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Chemical Engineering Education

Volume 27 Number 2 Spring 1993

EDUCATOR

66 Larry Duda, of Penn State, Written by His Colleagues

DEPARTMENT

72 Howard University,

Joseph H. Cannon, Ramesh C. Chawla, Dorian Etienne

KNOWLEDGE STRUCTURE

78 Introduction, Donald R. Woods

80 Fundamentals of Chemical Engineering,

Donald R. Woods, Rebecca J. Sawchuk

86 Mathematics, Stuart W. Churchill

92 Knowledge Structure of the Stoichiometry Course, Richard M. Felder

96 Thermodynamics: A Structure for Teaching and Learning About Much

of Reality, John P. O'Connell

102 The Basic Concepts in Transport Phenomena, R. Byron Bird

110 An Appetizing Structure of Chemical Reaction Engineering for

Undergraduates, H. Scott Fogler

CURRICULUM

118 On Letting the Inmates Run the Asylum, Alva D. Baer

CLASSROOM

120 What Works: A Quick Guide to Learning Principles, Phillip C. Wankat

144 Helping Students Communicate Technical Material,

William R. Ernst, Gregory G. Colomb

CLASS AND HOME PROBLEMS

122 Czochralski Crystal Growth Modeling: A Demonstrative Energy

Transport Problem, David C. Venerus

RANDOM THOUGHTS

128 Speaking of Education, Richard M. Felder

LABORATORY

130 Introducing Statistical Concepts in the Undergraduate Laboratory:

Linking Theory and Practice, Annette L. Burke, Aloke Phatak,

Park M. Reilly, Robert R. Hudgins

136 Purdue-Industry Computer Simulation Modules: 2. The Eastman

Chemical Reactive Distillation Process, S. Jayakumar, R.G. Squires,

G. V. Reklaitis, P.K. Andersen, L.R. Partin

140 An Inexpensive and Quick Fluid Mechanics Experiment,

J.T. Ryan, R.K. Wood, P.J. Crickmore

150 An Interesting and Inexpensive Modeling Experiment,

W.D. Holland, John C. McGee

77 Division Activities

95 Letter to the Editor

85,109,117 Book Reviews

CHEMICAL ENGINEERING EDUCATION (ISSN 0009-2479) is published quarterly by the

Chemical Engineering Division, American Societyfor Engineering Education, and is edited at the

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Defective copies replaced if notified within 120 days of publication. Write for information on

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Spring 1993

l =F educator

BY HIS COLLEAGUES

Pennsylvania State University

University Park, PA 16802-4400

.Larry Duda was born and raised in Donora,

Pennsylvania, a small steel-mill town twenty

miles down the Monongahela River from Pitts-

burgh. It was considered a good omen when he was

delivered by the high school football team physician

since his was a family in which most of the sons

went to college on football scholarships. In spite of

his lack of weight, skill, and interest, when he fi-

nally got to high school he too fulfilled the family

obligation of trying out for the "Donora Dragons,"

which had given the country not only such great

players as "Deacon Dan" Tyler, "Pope" Galiffa,

"Bimbo" Ceconi, but also Stan Musial. Although

Larry did not make the team, he did hear the first

pep talk wherein the coach indicated that there were

two paths down from the football field, which tow-

ered on the hill above the town-"One can graduate

from high school and go down into the mill, or one

can play good football and go to college." Fortu-

nately, Larry found a third path: a scholarship at

Case Institute of Technology. He decided to study

chemical engineering because he liked math and

chemistry and also because he was fascinated by

the old lead chambers which produced sulfuric acid

in the zinc works section of U.S. Steel.

He started out as a mediocre student at Case,

ARRY

PUDA

of Penn State

hampered by a poor high school background and a

dyslexia problem which he did not recognize at that

time. He was struggling along with Cs and some Bs

until he took his first chemical engineering course

in stoichiometry and found that his forte was in

solving problems. Even in high school, when he had

difficulty with formal algebra, he found he could

always solve the statement problems through his

own devious techniques. As a consequence, he ex-

celled in stoichiometry and became the top student

in the class. Upon graduating, he decided to go to

graduate school since he felt he did not yet fully

understand chemical engineering and was a little

fearful of going out and practicing the subject with

his limited knowledge.

THE DELAWARE YEARS

Larry blossomed as a graduate student at the

University of Delaware and was particularly stimu-

lated by research and interactions with such chemi-

cal engineering greats as Bob Pigford, Art Metzner,

and Kurt Wohl. An outstanding group of graduate

students who were at Delaware at the same time

also contributed to the exciting intellectual climate.

In addition to learning how to do research under

the tutelage of Art Metzner, he honed his tennis

game, helped integrate restaurants in Delaware,

and met his future wife, Margaret Barbalich. He

worked in the area of catalysis with ion exchange

resins and likes to joke that he did so poorly

that neither he nor Art Metzner ever worked in

that area again. Larry reminisces that his years at

Delaware were the best, blending an intensity of

research studies, sports, and personal life. The spe-

cific subjects studied at Delaware were quite sec-

Copyright ChE Division ofASEE 1993

Chemical Engineering Education

Larry joined the Process Fundamentals Group of the Dow Chemical Company..., and...

his long and successful collaboration with Jim Vrentas began... it was [there] that they forged their

friendship and created one of the most productive teams in the profession. They

represented a contrast in styles and abilities, yet had an abiding

respect for each other's points of view and contributions.

ondary compared to the enthusiasm he

gained for learning and the creation of new

knowledge through research.

THE DOW DAYS

In 1963, Larry joined the Process Funda-

mentals Group of the Dow Chemical Com-

pany in Midland, Michigan, and it was there

that his long and successful collaboration

with Jim Vrentas began. Although the two

knew each other in graduate school, it was

in the Process Fundamentals Laboratory

that they forged their friendship and cre-

ated one of the most productive teams in

the profession. They represented a contrast

in styles and abilities, yet had an abiding

respect for each other's points of view and

contributions.

Their differences were demonstrated by

an incident one Friday when they had a

very difficult problem which they could not

solve. Late that afternoon, Larry concluded

that they had been pounding on the prob-

lem too long and had actually begun recy-

cling potential solutions that they had al-

ready considered. He felt they were burned

out, and he was going to take the evening

off, see a play with Marge, have dinner, and

hopefully wake up the next morning with

fresh insight. In contrast, Jim decided to

stay on through the wee hours of the night,

continuing to work on the problem. When

Larry and Marge returned home later that

evening, they found Jim's solution nailed to

their front door! He wanted to make it crys-

tal clear that he had come up with the solu-

tion first, just in case Larry woke up in the

morning with a bright idea of his own.

Larry and Marge quickly established a

family in Midland, and within less than

three years had four children (twins John

and David, Paul, and Laura). Larry likes to

kid the Dow people that there was nothing

else to do in Midland in those days.

During the Dow days, Larry and Jim's

basic work in the area of diffusion in poly-

Spring 1993

THE

DUDA

DISGUISES

Cleverly disguised as a young

student, circa 1962, at Brown

Laboratory, University of Delaware

(right)

... and...

as jolly old Saint Nick himself

(below), with co-disguised

John Phillips in an interesting

impersonation of an elf...

as the

Shiek of... ah ... University Park

as... whatever...

with sons Paul, John, wife Marge, son David, and daughter

Laura all getting in on the act.

mer systems was initiated. To their dismay, how-

ever, they were not free to continue along the paths

of scientific interest-instead, they had to respond

to the more direct economic needs of the company.

Nevertheless, they were at Dow during the golden

days when great advancements were being made in

polymer science, led by such individuals as Turner

Alfrey and Ray Boyer. It was natural that in this

environment they would be drawn into considering

problems associated with polymer production and

processing. In addition to Jim Vrentas, Turner Alfrey

and Art Metzner (as a Dow consultant) also exerted

great influence on Larry's professional development.

Despite Larry's successful career development at

Dow in the late 1960s, he and Jim decided that they

should consider academia if they wanted to con-

... it became clear to him

that he would rather stay at Penn State

without research and just teach than to take a

position where he could concentrate on

his desired research with no

opportunityfor teaching.

tinue along their main avenues of interest. In his

last years with the company, Larry made his most

successful contribution through his work on design-

ing insulation systems for the trans-Alaskan pipe-

line that would keep it from melting the permafrost

during the short Alaskan summer.

Although Larry left Dow for Penn State in 1971,

he has maintained strong contacts with Dow. In

many ways, Larry has tribal instincts and develops

a strong devotion to groups he lives and works with.

In addition to his family, he still has vital attach-

ments to his home town of Donora and to the Dow

Chemical Company. He stays in touch with several

friends at Dow, including Doug Leng and George

Shier. Larry was most recently named a charter

member of Dow's Academic Advisory Council.

THE PENN STATE YEARS

Over the past twenty years, Larry has devoted

most of his energies to the development of the De-

partment of Chemical Engineering at Penn State.

The dominant characteristics of Larry's work are in

its diversity and its strong emphasis on collabora-

tion. He has conducted collaborative research work

with almost every member of the chemical engi-

neering faculty as well as with several researchers

outside the department. Besides his work with Jim

Vrentas in the general area of diffusion in polymer

systems, Larry has made contributions in many other

fields, most significant of which has been his joint

research with Elmer Klaus in the area of tribology.

Although Larry was attracted to academia because

he sought to define his own research work, he quickly

became enthralled by teaching. In fact, within

a few years it became clear to him that he would

rather stay at Penn State without research and

just teach than to take a position where he could

concentrate on his desired research with no oppor-

tunity for teaching.

The meetings of his research groups with their

inevitable interplay of ideas are the most enjoyable

parts of Larry's working schedule, and the most

attractive feature of these interactions comes from

the general thrill of exploring the natural world. In

these group meetings, Larry often makes bets with

Elmer Klaus that the results of the new experi-

ments will turn out a certain way. But Elmer is an

expert at oracle statements, and no matter which

way the results come out he can be counted on to

argue that he had already predicted the results.

Second only to chemical engineering is Larry's

continued interest in tennis. In fact, it is rumored

that Lee Eagleton originally hired him only be-

cause they were great tennis partners who together

could take on opponents from the chemistry depart-

ment. At present, Jack McWhirter and Larry offer a

standing challenge to take on any two students in

the department.

On the home front, Larry is proud of his belief

that the way to educate people is to help them be-

come themselves. This freedom of spirit is strongly

exhibited in his children. None of them has become

an engineer, or has even gotten close to engineer-

ing-they have been students of art, English litera-

ture, and medicine. Now that the children are grown,

Larry and Marge are able to nurture their interest

in international travel, and when at all possible

they try to couple it with Larry's technical interests

and Marge's photographic interests.

DUDA-THE RESEARCHER

Through the years at Dow and at Penn State,

Larry's work has exhibited a common thread of re-

search on polymers and transport phenomena. His

well-known collaboration with Jim Vrentas on mo-

lecular diffusion in polymer systems has yielded

many results which have been presented in over

seventy journal publications.

At the time Duda and Vrentas initiated their work,

the area of diffusion in concentrated polymer solu-

Chemical Engineering Education

tions and melts was in a state of disarray, and no

techniques were available to the design engineer for

the prediction or even the correlation of diffusivity

data. In fact, available experimental data revealed

many apparent contradictions. Some experiments

showed that the binary mutual diffusion coefficient

in polymer-solvent systems were strong functions of

concentration, while in other studies these coeffi-

cients were found to be independent of concentra-

tion. Some investigators found that diffusion in poly-

mer systems depended strongly on temperature and

did not follow an Arrhenius-type behavior, while

other studies indicated that the data could be corre-

lated with the Arrhenius equation with relatively

low activation energies for diffusion. Superimposed

on this perplexing situation were the experimental

observations that, in some cases, diffusion in con-

centrated polymer systems did not even follow Fick's

law. Numerous investigations showed that anoma-

lous effects were present which were not consistent

with the classical diffusion theory.

In response to this situation, the studies of Duda

and Vrentas led to the concept that molecular diffu-

sion processes involved the coupling of migration

and relaxation of molecules. Up to this time it had

been implicitly assumed that the molecules partici-

pating in a diffusion process could relax very quickly

to new equilibrium states and that local thermody-

namic equilibrium was maintained. Duda and

Vrentas quantified their theory with the introduc-

tion of the diffusion Deborah number, which is the

ratio of the characteristic relaxation time of the mol-

ecule to the characteristic time of the diffusion pro-

cess. This dimensionless group revealed under what

conditions classical diffusion theory is appropriate

for the description of diffusion in polymeric systems.

Probably the most important outcome of the col-

laborative work of Duda and Vrentas is the develop-

ment of the free volume theory in which the viscous

behavior of polymer melts is coupled to the diffu-

sional behavior in binary solutions. Their theory

allows the prediction of diffusion coefficients as a

function of temperature and concentration from vis-

cosity and thermodynamic data obtained essentially

for pure component systems. The free volume theory

as developed by Duda and Vrentas has been shown

to be applicable up to at least 80 C above the glass

transition temperature and for concentrations as

high as 70 weight percent solvent. Interestingly, the

theory is also capable of predicting anomalous abrupt

changes in the diffusivity observed in the vicinity of

glass transition temperature.

