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EDITORIAL AND BUSINESS ADDRESS:
Chemical Engineering Education
Department of Chemical Engineering
University of Florida
Gainesville, FL 32611
FAX 904-392-0861

EDITOR
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MANAGING EDITOR
Carole Yocum (904) 392-0861
PROBLEM EDITORS
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University of Michigan

PUBLICATIONS BOARD

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

PAST CHAIRMEN
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MEMBERS
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Thomas F. Edgar
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Richard M. Felder
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Purdue University
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McMaster University

Summer 1992

Chemical Engineering Education

Volume 26

Number 3

Summer 1992

DEPARTMENT
114 University of Virginia,
Peter T. Cummings, Roseanne M. Ford, John P. O'Connell

EDUCATOR
120 Phillip C. Wankat, of Purdue University, Frank Oreovicz

CLASSROOM
122 Confirming Thermodynamic Stability: A Classroom
Example, Kenneth R. Jolls, Jeffrey L. Butterbaugh

146 "Product in the Way" Processes, Noel de Nevers

152 A Statistical Look at Significant Figures, Park M. Reilly

164 Design of CSTRs in Tandem Revisited, A. A. Adesina

CLASS AND HOME PROBLEMS
130 Three Problems in Fluid Mechanics,
James 0. Wilkes, Stacy G. Bike

CURRICULUM
136 A Course Sequence for Instrumentation and Control,
Carlos A. Smith, Richard A. Gilbert

160 Molecular Enrichment of the Core Curriculum,
Henry A. McGee, Jr.

LABORATORY
142 The Effect of Agitation on Oxygen Mass Transfer in a
Fermentor, Ronnie S. Roberts, James R. Kastner,
Maqsood Ahmad, D. William Tedder

156 Add Some Flavor to Your Agitation Experiment,
M. Elizabeth Sensel, Kevin J. Myers

134 RANDOM THOUGHTS
What Do They Know, Anyway? Richard M. Felder

119, 133, 168 Book Reviews

CHEMICAL ENGINEERING EDUCATION (ISSN 0009-2479) is published quarterly by the
Chemical Engineering Division, American Society for Engineering Education, and is edited at the
University of Florida. Correspondence regarding editorial matter, circulation, and changes of
address should be sent to CEE, Chemical Engineering Department, University ofFlorida, Gainesville,
FL 32611. Copyright 1992 by the Chemical Engineering Division, American SocietyforEngineering
Education. The statements and opinions expressed in this periodical are those of the writers and
not necessarily those of the ChE Division, ASEE, which body assumes no responsibility for them.
Defective copies replaced if notified within 120 days of publication. Write for information on
subscription costs and for back copy costs and availability. POSTMASTER: Send address changes
to CEE, Chemical Engineering Department., University of Florida, Gainesville, FL 32611.

artment

UNIVERSITY OF VIRGINIA

7..

l.- A

The beauty of Mr Jefferson's handi-
work lives on: top photo is the his-
toric "academical village" and bot-
tom photo frames and reflects the
elegance of e-school building.

~- -~-
The Center for Bioprocess Develop
state-of-the-art instruments

View of the new (Phase 1) chemical engineering/biotechnology building.

PETER T. CUMMINGS, ROSEANNE M. FORD, JOHN P. O'CONNELL
University of Virginia
Charlottesville, VA 22903-2442

A after retiring from public life, Thomas Jefferson's preoccupation
was the founding of the University of Virginia as the first truly
public university in the United States. He formulated its first
curriculum, recruited the first faculty, and designed and supervised the
construction of all the original buildings. Jefferson had a singular vision
for the university: faculty and students would live together in the
"academical village," an environment of unparalleled beauty where they,
as equals, would pursue and expand knowledge. As he wrote to William
Roscoe in 1820,
This institution will be based on the illimitable freedom of the human mind, for
here we are not afraid to follow truth wherever it may lead, nor to tolerate any
error so long as reason is left free to combat it.
His legacy to the students and faculty at UVa includes the historic
campus-known as The Grounds-containing perhaps
the most famous and beautiful university buildings in
the United States: the Lawn and the Rotunda. Jeffer-
son also left UVa's students and faculty a unique and
rich educational tradition. This article will attempt to
convey how the Department of Chemical Engineering at
the University of Virginia strives to fulfill Jefferson's
educational vision.
The department is a blend of old and new. The "old" is
UVa's long history of engineering in general and chemical
engineering in particular. Jefferson had a strong personal
ment with its interest in science and the "mechanical arts." The earliest
nation. Copyright ChE Division ofASEE 1992
Chemical Engineering Education

ChEde

.. fulfilling Thomas Jefferson's vision

The educational philosophy of the department reflects a
commitment to continuing the Jeffersonian ideal
of students and faculty as equal partners
in the pursuit of knowledge.
curricular plans for the university included instruction in mili-
tary and civil architecture. Engineering courses were offered in
1827, about one year after the university's opening, and the
School of Engineering and Applied Science was established in
1836. This makes it the oldest university-based engineering
school in America.
The Department of Chemical Engineering was established
by several faculty from the Chemistry Department in 1908,
the same year that the American Institute of Chemical Engi-
neers (AIChE) was founded. The Masters program began in
1949 and the first PhD was awarded in 1961. Both our under-
graduate and graduate alumni have distinguished themselves
through outstanding contributions in many branches of indus-
try and in academia.
The "new" is a recent significant change in personnel and
facilities. Of the eleven full-time and one half-time faculty, four
have joined in the last five years and six are new in the last ten
years. John O'Connell joined the department as Chair in 1988
after twenty-two years at the University of Florida, while the
other new faculty all began their academic careers at UVa.

Phase I of a new 50,000 ft2
building was completed in
March of this year. It houses --- 7-:
the faculty offices and half of
the chemical engineering re-
search laboratories. The other
research laboratories, all in-
volved in various aspects of
biotechnology, are currently -
located in 15,000 ft2 of nearby
space that was renovated in
1986. All faculty have active,
funded research programs,
with over $3M in current
sponsored research grants.
There are more than fifty
graduate students, mostly
PhDs, using state-of-the-art Two views of the new ChE building. Part of the lobby (dedicated in honor of
laboratory and computational Charles Brown, alumnus and a former CEO of AT&T) above, and the Mobil
equipment for advanced-level classroom, used for essentially all undergraduate and graduate chemical engi-
research in contemporary neering courses, below. Itfeatures a state-of-the-art lighting system and seats 72,
chemical engineering, with handicapfacilitiesfor both listeners and speakers.
Summer 1992 11

EDUCATIONAL PHILOSOPHY
The educational philosophy of the department re-
flects a commitment to continuing the Jeffersonian
ideal of students and faculty as equal partners in the
pursuit of knowledge. Jefferson's academical village
began with sixty-eight students and ten faculty
drawn together in an atmosphere of close inter-
action and learning. This continues today in the
close relationships our faculty develop both with
undergraduate and graduate students, leading to
friendships that continue many years beyond gradu-
ation. In keeping with the idea of equal partnership
in the educational process, academic titles are not
used for faculty; they are addressed by the students
as Mr., Mrs., or Ms.

THE UNDERGRADUATE PROGRAM
The engineering school at UVa is renowned for
the quality of its undergraduate students. Several
published surveys indicate that the average SAT
scores of our engineering undergraduates are the
highest of any public university in the country. Only
one out of every six applicants is admitted, and a
significant fraction is from out of the state.
All of the courses offered by the School of Engi-
neering and Applied Science are taught by faculty-
none by teaching assistants alone. This is only
possible because UVa has the lowest student-to-
faculty ratio (9 to 1) of any US public engineering
school. Faculty are expected to maintain an "open
door" policy of being available during all normal
working hours (not just during posted office hours)
to assist students in every aspect of their personal
and scholastic development.
The undergraduate program is typical of ABET-
accredited programs, with preparatory courses in
mathematics, physics, chemistry, and computer sci-
ence and engineering fundamentals, followed by
traditional and modern chemical engineering courses.
In addition, the engineering school has its own
Humanities Division which focuses on technical
reading, writing, and presentation. In recent
years the department has graduated fifteen to fifty
BSChEs per year. The faculty recognizes exceptional
graduating students with a variety of academic and
leadership awards.
In the final year, each undergraduate student is
required to write a senior thesis with both technical
and Humanities Division advisors. Students often
use original research done in our laboratories for
their thesis topics. Besides producing a detailed
project plan and a final written document, students
orally defend their thesis proposal and summarize
116

their findings to their Humanities class. Currently,
the best eight theses are presented to a panel of
industrial and faculty judges in an Undergraduate
Research and Design Symposium who select the win-
ners of research awards. Chemical engineers have
been prominent in these design symposia.
Students are very active in professional service
and social organizations. The focus of chemical engi-

Table 1
Faculty and Research Interests

Giorgio Carta, Associate Professor
PhD (ChE), Delaware, 1984
separation technologies hioseparations adsorption and ion
exchange
Peter Cummings, Professor
PhD (Math), Melbourne, Australia, 1980
physical properties and phase equilibria optimization and
synthesis of chemical processes modeling of bacterial
migration
Bob Davis, Assistant Professor
PhD (ChE), Stanford. 1989
heterogeneous catalysis kinetic studies of selected probe
reactions
Erik Fernandez, Assistant Professor
PhD (ChE), UC Berkeley. 1989
Nuclear magnetic resonance (NMR) characterization of biochemi-
cal reactors and mammalian tissues NMR imaging offlow in
porous media
Roseanne Ford, Du Pont Assistant Professor
PhD (ChE), Pennsylvania, 1989
application of chemical engineering principles to microbial
ecology bacterial chemotaxis bioremediation
Elmer Gaden, Wills Johnson Professor
PhD (ChE), Columbia, 1949
biotechnology and bioprocesses social impact of technological
development
John Gainer, Professor
PhD (ChE), Delaware, 1964
immobilized biocatalysts two-phase aqueous extraction oxygen
transport in living systems
Jack Hudson, Wills Johnson Professor
PhD (ChE), Northwestern, 1962
dynamic behavior of chemically reactive systems stability,
periodic oscillations, and chemical chaos electrochemical
engineering
Don Kirwan, Professor
PhD (ChE), Delaware, 1967
biochemical engineering mass transfer, crystallization *
Director of Center for Bioprocess Development
Doug LeVan, Professor
PhD (ChE), UC Berkeley, 1976
fixed-bed adsorption thermodynamics of adsorption equilibria *
modeling offixed-bed adsorption systems computer-aided
design
Lem Lilleleht, Associate Professor
PhD (ChE), Illinois, 1962
nucleation of refractory vapors in microgravity environments *
utilization of solar and other alternative energy resources
John O'Connell, Professor and Chair
PhD (ChE), UC Berkeley, 1967
applied molecular theory strongly nonideal liquids surfactant
solutions

Chemical Engineering Education

neering involvement is the student chapter of the
AIChE, advised by John O'Connell. Last year the
group was selected as a national Chapter of Excel-
lence (no more than ten percent of all chapters are
cited for this award). The major activities of the
chapter include presentations during the semester
by industrial speakers, a symposium on graduate
school, the securing of industrial sponsorship to sup-
port attendance of about ten members at annual
AIChE meetings and regional student chapter con-
ferences. There are several social events for both
faculty and students, and the chapter also has a
novel outreach program called "Wahoo Wizards" (Wa-
hoos being one of the nicknames for UVa sports
teams) where students visit local elementary and
middle schools to perform experiments that stimu-
late children's interest in science and engineering.

THE GRADUATE PROGRAM
The closeness that exists between undergradu-
ates and faculty is paralleled in the relationships of
graduate students and faculty. Graduate students
undoubtedly benefit from the open-door policy at
least as much as the undergraduates do.
The graduate program offers MS, ME, and PhD
degrees. The two Masters degrees include a group of
five core courses in the fundamentals of chemical
engineering. The primary difference between them
is that the MS requires a research thesis. There is
also a special program for highly qualified students
with degrees other than in chemical engineering. It
begins with an intensive summer program covering
the undergraduate-level material, followed by en-
trance into the regular graduate program.
The ME degree can be taken as a nonresident

BIoproce

un tilzatic. Engineering

Physical Propeitta
tDiffuilon and
S Reaction Millu ranks fer Separations
S Engineering ineerin n en s and
Reaction
Electrochterr.i- K. nl c
Engineering heterogeneous
Process Synthesis,
Engineering E Optimization and Applications and
Fundamentals control E Technologies

Figure 1. Schematic illustration of faculty research inter-
ests divided into engineering fundamentals and applica-
tions. Placement of fundamentals at the center and appli-
cations at the periphery indicates how applications-
oriented research depends on advances in fundamentals.
Summer 1992

...research interests range from
applied chemistry, biotechnology, and chemical
technology to mathematical modeling, molecular
and process simulation, and design.

through the Virginia Cooperative Graduate Engi-
neering Program (VCGEP). Each term, one of the
regular graduate courses is broadcast via satellite
throughout Virginia and the U.S. using one-way video
and two-way audio capabilities. Many companies
have established classrooms at their industrial loca-
tions in order to allow their employees to participate
in this program. There are now more than thirty
nonresident students enrolled in the ME ChE pro-
gram through VCGEP, and more than a dozen ME
degrees have been awarded in the last three years.
The chemical engineering faculty view research
as an integral part of graduate education. The re-
search interests range from applied chemistry, bio-
technology, and chemical technology to mathemati-
cal modeling, molecular and process simulation, and
design. Figure 1 illustrates how the ongoing research
programs at Virginia cover the two broad categories
of fundamentals and applications. The major funda-
mental research programs are:
Diffusion and mass transfer Gas-liquid and solid-liquid systems *
transport processes in biological systems homogeneous nucle-
ation
Thermodynamics, physical properties, and adsorption Statisti-
cal thermodynamics prediction of physical properties fluid
phase equilibria adsorption equilibria ion exchange solubil-
ity of biochemicals
Fluid mechanics Low Reynolds number flow surface-tension
driven flow multiphase flow and stability
Reaction kinetics Oscillations and chaotic behavior; heterogeneous
catalysis
The programs in applications and technologies in-
clude:
Separations technology Fixed bed adsorption ion exchange and
chromatography precipitation and crystallization extraction *
air pollution control
Bioprocess technology Immobilized enzymes, microorganisms,
and cells aeration and oxygen transfer bioseparations *
bioremediation
Biochemical engineering Modeling of metabolic processes sec-
ondary metabolite regulation
Biomedical engineering Mammalian cell biocatalysis metabo-
lism in diseased tissues enhanced oxygenation in living sys-
tems NMR spectroscopy
Reaction engineering Bioreactors multiphase reactors flow
reactors
Electrochemical engineering Corrosion dynamics of electro-
chemical reactions
Heterogeneous catalysis Structural characterization of metal clus-
ters acid-base properties of solid oxides
Process synthesis, design, and control Mathematical modeling

117

and simulation computer control computer-aided process
design.
Solar energy utilization Thermal energy conversion and storage *
photovoltaics
While faculty direct independent research pro-
grams, there is considerable collaboration both
within and outside of the department. Many of our
faculty are involved in multidisciplinary research
efforts at UVa.
Six faculty members from chemical engineering
(Carta, Fernandez, Ford, Gaden, Gainer, and Kirwan)
participate in the Center for Bioprocess Develop-
ment along with several faculty from the Medical
School and Department of Biology. Founded in 1987
under the sponsorship of Virginia's multi-program
Center for Innovative Technology (CIT), the
Bioprocess Center conducts research in biotechnol-
ogy applications such as large-scale use of biological
catalysts (microbes, cells, and enzymes) and novel
processing for producing valuable products in medi-
cine, agriculture, and the food, energy, and chemical
industries. The center's annual budget is over $1M
from federal agencies (including NSF and NIH), state
funds through CIT, and fifteen companies.
Four faculty (Cummings, Ford, Fernandez, and
Gainer) are involved in UVa's Biophysics Program,
an interdisciplinary degree program with over forty
other faculty members from the Medical School, the
School of Engineering and Applied Science (Biomedi-
cal and Chemical), and the College of Arts and Sci-
ences (Biology, Chemistry, and Physics). Jack Hudson
participates in the Center for Electrochemical Sci-
ences and Engineering which draws together faculty
from chemical engineering, materials science, and
nuclear engineering around the themes of corrosion,
electrochemical reactions, and electrochemical phe-
nomena. Its research support of several million dol-
lars annually comes from a variety of federal agen-
cies, CIT, and industry.
ENVIRONMENT
The university is located in the historic city of
Charlottesville in beautiful Albemarle County,
nestled in the foothills of the Blue Ridge Mountains.
The area's mild climate, historical significance (three
presidents-Jefferson, Madison, Monroe-all resided
nearby), academic stature, and physical beauty
attract a wealthy and culturally diverse popula-
tion of about 120,000. The locale combines the ameni-
ties and attractions of a city with the charm and
ambience of rural America. Furthermore, Washing-
ton, DC, and Richmond are both less than two
hours away by car, while the Skyline Drive can
be reached in less than one-half hour. The

Charlottesville/Albemarle airport is serviced by
several major airlines.
UVa is often regarded as one of the finest univer-
sities in the US, with outstanding undergraduate
and graduate programs in the arts, law, medicine,
business, and engineering. For the last two years
it has been ranked by the New York Times' "Selec-
tive Guide to Colleges" as one of the three best
universities in the U.S. In a recent U.S. News
and World Report article surveying American
universities, UVa was the only public university
ranked in the top twenty.
The current enrollment is 17,000 students, with
7,000 of them in our graduate and professional pro-
grams. Thus, it is one of the smallest PhD-granting
state universities in the country. Combined with the
historical buildings and grounds, this gives the uni-
versity the look and feel of a small private school.
Much of chemical engineering is now housed in
the first phase of a new building designed specifi-
cally for chemical and biochemical engineering re-
search. Its dedication was on April 25, 1992, with
John M. Prausnitz of UC Berkeley giving the princi-
pal address. In keeping with Jefferson's view of close
faculty and student interactions, the building's fac-
ulty offices are dispersed throughout the building,
generally across the hall from their laboratories and
graduate student offices. The second phase of this
50,000 ft2 facility will house the bioprocessing re-
search laboratories, the undergraduate laboratory
and mechanical shop. Funding for both phases does
not include any state-allocated money. The generos-
ity of alumni, industry, and philanthropic founda-
tions to complete this $11M building demonstrates
how highly our program is regarded by these groups.
CONCLUSION
The goal of our department is to make measur-
able and distinctive contributions toward enhancing
the quality of life consistent with the rich educa-
tional tradition entrusted to us by Thomas Jefferson.
In doing so our objectives are to satisfy our public
and private benefactors and stimulate growth in all
of our students. Our energetic faculty members are
strongly committed to both teaching and innovative
research, deeply involved with undergraduates and
graduates in a community of shared learning and
research, and housed in a new building of architec-
tural beauty that promotes scholarly and profes-
sional interactions in much the same way as Tho-
mas Jefferson's beloved Lawn. We invite you to visit
us and experience first-hand the ways in which
chemical engineering at UVa is meeting its objec-
tives and fulfilling Thomas Jefferson's vision. J
Chemical Engineering Education

1 book review )

PLANT DESIGN AND ECONOMICS
FOR CHEMICAL ENGINEERS
4th Edition
by M. S. Peters and K.D. Timmerhaus; McGraw
Hill, Inc., New York, NY 10020; 910 pages, $60.45
(1990)

Reviewed by
Reena Chakraborty, Martin C. Hawley
Michigan State University

The fourth edition of this classic text retains the
same layout and philosophy as its predecessors. The
first third of the book covers the principles of process
design development and plant design and safety in
four chapters: 1-Introduction, 2-Process Design De-
velopment, 3-General Design Considerations, and
4-Computer-Aided Design. The second third of the
book, economics, is covered in the next five chapters:
5-Cost and Asset Accounting, 6-Cost Estimation,
7-Interest and Investment Costs, 8-Taxes and In-
surance, 9-Depreciation, and 10-Profitability,
Alternative Investments, and Replacements. The
remaining third deals with the technical design
problem: 11-Optimum Design and Design Strategy,
12-Materials Selection and Equipment Fabrication,
13-The Design Report, 14-Materials Transfer, Han-
dling, and Treatment Equipment: Design and Costs,
15-Heat Transfer Equipment: Design and Costs,
16-Mass Transfer Equipment: Design and Costs,
and 17-Statistical Analysis in Design. Chapters 11,
17, and 13 could be dealt with, in that order, as a
sequence in setting up and representing the solution
to a design problem.
Most of the solved problems and most of the
charts still use engineering units despite the stress
on SI. Surely the sample problems could have at
least incorporated both sets of units, since this was a
problem with the third edition and the authors have
had ten years to work on it! To the authors' credit,
many of the unsolved problems at the end of each
chapter are in SI. The extensive lists of references at
the end of each chapter that added to the utility of
the third edition have been deleted in this edition.
Perhaps these will be compiled and added as an
appendix in a future printing. They will be sorely
missed in this one.
The first two chapters remain unchanged from
the third edition, with no new problems. The third
chapter has been greatly expanded with much new
Summer 1992

material on health and safety hazards, including
sources of exposure, exposure evaluation, exposure
hazard control, fire and explosion hazards, person-
nel safety, and safety regulation. In each of the sub-
sections, relevant material on measures and stan-
dards of hazards, measures and standards of safety,
and pertinent references to codes and regulations
and the agencies which administer them have been
made. A new section on HAZOP studies has been
added which is clear, concise, and comprehensive,
and the material on environmental protection
and pollution control has been updated. The rest
of the chapter is generally unchanged, with the
exception of the section on patents, which has
been streamlined. There are twenty-five new
problems at the end of this chapter on hazard pre-
vention which are simple, but instructive. Many of
them have been adapted from Safety, Health, and
Loss Prevention in Chemical Processes: Problems for
Undergraduate Engineering Curricula (copyrighted
by the AIChE in 1990).
Computer-Aided Design, Chapter 4, is a concise,
comprehensive, well written and referenced section
on the various aspects of computer-aided design and
covers everything from the use of spreadsheets in
material and energy balance calculations to
flowsheeting software. The eight problems at the
end of the chapter vary from fairly straightforward
material and energy balances to fairly complex evalu-
ations of alternative process designs.
The material in the economics section of the book
is virtually unchanged, with the following excep-
tions: the section on evaluating interest has been
expanded into a chapter with fifteen elementary but
illustrative problems at the end, and one new prob-
lem each has been included at the end of Chapter 6
and Chapter 8 (neither is complex). A section on the
accelerated cost recovery system (ACRS) and the
modified accelerated cost recovery system (MACRS)
has been included in Chapter 9, along with three
related unsolved problems and a solved sample prob-
lem. Some of the unsolved problems at the end of the
chapters in the third edition have been deleted here.
All the cost data and charts have been updated.
Some of the charts for costing are now smaller than
their predecessors and thereby are harder to inter-
polate. The example on reactor design has been up-
dated and includes programs in BASIC, FORTRAN,
and PASCAL. There are no new problems in this
section of the book. Five new unsolved practice ses-
sion problems have been included in Appendix C.
Continued on page 155.

educator

PHILLIP C. WANKAT

of Purdue University

FRANK OREOVICZ
Purdue University .
West Lafayette, IN 47907

F or many young
people, the choice of
a career is a trial-
and-error process that lasts
for years. But not for Phil
Wankat. His father sug-
gested that he become a
chemical engineer, Phil
said "OK" ... and that was
that. His father, an ana-
lytical chemist, was actu-
ally making an informed
suggestion, knowing as he
did the engineering world
and Phil's penchant for sci-
ence and math.
Phil's other major deci-
sion-to become a profes-
sor-also came early and
easily. However, Phil chose
a roundabout way of
achieving his goals by de-
ciding to take advantage
of the opportunity for get-
ting an education in one of the military academies.
His first and second choices, the naval and air force
academies, were unavailable to him, so he went to
West Point. It didn't take long for him to realize that
military life wasn't for him (roughly one month, to
be exact!) but he felt he had to give it a fair shake
and he stayed two years. To those of us who have
never seen him without his beard, the image of "Gen-
eral Phil" is intriguing, to say the least.
He has no regrets, however, and claims that
three valuable lessons came out of his Academy ex-
perience. First, he learned that you could want some-
thing very badly, work very hard for it-and still not
attain it. This proved to be equally true for his
expectations of the military and for his hopes for

fluency in French. Second,
he learned discipline (a valu-
able but difficult lesson for
many college students to
learn), and he became accus-
tomed to "being yelled at."
And third, he decided in his
second year that he wanted
to earn a PhD and become a
Professor; through some in-
formal tutoring he was do-
ing in math, chemistry and
physics, he had discovered
he greatly enjoyed working
with people and explaining
things to them.
Phil transferred to
Purdue after two years at
West Point, and eventually
graduated first in his class
(in 1966). His interest in
separations was kindled by
Lowell Koppel's lectures on
distillation. He also contin-
ued tutoring, nurturing his
interest in teaching. When
he applied for graduate school he made note of his
interest in teaching, which (it turned out) qualified
him for a National Defense Education Act Scholar-
ship. Princeton offered him one and he accepted.
At Princeton his interest in separations was side-
tracked for a while since the only person doing re-
search in separations was Dick Wilhelm (who was
doing parametric pumping). Unfortunately, Phil
"couldn't understand the research at all, the way it
was presented," so he went to work with someone
else, in the area of Monte Carlo simulation in ther-
modynamics. But when his advisor was denied ten-
ure, Phil had to switch again! This time he decided
to talk only to full professors, and he eventually
went to work for Bill Schowalter, who not only taught

@ Copyright ChE Division of ASEE 1992

Chemical Engineering Education

him how to do research but also served as Phil's
model of how to guide grad students. His research
was on hydrodynamic stability analysis, specifically
on the Bernard problem. Although it was a far cry
from separations, his experience taught him some-
thing he still strongly believes today: that the area
of one's PhD is not all that important since the real
purpose of grad school is to train one how to do
research and how to formulate problems.
It was in graduate school that Phil learned how
to ask questions. In his own research and in his
relationships with his grad students, he still regards
questioning to be one of the main purposes of
grad school. A student at the Master's level may
need to be given a problem, but he or she should
have the freedom to work out the solution, with
the advisor acting only as a coach along the way.
At the PhD level, a student should be exposed
to a broad area and then guided toward framing
important questions.

