinylcyclohexane.

N ITRATION: Nitric acid is the most common source of this
attack. Polymers with aromatic groups are susceptible
to nitration reactions on the aromatic ring. For example,
polystyrene in the presence of both nitric and sulfuric
acids yields the corresponding poly(nitrostyrene). With
aliphatic polymers, the nitro group attaches to the
chain or to a suitable substituent on the chain.

Many additional specific reactions could be in-
cluded, but only a few of the more common ones are
described, and the students are warned that they
must do their own homework on the job for each appli-
cation which presents itself.

High-Temperature Effects
In addition to the fact that high temperatures
cause softening (loss of strength) of polymers, organic
polymers are unstable at temperatures above 150-200
degrees centigrade and undergo some chemical reac-
tions. the kinds of reactions include:

ISOMERIZATION: Polymers containing certain side chains
such as cyano(nitrile), chloro, carboxylic acid, or cster
groups, when subjected to high temperatures,
undergo isomerization to yield new products. A classic
example is the cyclization of natural rubber to produce
cyclohexane rings in the polymer chain. (This reaction
is exploited by the Goodyear Tire and Rubber Com-


pany to produce Pliolite rubber using chlorostannic
acid as a reagent.)

DEPOLYMERIZATION: High temperatures can cause de-
polymerization to yield the monomer or chain cleavage
to yield low molecular weight products or degradation
of side chains. The result is a general breakdown of the
polymer. For example, poly(tetrafluoroethylene),
poly(methyl methacrylate) and poly(alphamethyl
styrene) undergo complete conversion to the
monomer when heated to high temperatures.
The students should be alerted to the possibility of
polymer degradation from factors other than contact
with reactive chemicals. Such factors include X-ray
irradiation, electric discharge, ultra-violet radiation,
etc., which may result in cleavage and reformation of
the polymer chains. However, no simple theories are
available to predict the effects of such phenomena.
With this background, the students are prepared
to understand some of the general trends seen in the
empirical tables provided by the polymer vendors.
For example, the extracted information in Table 2
shows that polyamides, polyesters, and rubber are not
good candidates for use in the presence of acids and
bases, while PE and PVDF are much better candi-
dates.

TABLE 2
Selected Date on Chemical Resistance at 70'F
from Gates Rubber Co.
Chemical Resistance for Industrial Hose Stocks
Nat Rubber Cmss-#nked PVDF Polyester
SStyrene PE + HFPP Elastomer Polyamde
But. (Gatron) (Vton) (Hytrel) (Nylon)


Acetic Acid (25%-50%) N


Agua Regia
Chromic Acid (10%)
Chromic Acid (25%)
Chromic Acid (50%)
HC((15-37%)
Nitric Acid (10-60%)
Sulfuric Acid (10%)
Sulfuric Acid (30%)
Sulfuric Acid (50%)
Sulfuric Acid (93%)


Sodium Hydroxide (40%) E
(50,115-F) E
(50,180sF) N
(60%) G
Potass. Hydroxide (30%) G
Potass. Permanganate N


E = Excellent: G = Good: N =Not Recommended:


G N G N


N G G N N


G G E N N
N G E N N


G G N N
E G N


- = Insufficient Data


SPRING 1990









SOLVENT EFFECTS
Solvents interrupt the weak, secondary bonds be-
tween polymer chains. With thermosetting polymers,
this can result in swelling of the polymer. In thermo-
plastic polymers, where chains are not necessarily co-
valently attached to each other, solvent effects can
include the "dissolving" of some polymer material
(i.e., liquifying and removing it from the original bulk
of polymer). Obviously, the extent of the solvent ef-
fects is influenced by the access of the solvent to the
polymer chains, so amorphous, low-density (loosely-
packed) polymers with minimal cross-linking or with
long cross-links will be more susceptible.
To actually dissolve a polymer, the solvent must
completely surround the chains, so short-chain poly-
mers are more susceptible. For example, foams typi-
cally have very low molecular weights, are very
amorphous, and dissolve relatively easily (a good dem-
onstration here is to compare the effects of a mild acid
on a styrofoam cup versus a polystyrene beaker). This
principle is used to good advantage by manufacturers
who solvent-treat polymer formulations to carry away
low-molecular weight chains to produce high-molecu-
lar weight products.
The prediction of which solvents will be more effec-
tive with a given polymer begins with the hypothesis
that solvents must compete with the cohesive forces
between polymer chains. Such forces can be charac-
terized by the "cohesive energy density" which, for
liquids, can be defined as the energy needed to vap-
orize a certain volume of the liquid. Thus

Cohesive Energy Density = 82 = E0/Vo

where
Eo = latent energy of vaporization of volume Vo
8 = "solubility parameter"

The hypothesis is that a solvent with an energy
density similar to that of the polymer will be able to
exchange weak bonds with the polymer molecules
(chains) and to disrupt the polymer. This is presum-
ably the reason for observation of the "like-attracts-
like" relationship (polar solvents attack polar poly-
mers, aromatic solvents attack aromatic polymers, al-
kane solvents attack alkane polymers, etc.). If the
hypothesis is correct, a value of 8 exists for the
polymer (determined from exposure to solvents, since
polymers are not volatile) at which a maximum solvent
effect will be achieved (i.e., when 8solvent Spolymer).
In fact, swelling and/or dissolution in most polymers
is observed when solvent is within + 2-3 (cal/cm3)"1
of a central value, which is then reported as polymer
(examples of this effect are given in references 4 and


5). Values of 8 for polymers and solvents are tabulated
in several references (4, 6), and it is instructive to
have the students plot a vendor's recommendations of
solvents for a polymer against the values of solvent,
such as illustrated in Figure 4 for a PVDC formulation
from Dow Chemical Company.

200


soC,
Max. 150
Usable
Temp.
(F)
100


50
5 10 15 20 25
8 (cal/cm3)l2
FIGURE 4. Recommended maximum usable tempera-
tures of solvents with PVDC (Saran@) extracted from
Dow Chemical Company "Chemical Resistance Guide for
Systems Using Plastic Lined Piping Products" (values of
8 were compiled from reference 4).


The value here is that for a particular polymer,
given the value of 8 for that polymer or given a table
with recommendations for a few solvents, the student
will be able to quickly guess if a particular solvent is
safe or questionable by referring to the value of 8 for
that solvent. For example, suppose that an engineer
wishes to know if dimethyl sulfoxide will cause serious
swelling and/or dissolution with the PVDC from Dow
Chemical Company. First of all, a dilemma arises, be-
cause the value of 8 for PBDC is reported by Hall (6)
as 9.8 (cal/cm3)1/ and by Rodriguez (4) as 12.2 (cal/
cm3)12. From Figure 4, it is obvious that the formula-
tion from Dow Chemical Company is closer to the ma-
terial reported by Hall, and that dimethyl sulfoxide (8
= 13.0 (cal/cm")1') will probably not induce significant
solvent effects with this polymer.

REFERENCES
1. Seymour, R.B., Introduction to Polymer Chemistry,
McGraw-Hill, Inc., New York (1971)
2. Fettes, E.M., High Polymers, Vol. XIX, Chemical
Reactions of Polymers, John Wiley & Sons, Toronto,
Canada (1977)
3. Seymour, R.B., Plastics vs. Corrosives, John Wiley &
Sons, New York (1982)
4. Rodriguez, F., Principles of Polymer Systems, 2nd ed.,
Hemisphere Publishing Corp., New York (1982)
5. Allcock, H.R., and F.W. Lampe, Contemporary Polymer
Chemistry, Prentice-Hall, Englewood Cliffs, NJ (1981)
6. Hall, C., Polymer Materials, Halsted Press, John Wiley
& Sons, New York (1981) 0


CHEMICAL ENGINEERING EDUCATION










REVIEW: Equipment Design
Continued from page 93.
presented and recalls Gregorig waved surfaces. This
chapter concludes with a nice review of the in-tube
condensation which describes recent improvements in
the methods for predicting flow patterns, pressure drop,
and heat transfer during condensation in horizontal and
vertical tubes.
The thermal design of two-phase exchangers is
treated in chapter six, with a well-posed set of condenser
design approaches for pure vapor, mixture of vapors,
and multicomponent mixtures with the presence of non-
condensables. Special care is devoted to the design
methods for the cross-flow and reflux condensers. A
critical evaluation of cooling tower design methodology
is presented which outlines exact design procedures
and assesses the errors associated with the approximate
method. Next there is a brief discussion of the basic heat
pipe theory, followed by the preliminary design consid-
erations. Thus, an overall design methodology is pre-
sented for heat pipe exchangers. Detailed solution proce-
dures are outlined for rating and sizing problems with
an example. The chapter concludes with a review of the
types of heat pumps, their economics, and the state-of-
the-art of chemical absorption heat pumps for industrial
applications.
Chapter seven on heat transfer augmentation is
primarily directed to enhanced forced convective va-
porization and condensation inside tubes. A nice review
is presented, and the two-phase different approach is
compared to the heat transfer evaluation of single phase
behavior. This is followed by a discussion of the perfor-
mance evaluation criteria for enhanced tube geometries
used in two-phase heat exchangers, which is resolved in
terms of the heat transfer area ratio.
Chapter eight includes a brief introduction to the
fundamentals of rheology and the thermal design of
heat exchangers for non-Newtonian fluids. Specific in-
formation on the role of theological behavior and geom-
etry on heat transfer is presented. One should notice that
special emphasis has been given to the adoption of
Newtonian fluid correlations in dealing with non-New-
tonian materials.
To complete the design analysis, chapter nine goes
through a treatment of flow-induced vibration mecha-
nisms, and some correlations for their prediction in heat
exchangers are discussed. A single-component, two-
phase (boiling or condensation) flow instability analysis
is also presented which concentrates on the practical
aspects of two-phase flow instability in large steam or
vapor generators.
While reviewing the book, I got the impression that
the authors accomplished the main objective of the Insti-
tute. The material presented may be utilized in modern
engineering education. The book is not a teaching text in
the usual sense-there are too many gaps for a new
learner to bridge. But it may be utilized, with a


reasonable amount of success, in an advanced design
course of heat transfer equipment. O


a SE


book reviews


GRANULAR FILTRATION OF AEROSOLS
AND HYDROSOLS
Chi Tien
Butterworths, 80 Montvale Ave., Stoneham, MA 02180;
1989 pages, $69.95 (1989)


Reviewed by
Richard H. Heist
University of Rochester

This book deals with granular filtration of liquid
and gaseous suspensions and is directed specifically at
this one type of separation process. It fills a gap in the
separations literature since most of what has been pub-
lished is spread throughout the journal literature. This
book will be particularly useful to anyone new to the
field of granular filtration who wants to get started as
quickly as possible. Although the author asserts that the
level of the text is consistent with material in accredited
chemical and mechanical engineering degree programs,
I am not so sure this is true. However, the text could cer-
tainly be used as a text or a supplemental text in gradu-
ate level, research-oriented courses dealing with sepa-
rations.
Although both the filtration of liquid suspensions in
granular media and aerosol filtration in granular beds
are usually treated as two distinct subjects, the author
departs from this traditional practice and takes a unify-
ing approach with the result that a majority of the chap-
ters in the book apply equally well to both processes. The
principles presented and discussed in the text provide
the framework for obtaining information that will aid in
the design, operation, and control of granular filtration
systems.
In Chapter One the author provides a brief
overview of granular filtration, a bit of historical per-
spective, and a comparison with other, related separa-
tion technologies. Several examples of commercial scale
granular filtration applications for both liquid and
gaseous suspensions are discussed.
In Chapter Two, the governing equations that de-
scribe the macroscopic behavior of granular filtration
are derived. The formulation, solution, and application
of these equations to provide information describing the
time dependence of effluent concentration and pressure
drop are the primary focuses of this chapter. The author
also provides an interesting description of filtration as a
stochastic process.
Continued on page 105.