Concurrently, Duda and Vrentas developed experi-

Spring 1993

mental techniques and associated analyses for the

determination of accurate diffusivity data over the

wide ranges of temperature and concentration

needed for various polymer processes. Their work

led to the development of a widely used high-

temperature sorption apparatus as well as a novel

oscillatory sorption experiment. The latter tech-

Duda and Mary Eagleton presenting the Lee and

Mary Eagleton Design Award to Heather Bergman.

nique is the only method available to study unam-

biguously the coupling of diffusional transport and

molecular relaxation.

Not well known to the academic chemical engi-

neering community are Larry's contributions to the

area of tribology and lubrication. Larry recognized

how fundamental principles of chemical engineer-

ing can be successfully applied to bring order into

a traditionally empirical field of research that

has remained largely proprietary over the years.

This led to his collaborative research with Elmer

Klaus, the results of which are summarized in over

forty publications.

Probably the most important outcome of this re-

search has been the development of a micro-reactor

technique to study the thermal and oxidative degra-

dation of lubricants under conditions that simulate

automotive engine tests, heavy-duty diesel engine

performance, electrical power generating equipment,

and gas turbine engines. The test has been adapted

by over fifteen industrial research groups as a way

to minimize costly engine tests and has been suc-

cessfully used to study the performance of lubricant

additives as well as the catalytic effects of metal

surfaces on lubricant degradation.

Another important result from this research is the

development of a novel lubricant delivery system,

69

for applications at elevated temperatures. In this

system, a lubricant film is formed on a hot surface

from a homogeneous vapor phase. The lubricant-

forming vapor is adsorbed on the solid surface and

reacts to form the lubricant film. This new lubricant

system is being evaluated for applicability in di-

verse areas, including the lubrication of an adia-

batic ceramic engine and metal-forming operations.

Duda's work has also led to development of methods

for the theological characterization of lubricants

under extreme conditions of temperature, pressure,

and shear rate.

By his work, Duda has taught his colleagues and

students how to carry out fundamental research that

leads directly and tangibly to industrially signifi-

cant results. A unique indicator of this success is

the fact that virtually all of his research support

comes from industry.

DUDA-THE TEACHER

Larry has been a teacher with great impact. Over

the years he has developed a unique teaching style

and educational philosophy. For example, he starts

out each lecture in his graduate course with a quote

from a famous engineer, scientist, philosopher, or

religious leader. He feels that each lecture should

not only present some specific segment of technol-

ogy, but also should incorporate some thought or

philosophy concerning the general aspects of life it-

self. To illustrate, one of his classroom techniques is

role playing. He will introduce himself as an inven-

tor, while the students play the role of engineers in

a company that is considering buying the inventor's

latest creation. His "inventor" is usually a super-

salesman who is very close to playing a con game.

The students' roles are to analyze the proposed in-

vention for its scientific merits and to find its fatal

flaws, if any. A quote from Harold McMillan sets

the stage for this particular lecture: "Nothing that

you will learn in your studies will be of the slight-

est possible use to you in the afterlife. Save only

this: that if you work hard and intelligently, you

should be able to detect when a man is talking rot,

and that, in my view, is the main, if not the sole

purpose of education."

Larry's classroom emphasis is on creativity and

the ability to solve unique problems, as opposed to

the mere accumulation of specific knowledge or so-

lution of conventional problems. He stays awake at

night thinking up problems for homework or exams

which at first glance appear to be unrelated to the

topic at hand but that can be solved by using the

course fundamentals. For example, to illustrate the

use of the Flory-Reiner model for crosslinked poly-

mers, he considers the case of how the ancient Egyp-

tians cracked stones in their quarries. They drove a

wooden wedge into a crack, poured water on the

wedge, and let the swelling wedge crack the rock.

By giving properties of polymeric wood, students

can develop equations to predict the pressures that

such swelling wedges will develop.

Larry's success as a teacher stems not only from

his classroom lectures, but also from his close work

with undergraduate and graduate students in their

research. He has advised sixty-one masters' students

and thirty-two doctoral students at Penn State, in-

cluding the forty-six students who have worked with

him and Elmer Klaus in the area of tribology. It is

fair to say that almost every industrial tribology

researcher with a chemical engineering degree has

been trained at Penn State. Duda is a much sought-

after member of graduate student thesis commit-

tees. Over the last twenty years, in addition to the

students whose work he has supervised he has also

served on 100 doctoral committees and 120 masters'

committees. The students have been from chemical

engineering, chemistry, polymer science, petroleum

engineering, mineral processing, agricultural engi-

neering, fuel science, bioengineering, etc. An impor-

tant reason for the diverse backgrounds of students

seeking Duda's guidance is the active collaboration

Duda has developed and maintained with over

twenty faculty members in other disciplines. He has

also been unusually active in guiding over seventy

undergraduate students on their honors research

projects. Many of them have gone on to graduate

schools, inspired by their research experience.

HONORS AND AWARDS

Larry has been recognized for his teaching and

research through a number of awards. In 1980 he

received the Outstanding Research Award from the

Pennsylvania State Engineering Society, and in 1981

Larry and Jim Vrentas were co-recipients of AIChE's

William H. Walker Award in recognition of their

work on molecular diffusion in polymers and the

analysis of complex transport phenomena. Larry was

chosen by Penn State's senior ChE class as the Out-

standing Professor in 1983, and in 1989, along with

Jim Vrentas, he received the Charles M.A. Stine

Award in Materials Engineering and Sciences from

the AIChE Materials Division in recognition of their

development of the free volume theory and the oscil-

latory sorption technique. Also in 1989, Larry was

selected to receive the ASEE Chemical Engineering

Lectureship Award. The Pennsylvania State Engi-

Chemical Engineering Education

One oJ Duda's happier duties as Department Head-

receiving a check for the department!

neering Society honored Larry and Jim Vrentas in

1991 with its Premier Research Award, and also in

that year Larry was chosen as the Alumni Delegate

representing the Class of 1963 at the 1991 Com-

mencement Ceremony of the University of Delaware.

DUDA-THE ADMINISTRATOR

Larry has been an unusual department head for

the past ten years. He has demonstrated that taxing

administrative duties need not diminish one's in-

tense involvement in teaching, research, and guid-

ing students. Under his stewardship, the depart-

ment has increased its visibility, with many of the

faculty receiving national awards from AIChE, ACS,

ASEE, ASME, etc. The department has recruited

several outstanding young faculty in John Frangos,

Kristen Fichthorn, Lance Collins, Ali Borhan, Wayne

Curtis, and Themis Matsoukas. Two of these new

faculty, Frangos and Fichthorn, were honored with

Presidential Young Investigator Awards. The de-

partment also added two nationally prominent se-

nior scientists to its ranks in Art Humphrey and

Paul Weisz. Duda's leadership has been responsible

for the creation of a strong research program in

biotechnology at Penn State, capped by the recruit-

ment of Art Humphrey as the Director of the Bio-

technology Institute.

PROFESSIONAL INVOLVEMENT

Larry has been a spokesperson for academic inter-

ests to industry. His own experience of having al-

most all of his research sponsored by industry gives

him unusual insights into the mechanisms for and

the benefits of university-industry collaboration. He

has been a member of the Council for Chemical

Research (CCR) for the past ten years and served on

its Governing Board and on the latter's Executive

Spring 1993

Committee. He has served on the CCR Committee

on Industrial College Relations and as CCR Liaison

with the NSF, and has also been active on the Aca-

demic Advisory Council of Dow Chemical. His ad-

vice as an educator has been sought after by other

departments of chemical engineering: he has served

as the external reviewer for Rutger's University;

he has served on the Promotion and Tenure Re-

view Committees of the Illinois Institute of Tech-

nology and the University of Rochester; he serves

on the advisory committees of the chemical engi-

neering departments at West Virginia University,

University of Delaware, and Carnegie-Mellon

University. An example of the esteem in which

Duda is held by other department heads is their

election of him as the Chair of the Board of Judges

for the McGraw-Hill Kirkpatrick Award in

Chemical Engineering.

Larry has been active in the AIChE in a number

of ways. He has served as a member of the National

Program Committee, Public Relations Committee,

Polymer Engineering Subcommittee of the Research

Committee, Walker Award Committee, Charles M.A.

Stine Award Committee, and the National Awards

Committee. He is currently a Director of the Materi-

als Engineering and Sciences Division. He also serves

on the Publications Committee of the ASEE.

DUDA-THE PHILOSOPHER

Larry has made unique contributions to his field

through his role as a philosopher of graduate educa-

tion. His three articles in Chemical Engineering Edu-

cation, "Common Misconceptions Concerning Gradu-

ate School," "Graduate Studies: The Middle Way,"

and "Graduation: The Beginning of Your Education"

are necessary reading material for all graduate stu-

dents. They outline a philosophy that has guided

Duda's work and offer much-needed perspective to

beginning graduate students. To quote from the con-

clusion of the second article, Duda says

From my presentation, you might conclude that

there is a middle way in every aspect of graduate

work that is the most appropriate approach. Al-

though I have attempted to illustrate that this is

certainly true in many instances, there is one very

important exception. Some students say to them-

selves, "This is not the best that I can do but it's

good enough." Well, it's not good enough. Push

yourself-take time and make the effort to perform

at the very highest level of which you are capable.

There is no middle way when it comes to the pur-

suit of excellence.

Duda's contributions to chemical engineering epito-

mize the above philosophy in action. I

epartmen t

HO WARD

Frederick Douglass Hall-

houses Liberal Arts Departments and classrooms

JOSEPH N. CANNON, RAMESH C. CHAWLA,

DORIAN ETIENNE*

Howard University

Washington, DC 20059

Howard University is a private, co-educational institution

located in Washington, DC. Named for General Oliver

Otis Howard, a Civil War hero who helped found the Uni-

versity, it was incorporated in 1867 by an Act of Congress, and its

founding mission was to help educate the four million freed slaves

and others to whom education had previously been denied.

The University offers degree programs in about two hundred

*Graduate Student in chemical engineering.

There is strong interaction among

faculty members across research areas

[that] provide three research focal

areas... transport phenomena in

environmental engineering,

separation processes, and

kinetics and reactor modeling.

specialties and its four campuses encom-

pass 241 acres. Most of its schools and

facilities, including the radio and televi-

sion stations, a full-service hotel, a hos-

pital, and a number of research centers,

are located on its eighty-nine-acre main

campus three miles north of the Capitol

in the heart of Washington, DC.

Howard's more than 1,200 full-time fac-

ulty members are a microcosm of the

world population of scholars, and its ap-

proximately 12,000 students come from

all over the United States and more than

one hundred countries.

THE SCHOOL OF ENGINEERING

Howard University introduced its en-

gineering programs in 1911 and they

were among the first accredited programs

in the United States. Historically,

Howard has been the nation's major

source of minority engineers, particularly

African American engineers. Bachelor's

and master's degrees are offered in

chemical, civil, electrical, and mechani-

cal engineering, and in systems and com-

puter science. The departments of elec-

trical and mechanical engineering also

have PhD programs. Each year about

850 undergraduate and 200 graduate

Copyright ChE Division ofASEE 1993

Chemical Engineering Education

UNIVERSITY

Downing Hall of Engineering:

Chemical Engineering Wing on the left.

students enroll in the various programs offered.

Modern instructional and research laboratories,

together with computing facilities, support both

student and faculty research pursuits. The

Computer Learning and Design Center (CLDC),

the school's centralized computing facility, and

the Computer Laboratory for Instruction and

Design in Engineering (CLIDE), provide a full

spectrum of computer resources for faculty

and students. These include PCs, HP and DEC

VAX minicomputers, Sun Workstations, and

access to an Alliant mini-supercomputer. These

resources are linked via networks to each other,

to the university's IBM 3090 mainframe, and

to INTERNET.

THE CHEMICAL ENGINEERING DEPARTMENT

The Chemical Engineering Department was es-

tablished in 1969 with the appointment of Dr.

Herbert Katz as the Chair and with five stu-

dents at the sophomore level. Between 1970 and

1972 three more faculty joined the department:

Pradeep Deshpande (now at the University of

Louisville), Joseph Cannon (current Chair of the

Spring 1993

ivegnoors of nowara umverslry: ne Lincol

Memorial, the Washington Monument, and the

U.S. Capitol building.

^lv t~lA-i

Graduate students reviewing laws of motion.

department), and Franklin King (now Chair at NCA&T

State University). In June 1972, the five original stu-

dents successfully completed the curriculum and were

awarded the first BS degrees granted by the depart-

ment. Presently, there are six full-time faculty posi-

tions (one vacant), one part-time faculty, approximately

73

one hundred undergraduate students, and twelve

MS students.

In 1975 a modern chemical engineering wing

was added to the L.K. Downing Hall of Engineer-

ing. This facility contains a number of research

laboratories, each equipped with state-of-the-art

equipment to meet the experimental research

needs of the faculty.

The Fluid and Thermal Engineering Laboratory

houses equipment and instrumentation for the

measurement of flow and heat transfer. A

Laser Anemometry System, a rotational vis-

cometer, along with other instruments enable

researchers to measure velocities, map shear-

stress patterns, and conduct routine measure-

ments of shear viscosity.