RESEARCH
During Phil's first semester as an assistant pro-
fessor at Purdue, Robert Greenkorn (department
head at the time) suggested that he go to Puerto Rico
for an AIChE meeting. Although Phil wasn't very
interested in attending, money was available-so he
went. At a conference session on separations, he
talked at length with Norm Sweed, who suggested
that since Phil was interested in separations he
should do some parametric pumping. The result: he
did just that ... for the next ten years.
One of Phil's major research interests has been
in developing new operating cycles for adsorption
and chromatography. Early work in this area fo-
cused on parametric pumping and cycling zone ad-
sorption. However, since industry saw little advan-
tage in operating in this mode, Phil later switched to
Pressure Swing Adsorption (PSA) and chromatogra-
phy, where there is considerable industrial interest.
Industrial research is usually driven by the
need to solve a specific separation problem, and this
need often results in interesting and novel ideas.
Working in a university atmosphere, Phil has been
able to define his problems in more abstract and
general terms, without having to tie the research
to a specific problem. Although this approach can
lead to sterile solutions, it can also lead to solu-
tions that are different from (but every bit as
useful as) industrial solutions. In PSA, Phil's re-
search led the way to multicomponent separations
and showed the importance of pressure drop in ordi-

...his [grad school] experience taught him
something he still strongly believes today: that the
area of one's PhD is not all that important since
the real purpose of grad school is to train one how
to do research and how to formulate problems.

An early (1965, Phil's junior year) experiment in
tensile strength?

nary operations. Both of these advances have since
been adopted by industry.
In chromatography, Phil has been interested in
developing generic operational methods, treating
chromatography as a unit operation. One example is
moving withdrawal chromatography which can in-
crease throughput by one or two orders of magni-
tude and which is generally applicable to migration
chromatographic systems. This approach is easy to
scale up and easy to generalize, contrasting with the
biotechnological approach that looks at each separa-
tion problem as chemically unique. The combination
of these approaches will eventually make chroma-
tography a standard separation method.
Phil has always mixed independent and collabo-
rative research. He is currently working with a cross-
disciplinary team of chromatographers in an NSF-
sponsored mini-center. This group includes George
Tsao and Linda Wang (chemical engineering), Mike
Ladisch (agricultural engineering), and Fred Regnier
(chemistry). In addition, he has a long-term collabo-
ration with Martin Okos (agricultural engineering)
on combined fermentation and separation, which
has resulted in a patent. He has also worked with
Alden Emery and Dave Kessler (chemical engineer-
ing) on separations, and with Fritz Friedlander (elec-
trical engineering) on high gradient magnetic sepa-
ration. Even further afield, he has coauthored pa-
pers with Bud Homsy of Stanford (an outgrowth of a

Summer 1992

sabbatical at Berkeley), with Rich Noble of the Uni-
versity of Colorado, with Daniel Tondeur of ENSIC
in Nancy, France (from another sabbatical), and with
Renato Rota of the University of Milan.
Research, scholarship, and teaching are inextri-
cably linked for Phil. His research in separations led
to the development of his course on advanced sepa-
rations; this course fed into his work on adsorption
and chromatography, ion exchange, and membrane
separation; this work in turn led to modifications in
the course, out of which came his book on rate-
controlled separations. Clearly, this book has a solid

0

Neal Houze, Phil, and Ron Barile making a philo-
sophical statement. (1976)

background in research. Among his projects, Phil
considers his intensification work on adsorption
and chromatography, as well as his chromato-
graphic research on developing large-scale systems,
to be the most significant.

TEACHING
His first experiences in teaching taught him that
he didn't know what he was doing. He wanted to
give the students in a sophomore distillation class a
strong, abstract, theoretical base of separations, us-
ing a deductive, top-down approach. The result was
a disaster. The material was entirely over their heads.
Although his years of study had enabled him to
distill the knowledge for himself, his students didn't
have that preliminary study to build upon. After
that experience, he "became more concrete in his
teaching"-he talked about equipment and took stu-
dents to the unit ops lab so they could see the equip-
ment, enabling them to visualize it in the future.
Another experience occurred later, during his re-
search. When he was a grad student, he studied the
Thomas method for adsorption, but the material was
covered only in lectures and he had never solved any
problems with it. Later, while doing research, Phil
came across the Thomas method again, but he had
no memory of the earlier encounter. He studied it
and figured it out-but it wasn't until two years
later that he came across some old notes and real-
122

ized that he had studied the method during his
grad-student days! Apart from making conclu-
sions on the quality of Phil's short- and long-term
memory, we can appreciate the import of his real-
ization that "the incident convinced me that you
have to make students do things. Lecturing isn't
enough. They have to do problems and derivations,
and make connections."
Phil learned why that earlier class hadn't worked
when, in 1972, he took a course entitled "Educa-
tional Psychology for College Teachers," taught by
John Feldhusen at Purdue. The course opened up
whole new ideas about teaching, and it became the
seed out of which his Masters degree in counseling
and his own course on teaching grew.
After his unhappy experience with the separa-
tions class, Phil converted his class to a self-paced
format. Anyone who has ever been involved in in-
structional development knows what a risk it is for a
young assistant professor to make this kind of class
change. (The phrase "professional suicide" comes to
mind.) Such conversions consume a great deal of
time-time regarded by primary committees as bet-
ter spent on research and becoming promotable. But
Phil admits that he was immodest (or cocky?) in his
belief that he could do it all. Events have validated
that decision, of course, but that first semester re-
quired about thirty hours a week simply to develop
test problems and study guides. His students had to
meet an absolute standard, but if they didn't meet it,
the only "penalty" was a retest. In this way students
determined their own grades and did not finish until
they showed evidence of mastery. The class was
taught this way until 1982, when it ended after a
curriculum revision.
Phil felt that new faculty members could be helped
greatly in their first few years as professors if they
had some prior knowledge of what being a teacher
entailed. His idea was to teach a graduate course on
educational methods, and the idea resulted in a
course that has been taught biennially since 1983.
In 1990-91, with an NSF curriculum development
grant, the course was expanded to include all of
engineering, and a workshop was conducted in July
of 1991 for professors from ten major research uni-
versities. A book has been developed for this course,
and it should be published in 1992.
Phil used the ideas first encountered in the teach-
ing class and extended them to engineering, relying
along the way on a number of noted educators in
engineering as well as in science and education. In
addition to those already mentioned: Rich Felder
and Karl Smith, for getting away from lecturing and
Chemical Engineering Education

One thing which makes Phil unique ... is that during a time when he was a full professor he also
became a student again and earned a Masters in counseling [in 1982] .... he was only the
second professor at Purdue who was allowed to enroll as a grad student...

towards student learning; Jim Stice, for teaching
methods; Rich Noble and Don Woods, for problem
solving; Dick Hackney and Janine Bernard, who
helped foster his early ideas on education; and Dendy
Sloan, for combining caring and professionalism.

COUNSELOR
One thing which makes Phil unique (or odd, de-
pending on your point of view) is that during a time
when he was a full professor he also became a stu-
dent again and earned a Masters in counseling. The
incident that triggered this move occurred in 1975
when he had a student who was, by all accounts,
very "strange." Exasperated and completely at a loss
as to what to do with the student, Phil finally told
him that his behavior was abnormal and bizarre and
that he needed help-but Phil had no idea where to
send him for such help. "It devastated me, having to
tell that to a student. It left me in a state of shock."
Then, a friend of Phil's in Purdue's counseling
program told him about a course that covered the
basics of counseling. (Actually, it was quite an intro-
duction: five credits with about twenty hours of work
per week.) During that course, Phil discovered other
interests in the area and wound up taking another
course the following semester. Then, after a sabbati-
cal, he applied for degree status in the program, but
found himself confronting a bureaucracy that wor-
ried about conflicts of interests when faculty in one
area wanted to study for a degree in another area.
Phil argued that no conflict of interest existed since
he was already a full professor and that he simply
wanted to improve his teaching and counseling abili-
ties. He finally got his wish, and he became only the
second professor at Purdue who was allowed to en-
roll as a grad student. He finished the Masters in
Education in Counseling in 1982.
Because of his interest in people and his desire to
gain some practical counseling experience, he volun-
teered to work at the Crisis Center in Lafayette.
Over the span of seven years he estimates that he
gained at least a year's worth of valuable experience
as a working counselor through this volunteer activ-
ity. An added dividend from this work was meeting a
lady named Dot, who became his wife in 1980.

AUTHOR
It is not unusual for a professor to entertain
thoughts of writing a book. The reasons, both peda-
Summer 1992

gogical and personal, are many and varied. For Phil,
it was simply a "huge desire to write a book." Ever
since 1975 he had wanted to write a book, but there
were already a number of good texts on equilibrium-
staged separations in the marketplace. With his back-
ground, however, he felt he could write a book that
was pedagogically sound, with an emphasis on what
helps people to learn. For example, he would give
specifics, be concrete, build up to a general argu-
ment, give detailed example problems, and follow
a specific problem-solving strategy (based on
the ideas of Don Woods). He would present the
strategy in the first chapter and then use it in
all of the example problems, giving the student a
clear method to follow. He would also try to have
at least one homework problem drawing on each
and every section of the book, so that profes-
sors could have a choice. And he would list objectives
for each chapter and provide numerous figures. The
result, after ten years of intermittent labor, was
Equilibrium-Staged Separations.
In addition to over one hundred and twenty pub-
lications, he is the author of four books: Large Scale
Adsorption and Chromatography (CRC Press, 1986);
Equilibrium-Staged Separations (Elsevier, 1988);
Rate-Controlled Separations (Elsevier, 1990); and,
with Frank Oreovicz, Teaching Engineering
(McGraw-Hill, in press). He was a coeditor of Ad-
sorption and Ion Exchange: Fundamentals and Ap-
plications (AIChE Symposium Series) and is Editor-
in-Chief of the journal Separations and Purification
Methods. His publications on education and teach-
ing number more than thirty articles and include
coauthors such as Ron Barile, Alden Emery, Neal
Houze, and Frank Oreovicz.

ADMINISTRATOR
At one time, Phil swore he would never be an
administrator, but his Dean looked at Phil's resume
(after being prodded by Nick Peppas) and thought
Phil would be a perfect match for Head of Freshman
Engineering. The more Phil thought about heading
up the freshman engineering program at Purdue,
the more intrigued he became. For one thing, he had
been a professor for seventeen years and felt he
could benefit from a new challenge (while still main-
taining his research and teaching). For another, the
new program was clearly focused on students, with a
Continued on page 159.

classroom

CONFIRMING

THERMODYNAMIC STABILITY

A Classroom Example

KENNETH R. JOLLS, JEFFREY L. BUTTERBAUGH1
Iowa State University
Ames, IA 50011

Stability theory is a topic that has begun to
appear more frequently in modern thermody-
namics courses. The recent chemical engineer-
ing texts by Sandler[l] and Kyle[2] and the mechani-
cal engineering text by Bejan[31 discuss the subject
briefly, and the more advanced monographs by
Glansdorff and Prigogine,[4] Callen,[51 and Modell
and Reid161 treat it in greater depth. Stability consid-
erations underlie much of the thinking in classical
thermodynamics and are essential to any thorough
understanding of processes involving phase change.
Teaching stability theory, however, is hampered
by a lack of practical examples. Students are accus-
tomed to systems that are presumed to be in stable
equilibrium, and they have little experience with
states removed from that condition. While one
may memorize stability precepts formally-entropy
maximization under isolation or other potential
minimizations under corresponding constraints-
translating such notions into an understanding of
their significance is not easy. Thermodynamics has
its share of skeptics among students, both in regard
to its content and to its conventional pedagogy. Ex-
pecting such individuals to give serious thought to a
difficult theory describing states rarely (or never)
observed is naive at best.
But everyday examples certainly exist. Common
among these are supersaturated solutions and su-
perheated liquids, both predictably metastable and
both primed to revert to the more stable, two-phase
conditions in response to nucleating stimuli. Experi-
ments involving superheated liquids have been per-
formed by Patrick-Yeboah and Reid,171 and class-
room demonstrations have been developed by Jolls
and Prausnitz.181 Still more deeply metastable liquid
states were discussed in the interesting articles by
Address: Procter and Gamble Company, Winton Hill Technical
Center, Cincinnati, OH 45224-1797

Hayward[9l and Scholander[i01 on "negative pressure"
and "tensile water."
In the absence of such experiments, however, one
must develop descriptions of stability-related phe-
nomena that are sufficiently concrete to be convinc-
ing. Students must be persuaded that these ideas
are real and merit the same level of attention as the
more tangible aspects of thermodynamic analysis.
INTRODUCTION
We have found a way to reinforce stability con-
cepts that both satisfies the pragmatist and retains
theoretical rigor. We use the tabulations of stable
and metastable states for water and steam found in
the well-known Steam Tables by Keenan, Keyes,
Hill, and Moore (KKHME111). Students use these
data to locate pairs of matched states in stable-
metastable combinations. Then, using the appro-
priate thermodynamic potential for a given pair,
they compare the stability levels of the states and
confirm the rankings.
In this paper we show a typical set of comparisons
for the five potentials customarily applied to pure
fluids. Before proceeding, however, we give a brief
review of the principles of stability analysis, pre-
sented in the style of Modell and Reid.[61
Kenneth R. Jolls has undergraduate degrees
from Duke and North Carolina State and gradu-
ate degrees from the University of Illinois. His
specialties include electronic instrumentation,
thermodynamics, and the use of computer visu-
alization in chemical engineering research and
practice.

Jeffrey L. Butterbaugh received his BS and ME
from Iowa State University. His graduate minor
was in Business Administrative Sciences, and he
is presently working as a process development
F engineer for Procter and Gamble Research and
Development.
@ Copyright ChE Division ofASEE 1992
Chemical Engineering Education

The following inequalities are associated
with the stable equilibrium states of vari-
ously constrained systems:

ASM <0

AUM >0
AAT,V,M > 0

All >0
AHS,P,M > 0
AG > 0
-T,P,M

(2a)
(3a)

In these expressions the underbar signifies
an extensive property, subscripts specify the
constraints imposed for a given comparison,
and the symbolism is conventional.
Inequality (la) expresses the entropy-
maximum principle: for an isolated system,
unconstrained internally and in a stable
equilibrium state, the entropy decreases in
response to all perturbations that preserve
isolation. One tests this idea through a so-
called "thought" experiment in which an iso-
lated system in a stable equilibrium state is
partitioned into two contiguous sections and
perturbed by means of a "virtual" process.
The two (intensively) identical parts pro-
vide the mutual "give" needed for the ther-
modynamic properties to change locally
while overall isolation is maintained. Kyle's
discussion[2] provides a helpful background
for conceptualizing such processes.
Inequality (2a) reflects the duality of the
entropy and energy representations of the
fundamental equation-the entropy maxi-
mum implies an energy minimum.* Inequali-
ties (3a), (4a), and (5a) follow from (2a) and
are derived by contriving a subsystem within
the (S,Y,M)-fixed composite whose tempera-
ture and/or pressure may be held constant
during the perturbation process.
Paraphrasing inequality (3a), for example,
we note that any extensive state, known to
represent a stable equilibrium condition, will
possess a value for the Helmholtz energy
less than that of a second state, remote from
the first but having the same temperature,
mass, and total volume. Analogous state-
ments characterize the comparisons implied
by the other four constrained inequalities.
For single-phase states well removed from
any phase-change boundary, verifying in-
* Page 126 of Reference 6.
Summer 1992

Paraphrasing inequality, we note that any extensive state,
known to represent a stable equilibrium condition, will
possess a value for the Helmholtz energy less than that of a
second state, remote from the first but having the same
temperature, mass, and total volume.

/'B (T/T) = 0.85
p = G = A,q + (-P*)(' V1qd)
D= Avapor + (-P*)(-V p ,)

^ Slope at any point
energy Slpatp
A, slope of, --
mass Ithe common
Aaor tangent ine, -P*

I liquid volumes of the vapor
I coexisting phases

0 1.0 3.0 5.0 7.0 9.0
V (multiples of V.), L3M
Figure 1. Subcritical isotherm of the Helmholtz energy from the
Peng-Robinson equation (P* denotes vapor pressure).
qualities (la) through (5a) can be carried out only through
statistical reasoning-examination of molecular configurations
that are allowed but less probable. (Balzhisert12] presents simple
but effective examples of these.) For two-phase conditions, how-
ever, particularly where the equilibrium state lies only a short
distance inside the coexistence boundary, more tangible com-
parisons are possible.
In Figure 1 we show a typical isotherm of the specific Helmholtz
energy* for a temperature below the fluid-phase critical point in
a pure system. Intrinsic stability is guaranteed for states where
(a2A/aV2), is positive (volumes to the left of point C and to the
right of point D). The line tangent to the two lobes of the curve
identifies states B and E that have the same temperature, pres-
sure, and chemical potential. These states can thus coexist in
equilibrium at any fraction vapor so as to yield (through lever-
rule proportioning) values of A and V for the two-phase mixture
intermediate to those for the individual states.
The dotted line in Figure 1 intersects the metastable, single-
phase state I and the stable, two-phase state II--each at the
same temperature and volume but with the latter possessing a
lower value of A to coincide with its more stable condition.
Similar arguments applied to a subcritical isobar on H-S coordi-
nates show that the more stable state has a lower value of H
when entropy and pressure are the constraints.
* Based on a cubic equation of state.

In the following sections we will quantify these
comparisons for inequalities (la) through (4a)
and show analogous stable/metastable pairs for
inequality (5a).

THE KKHM TABLES
The data tabulated in the Steam Tables[111 are
based on an empirically determined expression for
the Helmholtz energy per unit mass of water sub-
stance A(T,V).* The form of this function is shown in
the Appendix of the Steam Tables, which also in-
cludes tabulated values of the sixty-one constants
used and discussions of the supporting experimental
data. In addition to the usual coverage of properties
in the fully stable regions, data for the metastable,
single-phase states that lie just inside the satura-
tion curves are given for both the liquid and vapor
phases. In compiling the Steam Tables this informa-
tion was generated by extrapolating the fundamen-
tal equation inside the coexistence boundary and
tabulating property values as continuous extensions
of the fully stable iso-lines outside. (Italics are used
to designate metastable conditions.) While no ex-
perimental values were used to control these exten-
sions, the authors refer to them as "reasonable" and
as providing "the best values available" (ca. 1978).
* Given in the Steam Tables as TY(T,p).

In Table 1 we reproduce a small portion of the
data for saturated and superheated steam (regular
face) and for subcooled steam (italic) in the vicinity
of the normal condensation point for a pressure of
0.38 MPa. The actual condensation temperatures
are shown in parentheses, and a dashed line is drawn
in each column to separate data for the two kinds of
stability.
It is thus possible to identify properties and prop-
erty changes in the metastable regions and also to
expect that conventional thermodynamic operations
will be borne out using those data. For example, one
might use numerical differentiation to verify the
following Maxwell relation:

pST \ Tlp
Substituting property values centered around the
metastable condition t = 95C, P = 0.38 MPa, into
the finite-difference approximations of the deriva-
tives, we obtain
( (6.5972-6.6600)(10-3)
APT 0.04 -5710(m/kgK
(408.9-424.5)(10-3)
(Y)p 10 -156x 10-3(m3 /kg.K)

The small error results from simple finite differencing

TABLE 1
Vapor-Phase Data (Steam Tables,'11 pages 28-29)
P(t Sat.) 0.36 (139.87) 0.38 (141.79) 0.40 (143.63)
t VX103 U H S Vx103 U H S Vx103 U H S
Sat 510.6 2549.9 2733.7 6.9311 485.3 2551.8 2736.2 6.9130 462.5 2553.6 2738.6 6.8959
75 407.9 2429.2 2576.1 6.5148 384.1 2425.9 2571.9 6.4800 362.6 2422.6 2567.6 6.4463
80 416.7 2439.4 2589.4 6.5528 392.5 2436.4 2585.5 6.5189 370.8 2433.2 2581.5 6.4860
85 425.2 2449.5 2602.5 6.5897 400.8 2446.6 2598.9 6.5564 378.7 2443.7 2595.2 6.5243
90 433.6 2459.3 2615.4 6.6254 408.9 2456.6 2612.0 6.5928 386.6 2453.9 2608.5 6.5614
95 441.8 2469.0 2628.1 6.6600 416.8 2466.5 2624.9 6.6280 394.2 2464.0 2621.6 6.5972
100 449.9 2478.5 2640.5 6.6935 424.5 2476.2 2637.5 6.6621 401.7 2473.8 2634.5 6.6319
110 465.7 2497.1 2664.8 6.7578 439.7 2495.1 2662.2 6.7273 416.3 2493.0 2659.5 6.6981
120 481.0 2515.2 2688.4 6.8187 454.4 2513.4 2686.1 6.7890 430.4 2511.6 2683.8 6.7605
130 496.0 2532.9 2711.5 6.8765 468.8 2531.3 2709.4 6.8475 444.2 2529.7 2707.3 6.8197
140 510.8 2550.1 2734.0 6.9318 482.8 2548.7 2732.2 6.9033 457.6 2547.3 2730.3 6.8761
150 525.2 2567.0 2756.1 6.9847 496.6 2565.8 2754.5 6.9567 470.8 2564.5 2752.8 6.9299
160 539.4 2583.7 2777.9 7.0355 510.2 2582.6 2776.4 7.0079 483.8 2581.4 2774.9 6.9815
170 553.5 2600.1 2799.4 7.0846 523.6 2599.1 2798.0 7.0573 496.6 2598.1 2796.7 7.0312
180 567.4 2616.3 2820.6 7.1320 536.8 2615.4 2819.4 7.1049 509.3 2614.5 2818.2 7.0792
190 581.2 2632.4 2841.7 7.1779 550.0 2631.6 2840.6 7.1511 521.8 2630.7 2839.5 7.1256
Properties at conditions below the saturation temperature for each pressure are italicized and correspond to metastable (subcooled) states.
Symbol and Meaning Units Symbol and Meaning Units Symbol and Meaning Units
P pressure MPa V specific volume m'/kg H specific enthalpy kJ/kg
t temperature C U specific energy kJ/kg S specific entropy kJ/kg.K
Energy and entropy are each taken to be zero for the saturated liquid phase at the triple point.

.26 Chemical Engineering Education

of these nonlinear functions.
Because the Steam Tables present data on a per-
unit-mass basis, we need not be concerned with
the fixed-mass constraint. Thus we can express
each of the conditions we wish to confirm in the
simpler, doubly subscripted form involving specific
properties only:
ASu,v < 0 (Ib)
AUsv > 0 (2b)
AAT, > 0 (3b)
AHSP > 0 (4b)
AGT,P > 0 (5b)
Inequalities (3b), (4b), and (5b) are the easiest to
verify because one or both constraints conform to the
temperature and pressure indexing of the data.[111
We show these calculations first.

Helmholtz Energy
To confirm inequality (3b), we must find two states
at the same temperature and volume-one that rep-
resents stable equilibrium conditions and the other
metastable. In Figure 2 we show the two-phase re-
gion in the vicinity of the 950C isotherm on pressure-
volume coordinates. (Note the difference in volume
scales for liquid and vapor.) Let us consider the
metastable (subcooled) vapor state at 950C, 0.38 MPa,
as our base point. From Table 1 we have the follow-
ing properties:
V= 0.4168 m3 /kg
U= 2466.5 kJ/kg
S = 6.6280 kJ/(kg.K)
Liquid water and steam at 95C will coexist in

Figure 2. Pressure-volume diagram, low-pressure range
(volume scales differ for liquid and vapor).
Summer 1992

stable equilibrium under a vapor pressure of 0.08455
MPa1 and with any fraction vapor. To find a tem-
perature-volume match for the base point, we need
only compute the fraction vapor in the two-phase
state that gives the same overall specific volume as
in the metastable state (0.4168 m3/kg). Noting that
the saturated-state liquid and vapor volumes at this
temperature are 1.0397 x 10-3 and 1.9819 m3/kg,
respectively, we solve for the desired fraction.
x = 416.8- 10397 0.2099
19819 0397
Thus, the stable, two-phase state at 950C (0.08455
MPa) and with vapor fraction 0.2099 has the same
temperature and volume as the metastable, single-
phase state at 95C and 0.38 MPa, and we can pro-
ceed to compare the Helmholtz energies.
metastable state:
A = U TS = 2466.5 (95 + 273.15)(6.6280)
= 26.4 kJ/kg
stable state:
saturated phases at 95C
liquid vapor
U 397.88 2500.6
S 1.2500 7.4159
from which
A = x[U TS]ap,r + (1- x)[U TS]iquid
= -97.4 kJ/kg (6)

Stable < Ametastable

Enthalpy
Confirming inequality (4b) requires a stable-meta-
stable pair at the same entropy and pressure. Figure
3 shows the two-phase region in the
vicinity of the 0.38 MPa isobar on t-
S coordinates. Again we choose the
metastable (subcooled vapor) base
state along the 0.38 MPa isobar at
950C [where S = 6.6280 kJ/(kg.K)
and H = 2624.9 kJ/kg]. From
entropy-matching calculations
analogous to the volume-matching
calculations in the previous case,
we find that the stable, two-phase
state at 0.38 MPa (t = 141.790C)
and vapor fraction x = 0.9447 has
=the same entropy.2 With satura-
SI tion properties
3400 Hiuid = 596.83
and

1 Reference 11, page 3.
2 Reference 11, page 10.

0.50
S 95TC '

0.38 0.38 MPa
base
0.30 point saturated vapor
point saturated vapor
0.30
95C (metastable vap
P, MPa
0.20 V=416.8

saturated liquid
0.10 0.08455 MPa
(1-x)=0.7901
0.00 ' '
1.02 1.07 400
V, m'/kg x 103

_1 I I I

or)

Hvapor = 2736.2
the enthalpy of the two-phase state is given by
Hstable = xHvapor +(1- x)Hliquid = 2617.94 kJ / kg (7)
and
Stable < Hmetastable

Gibbs Energy
Stable-metastable pairs that confirm inequality
(5b) involve liquid states that are either stably com-
pressed above or metastably expanded below satu-
ration. The limited amount of data for such states in
the Steam Tables requires that we move the region
of interest to a higher temperature. Figure 4 shows
the liquid and vapor branches of the 2600C isotherm
with the saturation points (at 4.688 MPa) dividing
each branch into stable and metastable sections.
Numerical data appear in Table 2.
Two Gibbs energy comparisons are

possible from these data. At 2.5 MPa
the liquid state (0) is metastable:

G = H TS = 1134.8 -(533.15)(2.8898)
= -405.9 kJ / kg
whereas for the stable (superheated) va-
por at this pressure (o)
G = 2907.4-(533.15)(6.4601)
= -536.8 kJ/ kg
and

Stable < Gmetastable
At 5.1 MPa the situation is reversed.
For the metastable (supercompressed or
subcooled) vapor (A)
G = 2770.4 (533.15)(5.9214) = -386.6
and for the stable (compressed or
subcooled) liquid (0)
G = 1134.3 (533.15)(2.8827) = -402.6
Again the inequality is confirmed. Re-

eating the calculation at the exact saturation pres-
sure confirms the equality of G for phases coexisting
at equilibrium.*
Glquid= -403.1

G va = -403.0
vapor

Entropy and Energy

Inequalities (Ib) and (2b) are more difficult to
confirm because the two-phase state in each case
must satisfy two nonindexed constraints. For the
entropy comparison one must find a stable-meta-
stable pair with the same volume and energy. Re-

* Properties of coexisting states are obtained from the fundamen-
tal equation at the observed vapor pressure for a given tempera-
ture-thus the insignificant difference in G-values for saturated
liquid and vapor phases (Ref. 11, p. 135).