SPRING 1990










f classroom


THE USE OF LOTUS 1-2-3 MACROS

IN ENGINEERING CALCULATIONS


EDWARD M. ROSEN
Monsanto Company
St. Louis, MO 63167

THERE IS A GROWING recognition of the potential
usefulness of spreadsheet programs throughout
the chemical engineering curriculum. This has been
confirmed by the Education and Accreditation Com-
mittee of AIChE in its listing of the CACHE Corpora-
tion's recommendation of "Desired Computer Skills
for Chemical Engineering Graduates" [1]. One of the
desired skills is the use of the spreadsheet.
For educational use, the spreadsheet provides
some appealing features:
The student must have a complete understanding of
the problem. He does not use a "canned" program
which may hide the solution method.
The spreadsheet allows the student to view the prob-
lem's solution directly without the need to print out
iterations or look at an output file.
The spreadsheet facility is generally available when
other computational facilities may not be.

For industrial users, the spreadsheet is also of con-
siderable interest:
The user can use one system for a variety of problems.
He need not leam multiple systems to carry out his job.
There is a certain level of integration the user of the
spreadsheet program can achieve by reading files from
and sending files to other programs.


Edward M. Rosen is a senior fellow in
the Monsanto Chemical Company. He re-
ceived his BS and MS degrees in chemical
engineering from Illinois Institute of Tech-
nology and his PhD from the University of
Illinois. He is coauthor (with E. J. Henley) of
the book Material and Energy Balance
Computations (John Wiley, 1969). A past
chairman of the CAST Division of AIChE, he
is currently chairman of the Process Engi-
neering Task Force of the CACHE
Corporation.


The use of the spreadsheet in chemical engineering
calculations has been recently reviewed [2]. However,
the use of macros was not indicated. Such macros ex-
tend the usefulness of the spreadsheet into a variety
of applications which would be quite improbable with-
out them. In this discussion, the macros of the popular
spreadsheet program LOTUS 1-2-3 [3] will be used
(Version 2.01).

MACROS
Macros were originally intended to simply allow
the user to store a series of keystrokes so that they
wouldn't have to be reentered in routine applications.
Macros, however, allow programming in a broader
sense. The early version of LOTUS 1-2-3 macros (/X
commands) were difficult to use and to follow. How-
ever, with Release 2 the Advanced Macro Commands
have become available. These are named in such a
way as to be much more understandable, and one can
follow a listing with comparative ease.
One of the limitations of the standard worksheet
is that it doesn't allow for the use of "loop within loop"
calculations which arise so often in chemical engineer-
ing. However, with macros, this limitation is removed
and the capability to use subroutines, much as in
FORTRAN, is possible.
A related limitation of the standard spreadsheet is
the inability to jump to an arbitrary location as a re-
sult of a conditional evaluation. With macros, this is
not only possible but also invaluable.
Since learning the macro language takes time and
effort, it is fair to ask whether it is worthwhile to
learn macros-especially if a calculation can be carried
out in another way, say by using FORTRAN or
BASIC. The answer certainly depends on system
availability, accessibility, familiarity, and the time
available for solution. However, it is worthwhile to
note that the advanced macro capability of LOTUS
1-2-3 can be made useful with about one day's effort.
E Division ASEE 1990


CHEMICAL ENGINEERING EDUCATION














SUBROUTINES

There are differences in using subroutines in

LOTUS 1-2-3 as compared to FORTRAN. The first is

the ability in LOTUS 1-2-3 to address and manipulate

any cell in the spreadsheet whether or not it is passed

as an argument to the subroutine. Results from the

subroutine cannot be placed in a relative location (i.e.,

the address cannot be passed on output). Instead the

output must be picked up from locations designated

by the subroutine.

These comments are illustrated in Figure 1 which

shows the coding for a general purpose subroutine,

ROOTX, based on Wegstein's method [4] for solving

a one dimensional equation in the form


f(x)= x (1)


The subroutine operates in two modes. If 'code'


To Run:
Set Hi
& H3
Then alt q

Problem 1
fro My ers
& Seider
Page 455

van der
eaels Eqn

Initial v
in H3: 600

Sotn: 222.4454


HI: Prob No. 2

H3: x 409.9927
H4: f(x) 409.9927

van der aals Constants

H8: a= 1351000
H9: b= 38.64
H10: R= 82.06
H11: T=(deg K) 173.15
H12: P=(ate) 50

H14: RT 14208.68
H15: a/v^2+P 77.30286

EVAL (LET H14,Hl0*H11)
(LET n15.H8/(H3*H3)+H12)
(LET M4,H14/H15+H9)


(cell P6) is set to 0, then the working cells (P7 to P16)

are cleared, and control is returned to the calling

routine. If 'code' is set to 1, then ROOTX will return

a new x for each pair of values x and f(x) supplied as

arguments which are passed to cells P4 and P5 using

the DEFINE keyword. Note that the upper and lower

bounds on the slope in Wegstein's method are set in

cells P1 and P2.

The calling program is given in the macro \q. It is

set up to solve either of two problems determined by

cell H1 (Problem Selection). The arguments passed to

the subroutine, H3, x, and H4, f(x), are specified in

the call to the subroutine,i.e., {ROOTX H3,H4}. The

new value of x generated by ROOTX is picked up

from location P4 and passed to location H3 with the

macro command {LET H3,P4}. The convergence

criterion is given in the calling program and can be

problem dependent.


paper
lower

x
f(x)
code
counter
x1
fl
x2
f2
slope
t
t*delte
ternl
detm


0.8
-9

409.9927
409.9927

4
409.3106
410.0009
409.9942
409.9927
-0.01200
0.988133
-0.00151
0.683556
0.683556


Problem 2 H25:
fre Reklaitis H26:
Page 445 M27:
M28:
M29:
Initial T
in H3: 700


Soln: 409.9927


3339.3
451.1603
613.8811
188.4174
18.65373


EVAL1 (LET H25,3339.3)
(LET n26,1.138E-2*(H3^2-298^2)/2.)
(LET H27.0.4338E-4(H3^3-298^3)/3.)
(LET H28,0.37E*7*(H3^4-298^4)/4.)
(LET H29,1.01E-11d(H3^5-298^5)/5.)
(LET N4.298+(H25+H26-H27MH28-H29)/29.88)


RODTX {DEFINE P4:VALUE,P5:VALUE)
(CALC)
(IF P6eO)(BRANCH P25)
(BRANCH P27)
/CP6-P7..P16-
(RETUIN)
(LET P7,P7T1)
(LET P8,PIO)
(LET P9,P11)
(LET P10,P4)
(LET P11,PS)
(LET P15,M BS(P10-P8))
(IF P15>0)(BRANCH P36)
(LET P16,1)
(BRANCH P37)
(LET P16,PIO-P8)
(LET P12,WRIN(Pl,I AX(P2,(P11-P9)/P16)))
(LET P13,1/(1-P12))
(LET P14,P13*(P11-PO10)
(LET P4,P4*P14)
(IF P7=1)(LET P4.P5)
(RETURN)


\q (LET P6,0) Clear
(RWOTX H3,H4)
(LET P6,1) Set ROOTX
G47: (IF HI9I)(BRAMCH G50) Select Prob 1 or 2
(EVAL1)
(80ANCH G51)
G50: (EVAL)
G51: (IF IES(N3-H4)<1.E-6)(BRANCH G55) Test Convergence
(R00TX 3,H4S ) Get new x
(LET 13,P4) Set x to f(x)
(BRANCH G47) Evalute function
G55: (CALC) Complete

FIGURE 1. Use of subroutine ROOTX in Macro\q.


SPRING 1990










Depending on the problem specification given by
H1(1 or 2) the macros EVAL or EVAL1 are used to
evaluate f(x). Problem 1 (EVAL) is taken from Myers
and Seider [5] in which the value of v is sought in the
van der Waals equation in the form v = f(v). Problem
2 is taken from Reklaitis [6] in which a temperature
is sought in an equation in the form T = f(T). The
solutions found in each case agree with those given by
the authors. Note that in each case (EVAL and
EVAL1) the value of H4, f(x), is calculated from the
value of H3, x.

PARTIAL DIFFERENTIAL EQUATIONS
The use of the spreadsheet to solve the steady
state LaPlace equation in two dimensions and the sim-
ple parabolic equation in one dimension and time was
discussed in [2]. In each of these cases the problem
could be set up in a single two dimensional table and
solved by an appropriate finite difference formulation
using the standard spreadsheet. However, this is not
possible in the following case.
Consider heat transfer in a cylinder of radius a and
height L:
PC = k I a2T a2T
DO R R iR R Z
where
p = density
c = heat capacity
k = thermal conductivity
T = temperature
R = radial coordinate
Z = height coordinate
0 = time


stable Crank-Nicolson method [7,8]. Let
i = index in the r direction
j = index in the z direction
n = index in time t

Then using finite difference approximations

u ui,J,n+l ui,J,n
at At

Ul+l,j,n 2Ui,j,n + Ui-l,j,n
2u 0.5 (Ar)2
r2 i+1,j,n+1 2ut,jn+1 + -l,J,n+l
(Ar)2


SU ,j, U-j,n Ui.,jn.+ -Ui-l.,J.n+
r ar 2iAr Ar Ar J


'UiJ+,n -- 2Ui,j,n + Ui,J-l,n
a2 (Az)2
I= 0.5
2 UlJ+I,n+l 2Ui,j,n+ + Uij-ln+l


Substituting these approximations into Eq. (4) and
solving for ij,n+ 1 there results

(D + B / i)u,, +(B B /i)(ui-1,, + Uil,j,n+1)
uj,n+l= --. + B(ui+1,j,n+l + ui+1,j,n)
A i- + C(ui,j-1,n+1 + ui,j_-,n + Ui,j+ln+l + Ui,j+l,n)


with boundary conditions


at9=0 T=TI at 0 at0>0 T=Tw at R=1 and Z=0 and Z=L

In order to put Eq. (2) into dimensionless form, let

R Z (T-T1) moe k
r=-, z=-, u= t=- where o=- (3)
a a (T,-Ti)' a2 pc


Then

au (1 2u a2u au
-- = +- + (4)
at r ar a8r az)

with boundary conditions
att=0 u=0 at 0 att>0 u=l at r=l and z=0 and z=L/a

Eq. (4) may be solved by finite differences using the


where
1A 1 1
A=-+I +
At (Ar)2 (A)2
1
B=
2(Ar)
C=- 1
2(Az)2
1 1 1
D=I-
At (Ar)2 (AZ)2

Eq. (5) allows the computation of u at time n + 1 from
the values at time n. This permits the following
scheme:

1. Set up a table to store the values of u at time n.
Initially this will be all zeros, except at the
boundaries. Call this table the Storage Table
(C100..AC125). It is shown in Figure 2 with the cells
labeled.