The undergraduate program is

structured to provide a broad background in

the fundamental areas of chemical engineering,

with special attention given to the development

of analysis and problem-solving skills.

The Biochemical Engineering Laboratory is

equipped to conduct research in microbial fermen-

tation, protein purification, bioremediation, and

protein adsorption. Specialized equipment in-

cludes an inverted phase contrast photo-capable

microscope, automated high-pressure and low-

pressure liquid chromatography systems with vari-

able wavelength detection capabilities, full-spec-

trum scanning spectrophotometry instrumentation,

and a microtome.

The Microelectronics Materials Processing Labo-

ratory features two chemical vapor deposition re-

actors (horizontal and vertical) and a sublimation

reactor, all for the growth of silicon carbide and

related materials. This laboratory is a part of the

NSF-funded Materials Science Research Center of

Excellence (MSRCE) located in Downing Hall of

Engineering where faculty and students from elec-

trical and chemical engineering, physics, and chem-

istry carry out interdisciplinary research.

The environmental engineering laboratories have

facilities dedicated to analytical instrumentation,

microbiology, incineration, water pollution, and air

pollution. Jointly shared by the environmental en-

gineering faculty in civil engineering, these labo-

ratories are the focus of several interdisciplinary

research projects. All the necessary equipment for

the growth, isolation, and analysis of microorgan-

74

Undergraduate unit operations laboratory

Undergraduate unit operations laboratory.

isms is located in the microbiology laboratory. Equip-

ment for studying the kinetics, chemistry, and heat

and mass transfer characteristics of high-temperature

reactions are available in the Incineration Laboratory.

This includes a Shirco infrared incinerator, a liquid/

gas combustion unit, and a fluidized bed high-tem-

perature reactor. Howard is one of a handful of aca-

demic institutions possessing the incineration facili-

ties capable of studying thermal degradation of waste

in all phases-solid, liquid, and gas.

The EPA-funded Great Lakes and Mid-Atlantic

Hazardous Substances Research Center (a con-

sortium of the University of Michigan, Michigan State

University, and Howard University) supports coop-

erative research efforts among chemical engineering

and other university faculty. These environmental

research programs are in the areas of bioremedia-

tion and composting.

UNDERGRADUATE PROGRAM

The undergraduate program is structured to provide

a broad background in the fundamental areas of chemi-

cal engineering, with special attention given to the

development of analysis and problem-solving skills. The

breadth of the undergraduate program is intended to

prepare students to either enter the chemical engi-

neering profession upon graduation or to successfully

continue their education at the graduate level.

The curriculum is particularly strong in providing

comprehensive design experience, basic engineering

technology in separation processes, and the fundamen-

tals of transport processes. Computer use is integrated

throughout the curriculum, with special emphasis on

digital simulation and software for analysis and de-

sign. Laboratories support undergraduate instruction

in momentum, heat, and mass transfer, reaction kinet-

ics, process control, and process design. Electives of-

Chemical Engineering Education

The EPA-funded Great Lakes and Mid-Atlantic Hazardous Substances Research Center [is] a consortium

of the University of Michigan, Michigan State University, and Howard University [which] supports

cooperative research efforts among chemical engineering and other university faculty.

feared by the department include: polymer engineering, bio-

medical engineering fundamentals, bioprocess engineering,

processing of electronic materials, transport phenomena,

energy systems, and environmental engineering.

Most of the BS graduates have found employment in in-

dustry, while about one-third of them have gone on to pur-

sue advanced degrees in chemical engineering, environmen-

tal engineering, business, or other professional areas such

as medicine, law, and dentistry.

GRADUATE PROGRAM

The goal of our Master's program is to provide the neces-

sary academic experiences to prepare students for challeng-

ing and responsible careers as practitioners and adminis-

trators in the chemical engineering profession and for the

numerous other opportunities associated with this level of

achievement. The program is intended to extend the student's

training in the mainstream areas of chemical engineering

at an advanced level, with sufficient in-depth study of a

n, selected area and involving both formal course work and a

osep thesis research project.

The instructional program is based on core courses in

TABLE 1 thermodynamics, transport phenomena, reaction kinetics,

Faculty and Research Areas advanced engineering mathematics, and elective courses re-

Joseph N. Cannon, P.E., Professor and Chair; lated to the student's area of specialization. Graduate the-

PhD, University of Colorado ses are generally based on faculty research.

Transport phenomena in environmental systems,

computational fluid mechanics, heat transfer FACULTY AND RESEARCH FOCUS

Ramesh C. Chawla, Professor;

PhD, Wayne State University Since ours is a small department, there is a great oppor-

Chemical kinetics, separation processes, bioremedia- tunity for interaction among students and faculty. Stu-

tion, incineration, environmental engineering dents feel comfortable visiting faculty at any time to seek

M. Gopala Rao, Professor; advice or assistance on matters related to their courses,

PhD, University of Washington, Seattle their research, or personal well-being. There is also strong

Separation processes, energy systems, radioactive

waste management interaction among faculty members across research areas.

Mobolaji E. Aluko, Associate Professor; These interactions provide three research focal areas for

PhD., University of California, Santa Barbara the department: transport phenomena in environmental

Process control, mathematical methods, reactor engineering, separation processes, and kinetics and

modeling, crystallization, microelectronic materials reactor modeling. Table 1 lists the research interests of

processing *

processing each faculty member.

John P. Tharakan, Assistant Professor;

PhD., University of California, San Diego Mobolaji Aluko's research is in three specific areas:

Reactor design and bioprocess engineering, protein experimental analyses and numerical modeling of gas-

separations, protein adsorption, biological hazardous phase deposition reactors for semiconductor materials; solu-

waste treatment

Robert J. Lutz, Visiting Professor; tion crystallization of ceramic materials; and control of non-

PhD., University of Pennsylvania linear chemical systems. Recent MS theses projects have

Hemodynamics, intra-arterial drug delivery focused on the analysis of mixed-suspension mixed-product

Herbert M. Katz, Professor Emeritus; removal (MSMPR) crystallizers and on the design of hetero-

PhD., University of Cincinnati generous catalytic reactors.

Environmental engineering

In addition, he directs the Engineering Coalition of Schools

Spring 1993 75

for Excellence in Education and Leadership (ECSEL)

program at Howard. This coalition consists of seven

universities funded by NSF to seek fundamental

changes in engineering education through active stu-

dent involvement in learning and by incorporating

interactive, open-ended teaching approaches. Dur-

ing the 1992-93 academic year he is spending a

sabbatical leave at two coalition schools-the Uni-

versity of Washington, Seattle, and the University

of Maryland, College Park.

In his spare time, he plays tennis, ping-pong, and

chess, and he is one-half of the 1991-92 Howard

University Tennis Doubles' Championship team. He

is always ready to argue politics and religion.

Joseph Cannon's research focuses on transport

phenomena with applications in environmental en-

gineering. He is currently studying the movement of

hazardous organic in soil and has both experimen-

tal and numerical work underway. He is also inter-

ested in the cooling of electronic equipment contain-

ing printed circuit boards. One of his students has

just completed a thesis on the numerical analysis of

conjugate heat transfer in electronic packages.

For over twenty years, Joe has been known to

frequently challenge a student to a one-on-one bas-

ketball game. It appears as though "Father Time"

has caught up with him, however, and he has re-

cently started taking tennis lessons. He also enjoys

pocket billiards and chess.

Ramesh C. Chawla's research combines the ap-

plication of the principles of mass transfer and ki-

netics to environmental systems. He has been in-

volved in an on-going EPA-funded research program

in hazardous waste treatment using physical and

chemical techniques such as soil washing, adsorp-

tion, acid protonation, and biodegradation of haz-

ardous wastes using indigenous microorganisms cul-

tured from the contaminated sites. He has also been

studying the combined technique of surfactant-as-

sisted biodegradation of hazardous wastes. His

projects on thermal treatment of hazardous wastes

deal with the assessment of organic emission and

heat and mass transfer limitations in incineration.

Ramesh loves to discuss politics and sports with

his colleagues and students. He is the faculty advi-

sor for the AIChE Student Chapter and frequently

conducts some of the chapter meetings with stu-

dents while bowling at the University Center.

Gopala Rao has been very active in the areas of

adsorption and ion exchange separation processes,

radioactive waste management, and alternative pro-

cess energy systems. His current research, funded

76

by the Office of Civilian Radioactive Management

(DOE), concentrates on sorption equilibrium mea-

surements of binary and ternary ionic systems of

radionuclides (such as cobalt, nickel, strontium, ce-

sium, and lead) in aqueous phases and on single

and mixtures of minerals such as clinoptilolite, mont-

morillonite, and goethite. These efforts are in sup-

port of the Yucca Mountain Site Characterization

Project being conducted at the Los Alamos National

Laboratory and the Sandia National Laboratory.

Gopala is an avid swimmer and jogger. When-

ever he is out of town for a meeting or a conference,

he can be found after hours on the jogging trails

around his hotel.

John Tharakan's protein separation research fo-

cuses on the effects of such parameters as ligand

distribution, resin structure, and flow configuration

on process efficiency. He has carried out cell culture

research to investigate the fundamental physico-

chemical parameters at the microenvironmental level

that affect cell viability and productivity in novel

bioreactor configurations for large-scale cell culture.

His bioremediation research focuses on the syner-

gistic effects of pathways and cofactors utilized by

individual and consortia of microbes in the biodeg-

radation of toxic wastes.

John enjoys discussing politics and is especially

interested in the interactions of science, technology,

and culture. He is a member of the local Chapter

of Science for the People. When not involved with

class or lab work, he can usually be found cooking

in the kitchen.

Robert Lutz has been studying methods of intra-

arterial drug delivery to achieve high concentrations

of an anticancer drug at the tumor site while main-

taining subtoxic levels at other sensitive sites in the

remainder of the body. He is investigating catheter

design and infusion methods that minimize

nonuniform drug distribution.

Bob has been teaching and participating in re-

search at Howard for the past twelve years. When

not working at NIH or Howard, he. can be found

playing basketball or golfing or participating in any

other sport for which the weather is suitable.

Howard University has come a long way since its

inception in 1867 with the mission of educating freed

slaves. Today it successfully conducts the daily busi-

ness of educating young people anxious to and ca-

pable of making significant contributions in many

ways and in many areas. We are proud of our gradu-

ates and look forward to the educational and soci-

etal challenges of the future. O

Chemical Engineering Education

lhE Division Activities

ASEE Annual Conference

When-June 20-24, 1993

Where-University of Illinois campus in Urbana-Champaign, Illinois

Since this is ASEE's centennial year, the overall

topic of this year's meeting will be the history of

engineering. With that theme in mind, the ChE di-

vision has organized three sessions pertaining to

our history: a lecture on the history of chemical

engineering education; a display of textbooks used

throughout our history; and a poster session on his-

tories of chemical engineering departments at the

various universities. Other sessions will deal with

new developments in education and research, such

as new environmental courses and curricula, high-

performance computing, new courses not tradition-

ally taught in chemical engineering, new chemical

engineering research areas, and new partnerships

with industry in chemical engineering The program

promises to be interesting and entertaining.

SCHEDULE

1213

1413

Monday

8:30-10:15

Monday

12:30-2:00

1613 Monday

4:30-6:00

2213 Tuesday

8:30-10:15

2413 Tuesday

12:30-2:00

2513 Tuesday

2:30-4:15

2613

Tuesday

4:30-6:00

2713 Tuesday

6:30-?

3213 Wednesday

8:30-10:15

3413 Wednesday

12:30-2:00

3513 Wednesday

2:30-4:15

3613 Wednesday

4:30-6:00

4213 Thursday

8:30-10:15

Lecture

Lunch

Tutorial

Papers

Lunch

Poster

Papers

Dinner

Papers

Lunch

Poster

Papers

Tour

The History of Chemical Engineering Education

Donald Dahlstrom, University of Utah

Moderator: James E. Stice, University of Texas-Austin

Chemical Engineering Chairpersons' Luncheon

Moderator: Richard Alkire, University of Illinois

Environmental Engineering Courses and Curricula

Moderator: Gary K. Patterson, University of Missouri-Rolla

High Performance Computing in Chemical Engineering

Moderator: Mark A. Stadtherr, University of Illinois

Chemical Engineering Executive Committee Meeting

Moderator: John Friedly, University of Rochester

Histories of Chemical Engineering Departments

Moderators: Ron Larsen, Montana State University

Susan Montgomery, University of Michigan

New Courses not Traditionally Taught in Chemical Engineering

Moderators: J. L. Zakin, The Ohio State University

L. S. Fan, The Ohio State University

Chemical Engineering Division Banquet and Division Lecture

Moderator: John Friedly, University of Rochester

New Chemical Engineering Research Areas

Moderator: Thomas Marrero, University of Missouri-Columbia

Chemical Engineering Division Luncheon, General Business Meeting

Moderator: John Friedly, University of Rochester

Textbooks in the History of Chemical Engineering

Moderators: Melanie McNeil, San Jose State University

Polly R. Piergiovanni, Lafayette College

New Partnerships with Industry in Chemical Engineering Research

Moderator: Neil Book, University of Missouri-Rolla

Tour of Research Facilities

Leader: To be announced

Spring 1993 7;

KNOWLEDGE

STRUCTURE

mnowo courtesy of ictoria nau, unwersaiy oT Uairornia, aong neacn

Participants in the AIChE session on Knowledge Structure in Chemical Engineering,

held in Los Angeles, November, 1991. Pictured, left to right: Scott Fogler, Stuart

Churchill, R. Byron Bird, Richard M. Felder, and John P. O'Connell

(not pictured, Donald R. Woods).