165

- . / 141.79C
'0 -=05

t,C S66280 saturated vapor
115 \

950 base point
95 /
saturated liquid 0 38 MPa
(metastable)

65 1 i l l1 l L I I I
0.5 1.0 1.5 2.0 2.5 6.0 6.5 7.0 7.5 8.0
S, kJ/kg-K
Figure 3. Temperature-entropy diagram.

saturated vapor

5.1 MPa
5.0-
4.688 MPa

P,MPa 4.0 -
saturated liquid 260C (metastable liquid) 260C (stable vapor)

3.0
2.5MPa

2.0
1.1 1.4 20 100
V, m3/kg x 103

Figure 4. Pressure-volume diagram, high-pressure range
(volume scales differ.)
Chemical Engineering Education

turning to Figure 2 and to the original metastable
base point, we search for a two-phase state with a
temperature and fraction vapor such that
xUvapr (t) + (1- X)Uiquid (t) = Umetstble =2466.5 (8)
and
xVvapor (t) + (1- X)Viquid (t) = Vmetastble = 0.4168 (9)
Trial-and-error solution of these equations (using
linear interpolation for saturation properties between
tabulated points) yields

t= 145.84 C

x = 0.9541 (P = 0.4251MPa)

with saturation values at this temperature*

U
103V
S

liquid
613.78
1.0859
1.7992

vapor
2555.7
436.8
6.8756

Thus, the entropy of the stable, two-phase state is

Stable = xSvaor +(1- X)Sliquid = 6.6426
This exceeds the entropy of the metastable state
(6.6280), and we conclude

Stable > Smetatable
For the energy comparison we must match the
volume and entropy of the base state. We replace Eq.
(8) with the analogous expression for entropy

xSvapor (t) + (1- X)Sliquid (t) = Smetastable = 6.6280 (10)
and solve as before through linear interpolation
t = 145.71C x = 0.9510 (P = 0.4236 MPa)
with saturation properties
liquid vapor
S 1.7979 6.8768
103V 1.0858 438.3
U 613.24 2555.5
From these data we determine Ustable = 2460.3 and

stable < Umetastable
The two-phase states for these latter comparisons
are indistinguishable at the scale of Figure 2, and
we represent both on the single horizontal line t'.

CLOSING REMARKS
The significance of these comparisons must be
explained carefully. They must not be characterized
as any form of proof of the validity of stability theory.
Indeed, they are not that at all. The principles of
stability theory are no more capable of proof than
are the Laws of Thermodynamics themselves. Given
our acceptance of the Laws (or of the Postulates that
* Reference 11, page 4.
Summer 1992

underlie the Laws in the neo-Gibbsian tradition[13]),
stability criteria follow logically. Thus, material be-
havior in violation of any criterion of thermodynamic
stability is in de facto violation of the Second Law.
These examples do, however, offer a tangible link
between real systems and abstract models. They
reveal the thermodynamic consistency of an empiri-
cally fashioned fundamental equation (the basis for
the KKHM Steam Tables), and they give support to
the too often rote-learned precepts of entropy maxi-
mization and Gibbs energy minimization.
We offer these exercises as a way to give students
a semiquantitative feeling for concepts usually rel-
egated to pure abstraction. They may be understood
even better when accompanied by descriptions of
"familiar" metastable-stable transitions-crystalli-
zation from a supersaturated solution or the explo-
sive (and potentially dangerous) vaporization of a
superheated liquid. Reid's series on the latter sub-
ject114] provides excellent background reading.

ACKNOWLEDGMENTS
Tabular data were reprinted by permission of
John Wiley and Sons. Financial support came from
Iowa State University and from the Camille and
Henry Dreyfus Foundation. Marcia Pierson edited
this paper and managed its production through the
Office of Editorial Services in the College of Engi-
neering. David Sauke used Aldus Freehand to pre-
pare the figures.

LITERATURE CITED
1. Sandler, S.I., Chemical and Engineering Thermodynamics, 2nd ed.,
Chap. 5, John Wiley and Sons, Inc., New York, NY (1989)
2. Kyle, B.G., Chemical and Process Thermodynamics, Chap. 7, Prentice-
Hall, Inc., Englewood Cliffs, NJ (1984)
3. Bejan, A., Advanced Engineering Thermodynamics, Chap. 6, John
Wiley and Sons, New York, NY (1988)
4. Glansdorff, P., and I. Prigogine, Thermodynamic Theory of Struc-
ture, Stability and Fluctuations, Chap. IV, Wiley-Interscience, Lon-
don, England (1971)
5. Callen, H.B., Thermodynamics and an Introduction to Thermosta-
tistics, 2nd ed., Chap. 8, John Wiley and Sons, New York, NY (1985)
6. Modell, M., and R.C. Reid, Thermodynamics and Its Applications,
2nd ed., Chaps. 6, 9, Prentice-Hall, Englewood Cliffs, NJ (1983)
7. Patrick-Yeboah, J.R., and R.C. Reid, Ind. and Eng. Chem., Funds.,
20,4,315(1981)
8. Jolls, K.R., and J.M. Prausnitz, "Laboratory Demonstrations for
Teaching Chemical Thermodynamics," paper presented at the An-
nual Meeting of AIChE, Washington, DC, November (1983)
9. Hayward, A.T.J., "Negative Pressure in Liquids: Can It Be Har-
nessed to Serve Man?" Amer. Sci., 59, 434 (1971)
10. Scholander, P.F., "Tensile Water," Amer. Sci., 60, 584 (1972)
11. Keenan, J.H., F.G. Keyes, P.G. Hill, and J.G. Moore, Steam Tables
(International System of Units-S.I.), John Wiley and Sons, New
York, NY (1978)
12. Balzhiser, R.E., and M.R. Samuels, Engineering Thermodynamics,
Appendix G, Prentice-Hall, Inc., Englewood Cliffs, NJ (1977)
13. Tisza, L., Generalized Thermodynamics, The M.I.T. Press, Cam-
bridge, MA (1966)
14. Reid, R.C., "Superheated Liquids: A Laboratory Curiosity and, Pos-
sibly, an Industrial Curse," Parts 1 and 2, Chem. Eng. Ed., 1, 60,
108 (1978) 0

O class and home problems

The object of this column is to enhance our readers' collection of interesting and novel problems in
chemical engineering. Problems of the type that can be used to motivate the student by presenting a
particular principle in class, or in a new light, or that can be assigned as a novel home problem, are
requested, as well as those that are more traditional in nature and which elucidate difficult concepts. Please
submit them to Professors James O. Wilkes and Mark A. Burns, Chemical Engineering Department, Univer-
sity of Michigan, Ann Arbor, MI 48109-2136.

THREE PROBLEMS

IN FLUID MECHANICS

JAMES O. WILKES, STACY G. BIKE
University of Michigan
Ann Arbor, MI 48109-2136

We present here (and solve) two homework
problems that we have developed in the
undergraduate chemical engineering fluid
mechanics course at the University of Michigan. The
first problem involves a fundamental principle of
hydrostatics and requires thoughtful but simple rea-
soning for its solution, while the second problem is a
good illustration of the application of potential-flow
principles. A third problem is also presented, but is
left for the reader to solve. The course is our second
required undergraduate course, taken in the second
term of the sophomore year, after thermodynamics
(mass and energy balances). After trying a few text-
books, we (and our students) have opted instead for
an extensive set of course notes that we have written
and typeset. We always attempt to set problems that
apply the principles of fluid mechanics to practical
situations, albeit simplified in some cases.

The authors are both faculty members in the Department of Chemical
Engineering at the University of Michigan. James 0. Wilkes, who is also
Assistant Dean of the College of Engineering, has current research inter-
ests in the flow of paint films and injection-molding of polymer composites.
Stacey G. Bike received her PhD from Camegie Mellon University in
1988, and conducts
research in the area
of colloid science,
including the fluid
mechanics of colloid-
al dispersions and
the theological char-
1 acterization of coat-
ings.

Copyright ChE Division of ASEE 1992

1 2 3

H h
t h
M -- 1 ---

Figure 1. Ship moving through locks.

PROBLEM 1
Water Supply for a Ship Moving Through Locks
A ship of mass M travels uphill through a series of
identical rectangular locks, each of equal superficial
(birds-eye view) area, A, and elevation increase, h.
The steps involved in moving from one lock to the
next (1 to 2, for example) are shown as A-B-C in
Figure 1. The lock at the top of the hill is supplied by
a naturally occurring source of water of density p.
Initially (A), the ship is isolated in lock 1, which has
a depth of water H. The gate between locks 1 and 2
is then opened (B), equalizing the depths of water in
the two locks. Finally (C), the ship moves into lock 2
and the gate is closed behind it.
1. Derive an expression for the increase in mass of
water in lock 1 for the sequence shown, in terms

Chemical Engineering Education

H t H+h

(a) Uphill (b)

fD n D-h
t^T D -__h_

(c) Downhill

Figure 2. Ship moving from one lock to the next.

of some or all of the variables M, H, h, A, p, and g.
2. If, after reaching the top of the hill, the ship
descends through a similar series of locks to its
original elevation, again derive an expression for
the mass of water gained by a lock from the lock
immediately above it. In this case, the initial depth
in the uppermost lock will be D (greater than H).
3. Does the mass of water to be supplied depend on
the mass of the ship if: (a) the ship travels only
uphill, (b) the ship travels uphill, then downhill?
Explain your answer.

SOLUTION
1. First, examine the ship as it travels uphill. As it
passes from one lock to the next (say, from lock 1
to lock 2), the new depth of water in lock 2 must
be H-exactly the same as it was in lock 1. The
depth of the water remaining in lock 1 is therefore
H + h. Figure 2 shows two appearances of lock 1:
(a) first, when the ship is still in it, and (b) after
the ship has moved into lock 2. Now examine the
corresponding masses of water in lock 1 under
these two conditions:
(a) From Archimedes' law, the weight of the wa-
ter displaced by the floating ship is the weight
of the ship itself, namely Mg. Therefore, when
the ship is still in the lock, the mass of water
displaced by the ship is M, so the mass of
water in the lock is pAH M.
(b) After the ship has moved out of lock 1, the
lock subsequently contains a mass of water
pA(H + h).
Hence, the mass of water to be supplied is the
difference between these two quantities:
pA(H + h)-(pAH-M)= pAh+M (1)

2. When the ship is proceeding downhill, as shown
in Figures 2(c) and (d), the amount of water lost

from the higher lock is likewise
(pAD- M)-pA(D h)= pAh- M (2)
3. In conclusion, we observe from the above that
0 The amount of water to be supplied is pAh
M, depending on whether the ship is proceed-
ing uphill or downhill, respectively.
> Thus, the amount of water does depend on the
mass of the ship, and is different for motion
uphill or downhill.
0 If the ship navigates both uphill and down-
hill-as in traversing the Panama Canal, for
example-the total water supply needed is
2pAh, which is independent of the ship's mass.
Thus, whether the Queen Mary or a rowboat is
involved, the total water supply required is
the same.

PROBLEM 2
Ground-Water Seepage
Figure 3 shows the seepage of water through the
ground under a dam, caused by the excess pressure
P (beyond that naturally occurring in the absence of
the impounded water) that arises from the buildup
of water behind the dam, which has (underground) a
semi-circular base of radius rD.

1. Verify the following relation, which has been pro-
posed for the (excess) pressure in the ground:

p=P(1-a) (3)
2. Determine the streamlines for the flow.
3. Between points A and B, a large amount of cop-
per-impregnated soil has been detected, with the
possibility that some of this toxic metal may leach
out and have adverse effects downstream of the
dam. To help assess the extent of this danger,

6=ir

Figure 3. Seepage of water under a dam.

Summer 1992

derive an expression for the volumetric flow rate,
Q, of water between A and B (per unit depth in
the z-direction, normal to the plane of the dia-
gram), in terms of P, K (the permeability of the
ground), i (the viscosity of water), rA, and rB.

SOLUTION
1. Start by observing that the flow of water in the
ground is governed by D'Arcy's law

v -KVp (4)

in which v is the (vector) superficial velocity and
p is the pressure. By applying the continuity equa-
tion
Sv = 0 (5)
and assuming constant permeability K and vis-
cosity T1, we find that the pressure obeys Laplace's
equation
V2p = 0 (6)
We are now reminded that the problem is essen-
tially one of potential flow; indeed, the flow is
irrotational, because the vorticity of a velocity
that is proportional to the gradient of a scalar is
zero, as may be checked by expanding
V x v = V x Vp and discovering that it is a vector
with three zero components.
Now examine the proposed pressure distribution
by checking to see if it satisfies the following
constraints:
(a) The conditions on pressure at the ground level.
For 0 = 0 and i, Eq. (3) gives p = P and p = 0,
respectively, confirming the known pressures
both upstream and downstream of the dam.
(b) Laplace's equation, V2p = 0, in cylindrical
(r/0/z) coordinates, in which all z derivatives
are zero, is

1 (P- 1 2 po
V2p =p a 2 = 0 (7)
r 2r rW
The first term on the right-hand side of Eq.
(7) is zero, because the proposed expression
for p is independent of r. The second term is
also zero, because p is only a linear function
of 0. Thus, Laplace's equation is satisfied.
(c) Zero radial flow at the base of the dam. It will
soon be seen that the radial velocity vr is
proportional to ap/ar, which is zero.
Thus, all constraints are satisfied by the pro-
posed solution, which indicates that the pressure

decreases linearly with the angle 0 between the
ground-level upstream and downstream values of
P and zero, respectively.
2. The r and 0 components of Vp in cylindrical (r/0/z)
coordinates are
_Dp 1 ap
(Vp), = and (Vp)e = (8)

from which it follows (in conjunction with D'Arcy's
law) that the radial and angular velocity compo-
nents are

V K p
v T =0
T ) j r

and ve = KP
Te I r T rr

The corresponding expressions in terms of the
stream function w are known to be

1 ra
Vr r as

and v= a-
0 ar

which, because of the minus sign in D'Arcy's law,
are the negatives of those usually encountered.
Substitution of the known values for vr and v,
from Eq. (9) into Eq. (10), and integrating, gives

S= f(r) and = KPnr + g(0) (11)
nil
in which f(r) and g(0) are functions of integration.
The two expressions for the stream function in
Eq. (11) must be compatible, so that f(r) = (KP/hri)
In r and g(0) is-at most-a constant, which may
be taken as zero, giving

S= KP Inr (12)

Since the streamlines are contours of constant y,
they must also be curves of constant r-that is,
semi-circles, as shown in Figure 3. The isobars (or
equipotentials) are, from Eq. (3), lines of constant
0 and are orthogonal to the streamlines. If both
streamlines and isobars were drawn, they would
appear as the circular arcs and radial lines of a
spider's web.
3. The flowrate between A and B (per unit depth,
normal to the plane of the diagram) can be ob-
tained in two ways. First, by definition of the
stream function, it is simply the difference be-
tween 4A and ~B

Q = B A = nr n rA) = KP nrB (13)
M = 1A rA

Second, the same result can be obtained by inte-
grating the velocity between the two points:

B B
Q = dr = KPdr = nB (14)
A AJ nilr -M rA
A A
Chemical Engineering Education

PROBLEM 3
Bubble Rise
We leave the reader with an intriguing problem
that originated with our colleague, Professor (now
Emeritus) M. Rasin Tek. As shown
in Figure 4, a hollow vertical cylin-
der with rigid walls and of height H
B 0 is closed at both ends and is filled
with a volume, V, of an incompress-
ible and non-volatile oil of density p
H at a uniform temperature T. A
gauge registers the pressure at the
top of the cylinder.
A When a small spherical bubble
Figure 4. of volume v initially adheres by sur-
Bubble rising in face tension to point A at the bot-
liquid in a tom of the cylinder, the absolute
closed cylinder, pressure at the top of the cylinder
is po. The gas in the bubble is ideal,
and has a molecular weight of M. The bubble is
liberated by tapping on the cylinder and rises to
point B at the top. Derive an expression in terms of
any or all of the specified variables for the new
absolute pressure pi at the top of the cylinder. Ex-
plain your answer carefully!
We leave the reader in suspense, requesting that
he or she solve this problem. It is instructive for a
fluid mechanics class because it shows that if you
proceed methodically, the answer is deceptively
simple. And, if you find it too easy, try it for the case
when the oil is slightly compressible, with an iso-
thermal compressibility p. 0

book review

CHEMICAL AND PROCESS
THERMODYNAMICS
2nd Edition
by B.G. Kyle
Prentice Hall, Inc., Englewood Cliffs, NJ 07632

Reviewed by
E. Dendy Sloan
Colorado School of Mines

In this useful second edition, the author has avoided
an encyclopedic "drink-of-water-from-a-fire-hydrant"
approach to thermodynamics in favor of pedagogical

digestion. The examples and problems with each chap-
ter are well conceived, and a complete solutions
manual is available. The text nomenclature and topic-
ordering will seem familiar to professors teaching the
topic.
Modern aspects of the book involve applications of
classically stated fundamentals to environmental con-
trol, electrolytes, biochemicals, and electronic materi-
als. Material on Jacobians, stability, and complex
chemical equilibria go beyond topics found in many
undergraduate texts.
A major asset of the book is its treatment of fluid
properties. The author has eschewed the use of three-
parameter corresponding states, providing graphic
visualization of changes in compressibility and re-
sidual properties as a function of reduced tempera-
ture and pressure. An IBM-compatible floppy disk
program (ca. 4000 lines) in the endpapers enables
more accurate calculation of pure fluid properties
(other than vapor pressure) through the Peng-
Robinson equation of state (EOS).
A second major asset is the treatment of phase
equilibria. After a brief treatment of principles, the
author goes straight to applications, with advanced
topics relegated to a later chapter. For example, in
the first chapter on phase equilibria principles the
author gives examples of activity coefficient hand cal-
culations to optimize van Laar and Margules param-
eters, but a floppy disk program (ca. 5000 lines) is
provided to either optimize or use Wilson equation
parameters. Regular solution and UNIFAC treatments
are delayed until the third chapter on phase equilib-
ra.
The floppy disk programs represent one approach
to introduce students to the foundations of ubiquitous
flowsheeting programs in the profession. As such, a
reader might wish for the unifying device of a Peng-
Robinson EOS program applied to mixtures so that,
for example, students could observe relative inaccu-
racies of an EOS versus activity coefficients for mix-
tures of alcohol+water or those of hydrocarbons.
Summing up, this book is a welcome addition for
students learning undergraduate thermodynamics. If
the author included an extension to molecular exposi-
tion and a final chapter on statistical thermodynam-
ics, the book might also be a foundation to address the
dearth of introductory graduate texts. O

Summer 1992

Random Thoughts...

WHAT DO THEY KNOW,

ANYWAY?

RICHARD M. FIELDER
North Carolina State University
Raleigh, NC 27695-7905

S ooner or later, the conversation at the commit-
tee meeting or in the faculty lounge turns to
student ratings of instructors. It's a sure bet
that within six seconds, someone will announce that
ratings are meaningless-students don't know
enough to evaluate the quality of their instruction.
Others agree: one grumbles that the high ratings
always go to the easy graders and entertainers; an-
other adds with complete assurance that the rigor-
ous instructors who are really the best teachers may
get low ratings now but in later years their students
will come to appreciate them.
What is interesting is that these assertions are
invariably offered without a scrap of evidence by
individuals with well-deserved reputations for ana-
lytical thinking. If someone offered such unsupported
arguments in a research seminar, most of us would
dismiss both the arguments and the arguer out of
hand. In discussions of teaching, however, we
routinely suspend the rules of logical inference
without a second thought.
It's not as if data on student ratings are lacking.
Cashin[11 notes the existence of 1300 articles and
books dealing with research on the subject;
Feldman[21 sees Cashin and raises him to 2000! So,
for the record and in case you happen to find your-

Richard M. Felder is Hoechst Celanese Profes-
sor of Chemical Engineering at North Carolina
State University. He received his BChE from
City College of CUNY and his PhD from
Princeton. He has presented courses on chemi-
cal engineering principles, reactor design, pro-
cess optimization, and effective teaching to vari-
ous American and foreign industries and institu-
tions. He is coauthor of the text Elementary
Principles of Chemical Processes (Wiley, 1986). i

Copyright ChE Division ofASEE 1992

self on a committee where student ratings come up,
here are some facts to throw into the conversation.

MYTH: Students lack the wisdom and experience to
evaluate the effectiveness of their current in-
structors. Those who give instructors low rat-
ings at the end of a course will in future years
appreciate those instructors.
FACT: High correlations exist between course-end
ratings and ratings by those who presum-
ably have the required wisdom and experi-
ence-peers,[31 administrators,[4] alumni,[5-71
and graduating seniors.s8'91 If professors in
your department who know how you teach
rated your effectiveness, the results would
probably not differ all that much from your
student ratings. If students rate you highly
now, they'll probably still do so when they
look back in future years; if they dislike you
now, the chances are that in their later wis-
dom they won't decide you were really a gem.

MYTH: Student evaluations are just popularity
contests. Easy teachers/easy graders get the
highest ratings.
FACT: Teachers who assign more work and more
difficult work tend to be rated as most effec-
tive.[3,9,101 Some studies show no effect of grad-
ing practices on overall student ratings,[11,12]
others find tendencies for teachers giving
higher grades to get higher ratings. The lat-
ter result does not invalidate the ratings,
however: as McKeachie[111 observes, if stu-
dents learn more from a teacher, one would
expect both their grades and their ratings to
be higher.

Chemical Engineering Education

... research shows that student evaluations of an instructor provide a reliable, valid assessment of that
instructor's teaching effectiveness, especially if they reflect the views of many students in several
different course offerings .... next time someone says that there's no good way to evaluate
teaching, quietly mention that one or two thousand research studies suggest otherwise.

MYTH: Even if student evaluations have some valid-
ity, there's no value in the multiple-choice
forms used to collect most of them. You've got
to interview students and ask open-ended
questions for the results to mean anything.
FACT: Comparisons have been run on student rat-
ings collected in three different ways: objec-
tive questionnaire items, written responses
to open-ended questions, and group inter-
views. The average correlation among the
rating methods was 0.86.[131

MYTH: Teachers who get high ratings aren't really
doing a better job of teaching.
FACT: Teachers rated as effective by students tend
to be those whose students perform best on
achievement tests.[31 Classes in which stu-
dents give instructors higher ratings when
multiple sections are taught tend to be those
in which the students score higher on com-
mon external exams.[P] Good teaching also
motivates interest and desire to learn; stu-
dents in courses taught by highly-rated teach-
ers are subsequently more likely to elect ad-
vanced courses in the same subjects[14] and
to major in those subjects.1151

MYTH: Student evaluations don't improve teaching.
FACT: Students of instructors who got student feed-
back scored higher on achievement tests and
assessments of motivation for learning than
students of instructors who got no feed-
back.[161

In short, the research shows that student evalua-
tions of an instructor provide a reliable, valid assess-
ment of that instructor's teaching effectiveness, es-
pecially if they reflect the views of many students in
several different course offerings. So, next time some-
one says that there's no good way to evaluate teach-
ing, quietly mention that one or two thousand re-
search studies on the topic suggest otherwise. You
may not change anyone's mind on the spot, but it
might raise the discussion to a higher level than it
usually occupies.

It remains to consider how evaluations can be
structured to have the maximum impact on teaching
effectiveness. That's another column.