CHEMICAL ENGINEERING EDUCATION















FIGURE 2. Spreadsheet solution to Eq. (4) using Macro \a.


Solution to Parabolic E qeton
Ion OD lnslenal Umtnedy State In Cylindrical Coordnrtes
To Run set E4 to 1 (I lit .) nd then 2
Center: 54: 50 Set 1-Initialize E4: 2
Set 2-mun
C vlttfd


50
57.87037037
0.162?7252
0.785714285
50


Physical Pr pertlee:

Iadiate Pte
It1dlu kft
Heijt Ieste

Init Ip Cent
MIllt 1 Cent
Irget 1Tp cent

Density K/II
Them Cond uI(i
eat Cap JI(i

Tierml Diff
Omega vi42

Table Incremnts:
Delta r (11/)
Detlta (Z/.)
Delta Diensionless lie
a*a/Omega


Table Voluen:
Inltial Tlreturte (cated)
Final Sctled TI eratur
at Tp-rature (Scaled)


I
C
D

Inlt ator


r E62:
rs E63:

E65:
E66:
E67:

3 E69:
*C) E70:
G*C) E71:


I E74: 6.0000E-0h


0.04
0.06
1.00OE- 03
4.1667E+06



0
0.7357142857


1701.25
312.5
78.125
218.75


\la (REAUN)
(IF E'2)(BRNCIIC G28)
(LIET ,40)
S5: /7CE-07...10-
ICEM-A1.. AT100-
ICEM-UI..AZ100-
/IDFC99.ACg-
-1-1--
10: /10m100.11125-
0-1--
ICEta -Coo. .AC0-
/C, 6-MCII. ..C125-
/CE6-C 25..AC125-
GI5: /DFC199.AC199-
-1-1--
,ID0FE03.225-
0-1-
/CE6-C200. ..C2O0-
G20: ICE6-AC201..AC225-
/CiS-C2N ..225-
ICEM--C01.AM124-
(LET A99,TINE MS)
(LET A199IlME *IS)
25: (LET E9r,O)
(LE 8m100.O)
(LET A00.O)
428: (CMIC)
(IF E4-1)(UIT)
G30: (LET 93,1)
(LET I4,0*1)
(LET A120, (E7 9 *E80)/3600.)
(LET AI010.MOD)
(LET 7,5 4)
G35: (LET A200)
(LET 010,EI5)
(CALC)
(KECALC C201..MA224,t(4<0),12)
/ITC201..AM226-

G40: CI01 .A124-
(LET 9.0.25(0112*41130l112PI13))
(CALC)
(IF 64=I)(HGODTATT-
(IF 84l)ODalI 1)(LEFT 1)
G45: /ItV8--
(EIGHT 1)

(IF IP>I10)(0UIT)
(IF 17-l11)(llIT)
650: (8ACKII G28)


1.157401407 0.000000003
2.314814814 0.0000000B7
Tim In hrs 3.672222222 0.000000716
(AT) ad 4. 2962929 0.0000374
scaled S.71817037 0.0o001ul1
Ipert ure 6.944444444 0.0000122
at 8.101851851 0.0001128I
a/2 and L/2 9.259259259 .0028133
(AZ) 10.41446666 0.000485837
u .5tu74407 0.o000u 05
12.714M148 0.101411i1
13.8Mi 0.11114161
15.1m4629M2 O.001Iu 92
16.2503731 .00u45556
17.M3111111 .0M0974040
18.51051M 1 0.00778144
19.61M59892 0.g0 8uu
20.m. mS 0.012210978
21.M740714 0.01482M04
25.14814114 0.01N7M274
24.30555555 0.00112I43
25.46292W 0.024153711
24.621370 0.02I77MO
27.77777777 0.03146521
28.19 51s51 0.03540270
30.09259 0.039512162
31.25 0. 0437 T7
32.40740140 O.048186412
33.M4601481 0.052724031
34.2222222 0.0573861
35.0872963 0.062148349
37.03713703 0.M0700971
38.194 444 0.07195031
39.35185Ii 0.076914146
40.50925925 0.012079706
41.6666466 0.0072363
42.R1404047 0.09248711
43 .90141141 0 .09770857
451.13088 0.103010338
46.2962929 0.101348481
47.453M379 0.113717919
48.61111111 0.119113971
49.M65151 0.124532344
0.92592592 O.129I 097
52.0333333 0.135420614
53.24074074 0.140M3577
54.3(14814 0.14654939
55.55555555 0.151831902
56.71296296 0.157311894
57.87037037 0.162722552


Center Line
C97/C197 D97/0197
C98/C198 D98/0198
-1 0
1 1
0.8019503696 0.801785688
0.616361832 0.616042838
0.4533459104 0.452891384
0.3190524537 0.318486287
0.2152089802 0.214556496
0.1397606841 0.139045490
0.0881935758 0.087435520
0.0550020135 0.054216366
0.03487747 0.034075089
0.0234283931 0.022616488
0.017458014 0.016641140
0.0149517193 0.014132758
0.0149517192 0.014132758
0.0174580139 0.016641140
0.023428393 0.022616488
0.0348774697 0.034075088
0.0550020132 0.054216365
0.0881935755 0.087435519
0.1397606837 0.139045489
0.2152089798 0.214556496
0.3190524533 0.318486287
0.45334591 0.452891384
0.6163618318 0.616042837
0.8019503694 0.801785687
1 1


E97/E197
E98/E198

1
0.8019503696
0.616361832
0.4533459104
0.3190524537
0.2152089802
0.1397606841
0.0881935758
0.0550020135
0.03487747
0.0234283931
0.017458014
0.0149517193
0.0149517192
0.0174580139
0.023428393
0.0348774697
0.0550020132
0.0881935755
0.1397606837
0.2152089798
0.3190524533
0.45334591
0.6163618318
0.8019503694
1


P97/P197
P98/P198
12
1
0.8282357983
0.6672779054
0.5258953404
0.4094218807
0.3193564049
0.2539176133
0.2091912275
0.1804025826
0.1629476435
0.1530174582
0.1478392427
0.1456655323
0.1656655323
0.1478392426
0.1530174581
0.1629476434
0.1804025825
0.2091912273
0.2539176131
0.3193564047
0.4094218805
0.5258953403
0.6672779053
0.8282357983
1


097/0197
Q98/0198
13
1
0.8351236273
0.6806200387
0.5449065092
0.4331029499
0.3466482528
0.2838327042
0.2408991162
0.2132643534
0.1965090051
0.1869768206
0.1820061544
0.1799195729
0.1799195729
0.1820061544
0.1869768205
0.1965090049
0.2132643533
0.2408991161
0.2838327041
0.3466482527
0.4331029497
0.5449065091
0.6806200386
0.8351236273
1


297/2197
298/2198
22
1
0.9502170828
0.9035656241
0.8625868594
0.8288267437
0.8027200517
0.7837509686
0.7707853961
0.7624396849
0.7573794531
0.754500637
0.7529994459
0.7523692811
0.7523692811
0.7529994459
0.754500637
0.7573794531
0.7624396849
0.770785396
0.7837509686
0.8027200517
0.8288267437
0.8625868594
0.9035656241
0.9502170828
1


AA97/AA197
AA98/AA198
23
1
0.9669669609
0.9360117568
0.908820593
0.8864192765
0.8690963093
0.8565094415
0.8479061644
0.842368376
0.8390106594
0.8371004192
0.8361043026
0.8356861562
0.8356861562
0.8361043026
0.8371004192
0.8390106593
0.842368376
0.8479061644
0.8565094415
0.8690963093
0.8864192765
0.908820593
0.9360117568
0.9669669609
1


AB97/AB197
AB98/AB198
24
1
0.9636623894
0.9683524371
0.9549041101
0.9438247564
0.9352570679
0.9290317776
0.9247767107
0.9220377909
0.9203771053
0.9194323234
0.9189396559
0.9187328457
0.9187328457
0.9189396559
0.9194323234
0.9203771053
0.9220377909
0.9247767107
0.9290317776
0.9352570679
0.9438247564
0.9549041101
0.9683524371
0.9836623894
1


AC97/AC197
AC98/AC198
25
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1


D201: [i12] OIF($SE930,0,(0D101*(SE91)+$Es89*(E201+E101)+3 E$89*(C201+CIOI3)+sES9(D102+D100+D200+D202))/(SE088))
E201: [114] 81F($E$93=0,0,(E101*(SE91+$E$89/ES99)+sESP9(F201+F101)s+SES9(l-1/ES99)*(0201+D101)tSES90(E102+E10+E202+E200))/(SE88-SE$89/E99))


SPRING 1990


Iter 87?
lime rs 1M1

Trant li"
1in *a111


Storage table after 50 iterations.