Chemical Engineering Education

------F>

Knowledge has structure;

structure to facilitate learning

and

structure to facilitate problem solving.

Research by cognitive psychologists has revealed the

characteristics of those different structures.

The Undergraduate Education Committee of the AIChE spon-

sored a session on knowledge structure at the Los Angeles

meeting in 1991. At that session (which I cochaired with Bill

Kroesser), Stu Churchill, Rich Felder, John O'Connell, Bob Bird,

and Scott Fogler shared their views of the fundamentals and

the structure of knowledge in the areas of mathematics, mass

and energy balances, thermodynamics, transport phenomena,

and reaction kinetics/reactor design.

The results were exciting and diverse. Some of the presenta-

tions focused on the importance of the subject and the process

of using the knowledge effectively, some on structure related to

learning, some on problem solving, and some on a combination

of these factors.

We are pleased to present those papers on

the following pages.

Don Woods, McMaster University

Guest Editor

Spring 1993

KNOWLEDGE STRUCTURE

FUNDAMENTALS

OF CHEMICAL ENGINEERING

DONALD R. WOODS, REBECCA J. SAWCHUK

McMaster University

Hamilton, Ontario, Canada L8S 4L7

he subject "Chemical Engineering" has struc-

ture. It is not an unrelated collection of about

three thousand equations that we somehow

put together to solve problems. The subject is built

upon fundamental laws, concepts that allow us to

use those laws, models, theories, semi-empirical cor-

relations, and data. English and mathematics are

the languages we use to work within the subject.

Unfortunately, some surveys of our graduating

seniors reveal that many see the discipline as a

"collection of isolated equations to be memorized

and 'cooked' to solve problems." They see no rela-

tionship between such courses as thermodynamics

and heat transfer-the topics are seen simply as

different courses taught in different semesters by

different instructors. Students fail to recognize links

between the courses and the concepts in chemical

engineering, and consequently they see little struc-

ture to the subject.

There are two vital types of structure: we use

a structure of the knowledge to facilitate learn-

ing, and we use a structure of the knowledge to

solve problems.

Structures to Facilitate Learning

To facilitate learning, Ausubelm emphasized the

importance of providing students with "advanced

organizers." Such advanced organizers help students

see the structure of the subject and provide a "big

picture" of the route ahead. The structure, selected

to facilitate learning, provides a framework that we

can hang new knowledge on as we learn it. One

considers which concepts are easier to learn first

and notes a certain sequence of topics. Most texts

attempt to provide such structure, and most of us in

the field of teaching attempt to provide such struc-

ture to facilitate learning.

The structures and relationships are created to

facilitate learning. The structures may pertain only

80

Don Woods is a professor of chemical engi-

neering at McMaster University. He is a gradu-

ate of Queen's University and the University of

Wisconsin. His teaching and research inter-

ests are in surface phenomena, plant design,

cost estimation, and developing problem-solv-

ing skills.

Rebecca Sawchuk is a senior in McMaster

University's chemical engineering undergraduate

program. The goal of her senior thesis project is

to link the fundamentals of chemical engineering

to form an organized "structure" of the knowl-

edge. She plans to work at Dow Chemical Canada

Inc. after graduation.

to the course and the subject we are teaching.

Rarely does the structure interlink with other

courses. Novak and Gowin[21 suggest "concept map-

ping" as a useful way of displaying the structure.

Our work with seniors shows that they can create

reasonable concept maps that reflect the structure

used to help them learn. However, they provide

separate and unconnected maps for each course.

Furthermore, the maps are very detailed and tend

to classify the information on the basis of the se-

quence in which it was taught. As they develop the

maps they say, "First we had this, and then this,..."

Thus, what we and the textbooks are providing

seems to help their recall. On the other hand, they

rarely have thought previously about connecting the

maps to see the bigger picture of all the under-

graduate subject matter.

Structures to Facilitate Problem Solving

A crucial finding about problem solving is that the

problem a person solves is their own internal, men-

tal image, or representation of the problem. We do

not simply solve "problem 6.3 at the end of Chapter

6." Although one reads the problem statement, the

mental task is one of reformulating the words and

images into some mental image of what "we think

the problem is all about." The creation of that inter-

nal representation is dictated by the problem solver's

Copyright ChE Division ofASEE 1993

Chemical Engineering Education

KNOWLEDGE STRUCTURE

internal structure of the subject knowledge.

For example, a student's internal representation

of chemical engineering for the purposes of problem

solving may be a "collection of unrelated equations."

Unsuccessful problem solvers tend to use a trial-

and-error tactic of using equations that will "use

up" the information they are given. For example, a

problem statement in Chapter 3 of a fluid mechan-

ics textbook included extraneous viscosity data. One

of the A+ students searched through the text until

he found, in Chapter 5, an equation that included

viscosity and all of the other information in the

problem statement!

This behaviour might be interpreted as being re-

lated to people whose grasp of the subject discipline

is only an unstructured collection of unrelated equa-

tions. Clement'31 and Larkin"'4 provide evidence in

the context of physics. Clement suggests that we

use four interconnected and hierarchical modes of

thinking with our internal knowledge: observations

Design of a solution

Write relations involving

known and desired Combine and solve

information

S10-14

Figure 1. Unsuccessful problem-solver's script (From Larkin;151 reproduced with permission)

POINTER Rotating object.

Motion of various

points on that object.

METHODS

PRINCIPLES

SDescription

Immediate Analytic s

Diagram showing object's rotation, Visualize separately motion of

path of center of mass center of mass and motion relative

to center of mass

| Motion of center of

v R mass is just like

motion of a particle.

POINTER

to another

area of physics

Particle Lotion

mx=F F

Relate by integration

SFgrav=mg

Beloci

Figure 2. Successful problem-solver's script. (From Larkin;ts5 reproduced with permission)

Spring 1993

POINTERS

Resistors

in series

i

R=R1+R2 C C1C

CC=1 C2

ap: i -tors

in neres

KNOWLEDGE STRUCTURE

and practical knowledge-leading to qualitative

physical models-leading to concrete mathematical

models-leading to written symbol manipulation.

Successful problem solvers tend to start solving prob-

lems by checking the observations, qualitatively un-

derstanding what is going on, invoking mathemati-

cal models, and then manipulating symbols to ob-

tain a quantitative result. Thus, they start with

observations and a qualitative understanding of what

is going on. Unsuccessful problem solvers depend

solely on symbol manipulation. Larkin's research

uncovered key differences between unsuccessful and

successful problem solvers: the unsuccessful prob-

lem solver, as illustrated in Figure 1, selects "point-

ers" in a problem in DC circuits that lead to a broad

set of relationships that then had to be played around

TABLE 1

Comparison Between Unsuccessful and Successful Problem Solvers' Use of Knowledge

UNSUCCESSFUL SUCCESSFUL

Problem Solvers' Use of Subject Knowledge Problem Solvers' Use of Subject Knowledge

cannot quickly and accurately identify the pertinent subject knowledge; tend rapid and correct identification of the pertinent subject (usually within

to play around with many equations;[4,5] tend to manipulate symbols and seconds of completing the reading of the problem statement)[51

combine what they select as being a relevant relationshipI3'4]

misinterpret and misuse "pointers"l51 identify and use "pointers" to zero in rapidly on key principles and

fundamentals[51

redescription and creation of mental image is limited, formal, and often not redescription is rich, accurate, and uses assumptions and approximations

helpfull51 rapidly to identify key features;[5] use qualitative analysis to point to

crucial concepts[61

a particular relationship is recalled independently of any general relationship strong structure connecting concepts, principles and laws[51 apply

upon which it is based;15] no restructuring and chunkingg" of knowledge; related "chunks" of subject knowledge[6]

work with independently applied individual principles(61

do very little qualitative analysis[61 do extensive qualitative analysis of the situation16]

unwilling to guess, to make approximations, and have no memorized, order- have memorized "tacit" or order-of-magnitude experience factors that

of-magnitude values to assist them in doing a qualitative analysis110'11,121 allows them to do rapid and extensive qualitative analysisl0',l1,12]

have incomplete and imprecise knowledge about knowledge[8] have a complete set of knowledge181

lack an organized, hierarchical and abstract knowledge structure that is based possess an organized, hierarchical, and abstract knowledge structure that

on fundamentals and tied to the real world by pointers[9'10] is based on fundamentals and tied to the real world by pointers19'101

do not know when to apply general theory and when to apply specific

subsets of the general theory that seem to apply[6,81

confuse specific and special cases with generally applicable relationshipsl81

have difficulty recalling/identifying conditions under which special case

equations apply and hence try to apply these when they are inapplicable[7,8]

have difficulty identifying and formulating the specific information to which

the general principles applyl81

have difficulty reasoning from basic principles; instead rely on "beginning"

and "end" events without reflecting on the chain of events between the two;

depend on redescriptive activities which merely rephrase the problem

situation without advancing one's understanding of it; depend on inappropri-

ate arguments by analogy181

cannot distinguish between additive and non-additive quantities;[81 have

difficulty working with "intensive" properties[81

place more emphasis on collecting sample solutions and working examples

than on understanding the fundamentals when "learning" a subjectll'0

replace precise technical definitions with imprecise, everyday usage, e.g.,

"velocity"l81

fail to realize that once certain physical parameters are set, other measurable

quantities cannot be varied independently181

have conceptual difficulty applying calculus in physics[81

82 Chemical Engineering Education

KNOWLEDGE STRUCTURE

with and "cooked" to see which one might apply.

The successful problem solver, illustrated in Figure

2, selects "pointers" in a problem on a falling disk

that show a direct and rapid connection with funda-

mental principles and methods. A summary of the

research on unsuccessful and successful problem

solver's use of subject knowledge is summarized in

Table 1. '3-13

More specifically, research has shown that suc-

cessful problem solvers have a structure to their

subject knowledge that-instead of being a collec-

tion of unrelated concepts and equations-is charac-

terized as follows:

1. The knowledge is structured hierarchically (with

fundamental laws and principles at the higher

levels and surface structure and pointers at the

lower levels. [6,9,14.15,16]

2. The highest levels in the hierarchy-or the under-

pinnings-are the fundamental laws, the abstrac-

tions.56.9.'141]

3. Related to the fundamentals are concepts and

"chunks" of information that allow us to apply the

fundamentals effectively. The knowledge is encoded

to include conditions and constraints when the

knowledge is applicable.t4'7'1,6

4. The lower levels are the surface structure (key words

in a problem statement that trigger one to use

certain approximations or concepts or descriptions

of the everyday events that work because of the

fundamentals) and "pointers" that link the surface

structure to the fundamentals.5'"'7''16171

5. Encoded with the subject knowledge is "tacit" or

memorized, order-of-magnitude numerical values

that allow qualitative application of the knowl-

edge. 10-121

6. Subject knowledge is organized in block or "chunks"

convenient for mental processing.6'7'121

Concerning the types of knowledge, there are

* the fundamentals

* concepts or defined terms to allow us to use the

fundamentals

the procedural knowledge about how to work with

the information

the pointers or links

a rich set of episodic knowledge that gives us a

qualitative understanding of what is going on, as

opposed to a series of symbolic equations that one

manipulates. This includes memorized, numerical,

and order-of-magnitude knowledge.

Glaser114' suggests that the knowledge structure is

not static; rather, as new knowledge comes in it

should be embedded in the hierarchy, attached to

the fundamentals, and related to the episodic knowl-

Spring 1993

KNOWLEDGE STRUCTURE

edge so that it relates to our past experience. This

embedding modifies the original structure.

IDEAS ABOUT THE FUNDAMENTALS

Identifying the fundamentals is not easy. Some-

times the things we call "laws" are "wishes," not

laws; sometimes "principles" are really laws, etc.

Some terminology might be:

Law A universally applicable explanation of how things

behave; e.g., the conservation of mass.

Constrained Law An explanation that is applicable over a

defined set of circumstances; e.g., the ideal gas law.

Balance An equation applied to a conserved entity-thus

one would have a "mass balance," but not a "mole balance" or

a "volume balance."

Model A representation of a situation for the purpose of

explaining how it behaves.

Theory A mathematical relationship between the dependent

and independent variables that is almost completely based on

fundamental laws and constrained laws. There may be a few

constants that have to be used to tune the theory to the

specific situation. There may be many different theories for

one particular behaviour.

Empirical Correlation A mathematical relationship

between the dependent and independent variables. No theory

or fundamentals were used in creating the relationship. It

considers the system to be a "black box."

Semi-Empirical Correlation A mathematical relation-

ship between the dependent and independent variables that is

based on some fundamental laws and constrained laws.

Concept A general term for an entity or idea that is useful

in applying a law; e.g., the concept of "force."

Convention An agreed-upon set of rules; e.g., Gibbs

convention for the dividing surface in surface phenomena.