REFERENCES
1. Cashin. W.E., "Student Ratings of Teaching: A Summary of
the Research," Center for Faculty Evaluation and Develop-
ment, Kansas State University, September (1988)
2. Feldman, K., quoted in The Teaching Professor, p. 5, De-
cember (1990)
3. Marsh, H.W., Students' Evaluations of University Teaching:
Research Findings, Methodological Issues, and Directions
for Future Research, Pergamon Press, Elmsford, NY (1987)
4. Kulik, J.A., and W.J. McKeachie, "The Evaluation of Teach-
ers in Higher Education," in Review of Research in Educa-
tion, Vol. 3, F.N. Kerlinger, ed., Itasca, IL, F.E. Peacock, p.
210 (1975)
5. Centra, J.A., "The Relationship Between Student and Alumni
Ratings of Teachers," Educational and Psychological Mea-
surement, 34(2), 321 (1974)
6. Drucker, A.J., and H.H. Remmers, "Do Alumni and Stu-
dents Differ in Their Attitudes Toward Instructors?" J. Ed.
Psych., 42, 129 (1980)
7. Overall, J.U., and H.W. Marsh, "Students' Evaluations of
Instruction: A Longitudinal Study of Their Stability," J. Ed.
Psych., 72, 321 (1980)
8. Aleamoni, L.M., "Student Ratings of Instruction," in Hand-
book of Teacher Evaluation, J. Millman, Ed., Sage, Beverly
Hills, CA, p. 110 (1981)
9. Marsh, H.W., "Students' Evaluations of University Teach-
ing: Dimensionality, Reliability, Potential Biases, and Util-
ity," J. Ed. Psych., 76, 707 (1984)
10. "Applicability Paradigm: Students' Evaluations of Teaching
Effectiveness in Different Countries," J. Ed. Psych., 78(1),
465 (1986)
11. McKeachie, W.J., Teaching Tips, D.C. Heath, Lexington,
MA (1986)
12. Palmer, J., G. Carliner, and T. Romer, "Leniency, Learning
and Evaluation," J. Ed. Psych., 70(5), 855 (1978)
13. Ory, J.C., L.A. Braskamp, and D.M. Pieper, "Congruency of
Student Evaluative Information Collected by Three Meth-
ods," J. Ed. Psych., 72, 181 (1980)
14. Marsh, H.W., and D. Solomon, "Student Ratings of Instruc-
tors: A Validity Study," J. Ed. Research, 51, 379 (1958)
15. Sullivan, A.M., and G.R. Skanes, "Validity of Student Evalu-
ation of Teaching and the Characteristics of Successful In-
structors," J. Ed. Psych., 66, 584 (1974)
16. Overall, J.U., and H.W. Marsh, "Midterm Feedback from
Students: Its Relationship to Instructional Improvement
and Students' Cognitive and Affective Outcomes," J. Ed.
Psych., 71,856 (1979) 0

Summer 1992

Curriculum

A COURSE SEQUENCE FOR

INSTRUMENTATION AND CONTROL

CARLOS A. SMITH, RICHARD A. GILBERT
University of South Florida
Tampa, FL 33620

At the University of South Florida we believe
that a controls and instrumentation back-
ground is vital for new chemical engineers.
Our curriculum specifies a required three-semester
course sequence in the area, with an additional
elective course also available. The three required
courses are
Mechanical Engineering Laboratory I (MELab), 3 credits
Instrument Systems I (ISys), 4 credits
Automatic Process Control I (APC-I), 3 credits
and the elective course is
Automatic Process Control II (APC-II),3 credits
The first course is taught by the mechanical engi-
neering department, and all the other courses are
taught by the chemical engineering department. The
first two courses are required for all mechanical
engineering and chemical engineering students.
This paper will describe the subject matter and
the goals the authors have set for each course. The
principal goals for the complete sequence are to pro-
vide the students with the technical background
to immediately begin productive careers in any
industrial controls group
to understand the fundamental principles involved in
data acquisition for experimentation and process
control
Carlos A. Smith is professor of chemical engi-
neering at the University of South Florida, where
he has been since 1972. He received his BSChE
from the University of Florida and his MSChE
and PhD from LSU. He is involved in continuing
education courses and consultancy and is coau-
thor of the text Principles and Practice of Auto-
matic Process Control (Wiley, 1985).

Richard Gilbert is an associate professor with
interests in instrumentation for experiment analy-
sis and process control. Current funded research
includes the investigation of optical sensors and
techniques for growth control in MBE, the appli-
cation of programmable controller-based control
systems in Florida's produce packing industry,
and the use of electrofusion and electroporation
techniques in cancer research and treatment.

to be able to keep up with future developments in this
very dynamic field
Because of the nature of the goals, all of the courses
are practice-oriented and heavily dependent upon
laboratory and project work.
Mechanical Engineering Laboratory I (MELab)
This one-semester course consists of one two-hour
lecture and one three-hour laboratory period per
week. The goals of the course are to introduce the
student to various physical variable measurement
devices and techniques and to develop proper report-
writing skills (Table 1 lists the contents of the course).
Initial lecture times are devoted to laboratory safety
issues, required elements in laboratory reports and
presentations, and the properties of measurement
and experimental procedure errors.
In the remaining weeks of lecture, students are
introduced to measurements of fundamental inter-
est to the process industry (i.e., temperature, pres-
sure, and flow) as well as measurements that relate
to the monitoring and control of mechanical systems
(i.e., strain, torque, and displacement). Laboratory
work during this phase of the course involves setting
up and taking measurements with sensors similar
to the ones discussed in class. The students provide
written reports for each of the ten experiments and
must include a summary of any required engineer-
ing calculations. They must also contain descrip-
tions of the experimental arrangement and any spe-
cial analog signal conditioning required to complete
the measurement, i.e., any temperature compensa-
tion technique used for a thermocouple measure-
ment, the type of measurement bridge used with the
strain gauge, and the flow element analog output
signal manipulation employed to obtain measure-
ment signals proportional to engineering flow units.
Instrument Systems I (ISys)
This one-semester course consists of three one-
hour lectures and one three-hour laboratory period
per week. Since MELab is a co-requisite and/or a
pre-requisite for this course, knowledge of various
types of sensors and their analog output signal char-
Copyright ChE Division ofASEE 1992
Chemical Engineering Education

acteristics is expected of the students. The course
introduces the various ways digital technology in-
corporates a sensor into an instrument system used
for process monitoring and control. Table 2 summa-
rizes the topics presented in the course.
Although the digital skills learned in ISys are
applicable in any research-oriented application, it is
convenient to present the course by using process
control examples. At this stage in their education,
the students are quick to appreciate how the sensor
and its digital interface can be used in an industrial
control situation. They also understand the useful-
ness of a computer or digital controller as the center
element of a control loop. By contrast, it is difficult
to find examples in their chosen fields of study that
are within the experience level of both the chemical
and mechanical engineering students in the course.
Finally, they are able to relate the digital technology
to monitor and control projects of immediate inter-

TABLE 1
Course Content:
Mechanical Engineering Laboratory I
TOPICS:
1. Laboratory safety 5. Force and torque
2. Technical reports measurement
3. Experimental errors 6. Flow measurement
4. Length, displacement, 7. Temperature measurement
and strain measurement 8. Pressure measurement
9. Humidity measurement

TABLE 2
Course Content: Instrument Systems I
WEEK CONTENT
1 Components of a control loop Properties of analog and
digital signals
2 Properties of logic operators Use of logic operations for
discrete element process control (start, stop, alarm, etc.)
3 Binary-, octal-, and hexadecimal-based counters Codes
and decoders Application of totalizer in process con-
trol
4 Analog-to-digital conversion Digital-to-analog conver-
sion
5 Signal conditioning Common industrial process sig-
nals
6 Multiplex concepts Latches and flip flops Memory
devices
7 Structure of an 8080 single-board microcomputer
8 8080 and Z-80 Assembly code as it relates to I/O opera-
tions
9 I/O ports and their bus connections to the CPU; Sensor to
A/D to I/O port interfacing
10 Intel 8250 series devices and their operational literature
11 DAS 8 data-acquisition board for IBM-type PCs
12 Sensor interface boards for IBM-type PCs (i.e., RTDs,
thermocouples, strain gauges, etc.)
13 Interrupt I/O strategies Memory map I/O
14 Parallel interfaces IEEE 488 interface boards

Summer 1992

est to themselves, i.e., digital display of wind speed
on a sailboard, a variety of home comfort and secu-
rity interlocks, etc.
Three aspects of control and data acquisition sys-
tem interfacing
discrete component technology
software drivers
dedicated computer interface boards
are covered. Lecture and laboratory time are divided
equally among them. Component technology is dis-
cussed first while the selection/operation of interface
boards is covered in the last four weeks.
The discrete component technology section of the
course covers TTL devices and their use as inter-
faces between a process sensor, a controller, and the
final control element. Presenting the discrete digital
technology concepts first has the effect of delaying
discussions about analog-to-digital conversion and
other aspects of interfacing an analog sensor output
to a digital system until those students taking MELab
as a co-requisite with ISys have been exposed to a
few examples of analog sensors. In this first part of
the course, students explore simple control schemes
that can be handled by an arrangement of discrete
components. Examples include elementary on/off in-
terlock logic, event counting, and time-delay situa-
tions. The function of open collector and three-state
devices as interfaces to traditional industrial control
voltages and computer circuits is also examined.
At this point in the course, our intent is to make
students feel comfortable working with control TTL
circuits. Example A (next page) summarizes a project
given in APC-I-the same assignment is also given
as an ISys lab. The problem is scaled down to facili-
tate the time base when discrete counters are used,
but the logic portion of the assignment is the same.
The full effect of the learning experience is not ap-
preciated until the controls course is taken, but the
lesson is not lost with time. Once the students solve
the problem by both methods, they can appreciate
the value and place for each.
Another reason for presenting discrete component
information is to show students the interrelation-
ship between operation of the components and the
function of a complete interface subsystem. This pre-
sentation is not an abstract academic exercise-it is
an opportunity for the student to develop skills that
can be employed in real instrumentation trouble-
shooting scenarios.
In a research environment these trouble-shooting
skills might be used to determine and maintain a
specific arrangement of triggering and then multi-
plexing the signals from several analog experimen-
137

tal measurements into a single A/D-based data log-
ger. In an industrial setting, trouble-shooting situa-
tions inevitably involve problem diagnosis of a sen-
sor, a controller, and a final control element in a loop
with no initial certainty of which loop element is at
fault. Understanding a loop's digital components fa-
cilitates the distinction between the analog and digi-
tal aspects of the control scheme. This helps the
engineer isolate the portion of the loop that is not
performing properly. Because control loops are so
intimately related to the process under control, the
person responsible for that part of the process usu-
ally directs the trouble-shooting "mission." More of-
ten than not, that person is a chemical engineer.
The course's software driver section focuses on
data transfer to and from a digital system. For this
purpose a software driver is defined as the subrou-
tine responsible for the data transfer operation. Stu-
dents learn to write code that directs interactions
between a CPU and its I/O ports. The intent is to
make them aware of the I/O port structure, how
those ports transfer sensor information to the CPU,
and the immediate operations required of a CPU to
accomplish that task. Once these operations are un-
derstood, an engineer can alter the computer inter-
face of an existing control system to meet the new or
modified needs of the project.
Laboratory experiences for the software driver
portion of the course include exercises in writing
code to operate digital I/O ports as well as A/D and
D/A converters. Students learn to write 8080 and
then Z-80 code. They may cross-assemble their pro-
grams on available IBM-type computers. Completed
programs are run on single-board computers that
the student has connected to the ports of interest.
Single-board computers are used in the labora-
tory because they are simple to operate, they sup-
port a variety of INTEL "smart chips," and they are

easy for the department to maintain. Because of the
simplicity of these computers, students are forced to
learn what the role of the I/O driver is and what
must be done to complete the interface. They also
develop valuable software debugging techniques that
can be used with any higher-level language.
The last section of the course covers the function
and operation of dedicated computer peripheral in-
terface boards. By this time students are expected to
understand the technical information provided by
the manufacturer of such boards. Lecture and labo-
ratory material cover A/D boards, thermocouple and
RTD interface boards, and how to use them.
Although some of the interface boards used in the
lab come with manufacturer-supplied menu-driven
software packages, the students are directed to de-
velop small routines that control the board. This
approach shows them that they understand what
the technical manual is trying to say, that they can
write code that actually takes a measurement, and
how to get maximum flexibility out of the board.
Students develop their programs in Quick BASIC
and use the program debugging skills they devel-
oped during the second phase of the course.
One laboratory assignment at this point in the
course is based on an RS-232 serial port card and a
serial printer. Requesting that the student create a
program that alters the font of the printer is identi-
cal in practice to setting up a RS-232 supporting
multimeter to take and store various research ex-
periment related voltage, current, and resistance
measurements. The same computer interfacing skills
are required to set up a PID temperature controller
so that all of its control parameters (i.e., set point,
gain, reset time, etc.) are under computer control.
The RS-232 card has to be set up to handle the
selected protocol. The correct command string has to
be sent to the instrument's control register, and

EXAMPLE A
Consider a tank where a dilution process takes place. The tank and accessories are
shown in the figure. A concentrated solution enters the tank where water is sprayed at a
significant rate to promote mixing. There are four water valves feeding the tank. Because
of process constraints not all valves can be open at the same time; maximum of two are
permitted at the same time. It has been proposed to open the valves in the following
sequence:

Concentrated
Solution
from PLC Irom PLC

V V2 V

Valves Time Duration, sec.
1 2 3 4
ON OFF ON OFF 5 -- to PLC
OFF ON ON OFF 10
ON OFF OFF ON 10
OFF ON OFF ON 5
Start/stop PBs are available to start/stop the sequence. In addition, a dilution sensor (conductivity sensor/transmitter) is
available to measure the amount of dilution. If the solution becomes too diluted (conductivity switch goes high) the valves must close
until the sensor indicates (conductivity switch goes low) to resume the valves sequence.
Desirn the logic for this process. develop the logic diagram, and program the PLC to accomplish this control strategy.

.38 Chemical Engineering Education

proper delimiters must be used to frame the mes-
sages. Finally, status information about the instru-
ment and the process must be imported through the
RS-232 interface back to the computer.
Using a printer instead of another instrument in
this experiment has several advantages: printers
are cheap, and even low-priced ones give several
protocol and delimiter options; students enjoy learn-
ing how to write their own software to drive a printer;
and finally, students have no trouble transferring
what they have learned to the more sophisticated,
more expensive, and more difficult to repair RS-232
driven measurement instruments.
Collectively, the device, the driver, and the dedi-
cated board portions of this course provide a sound
background for all phases of digital interfacing. A
detailed note set, a study guide, and a collection of
over twenty-five different subject-related books on
library reserve provide additional independent learn-
ing resources for the students.
The practical nature of the course materials, to-
gether with the hands-on concept of reinforcing labo-
ratory exercises, make the course immediately re-
warding for most of the participants. Those who do
not enjoy it usually complain about the lack of spe-
cific guidance during the laboratory periods. How-
ever, it is a conscious decision on our part not to
provide step-by-step laboratory projects. Several lab
periods are provided so that each student can work
with the isolated concepts. During this time, the
problems students have in working with example
circuits, programs, or subsystems are explored. They
learn alternative routes to diagnose the problems,

TABLE 3
Lecture: Automatic Process Control I
TOPICS
1. Introduction
2. First-order and higher-order systems
a. Modeling
b. Transfer functions
c. Block diagrams
d. Response to different forcing functions
3. Valves and transmitters
4. Feedback controllers
a. Types
b. Process identification and tuning
5. Analysis of closed-loop control systems
a. Modeling
b. Block diagrams and transfer functions
c. Stability
Routh test
Direct substitution
d. Effect of loop parameters and types of controllers on
stability
6. Case studies

Summer 1992

but little time is spent on telling them exactly how to
fix their problem. This approach of suggesting more
things to try instead of offering corrective instruc-
tion is just not what some students want.
Automatic Process Control I (APC-I)
This is a one-semester course consisting of two
hours of lecture and three hours of laboratory per
week. It is directed at the process industries and
includes several examples of environmental and ma-
terial handling processes. The textbook is Principles
and Practice ofAutomatic Process Control. [1
Table 3 presents the lecture content. Note that
the subject of Laplace transforms is not discussed-
it is assumed that the student has "learned" this
subject in differential equations. To test this as-
sumption and to help the students review the mate-
rial, a test is given during the second week of class.
Questions about temperature, pressure, level, and
flow sensors are also asked during the test as an aid
in helping the students review their MELab course.
The lecture begins with a presentation on system
dynamics, block diagrams, and transfer functions.
This material is usually perceived as very theoreti-
cal, mathematical, and in general boring. Therefore,
a deliberate, complete discussion on why the mate-
rial is necessary and how it is useful is presented on
the first day of lecture. We stress mathematical mod-
eling, the physical significance of gain, time con-
stant, dead time, how the response of systems in
series provides dead time, and the importance and
significance ofnonlinearities. We also provide a physi-
cal explanation of what the mathematics indicate.
Once the foregoing material is learned, we present
a discussion on controllers: the action of controllers,
the mathematics, the physical significance, and the
different types of controllers are discussed in detail.
Process identification, by low-order models, and con-
troller tuning are discussed in the lecture and prac-
ticed in the laboratory. The identification method
discussed is the step, or bump, testing procedure.
Students are organized into groups of two in the
laboratory, and each group is asked to tune the
controllers for two different simulated processes.
Each simulated process is connected to real control-
lers. The laboratory equipment consists of a
Honeywell TDC 2000[2] distributed-control system,
two CLC-002 Bailey,E[3 and two Yokogawa[4] stand-
alone controllers.
The topic of stability starts with a presentation of
the development of the mathematical model, block
diagram, and the closed-loop transfer functions of a
closed-loop control system. We continue with a defi-
nition of the characteristic equation and its relation-
139

ship to stability. Using the Routh Test and direct
substitution to study stability is then presented.
Finally, we demonstrate the effect on the stability
of the loop if any of its parameters change, i.e., if a
transmitter with a different span is used, if a faster
or slower sensor is used, or if the dead time changes,
etc. We also discuss the effect of the reset and de-
rivative actions on the loop stability. It is important
to notice that only the simple techniques of the Routh
Test and direct substitution are used in this presen-
tation (Pade approximations are used for dead times).
The idea is to show in simple, but effective, language
the effect of the different terms on the stability of
the loop and that these techniques do the job.
In addition to the lecture material and the home-
work, we ask the students to complete about three
simulation projects during the course. The simula-
tion software package used is TUTSIM.151 (If a stu-
dent wants to work with another simulation pack-
age, or with straight FORTRAN or BASIC, he/she is
allowed to do so.) The TUTSIM simulation package
is a PC-based system and is considered to be one of
the easiest packages for this purpose. The TUTSIM
package is highlighted in the recently published sec-
ond edition of the textbook Process Systems Analysis
and Control.[6] The projects usually involve the de-
velopment of the model for a process system, the
simulation, and the tuning of the control system.
Toward the end of the semester two design projects
are assigned. They provide an opportunity for the
students to design control systems for complete pro-
cesses. The students usually like these projects.
The laboratory presents another interesting part
of the course-Table 4 shows the weekly schedule.
The first week is used to stress the importance of the
course. We use this period to motivate the student to
learn the subject. We then present the TUTSIM
software package in the second week. This presenta-
tion usually takes about an hour and a half, and
once it is done a project is assigned.
During the next seven weeks we introduce the
subject of discrete or sequential logic. Using this
logic has become an important tool for process con-
trol engineers. The complexity of new processes, the
increasing use of batch processes, the increasing
concern with safety, and the development of the new
tools to implement this logic- such as program-
mable logic controllers (PLCs)[71 and distributed con-
trol systems (DCSs)-have precipitated the impor-
tance of this logic. These new capabilities provide an
easy way to introduce logic statements in continuous
control schemes. Until now, the design and imple-
mentation of logic systems have been principally the
140

domain of electrical engineers, but now chemical
engineers must also become acquainted with them.
The projects are all actual industrial cases that have
been collected over the years. Example A shows a
typical weekly project.
The laboratory contains ten Allen-Bradley SLC-
100[8] PLCs. Each is connected to a set of start/stop
push-buttons and to switches that represent field
signals. Lights are connected to the outputs and act
as final control elements. These systems provide a
realistic environment where the students can test
their control logic design. The PLCs are available
during lab periods as well as during the hours that
the College of Engineering's PC labs are open.
In the first week PLC relay logic (AND, OR,
latches, etc.) and instructions on how to develop
logic and ladder diagrams are presented. This is
usually accomplished in about one and one-half hours,
and then a project for the following week is assigned.
In week two, timers are covered and a project is
assigned. Counters are presented in the third week,
along with another project assignment. Finally, in
the fourth week, students read about sequencers,
and a new project is assigned.
During the fifth week of discrete logic lab, the
final project (exam) is presented. During the past

TABLE 4
Automatic Process Control I Laboratory
WEEKS) CONTENT
1 Introduction to process control
2 Introduction to TUTSIM
3-9 Discrete and sequential logic
10 Valves
11-14 Tuning of feedback controllers
15 Wrap-up

TABLE 5
Automatic Process Control II: Lecture
TOPICS
1. Control loop stability
a. Root locus
b. Frequency response
c. Pulse testing
2. Cascade control
3. Ratio control
4. Feedforward control
5. Selective, override, and constraint control
6. Multivariable control
7. Digital control
a. Z-transforms, sampling, and stability
b. PID discrete controllers
c. Dead-time compensation
Smith-prediction
Dahlin's controller
d. Filtering

Chemical Engineering Education

EDITORIAL NOTE

The following detachable pages describe some indus-
trial employment opportunities for graduating chemical
engineers. Please post the information in a conspicuous
place for the benefit of your students, or distribute the
pages to students who may be interested.

These companies have expressed a definite interest in
hiring chemical engineers in the areas described, and
we strongly encourage students seeking employment to
respond as indicated.

Ray W. Fahien
Editor

Chemical Engineering Education

L __

DOW USA
University Relations
Box 1713-CH
Midland, MI 48674

GENERAL INFORMATION
Dow manufactures and markets chemicals, plastics, metals, consumer prod-
ucts, and specialty products and services. Dow USA has over 2600 chemical
engineers working in all functions and geographic locations.

CITIZENSHIP REQUIREMENTS: Only U.S. citizens, aliens who have a legal right to work and remain
permanently in the U.S. or aliens who qualify as "Intending Citizens" under the Immigration Reform and
Control Act of 1986 are eligible for employment.
REGIONS WHERE BS/MS CAMPUS RECRUITING IS CONDUCTED: Nationwide
HOW TO APPLY IF UNABLE TO SCHEDULE A CAMPUS INTERVIEW: Send resume and letter to the
above address, stating your job interests and geographic preferences

ENTRY LEVEL OPPORTUNITIES FOR CHEMICAL ENGINEERS

BS / MS-
Functional Area Degree Level Major Hiring Locations
Design BS,MS Michigan, Texas, Louisiana, Ohio, Cali
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Tech Center Locations
Michigan, Texas, California
Michigan, Texas, California, Ohio
Michigan, Texas, California, Louisiana
Michigan, Texas

An Equal Opportunity Employer
Advertisement published in Chemical Engineering Education, Volume 26, No 3 (1992)

PhD

MERCK & CO., INC.
P.O. Box 2000
Rahway, NJ 07065

GENERAL INFORMATION
Merck & Co. is a worldwide, research intensive health products company that
discovers, develops, produces, and markets human and animal health products
and specialty chemicals. The company has 37,700 employees with sales of over
$8.6 billion in 1991.

CITIZENSHIP REQUIREMENTS: U.S. citizen, lawful permanent resident of the U.S., or otherwise authorized to work
in the U.S.
REGIONS WHERE BS/MS CAMPUS RECRUITING IS CONDUCTED: We recruit on campuses nationwide (U.S.)
HOW TO APPLY IF UNABLE TO SCHEDULE A CAMPUS INTERVIEW: Please submit resume or application which
clearly states educational background, objectives, and work experience to:
Office of College Relations
Merck & Co., Inc.
P.O. Box 2000
Rahway, NJ 07065

ENTRY LEVEL OPPORTUNITIES FOR CHEMICAL ENGINEERS
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In each division we have highly skilled chemical engineers and we will continue to hire
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MILLIKEN & COMPANY
College Relations Department, M-285
P.O. Box 1926
Spartanburg, SC 29304

GENERAL INFORMATION
Milliken is a major manufacturer of textile products for apparel, commercial, home,
and industrial markets, as well as specialty chemicals for a wide variety of applica-
tions. The company was founded in 1865 and has nearly 50 plants and 13,000 associ-
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CITIZENSHIP REQUIREMENTS: U.S. citizenship or Permanent Resident Visa
REGIONS WHERE BS/MS CAMPUS RECRUITING IS CONDUCTED: Southeastern United States
HOW TO APPLY IF UNABLE TO SCHEDULE A CAMPUS INTERVIEW: Send cover letter with
functional area interests and geographic preference statement, resume, and a copy of your transcript to
the above address.

ENTRY LEVEL OPPORTUNITIES FOR CHEMICAL ENGINEERS

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development in 32 R&D facilities in 19 countries, supported by over $800 million annual
R&D spending. More than half of our BS/MS entry-level hires are chemical engineers.

CITIZENSHIP REQUIREMENTS: U.S. citizens and individuals legally authorized for full-time employment without
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ENTRY LEVEL OPPORTUNITIES FOR CHEMICAL ENGINEERS
I I

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Major Hiring Locations
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Internally, five of the twelve Charter Members of the Victor Mills Society,
honoring excellence in technology at P&G, are chemical engineers.

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I

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technologies. Chemical engineers account for 60% of our entry hires.