TIME HRS
57.87037037
101/201:
102/202:
103/203:
104/204:
105/205:
106/206:
107/207:
108/208:
109/209:
110/210:
111/211:
112/212:
113/213:
114/214:
115/215:
116/216:
117/217:
118/218:
119/219:
120/220:
121/221:
122/222:
123/223:
124/224:
125/225:









2. Set up a second table (the Calculate Table,
C200..AC225) which will calculate the values of u at
time n+1 from the formula of Eq. (5). Since the
value of uij,n+l depends on the values at n+1 as well
as at n, iterate until convergence (say at least
twelve iterations). The cells are labeled together
with the cells for the Storage Table.
Figure 2 illustrates the spreadsheet setup for a
cylinder of radius 0.5 meters and a height of 1 meter
with the following physical properties:


p = 1000 kg/m3


density


k = 0.15 watts/(m deg C) thermal conductivity


c = 2500 J/(kg deg C)


heat capacity


The increments chosen (based on a table of 25 cells by
25 cells) were

Ar = 0.04

Az = 0.04* Height/Radius = 0.08

At = 0.001

The macro \a is set to run in two modes. If E4 is
set to 1, then the tables are both set to zero (the Cal-
culate Table is set to zero by having E93 set to zero
as shown in the commands for cells D201 and E201)
and the boundary values are set to 1. If E4 is set to
2, then the macro allows the Calculate Table to be
generated from the Storage Table. The values are
copied from the Calculate Table to the Storage Table
after the temperatures at time n+1 are determined
and the process is repeated until a fixed number of


TABLE 1
Spreadsheet Value
of u versus the Analytical Solution at L/2

Analytical
R L Spreadsheet Solution
Ar= 0.025 Ar =0.04 Ar = 0.04
Az =0.050 Az = 0.08 Az = 0.08
At = 0.001 At = 0.001 At = 0.0005


0. 0. 0.01421 0.01413 0.01413 0.01599
0.1 0.2 0.02897 0.02891 0.02892 0.03064
0.2 0.4 0.09399 0.09312 0.09313 0.09694
0.3 0.6 0.2684 0.2666 0.2666 0.2723
0.4 0.8 0.5922 0.5907 0.5907 0.5950
0.5 1.0 1.0 1.0 1.0 1.0


steps (i.e., time) is taken or a particular temperature
is exceeded. The macro uses columns AY and AZ to
record time and temperature at the location a/2 and
L/2. The results are shown in Figure 2. The computa-
tion stopped after 50 time steps (57.87 hrs) which was
reached before the specified target temperature. Each
of the time steps takes about 45 seconds on a Vectra
ES/12 (80286) with a math coprocessor (80287).
The Calculate Table was constructed by copying
the contents of cell D201 to cells D202..D224 and the
contents of cell E201 to E202..AB224. By symmetry
the values of column C were set to those of column E.
Carslaw and Jaeger [8] give an analytical solution
for this case:

8 (-1)k (Rm)
a k= m=1 (2k+l)amJ,(aam)
s(2k + 1)x
2h
exp-oham +(2k+ 1) / 4h2 ) (6)

where
h = L/2
-h < x < h
and am is calculated from the roots of the zeroth order
Bessel function Jo: i.e.,
a1 = (1st root)/a
a2 = (2nd root)/a

am = (mth root)/a
The upper limit on m was taken as 40 and the
upper limit on k was 50. The first forty roots of the
zeroth order Bessel function were taken from Jahnke
and Emde [10].
Table 1 compares Eq. (6) to the spreadsheet solu-
tion at L/2 (x= 0) at a number of values of R. Since
the spreadsheet solution is not given exactly at L/2,
the average value of the surrounding cells at a given
r was used. The table also gives values found when
the time increment was reduced to 0.0005 and the val-
ues of the coordinate increments were Ar= 0.025 and
Az = 0.050.
Reducing the values of Ar and Az (a 40 x 40 table)
improved the accuracy somewhat, but cutting the
value of At did not. Eq. (3) may be used to convert
the dimensionless solution to the scaled solution
sought. An error of 0.005 in u corresponds to an error
in T of 0.5 deg C if (T, Ti) = 100.

CONCLUSIONS
Macros allow the use of the spreadsheet for a
greater variety of problems than can be done without


CHEMICAL ENGINEERING EDUCATION










them. The LOTUS 1-2-3 advanced macro commands
are relatively easy to learn and apply. Their use
should be considered.

REFERENCES
1. AIChE Education and Accreditation Committee,
"Evaluating Programs in Chemical Engineering,"
August 1, 1988. Appendix VI
2. Rosen, E.M. and R.N. Adams, "A Review of Spread-
sheet Usage in Chemical Engineering Calculations,"
Computers and Chemical Engineering, 11 (6), pp 723-
736(1987)
3. LOTUS, 1-2-3 Reference Manual, Release 2
4. Henley, E.J., and E.M. Rosen, Material and Energy
Balance Computations, John Wiley & Sons, New York
(1969)
5. Myers, A.L., and W. D. Seider, Introduction to Chemi-
cal Engineering and Computer Calculations, Prentice-
Hall, Inc., New Jersey (1976)
6. Reklaitis, G.V., Introduction to Material and Energy
Balances, John Wiley & Sons, New York (1983)
7. von Rosenberg, Dale U., Methods for the Numerical So-
lution of Partial Differential Equations, Gerald L.
Farrar & Assoc., Inc., Tulsa, OK; p 86 (1977)
8. Carnahan, B., H.A. Luther, J.O. Wilkes, Applied Nu-
merical Methods, John Wiley & Sons, New York (1969)
9. Carslaw, H.S., and J. C. Jaeger, Conduction of Heat in
Solids, Clarendon Press, Oxford; p 227 (1959)
10. Jahnke, E., and F. Emde, Tables of Functions, Dover
Publications, New York; p 166 (1945) 0




REVIEW: Aerosols and Hydrosols
Continued from page 99.
In the third chapter, the author focuses on pro-
cedures for modeling granular media in filters. Rather
than utilizing a "black box" approach to describe the fil-
ter (inherent in the methods described in Chapter Two)
in order to determine concentration histories and pres-
sure drops, the specifications of the collector's structure,
geometry, size, size distribution, and the fluid flow fields
around the particles are considered.
In Chapter Four, a variety of mechanisms for the
deposition of particles on collectors from flowing sus-
pensions are discussed. Expressions for collection effi-
ciencies for these various deposition mechanisms are de-
rived, utilizing the media modeling methods described in
Chapter Three.
In the fifth chapter, the author illustrates that tra-
jectory analysis, along with the media models described
in the third chapter, can be used to estimate filtration
rates. Because of complexities associated with represent-
ing fluid drag forces acting upon suspended particles
and also representing particle surface geometry as
deposition proceeds, the method of trajectory analysis is
limited mainly to clean filters.
In Chapter Six we find that because of distinct dif-
ferences in the particle deposition mechanisms, it


becomes necessary for the author to depart from the
integrated approach he has followed up to this point and
to treat aerosols and hydrosols separately. In this
chapter he focuses on prediction and measurement of
initial collection efficiencies for the granular filtration of
aerosols. Collection efficiencies are predicted using the
trajectory analysis methods discussed in the fifth chap-
ter. A variety of experimental methods for determining
initial collection efficiencies are briefly discussed, and
appropriate experimental results are provided. Em-
pirical correlations and their relative merits are also dis-
cussed.
In the seventh chapter, the author describes the pre-
diction of initial collection efficiencies for hydrosols
using trajectory analysis. Results of these calculations
are compared with experimental data. Limitations of
the trajectory analysis approach and possibilities for
improving it are discussed.
In Chapter Eight the author begins to look at the en-
tire process of particle deposition, not just the initial
stages which have been addressed up to this point. Den-
drite growth of deposited particles and stochastic simu-
lations of particle deposition are the focus of much of
this chapter. The author points out that much of what is
covered in this chapter is still in the developmental stage
and, as such, is included to demonstrate general princi-
ples and the potential of the methods.
Finally, in Chapter Nine, the author focuses on a
number of actual investigations (case studies) dealing
with the granular filtration of aerosols and hydrosols.
Topics discussed include filter ripening, effects of
deposit morphology on filter performance, effects of
deposition on aerosol filtration, aerosol deposition in
fluidized filters, and the increase in hydrosol filter coeffi-
cient.
In summary, the author has done a nice job of
writing about a sharply focused area of separations
which, up to now, has been largely dealt with in
scientific journals. A great deal of information has been
brought together in a coherent, logical format. It is
particularly useful because it tells you how to do things.
The book is fairly easy to read, and the figures, graphs,
and tables are clear and easy to understand. The author
does not get bogged down in tedious mathematical
derivation. That which is not shown directly is usually
referenced adequately. The text is designed to bring
someone who is interested in further work in the area
"up to speed" in a reasonable period of time. The refer-
ences are extensive and will be particularly helpful to
anyone interested in the field. Since the subject matter of
the book is admittedly narrow, it would only be useful as
a course text or supplemental text for advanced, re-
search oriented graduate courses. O


SPRING 1990










laboratory


INCORPORATION OF

PROCESS CONTROL COMPUTERS IN THE

UNDERGRADUATE LABORATORY

A Case Study


WM. CURTIS CONNER, JR.
University of Massachusetts
Amherst, MA 01003

THE REBUILDING of our undergraduate unit oper-
ations laboratory was a substantial project and re-
quired the concerted effort of several individuals. To
understand the process, it is first necessary to realize
the state of our undergraduate laboratory before we
began the conversion (Background). A plan for trans-
forming the laboratory (incorporating state-of-the-art
computers) was created, and a method for accomplish-
ing the goals was developed (Implementation). The
eventual capabilities were dictated by the choice of
the computer systems to be used in the laboratory,
and this will be briefly discussed (Computer
Capabilities). A major aspect of the change was a
realization that both the existing philosophy of the
laboratory and the nature of the experiments needed
to be modified; further, new experimental approaches
would be available with the enhanced capabilities
(Course Content). The next-to-last section will discuss
the problems that occurred and our perception of the
process (Discussion). We have continuing plans to
modernize and update the laboratory to reflect cur-
rent and developing "state of the art" in personal com-
puters and their application to the measurement and
control of chemical engineering processes. They will
be discussed in the last section (Future Plans). The
last two brief sections include an overview of the pro-
cess (Final Comments) and Acknowledgements of the

A group of the faculty met and decided that
the laboratory should be restructured . Out-of-date
experiments were dropped, and other experiments
were combined into larger experimental projects

c Copyright ChE Division ASEE 1990


W. Curtis Conner, Jr., is an associate
professor of chemical engineering at the Uni-
versity of Massachusetts at Amherst. He re-
ceived his BES in chemical engineering and
his PhD in catalytic chemistry from Johns Hop-
kins University. After postdoctoral positions at
the University of Connecticut, the University of
Wisconsin at Milwaukee, and Zelinski Institut in
Moscow, he worked in catalytic research at
Allied Chemical Corp. His major research is
catalysis, and he is author of over eighty publi-
cations and patents.

myriad of people that made this whole process possi-
ble.