Postulate A simplifying set of agreed-upon conditions.

Examples of "laws" and "postulates" pertinent to

chemical engineers include1'18191

LAWS

1. Law: Mass is neither created nor destroyed; it is

conserved; the total mass is conserved; the mass of

an element is conserved (unless nuclear reactions

occur or E=mc2 occurs, in which case, mass and

energy will exchange).

2. Law: Electrical charge is neither created nor de-

stroyed; it is conserved.

3. Law: Energy is neither created nor destroyed; it is

conserved (unless nuclear reactions occur or E=mc2

occurs, in which case mass and energy will ex-

change).

4. Law: Momentum is conserved.

5. Law: The law of definite proportions is related to

compounds and their formation.

6. Law: The second law of thermodynamics-systems of

processes occur so as to minimize the total free

energy in the system. Concept: free energy.

KNOWLEDGE STRUCTURE

7. Law: If a process proceeds spontaneously, the reverse

process can never proceed spontaneously.

8. Law: If a system is left alone, it will go to a state of

dynamic equilibrium that has equal forward and

reverse rates and no available free energy.

Extensive details are needed for each law or corre-

lation.'4'12' The details include

a statement of the fundamental principle law of

equation

an identification of the meanings of all the concepts

used in the law

identification of the dependent and independent

variables

numerical units of measurement

listing of the region of application, identification of

the limitations and assumptions

hints to prevent errors in the application

utility hints (tacit information) about when a

particular principle is most useful

In addition, we must have a qualitative under-

standing bf what is going on as predicted by the law.

POSTULATES

To simplify our ways of thinking about nature and

how it behaves, we often define simplifying postu-

lates. Rase"1' provides the following examples of pos-

tulates:

1. Postulate: Isothermal (constant temperature)

2. Postulate: Isobaric (constant pressure)

3. Postulate: Isochoric (constant volume)

4. Postulate: Isentropic (constant entropy); simplifica-

tion for a compressor or turbine

5. Postulate: Isenthalpic (constant enthalpy); simplifica-

tion for flow through a valve

6. Postulate: Adiabatic (no exchange of energy between

the inside and the outside of the system); simplifica-

tion for perfect insulation

7. Postulate: Equilibrium exists (assume an infinitely

fast rate)

8. Postulate: Reversibility (neglect friction)

9. Postulate: Ideality (this has many subcomponents);

ideal gas when the ideal gas law applies; ideal liquid

(could be zero viscosity or Newtonian depending on

how ideal is defined); ideal Hookean solid, ideal

isotropic solid, ideal solution, ideal mixture, ideal

crystal, ideal catalyst

10. Postulate: Models for mixing; plug flow or complete

mixing

11. Postulate:Incompressible flow (Vv) = 0

12. Postulate: Unidirectional flow

13. Postulate: Black body radiation and grey body

radiation

14. Postulate for shape and configurations: infinite

shape, semi-infinite shape, perfectly smooth surface,

zero thickness surface region, point source, constant

total cross-sectional area, and perfect geometrical

shapes (flat, cylindrical, spherical)

15. Postulate for time: steady state, pseudo steady state,

zero time, infinite time

16. Postulates about limiting cases

As we move from laws to models, through con-

cepts and through to postulates and conventions, we

move down the structure. Indeed, the pointers that

connect the real world to the structure are usually

connected to "postulates."

SUMMARY

Knowledge has structure. Having the appropriate

structure facilitates learning and problem solving.

Key characteristics of the knowledge structure to

aid in problem solving are that knowledge is hierar-

chically organized with the fundamentals at the

higher levels and pointers at the lower levels. Knowl-

edge is "chunked" to include the bases, assumptions,

conditions of application, and tacit or experience

knowledge. Some example "laws" and "postulates"

have been given in this paper.

REFERENCES

1. Ausubel, D.P., Educational Psychology: A Cognitive View,"

Holt, Rinehart, and Winston, New York (1968)

2. Novak, J.D., and D. Bob Gowin, Learning How to Learn,"

Cambridge University Press, Cambridge (1984)

3. Clement, J., "Some Types of Knowledge Used in Under-

standing Physics," unpublished manuscript, Dept. of Phys-

ics and Astronomy, University of Massachusetts (1977)

4. Larkin, J.H., "Developing Useful Instruction in General

Thinking Skills," Paper JL010276, Group in Science and

Mathematics Education, University of California, Berkeley

(1975)

5. Larkin, J.H., "Cognitive Structures and Problem Solving

Ability," Paper JL060176, Group in Science and Mathemat-

ics Education, University of California, Berkeley (1976)

6. Larkin, J.H., "Processing Information for Effective Problem

Solving," unpublished paper, Group in Science and Math-

ematics Education, University of California; presented at

the Amer. Asso. of Physics Teachers, Chicago (1977)

7. Larkin, J.H., "Understanding Problem Representations and

Skill in Physics," Internal Report, Carnegie Mellon Univer-

sity (1980): Larkin, J.H., et al., "Expert versus Novice Per-

formance in Solving Physics Problems," Science, 208, 1335-

1342 (1980): Larkin, J.H., "Cognition in Learning Physics,"

Am. J. of Physics, 49(6), 534-541 (1980)

8. Lin, H.S., "Problem Solving in Introductory Physics: De-

mons and Difficulties," PhD Thesis, Department of Physics,

MIT, Cambridge, MA (1979)

9. Voss, J., "Problem Solving and the Educational Process," in

Handbook of Psychology and Education, R.Glaser and A.

Lesgold, eds., Lawrence Erlbaum Publishers, Hillsdale, NJ

10. Woods, D.R., et al., "56 Challenges to Teaching Problem

Solving," CHEM 13 News, 155, (1985); "Major Challenges

Chemical Engineering Education

KNO WLEDGE STRUCTURE

to Teaching Problem Solving," Annals of Engr. Ed., 70(3),

277-284

11. Mettes, C.T.C.W., A. Pilot, H.J. Roossink, and H. Kramers-

Pals, "Teaching and Learning Problem Solving in Science,"

J. Chem. Ed., 57(12), 882-885 (1980) and 58(1), 51, 55

(1981); B. van Hout Wolters, P. Jongepier, and A. Pilot,

"Studiemethoden," AULA, Uitgeverij Het Spectrum, Utrecht

(in Dutch), and K. Mettes and J. Gerritsma, "Probleem

Oplossen," AULA, Uitgeverij Het Spectrum, Utrecht (in

Dutch) (1985)

12. Reif, F., and J.I. Heller, "Making Scientific Concepts and

Principles Effectively Usable: Requisite Knowledge and

Teaching Implications," Paper ES-13; "Cognitive Mecha-

nisms for Facilitating Human Problem Solving in Physics:

Empirical Validation of Prescriptive Model," Paper ES-14b;

and "Knowledge Structure and Problem Solving in Phys-

ics," Paper ES-18; Physics Department, University of Cali-

Sbook review

FLUIDIZATION ENGINEERING

(Second Edition)

by D. Kunii, O. Levenspiel

Butterworth /Heinemann, Stoneham, MA 02180; 491

pages, $145 (1991)

Reviewed by

Roy Jackson

Princeton University

The first edition of this book, which appeared

over twenty years ago, enjoyed considerable success

in drawing together the research results available

at that time and synthesizing from them a con-

nected account of direct value to engineers involved

in the design of fluidized beds. It is, therefore, a

hard act to follow-but this second edition succeeds

in preserving (and even enhancing) the virtues of its

predecessor, while at the same time weaving many

newer ideas into the fabric of the text.

Though some passages from the earlier work are

retained, the present book is essentially a completely

rewritten text. Even where the material is similar

to the earlier presentation, it has been reorganized,

expanded, and supplemented with more worked ex-

amples. There is much more attention paid to mat-

ters such as the influence of the properties of the

particulate material on fluidization behavior, rest-

ing on concepts (such as the Geldart classification)

which have appeared since publication of the first

edition. Variants on the classical dense fluidized

bed are also treated; for example, a whole chapter

(entitled "High Velocity Fluidization") is devoted to

turbulent beds and fast fluidized beds, configura-

tions that have become increasingly important. On

the other hand, the many students and practitio-

Spring 1993

fornia, Berkeley (1982);

13. Woods, D.R., "Summary of Novice versus Experts Research

Results," PS News, 55, 55-2 to 55-21 (1988)

14. Glaser, R., "Education and Thinking: The Role of Knowl-

edge," Amer. Psychologist, 39(2), 93-104 (1984)

15. Boreham, N., "A Model of Efficiency in Diagnostic Problem

Solving: Implications for the Education of Diagnosticians,"

Instructional Sci., 15, 119-121 (1986)

16. Bransford, J., et al., "Teaching Thinking and Problem Solv-

ing," Amer. Psychologist, 41, 1078-1089 (1986)

17. Bhasker, R., and H. Simon, "Problem Solving in Semanti-

cally Rich Domains: An Example from Engineering Ther-

modynamics," Cognitive Sci., 1, 195-215 (1977)

18. Porter, S.K., "Ordinary Atoms Made in Stars," J. of Col.

Sci. Teach., Dec 1985/Jan 1986, p. 168 (1986)

19. Rase, H.F., Philosophy and Logic of Chemical Engineering,

Gulf Publishing Company, Houston, TX (1961) J

ners who have benefited from the information in

Chapter 3 of the first edition (which provided ex-

plicit instruction on how to estimate such elemen-

tary, but vital, properties as the terminal velocity of

fall and the minimum fluidization velocity) will be

happy to know that the same chapter of the second

edition provides the same help, but in an updated

and improved form.

My only criticism of the first edition was that the

very success of the authors in presenting the mate-

rial in such simple, clear exposition tended to give a

false impression that the material was well estab-

lished, reliable, and beyond controversy. In fact, this

was far from the truth. Many of the correlations

presented were extrapolations from limited data,

while the models, though reasonable and the best

available at the time, were gross simplifications

which had been subjected to only the most superfi-

cial testing. In short, the story was told so well that

it made the state-of-the-art seem much more firmly

based than it really was.

I have some of the same feeling about the second

edition. The unwary designer might easily be se-

duced into following the path so clearly marked out,

only to receive a rude awakening further down the

road. The subject remains today a very messy one,

in a state of continuing flux, with both the physical

principles and the tools available to apply them

changing very quickly.

But this is only a minor reservation about a book

which is likely to be as well received as was its

predecessor. We might even hope that the rapid

changes in the field will encourage the authors to

venture a third edition at some time in the future.

KNOWLEDGE STRUCTURE

KNOWLEDGE STRUCTURE

MATHEMATICS

STUART W. CHURCHILL

The University of Pennsylvania

Philadelphia, PA 19104-6393

he assigned objective for the presentation that

led to this paper was a discussion of the struc-

ture of knowledge in applied mathematics

which is appropriate to the undergraduate chemical

engineering curriculum. That presentation was, and

this paper is, actually focused on a limited aspect of

the assigned topic-namely, the form of exposition

of applied mathematics in the curriculum and its

reception and retention by students. The state and

consequences of current undergraduate preparation

in applied mathematics will be examined first, and

then proposals for improvement will be presented.

THE CHALLENGE

Doctoral students in chemical engineering have

sufficient time and a sufficiently narrow focus so

that they can master and utilize those aspects of

applied mathematics that are directly useful in their

research. On the other hand, undergraduate stu-

dents are currently exposed to a great amount of

material, including applied mathematics, in a form

and at a rate that precludes its mastery. The need

for such mastery as contrasted with exposure is first

considered, and then the degree to which it is cur-

rently accomplished. The superior preparation in

mathematics of students from Europe and Japan is

evident to all who encounter them in graduate

courses. Their preparation provides a measure of

what we might aspire to achieve.

Stuart W. Churchill is the Carl V.S. Patterson

Professor Emeritus at the University of Penn-

sylvania, where he has been since 1967. His

BSE degrees (in ChE and Math), MSE, and

PhD were all obtained at the University of Michi-

gan where he also taught from 1950-1967. Since

his formal retirement in 1990 he has continued

to teach and carry out research on heat transfer

and combustion. He is also currently complet-

ing a book on turbulent flow.

Copyright ChE Division ofASEE 1993

THE ESSENTIAL ROLE

OF MATHEMATICS IN ENGINEERING

"It's staggering to consider how much one's

social acceptance depends upon being quadrati-

cally integrable."

Snoopy

Most of those in the academic community do not

need to be convinced that innovative applications of

mathematics have made great contributions to the

advancement of the practice of chemical engineer-

ing in recent decades. Unfortunately this contribu-

tion is largely ignored and grossly underestimated

by its principal beneficiary-the chemical and

process industries (CPI). The leaders of the CPI

take for granted the improvements in process de-

sign, process control, process analysis, and process

safety that are a direct consequence of better

modeling and better understanding. They do not see

the link between those improvements and the

articles in mathematical language which have

appeared in the literature of engineering science,

such as the AIChE Journal.

Faculty members who read this article (and in

particular, the authors of the associated papers of

this symposium) owe their academic and professional

achievements at least in part to a superior grasp of,

and facility with, applied mathematics. A good un-

derstanding of applied mathematics and a willing-

ness to extend that understanding, as stimulated by

new topics in research or teaching, is a necessary

condition for successful academic practice today.