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Advertisement published in Chemical Eneineering Education, Volume 26, No 3 (1992)

five semesters this project has been prepared and
presented by Dow Chemical, U.S.A., Louisiana Divi-
sion. Dow's personnel present the project to the stu-
dents and then return two to three weeks later for
the students' presentation. The students are asked
to deliver an oral presentation and a written report.
Once the material on discrete and sequential logic
is presented, the lab continues with a one-period
discussion on control valves and subsequent periods
on controller tuning. Through these exercises the
students realize the effect of nonlinearities on the
controller tunings and loop stability.
We have described how APC-I has been taught for
the past five years. It is quite heavy in laboratory
practice and includes topics such as PLC logic which
are not usually covered in classical courses. We con-
tinually question whether such a departure from the
norm provides a correct education. Often, we try
new things, or modifications, such as a modification
in the spring 1992 semester that added a bit more
time to the subject of stability.
Automatic Process Control II (APC-II)
This is an elective one-semester course with a
two-hour lecture and a three-hour lab per week.
Usually twenty to thirty percent of the undergradu-
ates take APC-II, and it also serves as the first
graduate course. We use the APC-I textbook with
additional notes on digital controls provided.
Table 5 shows the material presented in the lec-
ture. Three modeling and simulation projects are
usually also assigned. Table 6 shows the weekly
assignment for laboratory practices. The equipment
is the same as that used in the undergraduate course.
Some exercises take a great deal of time because we
show the benefits of the techniques in detail. For
example, during the feedforward control, we first
ask the student to control a process with simple
feedback control. Then steady-state feedforward is
implemented and its performance is compared to the
performance of feedback control. We then add lead/

TABLE 6
Automatic Process Control II: Laboratory
WEEKS) CONTENT
1 Introduction to distributed control systems and
stand-alone controllers
2 Computing relays
3 4 Cascade control
5 7 Feedforward control
8 9 Multivariable control
10 Dead-time compensation
11 Level averaging control
12 "Catch-up"
13 14 Discrete and sequential logic

Summer 1992

lag and go through a similar comparison. Finally,
dead time compensation is added to the feedforward
and the results are compared. We ask the students
to do the same with two different processes.
In the lab, one to one and one-half periods are
used to explain about distributed control systems
and stand-along controllers. The students actually
learn to configure one system. The student also learns
in more detail about the available computing power
of these controllers, helping them to design and imple-
ment different control strategies.
In the spring 1992 semester a design project was
also assigned to each group of two students. Two
instrument and control engineers from the local Bad-
ger Engineers office provided the design projects
and acted as "leaders." Each group was asked to
design the control strategies for a process. In addi-
tion, each individual student was asked to completely
specify all the instrumentation for a control loop.

CONCLUSION
This sequence of required courses provides exten-
sive "hands-on" laboratory work and lectures that
are focused on the practical aspects of understand-
ing the elements, functions, and properties of a con-
trol loop. Although process control is used as the
unifying theme for the sequence, the students have
also been able to relate the material to their reaction
engineering course and their capstone project design
course. In addition, the department has several ac-
tive undergraduate research projects that provide
an opportunity for the students to use their knowl-
edge of sensors and computer interfacing in a more
traditional university laboratory environment.
The course descriptions refer to the courses as
they are taught today. As new sensors, computer
hardware, and control software become available,
the number of interfacing options increases and the
implementation of more advanced control strategies
becomes possible. It is our intent to make sure such
developments are reflected in our course sequence.

REFERENCES
1. Smith, C.A., and A.B. Corripio, Principles and Practice of
Automatic Process Control, John Wiley & Sons, Inc., New
York (1985)
2. Honeywell Inc., Phoenix, AZ
3. Bailey Controls, Wickliffe, OH
4. Yokogawa Corp. of America, Newnan, GA
5. TUTSIM Products, Palo Alto, CA
6. Coughanowr, D.R., Process Systems Analysis and Control,
Second Ed., McGraw-Hill, New York (1991)
7. Gilbert, R.A., and J.A. Llewellyn, Programmable Controllers
Practices and Concepts, ITC, Herndon, VA
8. Allen-Bradley, a Rockwell International Co., Milwaukee, WI
53204 0

laboratory

THE EFFECT OF AGITATION

ON OXYGEN MASS TRANSFER

IN A FERMENTOR

RONNIE S. ROBERTS, JAMES R. KASTNER,
MAQSOOD AHMAD, D. WILLIAM TEDDER
Georgia Institute of Technology
Atlanta, GA 30332-0100

Chemical engineers have traditionally been in-
volved in a wide variety of industries. Al-
though specific problems encountered in these
diverse industries may appear different, many of
them can be solved by using basic chemical engi-
neering principles. In the classroom and in the labo-
ratory, basic principles are generally demonstrated
by using problems from a number of different indus-
tries, allowing students to learn about both the in-
dustries and the application of these basic principles.
The increasing importance of industrial opera-
tions based on biochemical engineering has long been
recognized. Biochemical engineering problems have
been easily integrated into many courses, including
mass transfer, heat transfer, and reactor design.
Integrating biochemical engineering-type experi-
ments into chemical engineering laboratories, how-
ever, has been much more difficult.
Biochemical engineering experiments must be de-
veloped which demonstrate basic principles and
which can be easily incorporated into undergradu-
ate chemical engineering laboratories. An experi-
ment has been developed at Georgia Tech that dem-
onstrates the effect of agitation on oxygen mass trans-
fer in a fermentor and that can be conducted by
undergraduate students in an ordinary undergradu-
ate chemical engineering laboratory.

BASIC CONCEPTS
Fermentation is the production of chemicals from
a substrate by using microbes. Many fermentation
use microbes which require oxygen to convert the
substrates reactantss) into the desired product. Oxy-

gen is generally supplied by sparging air at one
atmosphere pressure directly into the fermentation
broth (aqueous mixture of substrates, products,
and microbes). The maximum dissolved oxygen par-
tial pressure in the fermentation broth would be
saturated. Dissolved oxygen levels in the fermenta-
tion broth of 30% of saturation or higher are re-
quired for many fermentations.
A high concentration of microbes in the fermen-
tor (reactor) is desirable in order to maximize
productivity per unit volume of the fermentor. Un-
fortunately, the high concentration of microbes con-
sumes oxygen at high rates and thus oxygen mass
transfer from the gas phase to the fermentation broth
is very important.

Ronnie S. Roberts is an associate professor of
chemical engineering at the Georgia Institute of
Technology. His research interests are in fer-
mentation and buffered solvent pulping. .

James R. Kastner is a PhD candidate in the
School of Applied Biology at the Georgia Insti-
Stute of Technology. His research interest is in the
fermentation of five and six carbon sugars.

D. William Tedder is an associate professor of
chemical engineering at the Georgia Institute of
Technology. His research interests are the treat-
ment of hazardous wastes and solvent extration.
Maqsood Ahmad is a visiting scholar in the School of Chemical Engineer-
ing at the Georgia Institute of Technology. His research interest is in the
production of ethanol and other products from lignocellulosic materials.
(Photo not available.)

Copyright ChE Division ofASEE 1992

Chemical Engineering Education

OXYGEN MASS TRANSFER IN A FERMENTOR
If the flowrate of air to the fermentor is large, a
negligible amount of oxygen will be consumed and
the mole fraction of oxygen in the gas phase will be
essentially constant. For suspension cultures, the
liquid film mass transfer generally controls the
overall mass transfer of oxygen from the gas phase
to the liquid phase. If we assume that liquid phase
mass transfer is controlling in the fermentor, the
change in oxygen partial pressure dissolved in the
bulk liquid with respect to time can be calculated as
shown in Eq. (1):

(1)

where
P02 = dissolved oxygen partial pressure; % of
saturation
t = time; unit time
k, = liquid phase mass transfer coefficient; unit
time, unit area-'
a = surface area; unit area
P2 = equilibrium dissolved oxygen partial pressure;
100% saturated
-r02 = rate of oxygen consumption; % saturation, unit
time'1

For a fermentor where the microbial population
remains relatively constant, the rate of oxygen con-
sumption is relatively constant and quasi-steady state
can be achieved for dissolved oxygen partial pres-
sure. Thus, kla can be determined as follows:

02 =kla(P0d -P02 )-(-r02)-0 (2)
(2 *)
dt O2 O(

ka= r2 (3)
P02 -PO2

Mass transfer from a gas phase to a liquid phase
in a stirred tank is very complex. In particular, agi-
tation strongly effects bubble size, bubble retention
time, and liquid mixing. All of these factors strongly
influence k1a. Generally, kla is correlated as shown
in Eq. (4):111

kla = a'( (Qair) (4)
where

a', '= constants which depend on vessel dimensions,
agitator dimensions, fluid properties, etc.
P/v = agitator power per reactor volume; unit power,
unit volume-'

Biochemical engineering experiments must be
developed which demonstrate basic principles and
which can be incorporated into undergraduate
chemical engineering laboratories.

Q. = volumetric flowrate of air; unit volume, unit
time

For a fermentor which contains a Newtonian
fermentation broth, the agitator power is a function
of agitator rpm.[2] Thus for a constant sparger
air flowrate, kla can be correlated to rpm as shown
in Eq. (5):
ka = a(rpm) (5)
where
a,P = constants
rpm = agitator rpm; revolutions, min'

From Eq. (4), a is equal to zero if the sparger air is
stopped. Thus, according to Eq. (1), the change of
dissolved oxygen partial pressure in the fermenta-
tion broth with respect to time is equal to the rate of
oxygen consumption.

dP
(-o2 ) (6)
The rate of oxygen consumption in the fermentor is
equal to the slope of a plot of the dissolved oxygen
partial pressure versus time.
Experimentally, the effect of agitation on kla can
be determined by setting the agitator rpm at various
levels and obtaining the corresponding quasi-steady
state dissolved oxygen partial pressures. Then kla
can be determined using the quasi-steady state dis-
solved data and the rate of oxygen consumption. A
plot of In(k1a) versus ln(rpm) should give a straight
line with a slope of P and an intercept of In a.
A good discussion of oxygen mass transfer in an
agitated fermentor can be found in Biochemical En-
gineering Fundamentals. [3
EXPERIMENTAL EQUIPMENT
A New Brunswick Scientific Bioflow IIc two-liter
fermentor (Edison, NJ) has been used for this ex-
periment. The fermentor is equipped with a galvanic
oxygen probe, temperature control, and a turbine
agitator. Compressed air is sparged directly into the
fermentation broth and is measured using a rotame-
ter. A less costly vessel such as a New Brunswick
Multigen fermentor or a similarly equipped stirred
vessel can be used instead of the Bioflow IIc.

Summer 1992

dPdt,=k 22 o) ',

Data are collected using an Austin 286 PC and an
A/D Board (Mendelson Electronics). Depending
on the application, the data are logged, manipu-
lated, and/or plotted using a PC-based system.
PC data collection is not necessary to conduct
the experiments. Data can be collected manually
with little trouble.
A schematic of the experimental equipment at
Georgia Tech is shown in Figure 1. The system
cost approximately $15,000 in 1990. The equip-
ment for this experiment is also used to conduct
both undergraduate and graduate fermentation
research projects.

EXPERIMENTAL PROCEDURES
One liter of distilled water containing 80 g glucose
is added to the fermentor. Temperature control is
set at 300C and agitation at 600 rpm. After the
system equilibrates, the dissolved oxygen probe is
calibrated. (Note: if the probe is being used for
the first time, place the probe in distilled water
overnight to equilibrate.) Air is sparged into the
aqueous solution at the rate of approximately 1.6
L/min until the dissolved oxygen meter indicates
quasi-steady state dissolved oxygen partial pressure
and saturated conditions. The dissolved oxygen
meter is then spanned to 100%. Next, nitrogen is
sparged at the rate of approximately 1.6 L/min until
the dissolved oxygen meter indicates steady state.
The dissolved oxygen meter is then zeroed at 0%.
The above is repeated by alternately spanning and
zeroing until the measurements replicate. Gener-
ally, twice is sufficient.
Next, the agitation is reduced to 500 rpm and
approximately 10 g of Fleischmann's dry active yeast
(approximately one and one-half 1/4 oz. packages) is
added to the water-glucose solution. Allow three
hours for the yeast to become fully active. The dis-
solved oxygen should be maintained at above 50%. If
required, increase the flowrate of sparger air and/or
reduce the yeast concentration to maintain the dis-
solved oxygen at above 50%.
After the yeast is fully active, increase agitation
to 700 rpm and allow the system to reach quasi-
steady state dissolved oxygen partial pressure. Next,
stop the sparger air and start the flow of nitrogen
(1.6 L/min) into the head space in the fermentor.
Nitrogen in the head space prevents incidental aera-
tion. Then obtain a plot of dissolved oxygen partial
pressure versus time. The initial part of the plot will
not be linear due to probe response. After the initial
nonlinear part, a linear plot should be obtained which
represents the rate of oxygen consumption in the

fermentor. After collecting the transient data the
nitrogen flow is stopped and the sparger air is turned
on. Repeat the above procedure. Compare the above
two runs for similarity and if they are not similar,
repeat the measurements.
Systematically vary the agitation between approxi-
mately 500 and 700 rpm. Allow the system to reach
quasi-steady state each time, and record the dis-
solved oxygen partial pressure. Generally, ten to
twenty minutes are required for the system to reach
quasi-steady state. After completing the above quasi-
steady experiments, set the agitation at 700 rpm
and allow the system to come to quasi-steady state.
Repeat the previous procedure again to obtain a
final plot of dissolved oxygen partial pressure versus
time. If the plot is not similar to previous plots,
repeat the procedure.
TYPICAL EXPERIMENTAL RESULTS
Plots of dissolved oxygen versus time are shown
in Figure 2. The nonlinear portion of the plots is
due to the response of the dissolved oxygen probe.
The slope of the linear portion of the plots represents
the rate of oxygen consumption in the fermentor.
The similar linear slopes of the plots, -20.4 and
-17.0% saturation min-1 for the initial and final
plots, respectively, indicate that the rate of oxygen
consumption is relatively constant during the course
of the experiment.
Quasi-steady state dissolved oxygen partial
pressures at various rpm are shown in Table 1.
Using the data in Table 1, kla's were calculated
using Eq. (3). A plot of k1a versus rpm is shown in
Figure 3. We estimated a and 3 to be 2.2*10-8min-1
and 2.75 (agitation in the form of rpm), respectively.

NewBrunswick Boflow II C Fermentor
Figure 1. Schematic of experimental equipment
Chemical Engineering Education

The correlation coefficient, r, was 0.986.

DISCUSSION
A major advantage for this biochemical engineer-
ing experiment is the simplicity of laboratory proce-
dures. Yeast (which can be obtained at most super-
markets) is inoculated at relatively high concentra-
tion in the fermentor. The high inoculum concentra-
tion and the relatively short time required for the
experiments eliminate the need for aseptic condi-
tions. Thus, only ordinary cleaning of the fermentor
(stirred vessel) and the use of distilled water is re-
quired to prepare for the experiments.
Initial preparation requires less than thirty min-
utes for the students or laboratory assistant. Little
or no additional effort is required during the three-

M 0 1 2 3
Time, minutes
Figure 2. Initial and final dissolved oxygen partial
pressures versus time

TABLE 1
Quasi-Steady State Dissolved Oxygen Partial
Pressures at Various RPM
Dissolved Oxygen Partial Pressure
RPM % of Saturation
600 82
700 87
700 87
500 67
600 82
650 85
550 77
500 68
700 88

hour yeast activation period. The experimental mea-
surements can be made in approximately three hours.
The experimental conditions previously described
were developed using a two-liter New Brunswick
Scientific Bioflow IIc Fermentor. If other fermentors
or stirred vessels are used, these conditions may
have to be adjusted. In particular, high shear from
the agitator can be detrimental to the yeast.
If a microscope and methylene blue stain are avail-
able, the students can also determine the number of
active and inactive yeast cells that are present.[a]
The concentrations of active and inactive cells are
not required to determine a and p. Inclusion of this
step does reinforce the biological nature of this ex-
periment. The total cell concentration for the typical
experiment previously presented was 3.6 x 108 cell/
ml (65% viable and 35% non-viable).
The general nature of this experiment should also
be emphasized. Although the system investigated in
this case involved a fermentation, similar experi-
ments could be conducted to investigate the effect of
agitation on mass transfer from a gas phase to a
liquid phase in other unit operations.

CONCLUSIONS
This biochemical engineering experiment involves
basic principles of mass transfer and chemical reac-
tions. In particular, the effect of agitation on kla is
demonstrated using a fermentor. The equipment and
material requirements for the experiment are mod-
est and students and laboratory assistants can gen-
erally master the experimental techniques with little
difficulty. It can be used to demonstrate basic chemi
Continued on page 163.
10 r

0.1 L
401

0

600 700 800

Fermentor Agitation, rpm

Figure 3. ka versus fermentor agitation

Summer 1992

I I

classroom

"PRODUCT IN THE WAY"

PROCESSES

NOEL DE NEVER
The University of Utah
Salt Lake City, UT 84112

any processes in chemical engineering have

the same basic physical description-that
the thing produced (or something propor-
tional to it) gets in the way of the process. These
diverse processes all lead to the same mathematics
and optimization, as will be shown here.
A wide variety of chemical engineering processes
lead to rate equations of the form
1 2= a(time)+b (1)
(production rate)
or
time g cumulative 2 +h cumulative (2)
time=g( product ) n product
Here time is measured from the start of production
or of the current production cycle, and a, b, g, and h
are constants (all symbols are defined in the nomen-
clature at the end of this paper). Although the pro-
cesses described by these equations cover the whole
range of chemical engineering (including heat trans-
fer, filtration, condensation, freezing, chemical reac-
tions, oxidations, etc.), the underlying mechanism is
the same for all. This paper is about that mecha-
nism, its mathematics, and the wide range of places
where a chemical engineer can encounter it.
In all of these processes, the characteristic physi-
cal fact is that the product, or something propor-
tional to it, gets in our way and the more we pro-

PI
Pressure
P3

Slurry Flow Filter Clear Filtrate Flow
Cake

Filter Cloth
Figure 1. Flow through a simple filter

Noel de Nevers has been a faculty member
at the University of Utah since 1963. His prin-
cipal interests are fluid mechanics, thermody-
S namics, and air pollution. He has also devel-
/oped a course and edited a book of readings
r on Technology and Society. He recently won
local fame by discovering a previously un-
known major arch in Arches National Park.

duce, the more the product is in our way and the
slower the process rate becomes.
One may easily show that Eqs. (1) and (2) are the
same by writing
t
cumulative product = (production rate) d(time) (3)
0
and then differentiating Eq. (2) and comparing it
term-by-term with Eq. (1). The two equations are
the same if a = 4g and b = h2.
FILTRATION
It is easy to see how these equations arise in the
classical treatment of constant-pressure filtration of
a solid from a liquid, to form an incompressible cake.1l]
The flow through a filter and its pressure profile are
shown schematically in Figure 1. A slurry (a fluid
containing suspended solids) flows through a filter
medium (most often a cloth, but sometimes paper,
porous metal, or a bed of sand). The solid particles
in the slurry deposit on the face of the filter
medium, forming the "filter cake." The liquid, free
from solids, flows through both cake and filter me-
dium. The flow is laminar in almost all filters, and
the changes in potential and kinetic energies are
negligible, so that the pressure drop is given by
Darcy's equation [(-AP/Ax) = gV/k]. Solving that equa-
tion for the superficial velocity, we find

V -APk (4)
=QA Ax
where g is the fluid viscosity and k is the cake
permeability. Here there are two resistances in se-
Copyright ChE Division ofASEE 1992
Chemical Engineering Education

Many processes in chemical engineering have the same basic physical description-
that the thing produced (or something proportional to it) gets in the way of the process. These diverse
processes all lead to the same mathematics and optimization...

ries with the same flow rate through them. If we let
the subscript "f.m." indicate "filter medium," we can
write Eq. (4) twice and equate the identical flow
rates (see Figure 1)

P P- 2 k P2 -P3(k
Ji \AX/cake x \.AXf.m.
When we solve for P2, we get

P2 = P1 v8 ( cake = P3 VV ( f.m.
and then, solving this equation for V., we get

(5)

(6)

= 3 Q (7)
()caLke k)f.m. Afil
This equation describes the instantaneous flow
rate through a filter; it is analogous to Ohm's law for
two resistors in series, so the gAx/k terms are called
the cake resistance and the cloth resistance.
The resistance of the filter medium is normally
assumed to be a constant independent of time, so
(Ax/k)f.m is replaced with a constant, a. If the filter
cake is uniform, then its instantaneous flow resis-
tance is proportional to its instantaneous thickness.
However, this thickness is related to the volume of
filtrate which has passed through the cake by the
material balance

'mass volume mass
of of of
ake cake 1 1 fitrate solids
area Pcake) Peake area volume (8)
) Afiltrate ,)
Customarily we define

mass of
w solids _1 volume of cake
volume of pake ) volume of filtrate (9)
filtrate )
so that

cake W (10)
Here the cake is assumed to be incompressible,
Pcake = constant, which is a good assumption for most
filtrations but not for filtration of flocs and gels. The
volume of filtrate here is V. (This implies 100% col-
lection efficiency for the solids in the slurry, which is
generally observed.) When we substitute Eq. (10) for
the cake thickness in Eq. (7), we find
Summer 1992

Time

Figure 2. Relation between production rate and
cumulative production

Q l(dV P1-P3 3
=A dt I +a (11)
r kA + a)
For most industrial filtrations the filter is supplied
by a centrifugal pump or blower at practically con-
stant pressure, so (P1 P3) is a constant, and Eq. (11)
may be rearranged and integrated to

2 _Wva =(P31-)t (12)
2A k +AWW
Eq. (2) and Eq. (12) are identical if
product = V/A
g = (gW)/2k(P1 P)
h = g a/(P -P3)
Intuitively, we can see what is happening in Fig-
ure 2. At time zero there is no cumulative product
and the production rate equals 1/(A). As soon as we
begin to produce filtrate, we also produce filter cake.
This increases the resistance, so the production rate
declines. The more filtrate we produce, the thicker
the filter cake and the higher the resistance. The
product (filter cake) gets in the way of producing
more filter cake.
Often one sees Eq. (2) rewritten as
timepr = g(cumulative product)+h (13)
cumulative product
This allows us to plot (time/cumulative product) vs.
cumulative product and to read the values ofg and h
as the slope and intercept of the straight line which
results. This is shown for filtration (using Eq. 12) by
McCabe and Smith.[21 It is equally applicable to other
processes described in this paper. That type of plot
has less intuitive content than Figure 2, but it makes

possible a visual check of whether or not the experi-
mental data agree with Eqs. (1) or (2) and allow a
direct determination of g and h from those data.
FREEZING
The second example of Eqs. (1) or (2) is the forma-
tion of ice on a cooled surface, such as occurs in an
ice maker.[31 Referring again to Figure 1, we see that
in this situation the flow is of heat, not fluid. We
would relabel that figure by replacing the slurry
with fluid being frozen, replacing the filter cake with
the ice which has formed, replacing the filter cloth
with the chiller surface (normally a highly conduc-
tive metal), and at the right the recipient of the heat
(normally a chilled brine or evaporating refriger-
ant). The pressure-distance curve would be replaced
by a temperature-distance curve, with the same
shape. If we ignore the heat transfer resistances
other than those due to conduction (which is an
excellent approximation for this case), then we can
rewrite Eq. (7) as

q d T _T
heat flux = -= A (14)
A dt r\ Ax
A dt L(k)ice k )metal wall ]

Where
T = temperature
k = (which were permeabilities in Eqs. 4 to 12) are
now thermal conductivities of ice and metal, re-
spectively
Q/A = total heat transferred per unit area (analogous
to the volume, V, of filtrate)
q/A = the instantaneous heat flux (analogous to V, =
(1/AXdV/dt) for filtration)

Here the analogs of Eqs. (8) to (10) are
mass of
ie _= ice (_1
ice area (Pice J

heat mass of

IPi. area heat A) (pX)icj
transferred
where h is the latent heat of fusion. If we substitute
this value of Axice into Eq. (14) and perform the
integration, we find

2(Q)A 1 ((p Q)(-{Ak )=(T1-T3)t (16)
which is identical to Eq. (2) if
product = Q/A
g = 1/[2(pk)ice(T T3)]
h = AXmetal/[kmetal(T T3)]

Again-the product (ice) gets in our way. The
thermal conductivity of ice is about 1% that of alu-
minum (the common metal in freezers) so the accu-
mulated amount of what we are producing (ice) is
the determinant of the rate of producing it.
This analysis ignores the sensible heat of the ice
and any convective heat transfer resistances. KreithE[3
applies the same analysis to the freezing of ice lay-
ers on ponds in cold weather. That situation is
sketched in Figure 3, which is practically the same
as Figure 1 if it were rotated by 900. However,
in Figure 3 the resistance of the metal wall is re-
placed by 1/(the ice-to-air heat transfer coefficient),
which is practically a constant. The resulting equa-
tions are the same as above, with (A eta/kmeta)
being replaced by an ice-to-air heat transfer resis-
tance, (1/ho). This analysis applies to any solidifica-
tion process if the solid is a poor heat conductor, but
not necessarily to the solidification of metals like
aluminum or copper.

EVAPORATOR SCALE FORMATION
The third example is scale formation in evapora-
tors.[41 In many such evaporators a scale layer forms
on the evaporator surfaces. This scale layer is nor-
mally a poor heat conductor, so its resistance to heat
flow largely determines the overall heat flow rate.
The experimental observation is that the thickness
of the scale is proportional to the amount of heat
which has been transferred to the evaporating solu-
tion since the last cleaning of the heating surface.
Clearly, this is the same as the previous example
with the variables renamed, i.e.,

d- T1 T3
heat flux =- A = T3(17)
A dt [Ax Ad +A
k )cae k metal wallJ
Normally, the scale thickness is taken as some con-
stant a times the cumulative amount of heat trans-
ferred per unit area, and the two fluid-film heat
transfer resistances are added to that of the metal
wall, so that the analog of Eq. (11) becomes

d
= dt
X dt

and the analog of Eq. (12) becomes

(q2( 01 +--(sum of other resistances)=(T1-T3)t
(19)
Normally this is seen in the form of Eq. (1).E4,5] The
Chemical Engineering Education

_- 1 -3 (18)
a + Ax l h h1J
scale )QA \ k metalwall h i

transition from Eq. (2) to Eq. (1) may be made by
solving Eq. (2) as a quadratic for the cumulative
product, finding

(cumulative product)= h + 4gt (20)
2 g 2g
then differentiating, and noting that the production
rate is d(cumulative production)/dt. Thus

q = heat transfer rate = 1 (21)
A h2+4gt
Squaring and taking the reciprocals leads to Eq. (1).