BACKGROUND
Seven years ago, when I came to the University
of Massachusetts, the undergraduate laboratory was
no more advanced than the ones I had been exposed
to in my undergraduate education. It had been built
in the 1950s and, without substantial state funds avail-
able for modernization, was essentially unaltered. The
limited funding provided through the years had been
used for maintenance of the existing equipment. At
one time, our undergraduate chemical engineering
laboratory course spanned three years and involved
one credit hour each semester. A sequence of several
small experiments was involved, e.g., calibration of a
thermocouple. Prior to that the laboratory had been
run during several summer weeks between the junior
and senior years, as a summer camp for chemical en-
gineering undergraduates.
The laboratory can provide a method of testing
and understanding the complexities of the concepts
learned in class. This should occur after, or concurrent
with, the class. Therefore, the laboratory was concen-
trated into two three-credit courses in the senior year.
The focus in the fall semester was on thermodynamics
and transport, and the focus in the spring semester


CHEMICAL ENGINEERING EDUCATION









was on kinetics and control. We also had been conduct-
ing a "senior seminar" course that gave the students
an opportunity to choose a general interest topic and
present a talk to the other students.
A group of the faculty met and decided that the
laboratory should be restructured. The first steps
were organizational. Out-of-date experiments were
dropped, and other experiments were combined into
larger experimental projects. As an example, an ex-
periment to measure the VLE diagram was combined
with distillation to reflect the design of a separation
based on a mixture of components for which the vapor
liquid equilibria were "unknown." The "senior semi-
nar" was incorporated into the course. The students
were required to orally present a proposal of their
intended experiments prior to going into the labora-
tory and then to orally report on the results after they
had finished. Written expression was also emphasized
as the students were required to write a one-page
proposal and a concise (less than ten-page) report.
Our primary concern was that the laboratory did
not reflect the "state-of-the-art" use of digital com-
puters in the acquisition of experimental data and did
not foster the ability to efficiently design experiments
and control the processes. A program (discussed
below) was developed by which this goal might be
realized. Catalyzing this proposal was the donation of
modern process control computers, MACSYM-350's,
from Analog Devices Corp., to the university. An un-
dergraduate student, John Melanson, had used this
system in our research in catalytic reaction engineer-
ing and found it was very easy to use and to interface
with real experimental measurements.

IMPLEMENTATION
It was first necessary to plan the laboratory trans-
formation. We initially proposed interfacing the com-
puters over a three-year period. Two or three com-
puters would be acquired each year and interfaced
with two of the six or seven experiments conducted
each semester in the laboratory. One or two com-
puters would be set up in the student AIChE office to
permit groups to write programs and to analyze data
outside of the laboratory. Modest funding was re-
quested for new experimental hardware (valves,
transducers, etc.) which was to be augmented by
funds from the university (generated by a new en-
gineering school laboratory fee). The proposal was
submitted to Analog Devices in the spring of 1983 and
was accepted for the first year.
We had decided to directly involve the under-
graduate students in the transformation of the labora-
tory. Two students, Ann-Marie Baker (a junior) and


The conversion ... to computer data acquisition
and process control involved . reorganization. Two
and one-half weeks at the beginning of the fall
semester are now set aside to introduce
students to the computer systems.



John Dorgan (a sophomore), were given jobs in the
Applications Group of Analog Devices during the sum-
mer of 1983. They returned to campus in August to
begin the conversion. Other students were employed
at the university during the summer (and on a continu-
ing basis since then) to transform specific experiments
and to develop new experiments.
We decided to make programming of the com-
puters an integral part of the course. Teaching
software was developed to instruct the students on
the use of computers and on the specific version of
BASIC (MACBASIC) employed on these process
control computers. Ten megabyte hard discs were ac-
quired for each computer system, and the teaching
and demonstration programs were loaded onto each
system. The demonstration programs (described
below) gave examples of all of the programming func-
tions required for the course. A 25-inch color monitor
(RGB input) was purchased for class instruction using
on-screen display of the programs with color graphics.
We found that classes of 25-30 could be conducted with
the monitor.
A technician and an instructor in our department
also became involved in the conversion. Each had been
involved in computer applications and readily volun-
teered their services and expertise. Graduate stu-
dents who had used these computer systems were
used as teaching assistants for the course.
The first year was so successful that we decided to
complete the transformation in two years instead of
the three years originally proposed. At the end of the
first year, a renewal proposal for the completion of
the conversion was submitted to Analog Devices and,
in view of our progress, was accepted. The retail price
was $250,000 ($200,000 in computer hardware and
$50,000 in experimental hardware).

COMPUTER CAPABILITIES
The capabilities of the computers used for the con-
version are essential for transforming our under-
graduate laboratory to primary computer data acqui-
sition and control. We decided to take the "quantum
leap" and use state-of-the-art process computers. The
language used by the computers had to be easy to
learn and readily adaptable to the measurement of


SPRING 1990










flow, force, temperature, and composition. We de-
cided to incorporate dynamic control as well as data
acquisition into the course curriculum; therefore, the
ability to perform simultaneous tasks ("multi-task-
ing") was important. The MACSYM line of com-
puters produced by Analog Devices was ideally suited
for this task. Analog Devices is a corporation based
on the conversion of analog to digital and digital to
analog signals.
MACBASIC is a "compiled basic" language that
is analyzed line by line as the program is written.
Syntax errors are noted immediately. "On screen"
editing is used. Analog to digital to analog conversions
and high resolution graphics (including color) are in-
herent in the language. This system seemed to be de-
signed specifically for the operations required in the
monitoring and control of a chemical engineering pro-
cess. Hence it was not necessary to adapt the com-
puter system for communication with the world of real
chemical processes. As an example, Table 1 illustrates
a first attempt at proportional-integral control.
It illustrates the ease of reading voltage inputs (line
30) and setting output voltages (line 100), in spite of
the simplicity of the control scheme. Decisions regard-
ing control and/or alarms are made in the program.
On/off inputs such as valves and switches are control-
led or recorded with comparable digital input (DIN)
and digital output (DOT) command syntax. A number
of commands are available to define simultaneous
tasks and to activate or suspend the tasks. This per-
mits the programming of simultaneous control, of
gathering and storage of data, of printing, and/or of
plotting.
We wanted to allow for expansion and the mea-
surement and control of as many as forty variables on
a single process (on a distillation column, for example).

TABLE 1
Program for PI Control


Command
10 INPUT "Setpoint, Gain, Integral Const. ? SP,G,I
20 zero timer, TOT = 0, PT= 0
30 X=AIN (2,3,10)

40 T= timer
50 ET=T-PT
60 E = SP-X
70 TOT = ETE +* TOT
80 N Abs (TOT))10 then TOT= 10TOT/Abs(TOT)
90 Y: G(E+TOT /I)


100 AOT(3,1)=Y
110 PT T
120 GOTO 30


Comment
Choose setpoint, control
gain and integral constant
Starts time clock, zero's
integral
Measures voltage on
card 2, channel 3 with
sensitivity 10
Records time
Calculates elapsed time
Calculates error
The integral
Preventing integral wind up
Calculate new output
voltage
Set channel 1 voltage on
output card 3 at Y volts
Saves time


Setting up the distillation column for a steady-state ex-
periment. Distillation column is seen on the right as is
the computer monitor depicting the schematic for the
column with temperatures and flow rates being shown
dramatically at the appropriate positions on the dia-
gram.


There are eight card slots on the MACSYM main-
frame and each slot can take up to 16 differential or
32 single ended inputs, or four voltage outputs.
Another twenty card slots are provided with the "200"
front end.
A further consideration was the availability of
service within twenty-four hours. Analog Devices is
located in Norwood, Massachusetts, and their service
hotline never failed to respond immediately.

COURSE CONTENT
The conversion of our laboratory to computer data
acquisition and process control involved a reorganiza-
tion of the course. Two and one-half weeks at the be-
ginning of the fall semester are now set aside to intro-
duce the students to the computer systems. Simple
test benches are set up for each computer to provide
voltage inputs and the display of voltage (analog) out-
put signals. The students are divided into groups of
two and are given three sets of homework during the
period in order to demonstrate their mastery of the
basic computer language. Five computer systems are
set up and available each afternoon for the students.
Teaching assistants are also available to assist in the
programming.
Five or six experiments are required each semes-
ter. In the spring, the students are required to per-
form four experiments and to choose one from two
additional experiments. The selection of experiments


CHEMICAL ENGINEERING EDUCATION


^
I












TABLE 2
Laboratory Experiments

Experiment Equipment 3-Hr periods Computer Interfaced
required

FALL SEMESTER
Vapor/liquid Equilibrium still and 1+3 Temp. on each tray and 12
equilibrium and gas chromatograph and other points on the column;
distillation 20', 13 plate, SS column all flow rates; reboiler level
Concentric pipe 16' steam-water and 40' 3 Temperatures at 24 points in
heat exchangers water-water co- or counter- the network; all flow rates
current heat exch. network
Fluid flow 120' pipe network of dif- 3 Flow rate over a broad
through pipes and ferent sizes with bends range; AP at 20 points; E &
fittings and fittings I for the water pump
Unsteady state Objects of different sizes 2 None yet but all tempera-
heat transfer and shapes immersed in tures possible
water
Compressibility Interconnected ballast 2 None
of gases and gas volumes and pressure
mixtures gages
SPRING SEMESTER
Control of distil- See above 3 As above with control of
lation steam, reflux and feed flows
PID control of Flow valve with trans- 2 Control valve and flow
flow ducer
Methanation Catalytic PFR with on- 3 Control of all flows; reactor
line CO analysis oven; analyzer
Water cooling 16' counter-current 2 None
tower packed column
Saponification Liquid-liquid CSTR 3 Temperature; flow rates; up
reactor and down stream PH's
Diffusion Capillary-column GC 3 Temperature; flow; concen-
tration at 10Hz