We owe our students an appropriate preparation

in mathematics, not only for the problems that are

current or foreseeable, but also as a foundation for

the acquisition of those mathematical skills that

will become important during their lifetime. If we

are successful, our students will have sufficient con-

fidence in their mathematical background and a suf-

ficient vision of its value to exercise, maintain, and

extend this competence throughout their career, or

at least as long as that career is focused on technol-

Chemical Engineering Education

KNOWLEDGE STRUCTURE

One of [my graduate students] devised a general method for deriving similarity transformations, and he

and others were among the first in engineering to use digital computers. They produced the first

numerical solutions of the partial differential equations governing laminar, transient, and

multidimensional natural convection, and subsequently they were among the

first to model the turbulent regime multidimensionally.

ogy as contrasted with management.

I assert that we now fail almost totally in this

respect-at least with those who do not pursue

graduate work in chemical engineering. The math-

ematical knowledge of those who enter industrial

practice with a bachelor's degree fades rapidly after

graduation owing to its disuse. An ancient but nev-

ertheless instructive study is re-examined below as

evidence thereof.

THE GOALS

OF ENGINEERING EDUCATION STUDY

The 1968 Goals of Engineering Study,'" sponsored

by the American Society for Engineering Education,

is still instructive despite its date. Although it floun-

dered for several reasons, the findings and recom-

mendations with respect to mathematics will be ex-

humed here. As a first step of the study, a survey

was conducted to determine the retroactive self-as-

sessment of their education by engineers in indus-

try who had been practicing five, ten, and twenty

years since receiving their baccalaureate degree. The

participants were asked to identify those aspects of

their undergraduate studies which had proved the

most and the least useful. An increasing majority at

each level of experience asserted that they had never

used mathematics (and in particular, calculus) in

their professional career. The only cited deficiency

in their mathematical preparation was in statistics.

This response was totally misleading; most, if not

all, of the participants had used mathematics in the

first few years of practice, but at the current stage

of their career the ambitions of many had become

more focused on skills and credentials required by

management. The technical and mathematical skills

they had used to reach the point of consideration for

management had been forgotten.

The authors of the Goals report used the results

of the survey as justification for recommending

more courses in managerial-related topics at the

expense of courses in engineering science and math-

ematics. This survey is an example of obtaining the

wrong answer by virtue of asking the wrong ques-

tion. Fortunately, a number of recommendations of

the Goals report, including those related to math-

ematics, were eventually rejected by the AIChE and

Spring 1993

other professional societies as unacceptable criteria

for accreditation.

My informal conversations with undergraduate stu-

dents at the University of Pennsylvania over the

past twenty-five years suggest that when they gradu-

ate they still lack confidence in their working knowl-

edge of engineering science and, to an even greater

extent, advanced mathematics. This is undoubtedly

a factor in the choice by many of positions in mar-

keting, sales, etc., that will not expose this pre-

sumed deficiency. Similar conversations with our

graduate students from other schools (consisting pre-

dominantly of students who performed exception-

ally well in engineering science and mathematics)

indicates that this insecurity is not unique to any

one school or group of students. If the Goals survey

were reconducted with industrial practitioners to-

day, a quarter of a century later, I suspect the same

general response would be obtained.

TEXTBOOKS

The standard textbooks in chemical engineering

provide additional insight into the role of applied

mathematics in the undergraduate curriculum. In

Elements of Chemical Engineering, by Badger and

McCabe,[2' (out of which I studied as an under-

graduate) the models were almost wholly algebraic.

Even Unit Operations, by Brown and Associates, 31 a

generation later in 1950, utilized very few differ-

ential models and then only elementary ones. Two

outstanding books on applied mathematics in chemi-

cal engineering appeared in the interim-Applied

Mathematics in Chemical Engineering, by Sherwood

and Reed in 1939,[4] and Application of Differential

Equations to Chemical Engineering Problems, by

Marshall and Pigford in 194751--but the material

therein was not required to solve any of the prob-

lems considered in the undergraduate curriculum

and had no direct impact thereon. Indeed, to this

day material of the level of mathematical sophisti-

cation of these latter two books is hardly recognized

in industrial practice, at least outside research de-

partments or their equivalent. As an aside, it may

be significant to note that no mention was made of

the former pioneering book in the citation for the

recent award of the National Medal of Science to

Charles E. Reed.

KNOWLEDGE STRUCTURE

Subsequent undergraduate texts, beginning in

1960 with Transport Phenomena by Bird, Stewart,

and Lightfoot,"6' have used more advanced notation,

models, and solutions, but otherwise have not greatly

extended the mathematical demands on students.

COMPREHENDING THE LITERATURE OF CHANGE

Several years ago, on the occasion of the 75th

Anniversary Meeting of the AIChE, I was asked to

review the role of mathematics in the history of our

profession and particularly in its publications.[7'

One of my conclusions was that our graduates were

no longer sufficiently prepared in mathematics to

read much of the AIChE Journal. That situation

has not changed significantly in the intervening

nine years. The mathematical sophistication of

our published research is certainly advancing more

rapidly than the preparation of our undergraduates

in this respect.

This inaccessibility of the articles in our archival

journals to our bachelor's graduates in terms of com-

prehension has at least two serious consequences:

1) the advances in knowledge, as described in the

journals, are a well-kept secret insofar as most of

our profession is concerned, and 2) the cultural gap

and the difficulty of technical communication be-

tween those with graduate education and those with-

out becomes ever greater.

How can we expect the results of analysis to

be implemented in industry if they are effectively

hidden from the practitioners and managers by

their expression in an unknown language? How can

we maintain professional continuity across the

division of degrees without a common language? This

is a relatively new phenomenon, and hence it is not

widely recognized.

A Personal Digression *

At this point I will take the liberty of citing some

of my own experiences as evidence of the impact on

chemical engineering practice of even modest skills

in applied mathematics. Such a personal digression

is perhaps tolerable since these experiences form

the basis for my commitment to, and proposals for,

improved instruction in this field.

As an undergraduate I majored in applied math-

ematics as well as in chemical engineering, and I

received a bachelor of science degree in each. The

decision to do this was one of the more felicitous

ones in my career since it set me somewhat apart

from my classmates in chemical engineering and

greatly enhanced my self-confidence. The added

88

Faculty members who read this article

(and in particular, the authors of the associated

papers of this symposium) owe their academic

and professional achievements at least in

part to a superior grasp of, and facility

with, applied mathematics.

mathematics was not very sophisticated by current

standards, and the topics themselves did not differ

greatly from those we now offer our undergraduates

in an elective or required course in "advanced math-

ematics for engineers." My courses were, however,

taught by mathematicians, and the classes included

students majoring in mathematics as well as in en-

gineering. Accordingly, the instruction included a

stronger focus on structure and rigor.

That focus has proven to be a long-term benefit-

one which is often denied our current students when

such courses are taught by engineers. For the short

term, including my first years of practice after gradu-

ation, the primary benefit of the added mathematics

was a capability to solve problems that my peers in

chemical engineering could not. Upon returning to

graduate school five years later, I was able to main-

tain this competitive edge by taking as many elec-

tives as possible in that lowly branch of mathemat-

ics known as analysis, and this had the unexpected

but happy collateral consequence of allowing me to

take advanced courses in physics.

In each phase of my subsequent academic career

I have been able to take advantage of this marginal

preparation in mathematics by my choice of and

approach to problems of research. My graduate

students have also been encouraged to undertake

problems involving advanced applications of ap-

plied mathematics. One of them devised a general

method for deriving similarity transformations, and

he and others were among the first in engineering

to use digital computers. They produced the first

numerical solutions of the partial differential equa-

tions governing laminar, transient, and multidimen-

sional natural convection, and subsequently they

were among the first to model the turbulent regime

multi-dimensionally. In the course of solving nu-

merically the integro-differential equations govern-

ing radiative transfer through dispersed media, we

were privileged to interact personally with Peter J.

W. Debye, John von Neumann, George Uhlenbeck,

and Subrahmanyan Chandrasekhar. My later stu-

dents solved models for radiatively stabilized com-

bustion that involved integro-differential equations

and complete free-radical kinetic models. My most

Chemical Engineering Education

KNOWLEDGE STRUCTURE

recent students devised the first numerical solu-

tions for flow and heat transfer with secondary mo-

tion in double-spiral heat exchangers and for

thermoacoustic convection.

These exciting and productive experiences have

all been a consequence of undertaking problems for

which no method of solution was yet known. We did

not necessarily even know in advance what forms of

mathematics would prove helpful; we simply were

confident (or foolhardy) enough to believe in our

ability to identify, master, and apply the necessary

techniques, whatever they might be.

This is not a unique story; it could be told with

slight differences by a number of others in our pro-

fession.[8' The only excuse for reviewing my own ex-

periences is that they illustrate the advantages that

accrue from a working knowledge of advanced math-

ematics and the confidence to use that knowledge.

This confidence, particularly when it extends be-

yond classical solutions, leads to boldness in tack-

ling problems of unpredictable difficulty and in de-

vising new techniques for their solution. Our objec-

tive as teachers should be to prepare and encourage

students to undertake such challenges rather than

to avoid them.

Although the above experiences were generally in

the framework of doctoral research, in most instances

one or more undergraduates also participated and

they often made significant intellectual contribu-

tions. Insofar as it is possible, such an experience

should be provided for our undergraduates as a

supplement to their regular course work. (As an

aside-within-a-digression, there appears to be a

strong correlation between undergraduate partici-

pation in exciting research and a positive decision to

attend graduate school.)

THE ROLE OF COMPUTERS

The principal technological event of our genera-

tion has been the rapid development of computers

and their software. This development has shifted

the emphasis on mathematics rather than replacing

it. Students are more receptive to computer use than

to mathematics, but some analogous problems have

arisen. Symbolic manipulators and canned numeri-

cal algorithms are often a convenience, but they

isolate the user from the mathematics and technol-

ogy of the process itself. Most computer scientists

show the same disdain as do pure mathematicians

for engineering-hence, we should anticipate some

of the same difficulties in instruction in numerical

methods that have been endemic in mathematics.

Spring 1993

TOPICS

Said the Mock Turtle with a sigh, "I only took the

regular course."

"What was that?" inquired Alice.

"Reeling and Writhing, of course, to begin with,"

the Mock Turtle replied; "and then different

branches ofArithmetic-Ambition, Distraction,

Uglification, and Derision."

Alice's Adventures in Wonderland

The choice of appropriate topics in applied math-

ematics is difficult, but perhaps less important than

the methodology used in the classroom. I have re-

cently attained the position in academic life desig-

nated as "emeritus." This title apparently means

that you are welcome to assist, but not to advise or

to expect compensation. From that perspective, it

would be unseemly for me to make recommenda-

tions concerning specific topics in applied mathemat-

ics to be included in the curriculum of the future. In

any event, I do not have a crystal ball with which to

predict those topics of engineering science that will

either fade, continue, grow in importance, or newly

appear in the decades ahead. Recently, in this same

journal, Ramkrishna91 mentioned some aspects of

mathematics which may become important to chemi-

cal engineers, but his focus was presumably on re-

search rather than on undergraduate education. I

will limit myself to a single guideline.

The topics of chemical engineering science that

were included in the knowledge structure sympo-

sium (physical chemistry and stoichiometry, ther-

modynamics, transport phenomena, and reaction

engineering) constitute one obvious criterion for the

choice of topics of mathematics to be included in the

curriculum-that is, the essential elements are those

needed to describe the laws and relationships of

these and other engineering sciences in the form of

algebraic, differential, integral, or stochastic mod-

els, as well as to derive solutions for these models

for general or specific cases. The elements and pro-

cedures of mathematics that are common to more

than one of the engineering sciences are of particu-

lar importance. It is, after all, the latter commonal-

ity that gives mathematics an all-encompassing role

and importance in the curriculum.

AN ANALYSIS OF MODELS

One technique which I have found to be successful

in the classroom and in homework for providing an

overview of applied mathematics is to emphasize

the analysis of models rather than the process of

solution. (This is not to say that instruction in meth-

ods and solutions should be neglected.) The models

89

KNOWLEDGE STRUCTURE

KNOWLEDGE STRUCTURE

which serve as a starting point for such analyses

should ordinarily be the general partial differential

equations of conservation, together with equations

of state, kinetic mechanisms for chemical reactions,

etc. If these equations are not familiar to the stu-

dents from their previous courses in engineering

science, they must be derived at this point as a

preliminary step. A list of questions which can then

be posed is presented in Table 1.

In some complex processes, for example in turbu-

lent flow1131 and in the motion of a rising bubble,[141

considerable information can be attained, even if a

simple list of variables rather than a set of partial

differential equations is used as the model. Conven-

tional dimensional analysis is then applied to deter-

mine a minimal set of linearly independent dimen-

sionless groups incorporating all of these variables.