GAS-SOLID CHEMICAL REACTIONS
The next application is a gas-solid chemical reac-
tion which forms or leaves a solid residue, e.g.
CaO(s)+SO2(g)- CaSO3(s) (22)
which is important in some gas-phase sulfur dioxide
capture processes, e.g., fluidized bed combustion, or
in catalyst regeneration, e.g.
Coked catalyst(s)+ 02(g) Cleaned catalyst(s)+CO2(g) (23)
in which carbon is burned off a solid porous petro-
leum cracking catalyst, leaving behind a cleaned
catalyst. In the first of these cases, the product of the
reaction is a less porous solid than is the solid reac-
tant, so that the layer of product forms the principal
barrier to diffusion of the gaseous reactant inward to
the surface of the unreacted solid. In the second
case, the reaction increases the porosity of the solid,
but as the regeneration continues the oxygen must
diffuse further inward to get to the unregenerated
part of the catalyst, and the carbon dioxide must
diffuse further to get out, so that the diffusion resis-
tance of the steadily growing cleaned catalyst layer
is the principal resistance in the process.
In general, such a reaction is described as[61
A(fluid)+bB(solid) fluid and solid products (24)

Tair < 0C

Air
SConvective resistance laver in air

Water

Heat Flow Twater = 00C

Figure 3. Solid ice formation on a body of water
Summer 1992

where b is the stoichiometric coefficient.
We may visualize these two reactions on Figure 3
if we visualize the ice as being replaced by the reac-
tion product (CaSO3 or Cleaned catalyst), visualize
the unfrozen liquid being replaced by the unreacted
solid reactant (CaO or Coked catalyst), and visualize
the air-to-ice heat transfer coefficient being replaced
by a gas-to-solid mass transfer coefficient. In place
of the heat flow we will have gaseous reactant diffus-
ing to the solid surface and then diffusing through
the reacted solid to the surface of the unreacted
solid; there will be no flow of anything beyond that
surface.
For this general reaction, the analog of Eq. (7) is

1 dNA CA Ai (25)
A dt (NA/A)b 1
LDolid product kG
where
(1/AXdNA/dt) = rate at which reactant A is delivered to
the surface of unreacted B
D = diffusivity of the gas
kG = an external mass transfer coefficient,
subscripts o, i = bulk gas phase and reaction interface,
respectively

The analog of Eqs. (8) to (10) is

X NAsop b (26)
solid product A Psolidproduct
NA is normally stated in moles, so that Psolid product
must be the molar density of the solid product. Sub-
stituting Eq. (26) into Eq. (25), we find the analog of
Eq. (11)

~-~N)2 CAo A1i ) Psolid product (27)
2( A j A -CA A o J (27)(k,=Ao

In most applications of Eq. (27) it is further as-
sumed that the concentration of A at the surface of
B, (CAi), is negligible, and that (1/kG) is negligible, so
that we have

2CA Dbt
Axsolidproduct = .o-- -
solid pduct Psolidproduct
or, solved for t

t Psolid product (29
2 bDC (29)
2bDCAo
Most often one sees this equation applied not to a
flat surface, but rather to a spherical particle.61 There
one sees[6, Chap. 12, Eq. 14]

,_ PeR2 2 3Y r
t= PBR2 1-3(r ) +2(-- )3 (30)
6bDCA R )(

where R is the radius of the particle (assumed con-
stant, which implies that PB/b = Psolid product), and rc is
the radius of the unreacted core of B. This is the
"shrinking core-ash diffusion controls" kinetic
model. In it, the attention is focused on the unreacted
B rather than on the reacted material
We may see how Eqs. (29) and (30) compare by
writing
r =R-Ax (31)
substituting in Eq. (30), and simplifying to find

t PAX2 2 Ax (32)
:2bDCAo [1- (32)
A0
If, as assumed above, pB/b = Psolid product, then Eq.
(32) is simply Eq. (29) multiplied by 1 (2/3)(Ax/R)],
which accounts for the spherical rather than planar
shape. For the planar configuration shown in Fig-
ures 1 and 3, R is infinite and Eqs. (29) and (32) are
identical. For spherical particles, Eq. (29) describes
only the initial stages of the process during which Ax
is small compared to R.
This same set of equations applies to the forma-
tion of oxide films on metals (e.g., rusting, but also
solid oxide formation on non-ferrous metals) if the
film is coherent and does not flake away,[71 and to
processes like fluidized bed powder coating and vari-
ous steps in the production of integrated circuits if
the deposited or diffused film is more resistant to
the flow of heat or material than the substrate.

FILM CONDENSATION
Nusselt's classic derivation of the behavior of a
vapor condensing on a vertical wall in laminar flow,181
as shown in Figure 4, provides the final example.
The derivation normally shown does not make clear
that this is one of the class of processes discussed
here. If we take the viewpoint of an observer riding
with a batch of fluid down the wall (the Lagrangian
view), we can see that the situation is exactly the
same as the problem of freezing of ice on a solid
surface and that Eq. (15) applies, with the proper-
ties of the condensate replacing those of the ice. In
the derivation, the heat transfer resistance of the
metal wall is normally ignored, as we do here, so by
combining Eqs. (15) and (16) we find
1A2 kATt (33)
2H pl
Here the appropriate value of t is the time it has

taken this batch of condensate to flow downward
from z = 0. At any value of z, for a slice perpendicu-
lar to the flow we may compute the average velocity
from the assumption of laminar flow as

(AVag g (34)
Vavg = 3g
(which ignores the buoyant effect of the vapor and
the shear stress between vapor and condensate film).
We assume that the piece of fluid we are riding with
begins at t = 0, at z = 0, with V = 0. At time t it will be
at location z and have the average velocity given by
Eq. (34). To find the value of t corresponding to any
z, we assume that the average velocity since t = 0 is
one-half of the velocity at t = t, which leads to t = z/
(Vav2). Substituting this value into Eq. (33) and
solving for Ax, we find

Ax= 12 ATz4 (35)
L kRP2g J
This is (3)1/4 = 1.3 times the value derived by Nusselt
and shown in most heat transfer books. The differ-
ence results from the approximation made in treat-
ing a laminar flow as if it were a plug flow. That
approximation is not as large a source of error in the
derivation as some of the other approximations.[8]

OPTIMIZATION
One benefit of seeing that all these processes have
the same form is that we can then use the optimiza-
tion equations developed for any one of them for all
of them. For any of the processes which require
regular shutdown and cleanout (e.g., batch filtra-
tion, batch freezing, evaporator operation with peri-

,Condenser Wall

Cooling Fluid

Condensing vapor

Heat Flow

Figure 4. Laminar film condensation
Chemical Engineering Education

4-
1-

odic shutdown and scale removal) if t is the operat-
ing time and tc is the time required to shut down,
clean out and restart, the average production rate is

cumulative product
average production rate = cumulative product (36)
t+t
If we substitute Eq. (20) for cumulative product, set
[d(cumulative product)/dt] equal to zero, and solve
for t, we find (after some algebra)

t=t,+h (37)

or, if the rate is formulated in terms of Eq. (1),

t=t +2 b (38)
The latter solution is shown in Peters and
Timmerhaus[51 for an evaporator with scale forma-
tion and regular shutdowns for cleaning, but it is
obviously equally applicable to all of the batch pro-
cesses shown here.

CONCLUSION

One fundamental kind of process-product gets
in the way of production-appears in many places in
chemical engineering. The mathematical presenta-
tions of these processes vary, but all can be shown to
fit a single pattern. By using that pattern, we can
use the results and ideas for any one of these pro-
cesses for all of them.

Where Should this Fit in the ChE Curriculum?
This material is regularly discussed in our senior-
year process design class. The students have previ-
ously taken courses in fluid mechanics, heat trans-
fer, mass transfer, and chemical reaction kinetics, so
the examples should all be review for them. The
design course seems a good place for them to see this
integration of several diverse topics in their previ-
ous courses. Professors who use the process design
book of Peters and Timmerhaus can introduce the
discussion of this topic by assigning the following
homework problem:
Problems 11-5 (page 417) and 14-16 (page 578)
of Peters and Timmerhaus have very different-
looking rate equations, for processes which are
physically similar. Show the choice of symbols
which makes the rate equations for these two prob-
lems the same.

NOMENCLATURE

a = rate constant in Eq. (1):
1/[(production rate)2 (time)]
A = area:m2
Summer 1992

b = rate constant in Eq. (1): 1/(production rate2)
b = stoichiometric coefficient: mols/mol
CA = concentration of A: mols/m3
D = diffusivity: m2/s
g = rate constant in Eq. (2): (cumulative
product2Xtime)
g = acceleration of gravity: m/s2
h = rate constant in Eq. (2):(cumulative
productXtime)
h = heat transfer coefficients: J/[(m2)(sXK)]
k = permeability: m2
k = thermal conductivity: J/[(m)(sXK)]
kG = external mass transfer coefficient: m/s
NA = moles of A: mols
P = pressure: Pa
Q = cumulative heat transferred: J
Q = volumetric flowrate: m3/s
q = heat flow: J/s
R = radius (of spherical particle): m
r = radius of unreacted core of spherical particle:
m
T = temperature: K
t = time: s
x = distance or thickness: m
z = vertical distance: m
V = volume of filtrate: m3
V = velocity: m/s
V = superficial velocity: m/s
W = cake volume/filtrate volume
a = cloth resistance/a = (Ax/k)Im.: 1/m
a = scale formation constant: m3/J
X = latent heat: J/kg
g = viscosity: Pa's
p = density or molar density: kg/m3 or mols/m3

REFERENCES
1. de Nevers, Noel, Fluid Mechanics for Chemical Engineers,
Second Edition, McGraw-Hill, NY, p. 426 (1991)
2. McCabe, W.L., and J.C. Smith, Unit Operations of Chemical
Engineering, Third Edition, McGraw-Hill, NY, p. 939 (1976)
3. Kreith, Frank, Principles of Heat Transmission, Third Edi-
tion, IEP, NY, p. 534 (1973)
4. McCabe, W.L., and C.S. Robinson, "Evaporator Scale For-
mation," IEC 16 478 (1924)
5. Peters, M.S., and KD. Timmerhaus, Plant Design and Eco-
nomics for Chemical Engineers, Fourth Edition, McGraw-
Hill, NY, p 357 (1991)
6. Levenspiel, Octave, Chemical Reaction Engineering: An In-
troduction to the Design of Chemical Reactors, Wiley, NY, p.
338 (1962)
7. Bakhvalov, G.T., and A.V. Turkovskaya, Corrosion and Pro-
tection of Metals, trans G. Isserlis, Pergamon, NY, p. 9
(1965)
8. Roshenow, W.M., and H.Y. Choi, Heat, Mass and Momen-
tum Transfer, Prentice Hall, Englewood Cliffs, NJ, p. 240
(1961)

classroom

A STATISTICAL LOOK

AT SIGNIFICANT FIGURES

PARK M. REILLY
University of Waterloo
Waterloo, Ontario, Canada N2L 3G1

Almost all of the numbers used by scientists
and engineers are approximations of some
t sort, and everyone recognizes the importance
of keeping in mind the uncertainty introduced by
these approximations. In spite of its severe limita-
tions, the significant numbers convention is still com-
monly used by engineers and scientists to express
this uncertainty and is widely taught in secondary
schools and in the lower levels of universities. The
purpose of this paper is to review the convention
and its limitations and to present an alternative
which is easy to use and is sound statistically. The
approach is similar to, but developed independently
of, that of Moffat.[1]
THE SIGNIFICANT NUMBER CONVENTION
Except in trivial cases such as the counting num-
bers, no decimal number can exactly represent a
mathematical or physical reality. The error in a deci-
mal number is the difference between the "true"
value of the reality and its decimal representation.
A significant number is defined as one in which
the error is less in absolute value than five in the
next digit beyond those shown, and under the sig-
nificant number convention all decimal numbers are
assumed to be significant ones. An important con-
sideration under the convention is the number of
significant figures present, which is the number of
figures in a significant number not counting preced-
ing zeros or following ones to which the error crite-
rion does not apply.[2-4]
There is one important area in which the use of
the convention is beyond reproach. That is in com-
municating purely mathematical numbers such as
logarithms, the values of trigonometric functions,
etc. The true values of such quantities are perfectly
knowable. As an illustration of this, it would be easy
in principle to express the base of natural logarithms
Copyright ChE Division of ASEE 1992

e correct to 100 significant figures. The significant
numbers convention should always be used, and un-
derstood to be used, in communicating this type of
number.
There are two basic rules for preserving signifi-
cance when significant numbers are combined arith-
metically. The first concerns addition and subtrac-
tion. Under it, a figure in a sum or difference is
significant only if all figures in the same position
relative to the decimal point in the numbers being
added or subtracted are significant. Thus, in adding
five numbers, each of which has one significant fig-
ure after the decimal point, the sum is said to be
significant to one figure after the decimal point. Ob-
viously this is not true. The maximum error in the
sum as indicated by the rule is 0.05, while in fact it
is five times that-because the maximum error in
each number being added is 0.05 by our hypothesis.
This is serious because it implies that the rule un-
derestimates the error. Even more important, the
probability of the actual error exceeding the figure
given by the rule has the high value of about 44% to
a good approximation. If we use the rule, we are in
effect guilty of the heinous sin of "showing too many
significant figures." Of course, the deficiency of the
rule is much more serious when adding, say, 100
numbers.
The second rule deals with multiplication and
division. Under it the number of significant figures
in a product or quotient is the same as in the one of
the quantities being multiplied or divided which has
the fewest. It is easy to show that this rule also is
seriously deficient.

Chemical Engineering Education

Park M. Reilly is a professor emeritus in the
Department of Chemical Engineering at the
University of Waterloo. He received his BASc
in Chemical Engineering at the University of
Toronto in 1943 and his PhD in Statistics at the
University of London in 1962.. He has spent
about twenty-five years in each of industry and
academe.

There is one important area in which the use of the convention is beyond reproach.
That is in communicating purely mathematical numbers such as logarithms, the values
of trigonometric functions, etc. The true values of such quantities are perfectly knowable.

The most important fault of the convention and
its rules is that they attempt to deal with the maxi-
mum possible error. While that concept has some
limited use, it is much more valuable to know how
much error is likely to occur than how much error
can occur.

MEASURED QUANTITIES
Except in trivial cases it is not possible in prin-
ciple to know the true value of a measurement. Here
measurement means the approximate numerical
value of a physical quantity obtained by comparison
with an accepted scale. The integer results of
counting are not considered measurements in this
sense. It is not possible to state that the error in a
measurement is not greater than five in some deci-
mal digit because we cannot know where the true
value is. Consequently, the significant number con-
vention cannot correctly be used in connection with
measurements. Also, as above it is almost always
more important to know how big an error is likely
to occur in a measurement than to know its maxi-
mum possible value. This is another serious limita-
tion on the value of the convention in dealing
with measurements.

AN ALTERNATIVE APPROACH
As established above, the significant numbers con-
vention is unsatisfactory. An alternative approach
can be developed which deals with which errors are
likely. It is based on writing measurements and
numbers derived from them in the form
x u(x)
The symbol x represents the number, and the ex-
pression u(x) represents the uncertainty in it. A nu-
merical example is
(2.693 0.024)
It is useful to enclose the numerical expression in
parentheses.
The uncertainty is that number which will exceed
the magnitude of the error "most of the time." To
those who are not familiar with the statistical ap-
proach it will be the number ordinarily used in stat-
ing how much error is expected, e.g., "The error is
0.3," or "The error is 2%." Such statements are very
commonly made and understood by engineers and
scientists. The quantity u(x) is the error magnitude
Summer 1992

in this sense. This is also the same sense in which
the error is said to be five in some decimal place
when using the significant number convention in
connection with measurements. This expression of
uncertainty is more flexible than the significant num-
bers convention because it is not restricted to a value
of five in some decimal digit.
Notice that the uncertainty expressed in this way
is additive, not multiplicative, and if the error is
taken to be, say, 2%, 0.02 must be multiplied into
the magnitude of the measurement to find u(x).
From the statistical point of view, u(x) is a con-
stant times the standard error. Often the constant
would be about 2, which would make the statement
of the number and its uncertainty consistent with a
95% confidence interval. Ideally, all uncertainties
should be half-confidence intervals or the equiva-
lent, calculated according to statistical theory. How-
ever, those who do not use statistical methods for-
mally may bring some statistical science into their
work by using somewhat informally the approach
presented here.
Some people will tend to be consistently higher
or lower than others in estimating the error. As
long as they interpret the results of this approach
consistently, and other people understand this, no
harm is done.
In reporting numbers in this form, the number of
figures shown in x and u(x) must be large enough
that the range is described finely enough. If too few
figures are used, the description is too coarse; for
example, u(x) = 1.4 represents a 40% wider range
than u(x) = 1, which is the same statement of uncer-
tainty with the last figure rounded. A reasonable
suggestion for presentation in most cases would be 2
to 4 arithmetically correct figures in u(x), not count-
ing leading zeros and the number of figures in x
made to correspond, as in the numerical example
above. There would be no harm in quoting more
except for its awkward appearance.

NEW RULES FOR MANIPULATING UNCERTAIN
NUMBERS
As expressed above, rules for manipulating un-
certain numbers which are sound statistically may
be developed by applying the well-known formula
for the propagation of variance.[51 For its correct
application, the uncertain numbers must be inde-
153

pendent random variables. This is ordinarily true in
the case of measurements. No particular form of
probability distribution is implied.
As applied to sums and differences, the formula is

u(x,X2 ...x)= {[U(x)]2 +[U(,)12+...+[u(x 1)]/2

Thus the uncertainty in a sum or difference of num-
bers is the square root of the sum of the squares of
the uncertainties in the individual numbers.
For products and quotients the rule is: let

y=x, X x2 x... x

Then

u(y) = y( ) + uX2 +... +
X1 X2 8

or equivalently
2+1/2x
y u(y)= y +U(

The relative uncertainty in a product or quotient is
the square root of the sum of the squares of the
relative uncertainties in the individual numbers.
If the uncertainties or relative uncertainties, as
appropriate, in either of these rules is the same for
all quantities being manipulated, the uncertainty or
relative uncertainty in the result is equal to that of
one of them multiplied by the square root of the
number of quantities manipulated.
The general rule for the uncertainty in a general
function f(xl, x2,... Xn), where the x's are uncertain
quantities is given by

U(f) = U(xi)
i=1 i
The formula for the propagation of variance is in
general only approximately true. In effect, it de-
pends on a linearization of the function which is
involved. Hence the formula for the uncertainty in a
sum or difference is strictly correct, but that for a
product or quotient or any nonlinear function is ap-
proximate. The approximation is good, however, as
long as the relative error in the x's is not too large.
Davies and Goldsmith[51 suggest a rule-of-thumb
which implies the generous rule here that u(x) should
not exceed 20% ofx.
It is interesting to note that at least the first two
154

of the above formulas are equivalent to the old rules
for manipulating significant numbers if the error in
one of the x's is large enough that it dominates the
others.
In dealing with mathematical numbers in the
above formulas it is possible to use 5 in the first
figure not shown, or some multiple of it, as the
uncertainty. However it is better, if possible, to ex-
press them to enough significant figures that their
error is negligible compared to those of the other
numbers involved.
USE OF THE APPROACH IN EDUCATION
No background beyond that required for the sig-
nificant numbers convention is needed to use and
understand this approach. It has, however, the di-
dactic advantage that it is consistent with the use of
confidence intervals and their equivalents. It can
therefore fill the gap which now exists with those
educators who recognize the deficiencies of the sig-
nificant numbers convention but have little or noth-
ing to take its place until the student obtains a
background in statistics.
It also has the considerable psychological advan-
tage that it requires the explicit statement of the
uncertainty in a number. Thus, when a student
quotes a number his or her attention is necessarily
focused on the uncertainty in it.

EXAMPLES
The following is a simple example of addition and
subtraction:

(42.63 0.21) (10 0.05) + (14.0 0.3)
= 42.63 -L0 + 14.0 (0.212 +0.052 +0.32)1/2
= (55.63 0.37)
The second example illustrates the use of significant
numbers and perfectly-known numbers along with
multiplication and division. The number 2 is per-
fectly known and requires no consideration in calcu-
lating the uncertainty. The number p is a significant
number and is carried to seven figures so that its
uncertainty has negligible effect.

2n1(10.623 0.500)
129 15
2(3.141593)(10.623) 1+[ 0.500 \2 ( 15 \)21/2
129 [-L10.6231 \129-
= (0.5174 0.0649)

The next example illustrates the use of the for-
mula for a general function.
Chemical Engineering Education

(2.31 0.26) exp(- 31 0.08)
= 2.31 exp(-L 31)

+ {[exp(-131) x 0.26]2 + [-2.31exp(-L31) x 0.08]2 1/2
= (0.6233 0.0861)

Summary of Suggested Approach to Calculating and
Expressing Uncertainty in Decimal Numbers
1. All mathematical numbers such as e, etc., should be
expressed using the significant numbers convention.
2. Enough extra digits should be carried in all arithmetical
calculations that the rounded result would not be
changed if more were carried. This usually requires two
or three extra digits.
3. The significant numbers convention should never be
applied for the purpose of expressing uncertainty in
measurements or the results of calculations on them.
4. Measurements and the results of calculations on them
should be presented by showing the decimal number
plus or minus its uncertainty. The best way to deter-
mine this uncertainty is by statistical treatment of the
data. Many people will, however, use their engineering
or scientific judgement, formally or informally, to
establish it.
5. The uncertainty in the sum or difference of uncertain
numbers is found as the square root of the sum of the
squares of the uncertainties in the individual numbers.
6. The relative uncertainty in the product or quotient of
uncertain numbers is the square root of the sum of the
squares of the relative uncertainties in the individual
numbers.
7. Providing the numbers used in expressing uncertainty
are arithmetically correct, there is no harm except
awkwardness in showing too many figures; if too few
are shown, however, the uncertainty may not be shown
precisely enough. Ordinarily, the uncertainty should be
shown with two to four arithmetically-correct figures,
disregarding leading zeros, and the number itself shown
with a total number of figures to conform with the
uncertainty.

ACKNOWLEDGMENT

The author is pleased to acknowledge the helpful
criticisms and suggestions of Professor Martin E.
Weber of the Department of Chemical Engineering
at McGill University.

REFERENCES

1. Moffat, R.J., "Describing the Uncertainties in Experimental
Results," Exp. Therm. and Fluid Sci., 3-17 (1988)
2. Anderson, T.W., and S.L. Sclove, The Statistical Analysis of
Data, The Scientific Press, 97 (1986)
3. Volk, W., Applied Statistics for Engineers, McGraw-Hill, 77
(1969)
4. Eshbach, O.W., Handbook of Engineering Fundamentals,
John Wiley & Sons, 2 (1936)
5. Davies, O.L., and P.L. Goldsmith, Statistical Methods in
Research and Production, Longman, 54 (1977) ri
Summer 1992

REVIEW: Plant Design
Continued from page 119.

Some of these have been developed from previous
AIChE Student Contest Design problems. They
provide the instructor with a good source of fairly
complex class assignments that he or she can then
build upon. The student may be able to use these as
practice problems in order to prepare for a design
contest problem.
Although this book is as complete a design text as
is possible in a single volume, it is intended to supple-
ment coursework rather than take its place. This
leaves each design instructor many opportunities to
embellish the material and give his or her design
course its own distinct flavor and personality. What
this text does not do (and does not claim to do) is
emphasize the importance of choice in design: the
alternatives involved in defining the problem, good
and bad design choices and how to tell the difference
between them, and process integration alternatives
and how to evaluate them. Design problems in the
less traditional areas of chemical engineering,
such as bioseparations, polymers, pharmaceuticals,
or food, could be presented in order to give the
student a realistic idea of the variety, complexity,
and inherent similarity of design issues in chemical
engineering practice. The text does not stress the
importance of thermodynamic principles in good
process design and with the exception of the
HAZOP study, neglects the importance of the prin-
ciples of process control. The instructor must take
over where the book stops.
Plant Design and Economics, in its fourth edition,
ntinues to provide a comprehensive source of
.sign principles and information that could be
,!use to both students and professionals. As a text,
it includes a wide variety of instructive problems,
both solved and unsolved, and many charts, logic
flowsheets, and worksheets which aid the student
in setting up and solving a design problem. The
text is lucid and readable. It serves as an excellent
aid to teaching a one- or two-term design se-
quence as well as a handy reference of up-to-date
information on regulations and cost. This would
be a good text for someone who does not already
possess the third edition. We would recommend
this text to an owner of the third edition because of
the updated and expanded material. We would be
happier still if an updated bibliography were in-
cluded and dual units were incorporated in a future
printing. This text remains an excellent buy in terms
of value for money. 0

I laboratory

ADD SOME FLAVOR

TO YOUR AGITATION EXPERIMENT

M. ELIZABETH SENSEL, KEVIN J. MYERS
University ofDayton
Dayton, OH45469-0246
Macias-Machin, Zhang, and Levenspiel[E1 re-
cently proposed the unstructured research
experiment as an effective means of im-
proving chemical engineering laboratory courses. This
type of experiment has great flexibility from year to
year, and it also forces students to be more indepen-
dent in developing a solution to the problem that is
presented to them. We have used this approach in
our unit operations laboratory, including the melt-
ing-ice heat transfer experiment discussed by Macias-
Machin and coworkers, and we would encourage other
departments to also make use of this type of labora-
tory assignment.
This paper describes one experiment that was
developed by students to determine the interphase
mass transfer coefficient for a solid dissolving into
an agitated liquid. The problem was presented to
the students in very general terms, and they were
required to search the literature to become familiar
with the problem, to develop a realistic mathemati-
cal model to describe the dissolution process, and to

M. Elizabeth Sensel received her bachelor of
chemical engineering degree in 1991 and is cur-
rently studying agitation in gas-liquid systems for
her master of science in chemical engineering
degree (both at the University of Dayton). While
she was an undergraduate student, she held a
I cooperative education position with the Depart-
ment of Energy's Mound Laboratory.