TABLE 3
Computer Programs Provided on Each System

Name Purpose De.srlllan
Temptest Data Measurement Conversion of a series of 16 thermocouples
to a displayed list of temperatures (updated
every second)
DTMX Data Manipulation Use of matrix to store data, to transfer to
disc and to print out tables
Datman Multi-tasked data Simultaneous collection, storage, display,
handling and printing of multiple analog inputs
Pltmx On-Screen and 8 Use of plotting graphics from data matrix
color plotting "on screen" and, if chosen, with plotter
(X vs Y or X us time)
AIN-OUT Settingoutputs On/off decisions, alarms, and proportional
based on inputs control based on measured analog inputs
Condem Demonstration of Setting of control constants and on-line
PID control screen plotting of set point, measured input
and output
Conplot Dynamic PID Multi-tasked control with data matrix stor-
control age and 8-color plotting...run dynamically
"LAB" Specific Basic programs for heat exchanger, distil-
lation, methanation, saponification, and
diffusion...includes flow diagrams


varies as the updating of the experiments is done on
a continuing basis. During each break between semes-
ters, groups of three students are involved in design-
ing new experiments and in updating earlier experi-
ments. This is a "modest" effort to keep the laboratory
program dynamic.
The current list of experiments is shown in Table
2. Three experiments in the fall semester and five in
the spring are interfaced with the computers. At least
one experiment each semester does not involve com-
puter data acquisition. The focus is on computer use
as a tool to measure more variables more rapidly than
was possible before. Further, the data can be stored
instantaneously and decisions can be made to control
the process variables and thereby the experiments.
The emphasis of the laboratory performance is on
chemical engineering principles and we are committed
to retaining this perspective. The advantage is that
computers are able to dramatically enhance the
analyses on-line and thereby to permit changes and
adjustments during the experiments.
The laboratory course is closely coordinated with
the ongoing courses during the senior year. As an
example, as the students learn PID control, Bode dia-
grams, cascade control, sensitivity analysis, or self-
tuning regulators in their control course, these con-
cepts are expected in their experimentation involving
control. As mentioned above, each successive group
performing experiments is required to go further than
prior groups did. Oral reports from the groups are
presented to the whole section (i.e., those not in the
laboratory conducting experiments). Students are en-
couraged to ask questions of other groups regarding
experiments.
To facilitate the student's use of computers for
data acquisition and control, a series of programs is
provided which demonstrates all the techniques re-
quired for computer use. These are listed in Table 3.
The programs are available on the 10MB Winchester
disc attached to each system and they are discussed
with the students in lecture sessions at the beginning
of each semester. During the fall semester the em-
phasis is on proper techniques of data acquisition,
management, and analysis. At the beginning of the
spring semester this is augmented with lectures and
demonstration programs on multi-tasking, on plot-
ting, and on control. As the students become involved
in the experimentation, they request assistance on
programming at increasingly higher levels. The dem-
onstration programs are employed (with encourage-
ment and coaching) to develop the students' own ap-
proaches to their problems. The effect is synergistic.
Basic data acquisition programs are provided for most


SPRING 1990









of the computer-interfaced experiments. This pro-
vides flow diagrams for the specific systems and starts
the students in the right direction. However, the stu-
dents are informed that the use of these programs
without substantial modification is unacceptable. Fi-
nally, a copy of the program that they used is ap-
pended to their final reports.
With a total of only 33 three-hour laboratory
periods each semester, it is obvious that a rotating
plan for the laboratory is needed. Friday are set
aside for make-up. For each experiment, each group
must provide a proposal and a report in addition to
the time spent in the laboratory. The assignments ro-
tate, and each student in a group of two is responsible
for at least two reports and two proposals each semes-
ter.

DISCUSSION
As we expected, we experienced several difficul-
ties during the conversion. The first semester was as-
sembled "on the fly" since the computers and all the
flow transducers and valves arrived just one week be-
fore the first class. Each computer system was con-
figured identically (this is crucial) as we scrambled to
install the valves and transducers. Each student was
given a formatted disc, and then the format command
was removed from the operating systems in the labo-
ratory. This was done after it was (painfully) discov-
ered that the hard disc could be inadvertently format-
ted and thereby erased in this manner.
We soon realized that homework needed to be as-
signed during these first weeks in order to focus the
student's practice on the computers. There is an acti-
vation energy with the use of a new computer system;
however, after the initial reluctance, the learning pro-
cess is autocatalytic.
The manual was not explicit in describing our spe-
cific needs. Several phone calls to Analog Devices re-
vealed that bleed resistors from voltage low to ground
were needed, and all the inputs had to be on common
ground. We included capacitors across the inputs to
decrease spurious noise. All the Foxboro transducers
required 20-24 volt DC power. A high capacity DC
power supply was requisitioned and was set up to
service all the needs from a single switchable source.
This worked well. Temperature measurements were
handled through a sixteen channel, zero compensating
subsystem. The example use software in the manual
needed to be consulted to determine the proper config-
uration.
The MACSYM system is very fast, and a certain
amount of signal averaging is desirable. The students


have to develop a perspective on the amount of data
needed to perform each experiment; otherwise, they
end up with reams of data and have difficulty extract-
ing the pertinent portions. Proper experimental plan-
ning is essential, and this is emphasized.
Since we had obtained the computer system di-
rectly from Analog, there was no salesperson involved
and the normal system-setup visit did not accompany
the delivery. However, by learning to configure the
systems "from scratch" and to set up the interfaces,
we gained invaluable experience and insight. This has
enabled us to correct problems and adjust the system
parameters as needed. Almost all of our difficulties
have occurred at the beginning of each semester when
the computer systems are changed to new or different
experiments.
The Macbasic language runs on a CCPM operat-
ing system, although DOS can be partitioned into the
MACSYM 120 systems. We have kept DOS off all
the systems and religiously excluded any word pro-
cessing software (or games) from the systems. These
are powerful minicomputers, but their exclusive use
for the laboratory needs to be maintained.
We initially attempted to prohibit students from
sharing computer programs already developed for
specific experiments, but this proved to be impracti-
cal. Subsequently, we encouraged the students to
share their software, but required successive groups
to do more and thereby improve on the prior experi-
ments. We have found that at least four to five times
as much data is gained by each group compared to our
prior experience with the same experiment. As an
example, prior running of the distillation column in-
volved steady state measurements to compute plate-
to-plate efficiencies. The students now start the sys-
tem, investigate the dynamics, and develop elaborate
control schemes to optimize the process.
The net results have been very dramatic. The tech-
nicians have developed programs to start up and check
out the functions of each experiment. The students
are stimulated to see how much they can extract from
each laboratory. We noticed this soon after we
started. Groups were asking to get into laboratory an
hour early to get started! They often ask how to do
various operations such as control, multi-tasking, or
plotting before we instruct or require them to use
these techniques. The most frequent questions start,
"How can I . .?" In addition to exercising their
abilities in programming, they are developing a "feel"
for chemical engineering processes and their state-of-
the-art monitor and control. The whole process has
been one of my most rewarding experiences in teach-
ing.


CHEMICAL ENGINEERING EDUCATION









FUTURE PLANS
The initial transformation of our undergraduate
laboratory was first envisioned in 1983. Full im-
plementation took several years. Since then we have
continued to update and expand the available experi-
ments. In particular, we realize the growing need for
expertise in solids processing. A tray drier has been
installed in the laboratory and is being interfaced with
the computer systems. Further, we are expanding the
separations/transport experimentation by adding a
dynamic Taylor dispersion apparatus and a continuous
membrane separation experiment. The first involves
moment analysis of pulses in a capillary G.C. column.
The second employs hollow fiber membranes to sepa-
rate oxygen and nitrogen from the air. In both exper-
iments temperature, flow rate, and composition are
manipulated variables subject to monitor and control.
Since the availability and capabilities of computers
has continued to change dramatically, we look at the
latest state-of-the-art and the obvious directions in
personal computers in order to plan for the next stage
of development of our undergraduate chemical en-
gineering laboratory. Further, Analog Devices has
chosen to concentrate its effort on subsystems that
are peripheral to the two major systems employed as
personal computers (IBM and Apple). Indeed, this
summer one of our students was employed at Analog
Devices to develop the "drivers" for Macintosh SE
and MAC II PC's to communicate with Analog's
newest measurement and control systems (the 1050-
1060 family of data acquisition subsystems). This seems
to be the way to proceed with the abundance of PC's
currently available. The computer driver would then
be able to be changed and updated, retaining the A/D
subsystems.
We look to the future and anticipate that we will
begin a conversion to state-of-the-art personal com-
puters with associated analog to digital to analog com-
munication. This conversion will start next year and
should be completed in three years. Ease of visualiza-
tion (graphics) and a low activation energy for learn-
ing the specific system leads us to investigate the use
of Apple Macintosh II and SE systems for our future
undergraduate chemical engineering laboratory.
Multi-tasking has not yet become an integral part of
either operating system; however, Apple seems to
have recognized its significance in Multifinder. For
chemical engineering applications, true multi-tasking
would be crucial as simultaneous monitor, display, and
control of the processes are essential to a viable chem-
ical engineering laboratory.
We have set up dedicated Apple Macintosh II and
SE computers and the associated A/D and D/A sys-


teams. The use of these systems for the collection and
control of analog inputs/outputs is being tested at this
time in our reaction engineering laboratories. Our
dialogue with Analog Devices continues as we and
they investigate the use of their A/D/A based on
Apple's Macintosh operating systems.

FINAL COMMENTS
Several aspects of the transformation might
be discussed. The integration of computer based
experimentation for one or two of the experi-
ments, as compared with the transformation of
the vast majority of the experiments at one time,
is not recommended. There is an activation en-
ergy to learn and to teach a new computer lan-
guage and the philosophy associated with digital
acquisition and control. If the students gain this
insight up front, they can focus on the actual
experiments being conducted. Use of the
computers becomes a tool by which they can
function more efficiently in the laboratory. With
only a few experiments, the computer and not
the chemical engineering principles becomes the
experiment.
It would be impossible to gain the same in-
sight into experimentation by conducting
"computer experiments" where all of the experi-
ments are conducted against a "simulator" within
a computer. I realize that this is a popular
approach to teaching "experimental" work.
However, this is not only naive, it is grossly un-
realistic. If we are preparing our students to work
in industry with real processes and materials,
they must come to grips with the nature of
experimentation. Throughout their education
they are exposed to an idealization of real pro-
cesses. The only place in our students' edu-
cation where they are exposed to real, albeit
simplified, engineering processes is in the
laboratory. The real world is not dimensionless
and represented by smooth curves. As they see
the valves turn and the flow, pressure, tempera-
ture, and products change, they learn some of
the limits to theory and the necessity of planning
the experiments and making the appropriate
measurements.
The undergraduate laboratory in chemical en-
gineering can be a course that brings together
the curriculum and allows the students to
visualize the application of theories in their
courses. If these experiments are interfaced with
data acquisition and process control computers,
and if they learn to use these to conduct the
experiments, they can visualize the applications
and learn to probe the more realistic aspects of
real processes.
ACKNOWLEDGEMENTS
This whole process could not have been ac-
Continued on page 116.