One or more procedures for identifying these group-

ings are described in most standard textbooks. They

generally fail, however, to indicate the possibility of

error owing to omissions or improper inclusions in

the list of variables. They also often neglect to indi-

cate the consequences of alternative choices of vari-

ables-for example, the shear stress on the wall

rather than the pressure gradient, and the mass

rate of flow rather than the mean velocity. They

frequently fail to stress the significance of alterna-

tive groupings and of the speculative deletion of

variables.[11"12141 These procedures often produce

asymptotic solutions whose only deficiency relative

to a complete analytical solution is a numerical value

for the leading coefficient. As a consequence, this

methodology may prove to be more useful to a stu-

dent and a practicing engineer than some particular

TABLE 1

Illustrative Questions to Stimulate the Critical Analyses of Models

1. Which terms can be dropped in general? Why?

2. Which terms can be dropped for particular cases on mathematical grounds? Which ones can be dropped on physical grounds?

3. Which terms must be dropped and which must be retained to obtain the appropriate model for classical limiting cases? For example, for fluid

motion the following limiting cases might be considered:

inviscid flow incompressible flow developing flow open-channel flow

purely viscous flow one-dimensional flow boundary-layer flow buoyant motion

purely inertial flow rectilinear flow steady flow free-streamline flow

slightly inertial flow fully developed flow unconfined flow turbulent flow

4. Which of the reduced models are linear?

5. What is the form of the reduced models from a mathematical point of view (parabolic, elliptic, hyperbolic)? What is the significance of this division

by form?

6. What are the relative advantages of the Eulerian and Lagrangian forms? (This question provides an opportunity to contrast the approaches in

engineering and in pure science.)

7. How can the model be dimensionalized? (This provides an opportunity to introduce the method of Hellums and Churchill'"" or the equivalent.)

8. What are the advantages and disadvantages, if any, of dedimensionalization?

9. Is a similarity transformation possible? (Exposition of the method of Hellums and Churchill"0' is again suggested.)

10. Can the model be simplified by a transformation of variables other than a similarity transformation? (Examples are the stream function, the vector

potential, and the vorticity.)

11. What is the physical significance of each of the boundary conditions? Are they physically realistic?

12. What is the physical significance of each term in the model? What are the criteria for dropping a term?

13. Will different methods of solution, such as 1) separation of variables and expansion in Fourier series, 2) conformal mapping, and 3) the Laplace

transform, lead to different solutions?

14. How can the Laplace transform be used to derive asymptotic solutions?

15. Try to conceive as many types of asymptotic behavior as possible. What reductions in the model are appropriate for these limiting cases? (See

Churchill" .121)

16. To what extent can the behavior of interest be circumscribed by asymptotic solutions?

17. What are the consequences of time-averaging an equation for conservation?

18. Is dimensional analysis of the equations of conservation applicable for turbulent flow in both time-dependent and time-averaged forms?

19. Does a numerical method of solution yield exact results as the subdivisions are increased?

20. What are the relative advantages of finite-difference, finite-element, and Monte Carlo methods?

21. What are the advantages of generalized computer programs as compared to special purpose ones?

22. What is the significance of a pseudo-steady state? Suggest possible applications.

23. What is stiffness with respect to numerical solution of a differential equation?

24. What are the advantages and consequences of developing a solution for the "phase-plane"?

25. What is the consequence of simplifications in a model which reduce the required number of boundary conditions?

26. What is the consequence of a transformation such as the introduction of the stream function which raises the order of the derivatives?

27. How can the required number of boundary conditions be identified?

28. What is the significance and consequence of an integral approximation such as for a boundary layer?

) Chemical Engineering Education

KNOWLEDGE STRUCTURE

analytical method such as conformal mapping.

The development of correlating equations that in-

corporate asymptotic solutions as components also

helps to provide an overview. The derivation of as-

ymptotic solutions may then be recognized as an

essential part of this process. The derivation of ei-

ther complete analytical or numerical solutions may

similarly be recognized as a means of generating

precise data with which the coefficients in the corre-

lating equation can be evaluated. In this context,

Shinnar~'15 has recently mentioned the need to base

correlations on the advances of engineering science,

and Churchill"161 has asserted that one of the princi-

pal roles of analysis is to support the construction of

correlating equations.

What are the advantages of the above approach?

It focuses on the model rather than on a

particular solution.

It focuses on the process and significance of

reducing the model rather than on the solu-

tion for some reduced model of unknown

applicability.

It emphasizes the possibility of more than one

method of solution and suggests an objective

basis for comparison of competitive solutions.

It integrates the physics and chemistry with

the mathematics.

It stresses a method of pure reasoning which

will be applicable to new problems.

It reveals the asymptotic character and

significance ofparticular solutions. (Most

solutions in closed form actually fall in this

category.)

It avoids excesses by focusing on possible

simplifications and their significance rather

than on general solutions.

It helps to alleviate one of the principal

sources of frustration for students, namely the

evocation of simplified models by the teacher

without explanation or justification in ad-

vance.

How and where can we incorporate the above ap-

proach in the curriculum? The simplest procedure is

to incorporate it in each of our present courses in

engineering science as applicable, rather than add-

ing or replacing a course.

Arthur E. Humphrey, my previous departmental

chairman and dean, has asserted that I teach the

same material and methodology in whichever course

I am assigned. In regard to this approach to analy-

sis, I am willing to confess to the crime, if it be one.

Spring 1993

SUMMARY

We are failing to prepare our undergraduates to

use mathematics in their professional work. This

failure has serious consequences relative to our

profession and to the recognition of new devel-

opments when they are expressed in the language

of advanced mathematics. The superior preparation

in mathematics of students from Europe and Japan

is a benchmark in this respect. Focusing on the

structure of models rather than only on detailed

analytical solutions is proposed as a partial correc-

tive. The increasing role of computers in the prac-

tice of chemical engineering can be expected to in-

fluence the choice of topics in applied mathematics

but not to eliminate the importance of proficiency

therein. The well-known problems of instruction in

mathematics can be expected to reappear in courses

in computer science.

REFERENCES

1. "Goals of Engineering Education," Amer. Soc. Eng. Ed.,

Washington, DC (1968)

2. Badger, W.L., and W.L. McCabe, Elements of Chemical En-

gineering, McGraw-Hill, New York (1931)

3. Brown, G.G., and Associates, Unit Operations, John Wiley

& Sons, New York (1950)

4. Sherwood, T.K., and C.E. Reed, Applied Mathematics in

Chemical Engineering, McGraw-Hill, New York (1939)

5. Marshall, Jr., W.R., and R.L. Pigford, The Application of

Differential Equations to Chemical Engineering Problems,

University of Delaware, Newark, DE (1947)

6. Bird, R.B., W.E. Stewart, and E.N. Lightfoot, Transport

Phenomena, John Wiley & Sons, New York (1960)

7. Churchill, S.W., "The Changing Role of Applied Mathemat-

ics in Chemical Engineering," AIChE Symp. Ser. No 235,

79,142 (1948)

8. Aris, R., and A. Varma, Eds., The Mathematical Under-

standing of Chemical Engineering Systems: Selected Papers

ofNeal R. Amundson, Pergamon Press, Oxford (1980)

9. Ramkrishna, D., "Applied Mathematics: Opportunities for

Chemical Engineers," Chem. Eng. Ed., 24, 198 (1990)

10. Hellums, J.D., and S.W. Churchill, "Simplification of the

Mathematical Description of Boundary and Initial Value

Problems," AIChE J., 10, 110 (1964)

11. Churchill, S.W., "The Use of Speculation and Analysis in

the Development of Correlations," Chem. Eng. Commun., 9,

19 (1981)

12. Churchill, S.W., "Derivation, Selection, Evaluation and Use

of Asymptotics," Chem. Eng. Technol., 11, 63 (1988)

13. Churchill, S.W., "New and Overlooked Relationships for

Turbulent Flow in Channels," Chem. Eng. Technol., 13, 264

(1990); 14, 73 (1991)

14. Churchill, S.W., "A Theoretical Structure and Correlating

Equation for the Motion of Single Bubbles," Chem. Eng.

Proc., 26, 269 (1989); 27, 66 (1990); also see Viscous Flows:

The Practical Use of Theory, Chap 17, Butterworths, Bos-

ton, MA (1988)

15. Shinnar, R., "The Future of Chemical Engineering," Chem.

Eng. Prog., 87, No. 9, 80 (1991)

16. Churchill, S.W., "The Role of Analysis in the Rate Pro-

cesses," Ind. Eng. Chem. Res., 31, 643 (1992) 0

KNOWLEDGE STRUCTURE

KNOWLEDGE STRUCTURE OF THE

STOICHIOMETRY COURSE

RICHARD M. FIELDER

North Carolina State University

Raleigh, NC 27695-7905

Most chemical engineering curricula in North

America begin with the stoichiometry

course. The content of this course is fairly

standard: definitions, measurement, and estimation

of various process variables and physical properties

of process materials; descriptions and flow charts of

unit operations and integrated processes; gas laws

and phase equilibrium relations; laws of conserva-

tion of mass and energy; and the incorporation of all

of the above into material and energy balance calcu-

lations on individual chemical process units and

multiunit processes. The material is not intrinsi-

cally difficult, especially compared to the content of

later courses in transport processes and thermody-

namics, but the approach required to set up and

solve course problems takes most students consider-

able time to grasp.[1

The course may conveniently be divided into two

parts for the purposes of defining a knowledge struc-

ture-material balances and energy balances. Pos-

sible structures for each part are shown in Figures 1

and 2. The following paragraphs comment on those

structures.

Knowledge Structure

Material Balances

(Figure 1)

E The concept of conservation is essential to the

course and is generally accepted implicitly. The prin-

Richard M. Felder is Hoechst Celanese Pro-

fessor of Chemical Engineering at North Caro-

lina 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 insti-

tutions. He is coauthor of the text Elementary

Principles of Chemical Processes (Wiley, 1986).

Copyright ChE Division ofASEE 1993

92

cipal concepts that all students must bring with

them from their prior education come from math-

ematics (basic algebraic and graphical manipula-

tions, solving sets of linear equations and word prob-

lems), physics (phases of matter, conservation of

mass), and chemistry (atoms and molecules, stoi-

chiometric equations, molecular weight, and molar

quantities).

O The building blocks of the course are properties

of process systems and materials including mass,

volume, pressure, temperature, and (later) en-

ergy. These properties are conceptually taken for

granted in the course, although both professors and

students might be hard pressed to define most of

them. Fortunately, they are familiar enough for us

to be comfortable with them, which is all we need to

be able to build on them successfully.

E Other broad concepts that may be presented in

first-year courses but are more likely introduced in

this one include (a) multistep chemical processing

and graphical representation of chemical processes

flowchartss); (b) the idea that a system has a state,

defined as the collection of all its physical properties

and determined by the values of a subset of those

properties; (c) various physical laws and relations

among system variables that allow some variable

values to be determined from specified values of

others; (d) the notions of equilibrium, dynamic equi-

librium, phase equilibrium, reaction equilibrium, and

steady-state and transient operation of a system; (e)

the idea that variables must sometimes be estimated

approximately rather than calculated to six signifi-

cant figures; (f) the idea that problems must some-

times be solved by trial-and-error; (g) the idea that

there's nothing illegal or shameful about (e) and (f).

E Most of the content of this part of the course

consists of definitions of and relations among the

variables that characterize chemical process sys-

tems-temperature, pressure, volume, density,

flow rate, mass fractions and concentrations, frac-

tional conversion, compressibility factor, vapor

Chemical Engineering Education

KNOWLEDGE STRUCTURE

pressure, relative humidity, etc.-and procedural

and computational algorithms for calculating values

of some of these variables from known values of

others. The sequence of the information flow is sug-

gested in Figure 1.

Knowledge Structure

Energy Balances

(Figure 2, next page)

All of the material listed in the previous section is

prerequisite to that which follows.

O Energy now takes its place as a basic course

concept that few involved with the course either

understand or question. Again, the fact that we think

we know what it is and feel comfortable about it

keeps us from hopelessly bogging down at this point.

D The integral of a function now joins the list of

prerequisite mathematical concepts and the prin-

ciple of conservation of energy joins the required

physical concepts.

ED Once energy and temperature are admitted as

working concepts, the three forms of energy (kinetic,

potential, and internal) and modes of energy trans-

fer (heat and work) can be introduced, setting the

stage for the first law of thermodynamics.

D A concept that arises in the context of the first

Figure 1. Knowledge structure-material balances

Spring 1993

KNO WLEDGE STRUCTURE

law is enthalpy, defined for convenience as a fre-

quently occurring combination of other system vari-

ables (H = U + PV). Perhaps because of its strange-

sounding name, students never get fully comfortable

with enthalpy-they eventually learn to work with

it (as in Q = AH), but they always have the feeling

that there is something fundamental and mysteri-

ous about it that puts it beyond their intellectual

reach. Trying to convince them that enthalpy is re-

ally a simple concept and things like mass and en-

ergy are concepts much more worth worrying about

is generally futile. (Later they will get into thermo-

dynamics, which will finish the job of overwhelming

them with variables defined for convenience and

given strange names.)

0 The previously introduced notions of the state

of a system and state properties now reappear, lead-

ing to the concepts of reference states and process

paths for calculating AU and AH. All the necessary

ingredients for energy balance calculations are now

in place.

Figure 2. Knowledge structure-energy balances.