Kevin J. Myers is an associate professor in the
Department of Chemical and Materials Engineer-
ing at the University of Dayton. He received his
Bachelor of chemical engineering degree from
the University of Dayton and his doctor of science '
in chemical engineering degree from Washington
University. His research interests are in the field
of multiphase agitation and chemical reactors.

develop a simple experimental technique to deter-
mine the mass transfer coefficient. Due to the suc-
cess that we experienced with this experiment, we
suggest that it be considered as a means of providing
flexibility for agitation experiments.
MATHEMATICAL MODEL
Badik and Servais[2] have demonstrated the value
of a mathematical model for the interpretation of an
experiment, and its usefulness is particularly impor-
tant for an unstructured research experiment. Al-
though the mathematical model and experimental
procedure are developed simultaneously in practice,
the mathematical model of solids dissolution will be
presented before the experimental procedure and
results. Briefly, the experimental method consists of
adding a number of solid particles of known mass to
the agitated liquid, removing the particles from the
liquid after a specified time, and then determining
the remaining mass of the particles. Thus, the math-
ematical model of the dissolution process must re-
late the mass of solid remaining in the solid phase
(the experimental data) to time and the interphase
mass transfer coefficient (the unknown parameter).
Examination of the agitation literature indicates
that the rate of mass transfer between a solid and an
agitated liquid is usually described by the following
relation (Nienow[31):
m=kLA (CSAT-C (1)
The experiment is conducted on a batch system,
with the result that a transient mass balance on the
dissolving solid takes the form
dM = -kA (CAT CL) (2)
dtSAT
while the corresponding mass balance on the liquid
phase is

O Copyright ChE Division ofASEE 1992

Chemical Engineering Education

dC
VL T = ln = kLsA (CSAT L) (3)
L dt A(CSAT-C) (3)
These model equations are coupled through the
liquid concentration term and must be solved simul-
taneously. The solution procedure can be simplified
by noting that the total amount of solid distributed
between the solid and liquid phases is constant at its
initial value.

Mo +VL CLo =M+V CL (4)
This equation can be combined with Eq. (2), which
can then be solved to yield the model predictions.
However, as the solids dissolve, they change their
size and shape, and the resulting changes in the
interfacial area must be taken into account before
the model equations can be solved. Any effect of
changing particle size on the interphase mass trans-
fer coefficient will be ignored in this analysis.
The particles studied in the experiment are ini-
tially spherical and are assumed to retain their
spherical shape as they dissolve. The solid particles
are also of the same initial size, and it will be as-
sumed that all of the particles dissolve at the same
rate. Under these assumptions, the mass of solid
remaining in the solid phase at any time for a sys-
tem of n particles with radius r is

M=4 r3 p n (5)

and the corresponding interfacial area is

A = 4 r2 n (6)
Substitution of Eqs. (4), (5), and (6) into Eq. (2)
yields the form of the model equation that can be
solved for the mass of solid remaining in the solid
phase at any time,

k = 2.5E-6 m/s

k LS = 5.0 E-6 mis

k15= 7.5 E6 -

... [the students] were required to search
the literature to become familiar with the
problem, to develop a realistic mathematical
model to describe the dissolution process, and to
develop a simple experimental technique to
determine the mass transfer coefficient.

1
dM_ k (36 n nM2 (3()) (7)
dP. -LSAT L VL

This equation can be solved numerically, but an
analytical solution is possible if the liquid-phase con-
centration is always much less than the saturation
concentration (CL << CSAT) which was the case for
the experimental results reported here. Under these
conditions, Eq. (7) can be integrated to yield the
following relation between time and the fraction of
solid remaining in the solid phase

M. IC 3 MopS ]

Figure 1 presents plots of the fraction of solid
remaining in the solid phase as a function of time for
typical experimental parameters and the range of
interphase mass transfer coefficients observed dur-
ing this study. Comparison of these model predic-
tions with experimental data yields the magnitude
of the interphase mass transfer coefficient for any
experimental run.

EXPERIMENTAL PROCEDURE AND RESULTS
The experimental procedure is based on the work
of Boon-Long, et al., [4 who studied the dissolution of
benzoic acid particles into water. After initial con-
sideration of working with benzoic acid, we decided
that there must be a better solid for use in an under-
graduate laboratory. The solid that was selected from
a number of possibilities was sourball candy, a mix-
ture of sugar, citric acid, and color additives. This
material is inexpensive and safe, and its high solu-
bility allows a number of successive experimental
runs to be made with a single liquid batch.
As described during the model development, the
experimental procedure is to add a number of par-
ticles of known weight to the agitated liquid and to
remove, lightly dry, and weigh the particles after
they have dissolved for a specified time. This tech-
nique yields an integral interphase mass transfer

Summer 1992

0
a0
Z

W"
0

0 s

0 50 100 150 20 250
TIME (S)
Figure 1. Model predictions for typical experimental
conditions

!

coefficient that is representative of the entire experi-
mental run.

Since the particle size changes during the experi-
ment, the mass transfer coefficient might also change.
To check this, experiments were performed to deter-
mine if a single value of the interphase mass trans-
fer coefficient describes the entire course of an ex-
periment. These results are presented in Figure 2,
and it can be seen that the model predictions with a
constant value of the interphase mass transfer coef-
ficient accurately describe the experimental data.
For the remaining experiments, only a single data
point was taken (usually after five minutes of disso-
lution), and it was assumed that the calculated in-
terphase mass transfer coefficient was representa-
tive of the entire experiment.

Two impeller types were studied: a four-bladed
450 pitched-blade impeller and a three-bladed high-
efficiency impeller. The dependence of the interphase
mass transfer coefficient on the agitation speed for
these impellers is shown in Figure 3. All results
were obtained using 0.178-meter diameter impellers
in a 0.445-meter diameter tank with a liquid level
equal to the tank diameter, an impeller off-bottom
clearance of one-fourth of the tank diameter, and
standard baffles.

The results of Figure 3 indicate that the inter-
phase mass transfer coefficient is not strongly af-
fected by operating conditions as has been discussed
by Nienow.[3] The magnitude of the interphase mass
transfer coefficients found in this study are some-
what lower than those reported in the literature, but
this can be attributed to the fact that the sourball
candy used in this study is considerably larger than
the solids used in other investigations (Miller[51).

The results presented in Figure 3 appear to indi-
cate that the pitched-blade impeller performs better
than the high-efficiency impeller, yielding similar
interphase mass transfer coefficients at lower speeds.
However, the pitched-blade impeller draws about
four times as much power as the high-efficiency im-
peller at the same operating conditions.

A proper comparison results when the interphase
mass transfer coefficient is considered as a function
of the power input per unit liquid volume, as shown
in Figure 4. This comparison indicates that the high-
efficiency impeller yields interphase mass transfer
coefficients that are about five percent higher than
those of the pitched-blade impeller at equal power
inputs. This small difference is near the limit of
accuracy of the experiments, and the performance of

~---~--A

MODEL PREDICTION (k LS = 5.5 E-6 m/s)

--\

*- EXPERIMENTAL DATA

0 60 120 180 240 300 360 420
TIME (S)

Figure 2. Comparison of the model prediction and
experimental data over the course of an experiment

0

* HIGH EFFICIENCY

0 PrTCHED-BLADE

0 L_____________Lr I
150 175 200 225 250 275 300 325 350
AGITATION SPEED (RPM)

Figure 3. Experimental results for pitched-blade and
high-efficiency impellers

, I''

*HIGH EFFICIENCY

O PITCHED-BLADE

0.02 0.04 0.06 0.08 0,10 0.12
POWER INPUT PER UNIT VOLUME (kW/M-3)

0.14 0.16

Figure 4. Comparison of impeller performance on an
equal power-per-volume basis

Chemical Engineering Education

. . . . I I I I I II' ' ' -l'' l'

, L I I I

the two impellers is essentially equal. The data of
Figure 4 indicates that the interphase mass transfer
coefficient increases with the power input to the one-
fourth power, which is consistent with the data dis-
cussed by Nienow.131

CONCLUSIONS
We have found that the study of sourball candy
dissolution can spice up an agitation experiment.
The technique is safe, inexpensive, rapid, and is
capable of yielding meaningful results. The interpre-
tation of the experiment requires the students to
develop a mathematical model of the dissolution pro-
cess which adds to the instructional appeal of the
experiment. Although the experimental technique
was developed as an unstructured research experi-
ment, it is also possible to supply the students with
the technique and instruct them to use it to solve
other problems, such as making a sugar solution
(make up a good assignment story), comparing the
performance of various impellers, determining the
effect of vigorous agitation on liquid-solid mass trans-
fer, and comparing the data with reported values in
the literature.

ACKNOWLEDGMENTS
The assistance of Bonnie Struble and Russ Logue
in developing this experimental technique is grate-
fully acknowledged.
NOMENCLATURE
A total liquid-solid interfacial area at any time (m2)
CL liquid-phase concentration of the solute (kg/m3)
CSA equilibrium liquid-phase concentration of the
solute (kg/m3)
km liquid-solid interphase mass transfer coefficient
(m/s)
M total mass of solute remaining in the solid phase
at any time (kg)
m rate of interphase mass transfer of the solute from
the solid phase to the liquid phase (kg/s)
n number of solid particles used in an experiment (-)
r radius of the solid particles at any time (m)
t time (s)
VL liquid volume (m3)
p, solid density (kg/m3)
o subscript indicating initial conditions
REFERENCES
1. Macias-Machin, A., G. Zhang, and 0. Levenspiel, "The Un-
structured Student-Designed Type of Laboratory Experi-
ment," Chem. Eng. Ed., 24(2), p 78 (1990)
2. Badik, C.S., and R.A. Servais, "Experiences with Revamp-
ing an Introductory Engineering Laboratory Including Data
Systems and Modeling," Proc. 1991 ASEE North Cent. Sect.
Conf., p 265 (April, 1991)
Summer 1992

3. Nienow, A.W., "The Mixer as a Reactor: Liquid/Solid Sys-
tems," Chapter 18 of Mixing in the Process Industries, ed-
ited by N. Harnby, M.F. Edwards, and A.W. Nienow,
Butterworths, London (1985)
4. Boon-Long, S., C. Laguerie, and J.P. Couderc, "Mass Trans-
fer from Suspended Solids to a Liquid in Agitated Vessels,"
Chem. Eng. Sci., 33, p. 813 (1978)
5. Miller, D.N., "Scale-Up of Agitated Vessels: Mass Transfer
from Suspended Solute Particles," Indus. Eng. Chem. Proc.
Des. and Dev., 10(3), p 365 (1971) C

EDUCATOR: Wankat
Continued from page 123.
strong emphasis on counseling. He felt he could put
his counseling experience to good use by dealing
with students who were at a critical stage in their
careers. He feels that the vast majority of students
who enter the freshman engineering program have
the ability to graduate and become successful engi-
neers, but that the lack of motivation is a problem
for some of them. Phil rejects the "sink or swim"
idea-that the best students will rise to the top
while the others sink. Rejecting the notion of teach-
ing only the intellectually elite, he believes that the
"purpose of a university is to nurture students' learn-
ing and to help them get past barriers." That is the
goal of the freshman engineering program.
PERSONAL
Phil has won numerous awards, among them
ASEE's Western Electric Award (1984), George
Westinghouse Award (1984), and Chester F. Carlson
Award (1990). In 1991 he was named a Fellow of
ASEE. He has also held several divisional offices,
including Chairman of the ChE Division of ASEE.
Phil and Dot have two children: Charles (7) and
Jennifer (4)-both of whom, alone or in tandem,
provide him with all of the exercise he needs. When
he feels contemplative, or simply in need of quiet
moments, he likes to head to a favorite fishing spot;
fishing is his Zen meditation. When it is possible, he
likes to go canoe camping (especially in the Quetico-
Superior area) and (hopefully) catch fish every day.
A Chicago-area native, Phil has never outgrown
his addiction for the Bulls, the Bears, and the Cubs.
For him, 1991 was "Bull Heaven." And finally, what
surely labels him as an eternal optimist, he still
believes the Cubs will win it all next year.
Phil Wankat is a busy man: teacher, researcher,
counselor, author, editor, administrator. "Just do it.
. but care!" would be a good slogan for him. His
career exemplifies what many others strive for-a
blend of excellence in both research and teaching. O

curriculum

MOLECULAR ENRICHMENT OF THE

CORE CURRICULUM

HENRY A. MCGEE, JR.
National Science Foundation*
Washington, DC 20550
he core courses of chemical engineering are
properly taught from the viewpoint of con-
tinuum physics. Thermodynamics, transport
phenomena, and reaction engineering, as they are
now presented to students, would be unchanged
whether molecules exist or not. This is a strength in
that one need never worry about underlying struc-
ture or mechanism. But it is also a weakness, for
so much of practice in chemical engineering, in
the thermal fluid sciences part of mechanical engi-
neering, in materials science and engineering, and
in aerothermochemistry rests directly upon molecu-
lar insights. It is truly molecular engineering. With-
out a molecular perspective to complement their
continuum perspective, our young graduates will
be ill-equipped to be full participants in modern
engineering practice.
Building on the courses in physical chemistry, we
can enrich our continuum-based core courses in
chemical engineering by having students study an
auxiliary textbook that discusses the same phenom-
ena and processes, but from a molecular point of
view. The molecular discussion can be read at the
same time that they read any of our good continuum-
based textbooks.
The needed enrichment must not delve into the
exotica of quantum and statistical mechanics that is
of interest only to the specialist, however; it must

Henry McGee was trained in chemical engi-
neering and in theoretical chemistry at Georgia
STech and the University of Wisconsin, and his
subsequent teaching and research reflect this
SS *7' continued dual interest. His research has cen-
tered upon chemical reaction and processing
under extreme or unusual conditions. While in
Washington, he has been conceded mainly with
science policy matters and with priorities in the
support of research.

* On leave from the Chemical Engineering Department at Vir-
ginia Polytechnic Institute and State University, Blacksburg,
VA 24061-0211
160

engage students and faculty alike at their existing
level of understanding. Molecular understanding and
practical examples must be compelling and memo-
rable to the engineering student rather than elegant
to the theoretical chemist.[13 The molecular perspec-
tive on thermodynamics, on transport, and on chemi-
cal kinetics may thereby be merged into the four or
five semesters now required for the core.
DEFINITIONS AND EXAMPLES
Molecular engineering encompasses those prob-
lems wherein a molecular perspective (whether it be
computational or merely phenomenological) is an
essential part of any optimum design. A number of
illustrative examples follow.
Chiral synthesis and separation is an essential
part of many problems involving pharmaceuticals,
manufactured foodstuffs, agrochemicals, flavors, and
fragrances. Chirality can be critical in drug manu-
facture. For example, one isomer of thalidomide
(shown below) is a useful sedative while the other is
a potent teratogen that caused thousands of birth
defects three decades ago.
H H

o0 0
0 0

Sedative

Teratogen

How is a stereoselective catalyst designed, or how
does one think about separation of chiral molecules?
To be sure, Pasteur first separated crystals ofd and 1
tartaric acid by using a pair of tweezers and a micro-
scope, for the salts of the two isomers have macro-
scopically recognizable differences in crystal
morphology. But more usually one thinks about spe-
cific completing agents that geometrically fit the
one molecule but not the other. Such catalyst and
separation designs are exercises in molecular
recognition. Designs frequently depend upon
either ab initio or semi-empirical quantum mechani-
Copyright ChE Division ofASEE 1992
Chemical Engineering Education

cal techniques to calculate structures and energies
of candidate host-molecules.
Although only well developed for separating ura-
nium isotopes, the best procedure for any isotope
separation seems to be the atomic vapor laser iso-
tope separation (AVLIS) scheme. Here one recog-
nizes small differences in the ionization energy of
each isotope and uses a fixed energy input from a
properly tuned laser to ionize the one desired iso-
tope, while producing no effect at all on the other
isotope. To produce reactor-grade enriched uranium,
one produces a low pressure vapor of natural ura-
nium and irradiates this vapor with laser-photons
selected to have energy sufficient to ionize 235U that
is present to 0.3 percent, but the 99.7 percent which
is 238U is transparent to these photons. The laser-
photons function as somewhat of a Maxwell's De-
mon. A negatively biased plate attracts and collects
the ions. This laser process has been pilot-planted,
and although still somewhat debatable, data sug-
gest that both installed and operating costs of the
laser plant will be an order of magnitude below such
costs for conventional gaseous diffusion technology.
This process would not have occurred to chemical
engineers unschooled in molecular thinking, and as
a matter of fact, this process was largely conceived
and developed by physicists and physical chemists.
It is disappointing to admit that researchers and
designers other than chemical engineers have pro-
duced attractive solutions to problems in separa-
tions on a practical scale. In a sense, chemical engi-
neers have here been beaten at their own business
due to a lack of molecular insight.
The physical and chemical properties of clusters
depend on the size and arrangement of the atoms
forming the cluster. Even the color of cadmium-sele-
nium particles can be red, orange, green, or black
due to slightly different particle sizes. Red Cd/Se is 5
nm across and has about 3000 atoms, while orange
Cd/Se is 3.5 nm across and has about 1000 atoms.
Such clusters are not molecules nor are they bulk
metal, but rather they are a new class of materials.
They may be effective catalysts, and materials made
from clusters may have superior properties. The mo-
lecular view suggests that a large fraction of the
constituent atoms are on or near the surface. Also
the conduction electrons are confined to a space only
a few atoms across, producing a quantum size effect
responsible for the colors of Cd/Se and other proper-
ties. Ionic Nb19 exists in two forms, jokingly called
"chocolate" and "vanilla," wherein the one is
highly reactive with hydrogen while the other is
unreactive. Presumably, this striking chemical
Summer 1992

Building on the courses in physical chemistry,
we can enrich our continuum-based core courses
... by having students study an auxiliary
textbook that discusses the same phenomena and
processes, but from a molecular point of view.

difference is due to the arrangement of the nine-
teen atoms of the cluster. The understanding and
application of clusters is impossible outside of the
molecular perspective.
Suppose we are interested in the specific impulse
that might be obtained from an electrothermal arc-
jet thrustor using H2 as the propellant. At plasma-
temperatures, we need the thermodynamic proper-
ties of H, H2, H+, and e, for it is necessary to calcu-
late the difference in enthalpy of the expanding gas
between the combustion chamber and the exit plane
of the nozzle if we are to estimate the thrust. There
is no way to measure the heat capacity or entropy of
atomic hydrogen or of protons. Rather, we calculate
all of the properties using the techniques of molecu-
lar physics. With values for all of the properties, we
can calculate the equilibrium extent of reaction of
H2 t42H
H t4 H+ +e
and then the specific enthalpy of the reacting and
expanding gas in the nozzle as a function of tem-
perature and pressure. From this, the expected thrust
levels for any particular motor design can be de-
duced. One believes the calculated values of thermo-
dynamic properties in regions not experimentally
accessible because in all instances where such com-
parisons between theory and experiment are pos-
sible, agreement is excellent. Without molecular in-
sight, such rational rocket motor design would be
impossible.
One of the best ways to grow diamond films is by
chemical vapor deposition (CVD). In the high-energy
environment of a low-pressure plasma, a large vari-
ety of reactive chemical species can exist, and each
may play a significant role in the formation and
quality of the resulting diamond film. With a feed-
gas stream ofH2 and CH4, reactive species including
CH, C2, C3, C2H2, and C2H are evident. Different
electronic and vibrational states are also evident,
and these may not be in equilibrium with the trans-
lation/rotation heat bath. How does the concentra-
tion of species vary in time and place in the CVD
reactor, or with temperature, or with pressure, or
with feed-gas composition? How do you even think

about the temperature of such a reacting gas
mixture in the presence of an electric field? Such a
CVD gas mixture may not be at equilibrium at all,
but rather the concentration of the various species
may be kinetically determined. All such questions
must be addressed from the point of view of molecu-
lar engineering, and the optimum design of CVD
reactors for diamond deposition depends upon these
molecular insights.
Such a listing of examples of molecular engin-
eering could continue, but these few suggest the
central importance of molecular insight in engineer-
ing design.
INNOVATION VS. DESIGN
The manufacturing ability of the United States is
being challenged by worthy competitors, particularly
in Germany and Japan. The NSF and the entire
federal research and development establishment is
developing a major initiative designed to help en-
sure that American industry maintains its interna-
tional competitiveness. Terms such as "agile manu-
facturing," or "21st Century manufacturing," or "en-
vironmentally benign manufacturing" are seen with
regularity. Creative innovation and design are cen-
tral to success in competitive manufacturing.
Whether one is substituting an alternative reaction
chemistry or optimizing a separation and heat ex-
change network, there is creative opportunity.
Molecular engineering addresses questions of in-
novation by stimulating the engineer to think about,
say, an alternative separation based on some newly
synthesized zeolite with heretofore unavailable pore-
size. After the innovation, process design allows its
optimization. Both are important-but the senior
design class in chemical engineering usually concen-
trates on process design alone (which has become
very logical and analytical).
Computerized design methodologies are a triumph
of modern chemical engineering. But in contrast,
molecular engineering gives the student more
opportunity to be imaginative. It gives the chem-
ical engineer an opportunity not unlike that afforded
to an architect who imagines the form of a building
and then performs structural design calculations
(just as in the chemical engineer's process design) to
judge whether that imaginative design is economi-
cally buildable.
Modeling and tools such as ASPEN are important
and powerful components of the curriculum. But
they will never invent AVLIS or a stereoselective
separation or a nanoparticle manufacturing scheme.
After the innovation has occurred, conventional teach-

ing allows the practitioner to pursue the important,
but subsequent, tasks of simulation, modeling, opti-
mization, and control. That initial innovation, how-
ever, is the point where molecular insight is so im-
portant. It is not a panacea, and it is not a sufficient
condition for innovation. But it does broaden one's
scope and opportunities.
Some curricula require a year of physical chemis-
try where some insights into partition functions,
energy levels, kinetic theory, and molecular dynam-
ics is learned. However, ABET requires only one
semester of physical chemistry (which is largely clas-
sical thermodynamics in most courses). Whether
the study of molecular physics in physical chemistry
is required or elective, it is to be applauded-but
it remains a subject apart from the mainstream
(like technical writing, or the German language) and
the student never integrates modern molecular
physics into his or her engineering Weltanschauung
(philosophical world-view). That now-missing in-
tegration is the goal of molecular enrichment of
the core curriculum.
SOLUTION
Teaching and learning molecular engineering, like
other subjects in the core curriculum, are not diffi-
cult if the sophisticated research-oriented aspects of
the subject are abandoned. For example, starting
with a thought experiment with a collection of a
half-dozen, labeled molecules, one immediately visu-
alizes the most probable distribution of molecules
among energy levels, with the distribution driven to
its most probably state by no other mechanism than
simple chance.11] Then, with the same Lagrangian
technique of undetermined multipliers learned in
calculus or in thermodynamics when calculating re-
action equilibria, the student immediately derives
the Boltzmann distribution; he/she gains immediate
insight into why so many macroscopic phenomena
(equilibrium constant, rate coefficient, vapor pres-
sure, etc.) depend on exp(-energy/RT).
Molecular insight also provides a powerful peda-
gogical tool in that it enables linkage between other-
wise (seemingly) disparate macroscopic phenomena
and processes. For example, it can be seen that the
same intermolecular collision frequency that gov-
erns the chemical reaction rate also governs thermal
conductivity. As a pedagogical tool, molecular engi-
neering is compelling, provided only that sophisti-
cated molecular physics is avoided.
Similarly, single particle partition functions are
easy to understand as compared to ensemble ideas.
To be sure, there are troubling consequences when
Chemical Engineering Education

real gases are studied, but sensible treatment is
possible and nothing has to be unlearned by those
very few students who later will wish to become
expert in statistical thermodynamics.
The Maxwell-Boltzmann distribution of molecu-
lar speeds is easily obtained from the most probable
distribution of energy, which itself was easily ob-
tained (as we saw) from simple thought-experiments
with a few labeled molecules. With the MB distribu-
tion, all the concepts of kinetic theory of average
speed, mean free path, and collision frequency may
be immediately shown. Similarly, and of more inter-
est to students, each of the transport properties can
be calculated and collision theories of chemical ki-
netics can be developed.[11 Compelling comparisons
of all such theories with experiment make it real
and believable to the students. With this kinetic
theory, it is natural to realize that chemical reaction
does not occur in one step as we typically write an
overall stoichiometric change, e.g.,
H2 + Br2 -- 2 HBr
Rather, reaction occurs by a complex array of usu-
ally bimolecular encounters which together constitute
the reaction mechanism, which for the hydrogen/
bromine flame is

Br2 -+ 2 Br
Br+H2 -- HBr+H
H+Br2 HBr+Br
S+ H Br-H H2 +Br
Br + Br Br2

The rate of each of these molecular events of the
mechanism depends on its particular reactant colli-
sion frequency, the relative energy involved in the
collision, the energy states of each colliding reac-
tant, and the relative geometry of the colliding reac-
tants at the moment of impact. Reaction occurs only
in collisions that occur with an above-some-mini-
mum threshold energy, and even then only in colli-
sions that occur with certain geometric orientation.
Finally, the macroscopic (or observed) rate of the
overall stoichiometric change is some sort of a com-
plex average of these many different microscopic
events. And, under a variety of assumptions, this
averaging can be calculated, and comparisons with
experiment may be made.
It is pedagogically essential to present numerous
comparisons with experiment and to present many
case studies and practice problems to inspire and
provide exercise for the students in their develop-
ment of new skills.[11
Summer 1992

CONCLUSION
You may invent a laser-based process for isotope
separation, or be concerned with fundamental prob-
lems in combustion leading to greater fuel efficien-
cies and less pollution, or be concerned with ion
implantation for the development of new alloys of
new and unusually doped materials of interest in
electronics, or require some property of matter that
may be unknown or unmeasurable. From whatever
perspective, however, a molecular view is essential,
and a purely traditional or classical perspective un-
acceptably slows invention, hinders creativity, and
frustrates original design.
This enrichment of the chemical engineering core
curriculum will have served its purpose if its atti-
tudes can be internalized. That is, long after the
student has forgotten just exactly how this or that
particular argument or calculation goes, he or she
will nonetheless instinctively think about any prob-
lem in terms of what the molecules must be doing.
That is the real, bottom-line goal of molecular en-
richment of our core curriculum.
ACKNOWLEDGMENTS
The author gratefully acknowledges helpful criti-
cism by the referees of this paper.
REFERENCES
1. McGee H.A., Jr., Molecular Engineering, McGraw-Hill, New
York (1991) 0

OXYGEN MASS TRANSFER
Continued from page 145.
cal engineering principles in undergraduate labora-
tories.