SPRING 1990










classroom


TEMPERATURE EFFECTS

IN HETEROGENEOUS CATALYSIS


CHARLES D. SCHAPER and C. O. BENNETT
University of Connecticut
Storrs, CT 06268

N THE STUDY of mass and heat transfer effects for
a first-order irreversible gas-phase reaction occur-
ring over a bed of catalyst pellets, it is interesting to
analyze the effect of temperature on the observed rate
of reaction. To a first approximation, it would seem
that a graph of effectiveness factor, i, versus Thiele
modulus, mo, could be used to easily calculate the
reaction rate, R, as a function of temperature from
the basic relation
R=kni (1)
where k0v is the rate constant at the gas-phase tem-
perature To. However, such charts (refer to [1], for
example) are usually based on constant values of the
Arrhenius parameter, y, the intraparticle thermal
parameter, 0, and the Biot number for mass transfer,
Bim. In reality, these three parameters vary appreci-
ably with temperature for a given reaction system, so
that the behavior of the system cannot be determined
by following rl versus mo on a single chart. Con-
sequently, in order to analyze the effect of tempera-
ture, one must return to the model that was used to
generate the charts, developed by Carberry and Kul-
karni [2], and solve the model without holding y, P and
Bim constant.
In this paper, we present an analytic solution of
the heterogeneous reaction model for the effect of
temperature on the system described earlier. Our an-
alytic formulation utilizes a "reference state," or sys-
tem characteristics at a single temperature, to
explicitly determine the behavior of the system at any
temperature.
The contribution which we want to make will be
more accessible if the derivation of the basic equations
of the heterogeneous reaction model is reviewed. We
have incorporated the isothermal pellet assumption [2]
into our model, realizing that a specific design problem
may deserve a more rigorous approach and that our
results do not apply to complex kinetics which may
show autocatalytic behavior. Although it is the be-


havior of the system parameters with the bulk gas
temperature To that is desired, we find that it is con-
venient to use the surface (i.e., pellet) temperature Ts
as the independent variable in our model. For any Ts
we calculate the appropriate To, but in regions of mul-
tiplicity a value of To corresponds to three values of
Ts at steady state, two of which are stable.

MASS TRANSFER EFFECTS
At steady state the rate of reaction in the pellet,
r, equals the rate of interphase mass transfer of reac-
tant A towards the surface,
S=ka (CA -CA.) (2)
where kc is the mass transfer coefficient, a is the out-
side area of the pellet per unit volume, and CAs is the
concentration of reactant A in the gas at the pellet
surface.
Intraphase diffusion occurs with chemical reaction
within the pellet and produces a concentration gra-
dient, described in slab geometry by

cosh z v
CA(z) D (3)
CA. cosh k
LDe.


Charles Schaper received his BS in
1985 and his MS in 1986, both from the Uni-
versity of Connecticut. He is currently a PhD
candidate in chemical engineering at the Uni-
versity of California, Santa Barbara. He plans to
begin postdoctoral research in the Department
of Electrical Engineering at Stanford University
this summer. His current interests include ro-
bust control and probability theory with
applications to IC manufacturing.


C. O. Bennett, presently professor
emeritus at the University of Connecticut, re-
ceived his PhD in chemical engineering from
Yale University in 1950. He was on the faculty
at Purdue University until 1959 when he left
academia and went to work for the Lummus
Company. He returned to teaching in 1964,
joining the faculty at the University of Con-
necticut. His principle research interest is in
heterogeneous catalysis.


Copyright ChE Division ASEE 1990


CHEMICAL ENGINEERING EDUCATION









where z is the distance from the center of the slab, L
is the half thickness of the slab, ky, is the rate constant
at the pellet temperature T,, and De is the effective
Knudsen diffusivity. The Thiele modulus at Ts is
m, =LD (4)

The effectiveness factor associated with the pellet
at T. is
D. -CzA (L)
T* dz (5)
k,. CA. k,. CA.

so that one can obtain
= tanh m (6)
m,
For sufficiently high temperature, the rate in-
creases so that the interphase temperature and con-
centration differences are important. Thus we need to
consider the inter-intraphase (overall) effectiveness
factor, ;q, defined through Eq. (1). The rate R, or the
apparent rate constant k, can be expressed in several
ways, as follows; through Eqs. (1), (2), (5) and
R=- r = Dakca (7)
CA.
The Damkbhler number Da is k,,/kca, and it is conve-
nient to consider together the product iDa. From Eq.
(7) is clear that FjDa is an observable, as defined by
Carberry [1]. This group measures the importance of
the interphase concentration difference, as shown by
combining Eqs. (2) and (7)


TiDa = 1 -A
CAo


(0o5 IDa< 1)


It is also useful to express 7IDa in terms of mi, at
conditions in the pellet. By combining Eqs. (5), (6),
and (7), we obtain
iDa tanh m. k, C. (9)
m, ka CAm
When CAs/CAo is replaced according to Eq. (8), the
result is ta
iDa= m tanh m. (10)
m, tanh m, + mk,-
kvs
Now Bim = dpkc/De and is used with Eq. (4), along
with the relation for spherical pellets of diameter dp,
L = 1/a = dp/6 following a common approximation
[3], to replace the second term in the denominator of
Eq. (10). The result is an equation for ;iDa in terms
of m. and Bim,
Da= m, tanhm, (11)
Da=Bim (11)
m, tanh m, + i
6


In this paper, we present an analytic solution
of the heterogeneous reaction model for the effect
of temperature on the system described earlier. Our
analytic formulation utilizes a "reference state," or
system characteristics at a single temperature ...

Although this equation permits the calculation of iDa
for a given T., we still need to find the corresponding
To and kvo in order to calculate '.

HEAT TRANSFER EFFECTS
The interphase temperature difference is deter-
mined by equating the rates of heat generation and
removal for the pellet.
F(-AH)=ha(T, -T,) (12)
where (-AH) is the reaction enthalpy difference and h
is the heat transfer coefficient. Substituting Eq. (7)
into Eq. (12) gives
iDa (-AH) kC^A = h(T. T,) (13)
This equation can be rearranged to
T. k,(-AH)C -
S=1+ T, Da (14)
T. hT.
According to the Chilton-Colburn analogy [4], JM =
JH, so that we can derive
h ,(L ,3 pop
S= (Le)2 pC, (15)
k,
where Le = Sc/Pr and write the temperature-effect
equation as
T -T. = IiDaTo (16)
where

(-AH)CA. (17)
S(Le)2/3 pCT,

REFERENCE STATE
In order to follow the effect of temperature easily,
a reference temperature Tr is defined at which the
rate constant k, is known. Usually Tr would be a
suitable low temperature. In the example we shall
give, Tr is 600 K. The appropriate ky, can then be
calculated by
(T M
k,,= k,r expl-Y 1 (18)


where the Arrhenius parameter y, = E/RTr is a con-
stant.
Clearly Eq. (18) can be used to calculate kvo at To.
We also need De at T,. We assume Knudsen diffusion,
so that


SPRING 1990










D, Der 2 (19)

Now ms can be computed at the chosen Ts. In Eq.
(11), which we need to calculate fDa, the parameter
Bim must be found. We write

Bim = Sh DAB = jReScI DA (20)
D. De
where Re = dpG/i, G is the gas mass velocity, (J is
the viscosity of gas, and DAB is the diffusivity of gas
A thru B. Among many possibilities, we choose the
following correlation for JM in a packed bed [4]:

JM =2.25Re 2 (21)
so that
1 I
Bim = 2.25 Re2 Sc3 DA (22)
De

As a first approximation we evaluate Bim at Ts; after
To is estimated, the solution could be iterated with an
average of To and Ts used for the estimation of I, and
DAB. Sc is little affected by temperature. If DAB is
proportional to T,3'2, and [i to Ts"2, then there results
3
Bim = BirJ. (23)

For a chosen Ts we now calculate Bim from Eq.
(23), ms from Eq. (4) with Eqs. (18) and (19), and then
use Eq. (11) to find IDa. Before using Eq. (16) to find
To, it is convenient to define
(-AH)CAo (24)
(Le)B pCpTr


1800


1500


1200


S900


300 600 900 1200
gas temperature, K
FIGURE 1: Surface temperature as a function of gas tem-
perature for the example pellet-reaction system.


so that


T,-T, = Pr DaTr


For a given mole fraction XAO, Pr defined by Eq. (24)
is approximately constant; CAo/P is constant, and usu-
ally the effects of temperature on (-AH)/Cp and Le
are small.
For a chosen T,, we now know iDa and To. Equa-
tion (24) can be used to find kvo at To, and mo is defined
by Eq. (3) with kvo replacing k,. It is interesting to


100




I50
o


300 600 900 1200
gas temperature, K

FIGURE 2: Overall reaction rate as a function of gas
temperature for the example.


0.1 1 10 100 1000
Thiele modulus, mo
FIGURE 3: Variation of the overall effectiveness factor
with the Thiele modulus nm, for the example.


CHEMICAL ENGINEERING EDUCATION









calculate the rate R, and Eq. (12) gives this quantity
once we evaluate kea. The Bim can be written as
kafBlmDe 6
k,a = 6 (26)
d, dp
Then Eqs. (19) and (23) are used so that
5
6Bi D., (T.
k~a -r' r (27)

This completes the calculation procedure; for a chosen
Ts, we can now calculate 7Da, To, mo, R and then i
by Eq. (1).

EXAMPLE
Let us consider the behavior of spherical pellets of
6 mm diameter. Experiments using a powder of 0.3
mm diameter, made by crushing the pellets, give a
value for k = R of 5 s-1 at 1 bar and 600 K. For these
conditions i is unity, and k, = kvs = kvo, since
Ts = To. This reaction is first-order and irreversible.
Considering Tr to be 600 K, we establish for the 6 mm
pellets the values ry = 20, Der = 2.0 x 103 cm2s-1,
and Bir = 1300, corresponding to Re = 50, Sc =
0.6 and DABr = 0.2 cm2s-'. Now we can follow the
procedure described in the previous section to find
the values of interest for this example. A simple com-
puter program with graphics gives the curves dis-
cussed below.
Figure 1 shows the surface temperature corres-
ponding to various bulk (gas) temperatures To. As To
is increased, for a large enough 0r, hysteresis loops
with multiple steady states are found. Recall that in
10 ....... .