ACKNOWLEDGMENTS
This work was partially supported by Grant DTD
910418, U.S. Agency for International Development,
Pakistan Participant Training Program, and the
Georgia Tech Foundation. The authors are very ap-
preciative of the assistance of Brenda Chand, Harolyn
Ingram, Susan Elliot, and William Ernst.

REFERENCES
1. Van't Riet, K, "Mass Transfer in Fermentation," Trends in
Biotechnology, 1(4) 113 (1983)
2. Ruston, J.H., E.W. Costich, and H.J. Everett, "Power Char-
acteristics of Mixing Impellers," Part 2, Chem. Eng. Prog.,
46, 467 (1950)
3. Bailey, James, and David Ollis, Biochemical Engineering
Fundamentals, 2nd Edition, McGraw-Hill Book Company
4. Lee, S.S., F.M. Robinson, and H.Y. Yang, "Rapid Determi-
nation of Yeast Viability," Biotechnol. and Bioeng., Symp.
No. 11, 641 (1981) 0

classroom

DESIGN OF CSTRs IN TANDEM

REVISITED

A. A. ADESINA
University of New South Wales
Kensington, NSW, Australia 2033

since the days ofDenbigh,'1] the optimal design
of chemical reactors has held a place of pride
in the chemical engineering profession. Aris'
unparalleled monograph[2] laid a solid mathema-
tical foundation for the treatment of this subject,
and application of dynamic programming tech-
niques in the determination of optimal interstate
conversions and reactor sizes was painstakingly
expounded. Chen[31 also utilized Pontryagin's maxi-
mum principle to solve this problem, while the
two-part serial papers by Chitra and Govind[41 offer
considerable insight into situations involving com-
plex reaction networks.
Chemical reaction engineering is usually taught
in the penultimate year of a four-year bachelor
(honours) program. Unfortunately, third-year stu-
dents, partly because of their limited exposure to
mathematics, are loathe to accept analytical meth-
ods as a substitute for a graphical procedure involv-
ing the maximization of rectangles (described in the
texts by Levenspiel[5] and Fogler[61). For instance,
until recently at the University of New South Wales,
introductory concepts in dynamic programming were
not encountered until the process optimization course
in the last year of the undergraduate curriculum.
Additionally, Levenspiel's approach has important
pedagogical appeal for the lecturer. Therefore, the
analytical techniques must be reserved for a more
advanced course in reaction engineering where the
students (such as those in the postgraduate pro-
gram) will then be able to savor the taste of these
mathematical treats.

Adesoji A. Adesina is a chemical engineering
faculty member at the University of New South
Wales, Australia. He obtained his BSc from the
University of Lagos (Nigeria) and his Masters
and PhD from the University of Waterloo
S(Canada). His primary research activities are in
Z catalysis and reactor design theory.

However, there is a compelling drive (especially
with the infiltration of computers into chemical
engineering) to let the students know that it may
sometimes be possible to dispense with a trial-and-
error design procedure and employ an appropriate
sequential technique that utilizes only the math-
ematical methods with which they are familiar (the
principle of vertical and lateral organization in a
curriculum-development model). The design proce-
dure suggested here assumes that the undergradu-
ate student has taken (or is currently taking) courses
in elementary calculus, vectors and matrices, and
introductory programming techniques. All of these
requirements are easily met by the average third-
year chemical engineering student at the University
of New South Wales.
DESIGN METHODOLOGY
Consider a train of N CSTRs whose inlet and
exit conversions (with respect to reactant A) are
Xo and XN respectively. The design problem is
to find the (N-l) intermediate optimal conversions,
X, X2 . XN-1 which will minimize the overall
reactor size. Following Levenspiel,[51 the optimal
selection of the conversion, Xi, (in the ith tank) on the
l/(-rA) vs X plot is such that the diagonal of the
rectangle must possess the same slope as the tan-
gent to the curve at the point Xi. Thus for the
1st reactor

f(X2)-f(X) df(X)
X1-Xo dX (1
where f(X) = 1/(-rA) and 1 means "evaluated at X."
Rearranging, we have

W1 = f(X2)- f(XJ)-(X1 XO) 0 (X)= O

(2a)

In general, for the ith reactor, we obtain
jit reactor
Wi =f(X,+1)-f(Xi)-(Xi-X ,_l) (Xi)=o (2b)

Copyright ChE Division ofASEE 1992
Chemical Engineering Education

(N-l)' reactor

wN- =f(XN)-f(XN-)-(XN1 -XN-2) D (XN)= 0 (2c)

The simultaneous solution of these equations

yields the unknowns X,, X2, . XN, whence the

optimal size (V/FA0)i for the ith reactor is

(V/FA )i=(Xi-Xi_)f(Xi) i=1,2,...N (3)

and D(X) = df(X)/dX.

Using the Newton-Raphson method for solving

the nonlinear system described by Eqs. (2), we find

(m) =x(m -X(m-1 __J- l(x(m-1))w((m-1)) m=t2,... (4)

where Xm) is the column vector of conversions at the

mth iteration and is written

X(m)=X[m) X(m) ...X(m) (5)
m T1 2 N-1 )

with X(o) being the guessed initial conversion vector

and the Jacobian matrix at the (m-l)th iteration,

J(X(m-1)) has dimension (N-l) x (N-l). Because Eq. (4)

has quadratic convergent property, the true solution

is obtained after very few iterations. An effective

TABLE 1

Computer Program

c This program calculates the optimal conversion in each tank
c in a train of isothermal cstr's
c The program was executed on an IBM compatible 386 machine
c using WATFOR77 compiler

c ********************SOME HELPFUL HINTS************ ******

C
c Reaction example: r kl*CA k2*CR (1st order reversible rxn)
c
c Declaring program variables
c
c The dimension of the variables should be at least, ntanks + 2
c where ntanks = number of tanks in the train
c
c
real xinit(22), a(22), c(22), d(22), x(22), w(22)
c
c
c The rate here is, r caO [kl*(l-xx)-k2*xx]
c
c Note that this program can handle any form of rate expression
c no matter how complex provided it is twice differentiable.
c Fortunately, this is always the case even for complex
c Langmuir-Hinshelwood and Michelis-Menten type kinetics.
c
c Defining the statement functions for the rate expression, its
c reciprocal and the first two derivatives w.r.t conversion, xx
c
c ***************************************************************
c
rate(xx)=ca0*(constl*(l.0-xx)-const2*xx)
rateinv(xx)l=.0/rate(xx)
der(xx)=(constl+const2)/(caO*(constl*(1.0-xx)-const2*xx)**2.0)
dder(xx)=2.0*(constl+const2)**2.0/(caO*(constl*(l.0-xx)-const2*xx
*)**3.0)
c
c open the input and output data files
c input data file = cstr.dat
c output data file = cstr.res
c
c
open(unit=l, file= 'cstr.dat')
open(unit=2. file= 'cstr.res')
read (1, *) ntanks, (xinit(i),i=2,ntanks),constl, const2, xO
*xf, caO, tol
c
write(2, 100) ntanks, caO
100 format(//,10x,'RESULTS OF THE REACTOR TRAIN DESIGN',//,15x,
*'number of tanks = ',i4,//,15x,'concentration of reactant, A. ir
*feed = ',f6.2,lx,'mol./lit')
c
n-ntanks-1
xinit(l)=x0
xinit(ntanks+l)=xf
c kounta is the iteration counter until tolerance limit is met
kounta=0
10 continue
kounta=kounta+l
c calculating elements of the principal diagonal, d(i);
c the lower diagonal elements, a(i),
c the upper diagonal elements, c(i) and
c the vector, w(i)

do 20 i=l,n
d(i)-(xinit(i) xinit(i+l))*dder(xinit(i+l))-2.0*der(xinit(i+l))
w(i)=ratinv(xinit(i+2))-ratinv(xinit(i+1))-(xinit(i+l)-xinit(i))*
*der(xinit(i+l))
20 continue
nn=n-1
do 30 j=l,nn
a(j)=der(xinit(j+l))
c(j)=der(xinit(j+2))

30 continue
call soln(n,a,d,c,w,x)
sum = 0.0
do 40 i=l,n
sum=sum+(abs(x(i)))**2.0
40 continue
c
c reinitialising the interstate conversions
c
do 50 j=l,n
xinit(j+l)=xinit(j+l)-x(3)
50 continue
c
c determining the average percentage conversion difference, apcd,
c in successive iterations
apcd=sqrt(sum/float(n))
if(apcd .gt. tol) go to 10
continue
write(2, 300)
300 format(//,5x,'final results satisfying tolerance limit',//,
*5x,'conversion in reactor train')
write(2, 400) (xinit(i), i=2,ntanks), xO, xf, kounta
400 format(//, 5(10x,el2.4/),//,10x,'inlet conversion = ',e12.4
*//,10x,'train exit conversion = ',e12.4,//,10x,
*'required number of iterations to achieve tolerance = ',i5,//,
*/////////,5x,'EXHIBIT 2: COMPUTER PROGRAM OUTPUT FOR 1ST ORDER RE
*VERSIBLE KINETICS')

close(unit=l)
close(unit=2)
stop
end
c
c subroutine for calculating the solution, y=JINV*b
c where p(i), q(i), and r(i) are the lower, principal and upper
c diagonal elements respectively of the matrix J whose inverse
c is JINV. The dimension of J is 'norder'.
c
subroutine soln(norder,p,q,r,b,y)
dimension p(norder), q(norder), r(norder), b(norder), y(norder)
do 2 i=2,norder
ymult=p(i-l)/q(i-l)
q(i)=q(i)-ymult*r(i-1)
b(i)=b(i) ymult*b(i-l)
2 continue
y(norder)=b(norder)/q(norder)
do 3 i=norder- 1, -1
y(i)=(b(i)-r(i)*y(i+l))/q(i)
3 continue
return
end

Summer 1992 1 i

convergence criterion is

yX(m)-X(m-i) 2
i ~
%I x(m)
Si <

Additionally, the Jacobian matrix is easily shown
to be tri-diagonal since the elements are given as

aw.i
-X
aq

q=1,2,...(i-2) (7a)

W = (Xi- 1- Xi) a(X) 2 (Xi)
"KiJ axxi(X- i)

awi
Xi1)= (Xi)

awi
Xi+ =N(Xi+l)
s^-9

aw. _
ax
pX,

p=i+2,i+3,...(N-1)

As such, the Jacobian matrix is

C
C
C
C
(i
8c
c
c

Vw1 aw
)X1 aX2
w2 w2 w2
)x1 ax2 ax3
0 aW 3 3Wa
ax2 8Xs

0

0

0

0

aw, aw awi
0 aWi oWi aWi
aXi_1 axi axi+1

0 WN-1 aWN-1
aXN-2 8N-l

As shown in the text by Cheney and Kincaid,17' it
is unnecessary to carry out the inversion required by
Eq. (4) at every iteration for the tri-diagonal matrix
J. In fact, the vector, ym), is easily computed from
simple operations between the tri-diagonal elements
of the Jacobian matrix and the vector, w. This simple
algorithm was utilized as a subroutine subroutinee
SOLN) in the accompanying program. Clearly, this
method is completely independent of the reaction
kinetics in question; the only requirement is that the
rate expression be differentiable with respect to the
conversion. To demonstrate the utility of this method,
we provide the following two illustrative examples.

Example 1
A Reversible 1st Order Reaction
Suppose the reaction A<-R occurs in a cascade of
six CSTRs isothermally. For 1st order kinetics in
both A and R we have
-rA=kCA -k R (9)

which rewrites as

-rA=CA [k,(1-X)-kX] (10)

in terms of conversion X. The results from the com-
puter program (see Table 1) based on the method
described here using k1 = 0.196 min-1 and k2 = 2.124
x 10-3 min-1 with 1 mol/lit of pure A in the feed is as
shown in Table 2. As expected, the number of itera-
tions needed (usually less than six) is not affected by
the values of initial conversion guesses (if each is
less than unity). Changing the number of tanks from

TABLE 2
Computer Program Output for 1st Order Reversible
Kinetics

RESULTS OF THE REACTOR TRAIN DESIGN
Number of tanks = 6
Concentration of reactant, A, in feed = 1.00 mol./lit
final results satisfying tolerance limit
conversion in reactor train
0.2302E+00
0.4069E+00
0.5439E+00
0.6519E+00
0.7342E+00
inlet conversion = 0.0000E+00
train exit conversion = 0.8000E+00
required number of iterations to achieve tolerance = 3

Chemical Engineering Education

TABLE 3
Computer Program Output for LH Kinetics

RESULTS OF THE REACTOR TRAIN DESIGN
Number of tanks = 6
Concentration of reactant, A, in feed = 1.00 mol.lit
final results satisfying tolerance limit
conversion in reactor train
0.2272E+00
0.4028E+00
0.5399E+00
0.6488E+00
0.7326E+00
inlet conversion = 0.0000E+00
train exit conversion = 0.8000E+00
required number of iterations to achieve tolerance = 3

six to as high as twenty neither influenced the rate
of convergence nor significantly the time for pro-
gram execution on an IBM compatible 386 machine
using a WATFOR77 compiler.

Example 2
Complex Langmuir-Hinshelwood Kinetics
This example shows that the proposed method is
robust with respect to the kinetics of the reaction.
The Pt-catalyzed oxidation of CO in an isothermal
CSTR is described byt81

kCco
-rA +KC2 (11)
[1+KCo 2
The program was used to compute the optimal
interstate conversions for the same number of tanks.
The results are shown in Table 3, along with the
reactor parameters. Again, in spite of the nature of
the rate expression, the conversions were obtained
in only three iterations. Considerably more complex
rate equations (involving, for example, more than
one reactant and product) could be handled since the
concentration of each species may be related to the
conversion, X, as

TABLE 4
Equations for Top, for a Class of Reversible

Type of Reaction Topt
1 aA <-rR

-r=k1CA1 -k2C01 E2 -E1
A 2R A 2E 2A10-" (OR -VR
S 2 2 Ao
Rg n A1Ei(1-X)a

2. aA + bB <- rR

-r = aB -kC1 E2 -E1
-r = kCCal2 k2 RE (al+a2)
A B -k2 R CP1-(-1+-2)
R in A2 2 Ao
Rg AE1(1- X)"a (0

3. aA+bB<->rR+sS

kCaC a2 -k2CPIC2 E 2-
-r=kC1 A CB 2 RS A2 2

RgA AE A1E(1-X)

4. aA<->rR+sS

-r=kCc -kCCi2 2AE E2-El
R in 2 2 Ao (OR
S e A1E9(1

Summer 1992

Ci= CA (0i +ViX)

DESIGN FOR A CASCADE OF NON-ISOTHERMAL
CSTRs
In certain situations, especially for highly exo-
thermic reactions, it may be desirable to let each
reactor in the train operate at a different tempera-
ture. Thus, it is important to find the optimum tem-
perature, T for each tank which will simulta-
neously yiel the optimum conversion and hence the
overall minimum reactor size. To carry out the de-
sign for a non-isothermal train of CSTRs, the pro-
gram can be suitably modified so that the kinetic
rate constants which were previously supplied as
data to the program can now be computed in situ
along the optimum temperature progression (OTP)
path. Table 4 contains the equations for the opti-
mum temperature, Topt, for a class of reversible reac-
tions frequently encountered in process design (see
reference 9 for detailed derivation of equations for
T ). The following is a modification of the algo-
rithm for this situation.
1. Supply an initial vector of interstate conversions,
X(O1,

X(O) =[X) X() ...X(O) T

Reactions 2. Evaluate the optimum tem-
peratures, Tpt, corresponding to
the conversion in each tank using
relations from Table 4 for the ap-
propriate kinetics.
3. Compute the kinetic constants
X)oil k, and k, for each reactor at the
optimum temperatures Topt1, Topt,
. ToptN-l)
4. Evaluate the elements of the
Jacobian matrix and hence X"(m us-
ing subroutine SOLN.
1 5. Use the new X(m" to estimate
0R + RX) new optimum temperatures as in
B + VX)a2 Step 2. Follow Steps 3 and 4.
6. Continue Step 5 until con-
vergence criterion for the conver-
sion is met. The corresponding Top,
E are the design optimum tempera-
R +v X) "(0s +vSX) 2 tures for the train of CSTRs.
----) It may be recognized that, in
S(0, + ) B practice, the equations in Table
4 are actually quite easy to use
since the orders of the reactions
a's and p's rarely exceed two,
v RX)(0S +v X), while the parameters Oi and vi
are usually given by the feed
-)j specification and the reaction
stoichiometry.

CONCLUDING REMARKS
A method for the design of a cascade of CSTRs
isothermall and non-isothermal) has been proffered.
The required level of mathematical rigor appears
suitable for undergraduate instruction in optimal
reactor design. Also, the procedure is particularly
amenable, even at that level, for computer coding.

NOMENCLATURE
A,A, = frequency factors in the Arrhenius relation
C &.s = concentrations of species A, B, R, S respec-
tively, mol/lit
E1,E2 = activation energy in the forward and back-
ward directions respectively, J/mol
FAO = feed molar flow rate, mol/min
J = Jacobian matrix
k1,k2 = rate constants in the forward and backward
directions respectively
-r = rate of reaction, mol/lit. min
R = universal gas constant, J/mol K
T = temperature, K (subscripts are obvious from
text)
V = reactor volume, lit
X = fractional conversion
a. = reaction order w.r.t. reactant i
pj = reaction order w.r.t. product
0BAss = feed concentration ratio of species A, B, R, and
S to that of A
VA.Rs = stoichiometric coefficient ratio of species A, B,
R, and S to that of A
By convention v is negative for reactants and
positive for products. Consequently, vA = -1,
vB = -b/a, and vR = r/a. Similarly, 8A = 1 and
0B = CB/CAO, etc.

REFERENCES
1. Denbigh, K.G., Chemical Reactor Theory: An Introduction,
2nd ed., Cambridge University Press (1971)
2. Aris, R., The Optimal Design of Chemical Reactors: A Study
in Dynamic Programming, Academic Press, New York, NY
(1961)
3. Chen, N.H., Process Reactor Design, Allyn and Bacon, Inc.,
Boston, MA (1983)
4. Chitra, S.P., and R. Govind, "Synthesis of Optimal Serial
Reactor Structures for Homogeneous Reactions: I & II,"
AIChE J., 31,177 (1985)
5. Levenspiel, O., Chemical Reactor Omnibook, Oregon State
University Press (1984)
6. Fogler, H.S., Elements of Chemical Kinetics and Reactor
Calculations, Prentice-Hall, Englewood Cliffs, NJ (1974)
7. Cheney, W., and D. Kincaid, Numerical Mathematics and
Computing, Brooks and Cole Publishing Company (1985)
8. Carberry, J.J., Chemical and Catalytic Reaction Engineer-
ing, McGraw-Hill, New York, NY (1976)
9. Omoleye, J.A., A.A. Adesina, and E.O. Udegbunam, "Opti-
mal Design of Non-Isothermal Reactors: Derivation of Equa-
tions for the Rate-Temterature-Conversion Profile and the
Optimum Temperature Progression for a General Class of
Reversible Reactions," Chem. Eng. Comm., 79, 95 (1989) 0

book review

AN INTRODUCTION TO NUMERICAL
METHODS FOR CHEMICAL ENGINEERS
by James B. Riggs
Texas Tech University Press, Lubbock, TX 79409-1037;
460 pages (includes Solutions Manual)(1988)
Reviewed by
R. Narayanan
University of Florida

This book is meant primarily for undergraduate
students in chemical engineering. It could be used by
other engineering students even though the physical
connection of the majority of the examples is related to
chemical engineering. It is aimed at students who
have some background in calculus and some differen-
tial equations-the student would typically be in the
junior or senior year of chemical engineering.
I found the book well structured. It deals with ma-
trix operations and inversion with clarity and with
minimum confusion. The examples from stage-wise
operations are delightful, and the chapter on single
nonlinear equations is well presented. However, some
elementary derivations on sufficient conditions for con-
vergence of the methods and the errors would have
been possible but were (unfortunately) omitted.
The section on multiple nonlinear equations was
adequate, but the geometric interpretation of Newton's
method was needlessly confusing. Also, the chapter on
polynomial approximations and integration could have
been strengthened by inclusion of error bounds, and a
section on Richardson's extrapolation method should
be included in any future edition.
I liked the chapters on ordinary and partial differ-
ential equations and the subsequent treatment on
boundary value problems. The chemical engineering
examples were particularly good. One of the most
useful chapters for students, I feel, deals with linear
and nonlinear regression.
In short, I feel that the book is thoughtfully written.
Its main weakness is that it lacks some theoretical
background (which can be provided by an instructor
without much ado). Its strengths are the apt chemical
engineering examples that are provided, and in this
regard, I find it a suitable alternative to other well-
established textbooks. I found the level appropriate
for our junior-level students and feel it can be taught
without essential knowledge of the main chemical en-
gineering courses. It is published by a relatively un-
known press and does not appear to have received the
publicity it deserves. O
Chemical Engineering Education

AUTHOR GUIDELINES

This guide is offered to aid authors in preparing manuscripts for Chemical Engineering
Education (CEE), a quarterly journal published by the Chemical Engineering Division of the Ameri-
can Society for Engineering Education (ASEE).
CEE publishes papers in the broad field of chemical engineering education. Papers generally
describe a course, a laboratory, a ChE department, a ChE educator, a ChE curriculum, research
program, machine computation, special instructional programs, or give views and opinions on
various topics of interest to the profession.

Specific suggestions on preparing papers *
TITLE Use specific and informative titles. They should be as brief as possible, consistent with the
need for defining the subject area covered by the paper.

AUTHORSHIP Be consistent in authorship designation. Use first name, second initial, and
surname. Give complete mailing address of place where work was conducted. If current address is
different, include it in a footnote on title page.

TEXT Manuscripts of less than twelve double-spaced typewritten pages in length will be given
priority over longer ones. Consult recent issues for general style. Assume your reader is not a novice in
the field. Include only as much history as is needed to provide background for the particular material
covered in your paper. Sectionalize the article and insert brief appropriate headings.

TABLES Avoid tables and graphs which involve duplication or superfluous data. Ifyou can use
a graph, do not include a table. If the reader needs the table, omit the graph. Substitute a few typical
results for lengthy tables when practical. Avoid computer printouts.

NOMENCLATURE Follow nomenclature style of Chemical Abstracts; avoid trivial names. If
trade names are used, define at point of first use. Trade names should carry an initial capital only,
with no accompanying footnote. Use consistent units of measurement and give dimensions for all
terms. Write all equations and formulas clearly, and number important equations consecutively.

ACKNOWLEDGMENT Include in acknowledgment only such credits as are essential.

LITERATURE CITED References should be numbered and listed on a separate sheet in the
order occurring in the text.

COPY REQUIREMENTS Send two legible copies of the typed (double-spaced) manuscript on
standard letter-size paper. Clear duplicated copies are acceptable. Submit original drawings (or clear
prints) ofgraphs and diagrams, and clear glossy prints ofphotographs. Prepare original drawings on
tracing paper or high quality paper; use black india ink and a lettering set. Choose graph papers with
blue cross-sectional lines; other colors interfere with good reproduction. Label ordinates and abscissas
ofgraphs along the axes and outside the graph proper. Figure captions and legends may be set in type
and need not be lettered on the drawings. Number all illustrations consecutively. Supply all captions
and legends typed on a separate page. If drawings are mailed under separate cover, identify by name
of author and title of manuscript. State in cover letter if drawings or photographs are to be returned.
Authors should include brief biographical sketches and recent photographs with the manuscript.

ACKNOWLEDGEMENT

DEPARTMENTAL SPONSORS

The following 155 departments contribute to the support of CEE 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

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	Front Cover
	Table of Contents
	University of Virginia
	Book reviews
	Phillip C. Wankat, of Purdue...
	Confirming thermodynamic stability:...
	Three problems in fluid mechan...
	Book reviews
	What do they know, anyway?
	A course sequence for instrumentation...
	The effect of agitation on oxygen...
	"Product in the way" processes
	A statistical look at significant...
	Add some flavor to your agitation...
	Molecular enrichment of the core...
	Design of CSTRs in tandem...
	Book reviews
	Back Cover

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