300 600 900 1200 1500 1800
surface temperature, K
FIGURE 4: Estimation of the difference between the tem-
peratures at the center and at the surface of the exam-
ple pellet, as a function of surface temperature.


the actual calculations, To is found from Ts. The vari-
ation of pr can be thought of as arising from changes
in CAo. If (-AH) were varied, this would imply a differ-
ent reaction with a different y, and other parameters.
Figure 2 demonstrates how the overall reaction rate
(or k) varies with To for the given example.
Curves can also be presented in terms of the usual
dimensionless parameters, 'Da or mo; the variation
of i with mo is presented in Figure 3. These diagrams
have the same general appearance as those of Car-
berry's text, for example [1]. However, they apply to
the chosen particle and reacting system with the
parameters already enumerated. Because of the de-
pendence on temperature of kvo, Bim, and De which
are built into the model, somewhat different results
for i would be obtained for a different set of paramet-
ers which might lead to the same values of mo.
It is worth noting that the assumption of a constant
pellet temperature is equivalent to choosing a Car-
berry number [5] of infinity, where
Ca = r = Bimr (28)
Ca (28)
P, Bihr
As the thermal conductivity X, of the pellet goes
to infinity, Pr and Bihr go to zero and Ca is infinite,
corresponding to an isothermal pellet. If we retain the
results already calculated with Ca = c, we can set
Ca = 100, a reasonable value [1], and estimate the
temperature rise inside the pellet. The result for our
example is shown in Figure 4. The AT's found are low
enough so that the isothermal pellet model seems jus-
tified.
In the design of a fixed-bed catalytic reactor, the
mass and energy balances written in terms of To and
CAo are integrated along the bed. The present simple
model for heterogeneous effects can easily be incorpo-
rated into an algorithm for the simulation of such a
reactor. Thus a realistic result can be obtained by sim-
ple methods.
ACKNOWLEDGEMENT
The authors wish to thank Professor Robert
Rinker for a helpful discussion of the paper.
REFERENCES
1. Carberry, J.J., Chemical and Catalytic Reaction Engi-
neering, McGraw-Hill, New York (1976)
2. Carberry, J.J., and AA. Kulkarni, "The Non-Isother-
mal Catalytic Effectiveness Factor for Monolith Sup-
ported Catalysts," J. of Catalysis, 31, 41-50 (1973)
3. Aris, R., Elementary Chemical Reactor Analysis, Pren-
tice-Hall, Englewood Cliffs, NJ (1969)
4. Bennett, C.O., and J.E. Myers, Momentum, Heat, and
Mass Transfer, 3rd Ed., McGraw-Hill, New York (1982)
5. Froment, G., and K. Bischoff, Chemical Reactor Analy-
sis and Design, John Wiley and Sons, New York (1979) 0


SPRING 1990










STUDENT-DESIGNED LAB
Continued from page 79.
block under water, calculate h for the top and sides, and
subtract to find h for the bottom. (Hopeless!)
Did they measure the thickness at more than one point,
and did they plot all their points? Or did they just average
all their readings ?
Did they state that they tried to make their measure-
ments with as little disturbance as possible (agitation will
greatly increase h)? Did they discuss this and verify this
with calculations?
Did they choose a large enough reservoir of water so
that the water temperature did not change significantly
during the experiment?
Did they choose to weigh the ice? (Not such a good
method because the edges of the slab melt faster than
the center.)
In the weighing approach, if that was used, did they re-
move the slab for weighing? (Poor, because the extra
agitation increases h drastically.) Or did they figure out
how to weigh the slab in place? (Better.)

Variations and Extensions

Many variations and extensions of this simple ex-
periment can be used by the teacher throughout the
years. For example:

Find h for vertical surfaces in water at different
water temperatures.
Find h for horizontal upfacing surfaces in
water. (This is more difficult experimentally and
is not recommended.)

Repeat all the above for ice in air.
Find the effect of fluid motion relative to the ice
surface. For air, all one needs is a regular
household fan and a pitot tube to study this.

For the teacher, there is the inescapable tempta-
tion to ask the student to study a number of these
factors, all in one experiment: upfacing, downfacing,
vertical, effect of velocity and of AT, etc. Try to resist
this as the lesson of this experiment can be learned
just as well by studying one factor alone.
FINAL COMMENTS
What do students learn from this type of experi-
ment?

They have to use their ingenuity and come
up with their own way to answer the
question.

The best way of approaching the problem
will not come to them right away, but only
after they have thought up a number of


schemes. This sort of exercise may give them
an appreciation of the value of group
discussion.

They had to develop their own analysis and
equations-no copying from books. This
should give them a taste for doing original
work.

The laboratory course can be challenging,
surprising, and interesting.
We feel that there is a place for this type of labora-
tory experiment in the undergraduate program. O


AWARD LECTURE
Continued from page 87.
neering Thermodynamics, 2nd ed., J. Wiley, New
York, p. 323
6. Hildebrand, J.H., J.M. Prausnitz, and R.L. Scott,
Regular and Related Solutions, Van Nostrand-Rein-
hold, Princeton, NJ (1970)
7. Wilson, G.M., J. Am. Chem. Soc., 86, 127 (1964)
8. Abrams, D.S., and J.M. Prausnitz, AIChE J., 21, 116
(1975)
9. See, for example, page 331 of reference 5.
10. Lee, K.-H, S.I. Sandler, and N.C. Patel, Fluid Phase
Eq., 25, 31(1986)
11. Lee, K.-H., and S.I. Sandler, Fluid Phase Eq., 34, 113
(1987)
12. Whiting, W.B., and J.M. Prausnitz, Fluid Phase Eq.,
9,119(1982)
13. Hu, Y., D. Ludecke, and J.M. Prausnitz, Fluid Phase
Eq., 17 217 (1984)
14. Shibata, S.K., and S.I. Sandler, IEC Research, 28, 1893
(1989)
15. Lee, K.-H., L.R. Dodd, and S.I. Sandler, Fluid Phase
Eq., 50, 53 (1989)
16. Sandler, S.I., and K.-H. Lee, Fluid Phase Eq., 30, 135
(1986) 0



PROCESS CONTROL COMPUTERS
Continued from page 111.
complished without the effort of several dedicated
people. Professors R. L. Laurence and B. E. Ydstie
helped with the initial proposal. Dr. Graham Sterling,
Alan Ryan, Michael Hajjar, and the whole educational
support committee from Analog Devices supported
and assisted in our development of this laboratory.
Their faith and vision were crucial to this project. Paul
Grabin and Frank Pulaski were central to the setting
up of the laboratory. We also acknowledge our under-
graduate classes of 1985 and 1986. With their pa-
tience, assistance, and feedback, this major transfor-
mation was completed with a minimum of problems
and an enhancement of the results. O


CHEMICAL ENGINEERING EDUCATION












ACKNOWLEDGMENT
DEPARTMENTAL SPONSORS
The following 157 departments are contributing to the support of CEEin 1990 with bulk subscriptions.
If your department is not a contributor, write to CHEMICAL ENGINEERING EDUCATION, c/o Chemical Engineering
Department, University of Florida, Gainesville, FL 32611, for information on bulk subscriptions.


University of Akron
University of Alabama
University of Alberta
University of Arizona
Arizona State University
University of Arkansas
Auburn University
Brigham Young University
University of British Columbia
Brown University
Bucknell University
University of California, Berkeley
University of California, Davis
University of California, Los Angeles
University of California, San Diego
University of California, Santa Barbara
California Institute of Technology
California State Poly Institute
California State University, Long Beach
Carnegie-Mellon University
Case Western Reserve University
University of Cincinnati
Clarkson College of Technology
Clemson University
Cleveland State University
University of Colorado
Colorado School of Mines
Colorado State University
Columbia University
University of Connecticut
Cooper Union
Cornell University
Dartmouth College
University of Dayton
University of Delaware
Drexel University
University of Florida
Florida Institute of Technology
Florida State University
Georgia Institute of Technology
University of Houston
Howard University
University of Idaho
University of Illinois, Chicago
University of Illinois, Urbana
Illinois Institute of Technology
Imperial College, London
University of Iowa
Iowa State University
Johns Hopkins University
University of Kansas
Kansas State University


University of Kentucky
Lafayette College
Lakehead University
Lamar University
Laval University
Lehigh University
Loughborough University
Louisiana State University
Louisiana Technical University
University of Louisville
Lowell University
University of Maine
Manhattan College
University of Maryland
University of Massachusetts
Massachusetts Institute of Technology
McGill University
McMaster University
McNeese State University
University of Michigan
Michigan State University
Michigan Technical University
University of Minnesota
Mississippi State University
University of Missouri, Columbia
University of Missouri, Rolla
Monash University
Montana State University
University of Nebraksa
University of New Hampshire
University of New Haven
New Jersey Institute of Technology
University of New Mexico
New Mexico State University
University of New South Wales
University of New York, Buffalo
Polytechnic Institute of New York
North Carolina A & T University
North Carolina State University
University of North Dakota
Northeastern University
Northwestern University
University of Notre Dame
Technical University of Nova Scotia
Ohio State University
Ohio University
University of Oklahoma
Oklahoma State University
Oregon State University
University of Ottawa
University of Pennsylvania
Pennsylvania State University


University of Pittsburgh
Princeton University
Purdue University
Queen's University
Rensselaer Polytechnic Institute
University of Rhode Island
Rice University
University of Rochester
Rose-Hulman Institute of Technology
Rutgers, The State University
University of Saskatchewan
University of Sherbrooke
University of South Alabama
University of South Carolina
South Dakota School of Mines
University of South Florida
University of Southern California
University of Southwestern Louisiana
Stanford University
Stevens Institute of Technology
University of Sydney
University of Syracuse
University of Tennessee
Tennessee Technological University
University of Texas
Texas A & M University
Texas Tech University
University of Toledo
Tri-State University
Tufts University
University of Tulsa
Tuskegee Institute
University of Utah
Vanderbilt University
Villanova University
University of Virginia
Virginia Polytechnic Institute
University of Washington
Washington State University
Washington University
University of Waterloo
Wayne State University
West Virginia College of Grad Studies
West Virginia Institute of Technology
West Virginia University
University of Western Ontario
Widener University
University of Wisconsin
Worcester Polytechnic Institute
University of Wyoming
Yale University
Youngstown State University






4 Do You Qualiffor Intemational? .1





CHEMICAL ENGINEERS

S... The World is Yours!

S...iEl Mundo es Tuyo!

S...Le Monde est a Vous!

...Die Welt ist Dein!



Return Home with an Exciting Procter & Gamble total sales are over 21 billion dollars
world-wide. Major product categories include beauty
Career Ahead of You! care, beverage, detergent, fabric care, food, health care,
Procter & Gamble has several entry-level product household care, paper, and pharmaceutical consumer
and process development openings for BS, MS, or products. Our technically-based corporation spent over
S PhD Chemical Engineers in Asia, Europe, Mexico 600 million dollars in research and product development
and South America. last year.
STo readily qualify, you must be bilingual We offer a stimulating environment for personal and
(including English) and possess ap-prop rate professional growth, highly competitive salaries, and
SCitizenship Immigration Visa or Work Permit excellent benefits package including pension, health
from one or more of the following countries: care and paid relocation.
Austria, Belgium, Brazil, Chile, Colombia, If interested, send your resume, including country
Denmark, Egypt France. Germany, Hong qualifications and language fluencies, to:
Kong, India, Ireland, Italy, Japan, Lebanon, F. 0. Schulz, Jr.
Malaysia, Mexico, Netherlands, Peru, International Ch E Openings
Philippines, Portugal, Puerto Rico, Saudi The Procter & Gamble Company
SArabia, Singapore, Spain, Taiwan, Turkey, Ivorydale Technical Center (#3CEE)
United Kingdom and Venezuela. 5299 Spring Grove Ln.
SCincinnati, OH 45217

PROCTER &GAMBLE
An EqualOpportunity Employer
4 An Equalopportuniy Employer
44 4 4 4 4 4 4 4 4 44 4 4 4 4 4 4 4 4 44 4 4 4 4 4 4 4 4 4