Chemical Engineering Education

KNOWLEDGE STRUCTURE

KNOWLEDGE STRUCTURE

E Most of the content of this part of the course

consists of (a) definitions of and procedures for

measuring and estimating the energy-related vari-

ables that characterize chemical process systems-

heat capacities, latent heats of phase change,

solution, and mixing, and heats of reaction, forma-

tion, and combustion; (b) procedural and computa-

tional algorithms for calculating internal energy

and enthalpy changes associated with transitions

from one system state to another; and (c) procedures

for solving the first law equation for unknown en-

ergy flows or changes in state in various unit pro-

cesses. The sequence of the information flow is sug-

gested in Figure 2.

TRANSIENT BALANCES

Most stoichiometry textbooks contain a chapter on

transient system balances. A key concept here is

that of a derivative. While students in the course

can differentiate functions on demand, they have no

physical or intuitive understanding of derivatives,

in part because most mathematics professors seem

to fear that they would harm their reputations by

putting applications in the elementary calculus se-

quence. Covering transient balances in the stoichi-

ometry course could help the students make signifi-

cant progress toward this understanding; unfortu-

nately, the course almost never gets to transient

balances and most introductory transport courses

take the underlying knowledge structure of this topic

for granted.

AFTERWORD

Once a knowledge structure has been defined, the

next logical step is to consider how it can best be

transferred into students' brains. I believe that for

stoichiometry there are two keys:

1. Provide explicit instruction and lots of drill in

basic problem-solving procedures,

especially the systematic use of the flow chart

coupled with informal degree-of-freedom analy-

sis to organize the solutions of material and en-

ergy balance problems.

2. Establish an active, cooperative learning environ-

ment.

Have students work in teams on problems in

class and on the homework, identifying concep-

tual and procedural sticking points and finding

out how to get past them, teaching and learning

from one another.

For specific ideas about how to accomplish these

tasks, see Reference 1.

REFERENCES

1. Felder, R.M., "Stoichiometry Without Tears," Chem Engr.

Ed., 24(4), 188 (1990) 0

RJR% letter to the editor

Dear Editor:

Due to an unfortunate oversight, the article on the Mark-

ovian approach to chemical kinetics (CEE, 27, 42-43) does

not discuss the importance of choosing properly the

duration of a stage for the sake of acceptable numerical

accuracy. In any discrete approximation to a contin-

uous phenomenon, the time increment in the former

must be sufficiently small, and Markov chains are no

exception.

In the numerical example of the article, the stage width

of 0.001 minutes is one appropriate choice, when 75% of

species A at a given time decompose to B and 5% of

species B at a given time decompose to species A in one

minute. With this choice, the Markov formulation

A(n+ 1) (0.99925 5.0e-5)(A(n))

B(n+ 1)) (7.5e-4 0.99995)(B(n))

and the integral rate equations

A(t) =0.075 +0.925 exp(-8.0 e 4t)

B(t)= 1.125-0.925 exp(-8.0 e 4 t)

Spring 1993

agree to at least a four-decimal accuracy when t=n=stage

number, as shown in the tabulation. Steady state condi-

tions are reached essentially at n = 10000.

The author regrets the omission of this material, and

wishes to thank Dr. Alan M. Lane at the University of

Alabama, Tuscaloosa, for drawing it to his attention.

n A(n) B(n)

Markov Rate Eq. Markov Rate Eq.

1 0.9993 0.9993 0.2007 0.2007

10 0.9926 0.9926 0.2074 0.2074

1000 0.4905 0.4906 0.7095 0.7094

5000 0.0919 0.0919 1.1081 1.1081

10000 0.0753 0.0753 1.1247 1.1247

inf. 0.075 0.075 1.125 1.125

Thomas Z. Fahidy

University of Waterloo

KNn)WLFf Qn= STRUCTURE

THERMODYNAMICS

A Structure for Teaching and Learning About Much of Reality

JOHN P. O'CONNELL

University of Virginia

Charlottesville, VA 22903

Thermodynamics is an amazing discipline. Its

two brief laws contain the complete basis for

establishing the states of pure and mixed sys-

tems and their tendencies for change. The founda-

tion for scientific investigations into all forms of

matter lie in its rigor. Constraints on engineers to

interconvert heat and work, separate components

from solutions, and obtain ultimate yields from

chemical reaction arise with its symbolic manipula-

tion. Reliable screening for feasibility and optimiza-

tion of nearly every type of process can be guided by

its procedures. Thermodynamics is fundamental and

applicable to all technical endeavors.

Though thermodynamics focuses on natural phe-

nomena, it is really just a deductive structure devel-

oped by creative and systematic human minds. Na-

ture has carried out her diverse processes for eons

without being explicit about energy, entropy, and

fugacity. We find these mental constructs useful be-

cause they give us a chance to assimilate extensive

amounts of real behavior, rather than being over-

whelmed by its totality or misguided by less general

alternatives. Further, we can use "always true" ther-

modynamics with appropriate information and ap-

proximation to effectively describe and predict mul-

titudes of reality.

Modern thermodynamic ideas originated over 150

years ago, but the subject still evolves. Although

some scholars claim that "there is nothing new in

thermodynamics," a few still find challenges in its

John O'Connell is H.D. Forsyth Professor of

Chemical Engineering at the University of Vir-

ginia. He received his BA from Pomona College,

his BS and MS from MIT, and his PhD from the

University of California (Berkeley). He taught

thermodynamics and statistical mechanics as

well as materials science for chemical engineers

at the University of Florida from 1966-88. His

research on varieties of fluids involves theory,

molecular simulation, and experiment.

Copyright ChE Division ofASEE 1993

Though thermodynamics focuses on natural

phenomena, it is really just a deductive structure

developed by creative and systematic human

minds. Nature has carried out her diverse

processes for eons without being explicit

about energy, entropy, andfugacity.

abstractness, rigor, and universality as well as in

debating the "best" way to phrase the principles and

their limits of application. But most current engi-

neering work deals with the practical uses of

thermodynamics-predominantly with models of

reality. Modern computers enable testing of

quantitative expressions for phenomena at every

level of complexity. As a result, we find thermody-

namics being used to an unprecedented extent to

mimic and predict Nature's behavior more easily

(and often more reliably) than experiment-espe-

cially for mixtures.

Unfortunately, the word "thermodynamics" pro-

vokes uneasiness or frustration in many well-edu-

cated people, especially in alumni of engineering

thermodynamics courses. This often arises from an

incomplete or insecure classroom experience com-

bined with insufficient background in assimilating

all the basics. Becoming really comfortable with ther-

modynamic concepts and proficient in their use re-

quires a comprehensive appreciation of the subject

in addition to care, maturity, and intelligence. Thus,

major objectives of thermodynamics education should

include overcoming confusion and antipathy while

fully integrating the concepts, knowledge, and pro-

cedures. The process, though quite demanding, must

guide students to appreciate the structure and rel-

evance of thermodynamics and to become effective

in its use. It should also enrich their vision of

Nature's unity and diversity.

What follows is one teacher's view of fundamental

thermodynamic structure and how it leads to ap-

plications that could foster a useful and satisfying

learning experience for chemical engineering stu-

dents. While integration and connection require

Chemical Engineering Education

KNOWLEDGE STRUCTURE

terms of study and often years of practice, the ideas

presented here may be valuable for others in en-

hancing learning.*

STRUCTURE

Because thermodynamics is a logical construct,

there are many ways that the subject can be devel-

* Jim Haile (Clemson) contributed much to these beginning

thoughts.

A Pedagogical Structure of Thermodynam

Category Elements

Observations PrimitjveConcepts ral Phenomer

S ns Mathema

Generalizations Measu les & Variables

& Constraints as kles & Vanables

onstraMaterial Conservation

( Initially For Energy Conservatio~ Nonequivlnce

\Fixed Composition I Degradation_ st& 2Tfaw Equatio

# ii eeident arables of Sti

Articulation & St te Prdperties & Boundaries' Conce pa

Quantification / fConnections Among Partial Deri

Pro rties........ ...Principles .of

Multicomponent Fluids :: Compoiion Variables Partial M

Equilibrium & Change Extrema of Conceptuals Pro

Phase Stability Diffe

Phases and Reactions Phas ilibum Phase Reaction

SRelations ia ams Relatio

ods Organization of Information

Models Data Tabulations Simulations

............................................................ ... ............ ...... ....... ........ .. ".

'-Mixing & Separation Chemic

Applications -, Transport Tendencie Heat &

"* Volumes and Heats

Direct Connection ------- Indirect Connec

Figure 1. A structure of chemical engineering thermod

PRIMITIVE CONCEPTS NATURAL PHEN

MEASURABLES HAPPENING

Things Properties & State Changes Thermal and Material

System Force Input mechanical transfer of

Surroundings Length Output effects on substances

Boundaries Pressure Accumulation fluids via various

Volume Generation and solids mechanisms

Consumption

Table 1. Observations

Definitions Mathemat

Identity Chemical species Algebraic equations a

System-surrounding interactions Functions of several

Quality Extensive and intensive Independent and depe

Reversible and irreversible Calculus derivatives

Quantities Mass Differential equations

Temperature Exact and inexact

Work Balance equations

Kinetic energy Path dependence of ii

Potential energy

Table 2a. Generalizations I

Spring 1993

oped. That is why there are so many textbooks. One

extreme approach is to begin with axiomatics and

mathematics, which then lead through formalisms

to applications (the most elegant and difficult trea-

tise on this is by Truesdellt11). The other extreme is

to note common observations, followed by generali-

zations and applications (Fenn has cleverly shown

this technique with a cartoon character called

"Charlie the Caveman"[21).

Present-day students tend to be

ics inexperienced in "the way things

work," so I find that discussing ob-

servations first can be motiva-

na

.--. ................. tional, informative, and organiza-

tional. The flow diagram I gener-

f Work & Heat ally follow is shown in Figure 1.

nns & Inequality

te ............. The way basics are initiated is

a Properties j through primitive concepts and

ves as Properties natural phenomena, as listed in

....... Table 1. The key to the concepts is

lar Properties

a high level of precision that will

ead easily to later mathematical

erty Differences .

rental Finite descriptions of the phenomena.

................These initial elements should

ns / be phrased and illustrated in what-

.... ever terms that will make the

Equation Solving

properties Flow group of learners relate to them.

alReactions Years ago, references to cars and

Work Machine farming worked. Nowadays it

needs to be connected to tele-

tion vision, sports, music, environ-

ment, and the materials and goods

dynamics. of affluence.

IOMENA The next step is generalizations

s and constraints, beginning with

Reactive definitions related to physics and

conversion chemistry as well as to mathemat-

with regular ics. Table 2a shows the kinds of

changes in things I define in familiar terms,

form and amount

in addition to the mathematical

tools that must be used with facil-

ity in the study and implementa-

ics tion of thermodynamics. One point

that I usually make is that we do

nd variables not know what temperature (hot-

1 variables

indent variables ness) really is-we only know it

ad integrals can make a difference to a system,

although not always. This uncer-

differentials tainty of what a property "really

integration is" often makes the later concep-

tual quantities of energy, entropy,

and fugacity less threatening since

KNOWLEDGE STRUCTURE

something as familiar as temperature

is really unknown yet easily utilized

with experience. Another device I have

used to deal with the unfamiliar prop-

erties is to read the story of 37 sugar

cubes, a small boy, and his mother.[31

(Some students, however, find that

these challenges make the whole pro-

cess even less appealing!)

Table 2b lists a set of "convenient"

observations, definitions and equations

which encompasses the conservation

of mass, the number of variables

needed to completely describe a sys-

tem, the definition and conservation

of energy, and the definition and gen-

eration of entropy. These particular

choices are made because they lead di-

rectly to the most widely used state-

ments of the laws and open system

results, even though at this stage only

systems of fixed composition are dis-

cussed. The level and amount of time

on this part depends on the students'

prior exposure-obviously, less is done

with graduate students.

Because the fundamentals given to

this point are often alien and abstract,

they are articulated further, as shown

in Table 3. The objectives are under-

standings, procedures, and recognition

that users must assimilate. It is es-

sential that learners understand at this

point that people invented state prop-

erties and conceptuals for their gener-

ality and directness, even if they were

not measurable like the things we pre-

fer to (and ultimately must) deal with.

The next step separates chemical en-

gineers from the rest because the de-

velopment is extended to multicompo-

nent systems (see Tables 4a,b). This

leads to a morass of definitions and

complexities as the dimensionality of

the system grows, and I know of no

way to simplify this. By this time I

have begun to insist that students have

a notebook of definitions and I give

the first part of each exam as a closed-

book set of definitions, asking both

word and equation answers for the

quantities previously defined. I also al-

ways use the symbol for the definitions to distinguish them from

mere qualities.

Particularly troublesome is fugacity. Students must recognize it is

not a "corrected partial pressure"; it is a practical substitute for the

chemical potential. Also, fugacity must be connected to temperature,

pressure, and composition. The "Four Famous Fugacity Formulae"

(FFFF) of Mike Abbott'41 (I use Five FFF) assures students that there

are only a few options for every problem of phase and reaction equi-

libria. Also, they should be aware that it is now routine, though

complicated, to connect complex composition behavior of activity co-

Convenient Observations Definitions

Mass conserved

(except in nuclear changes)

# independent variables

is # interactions

Work depends on path

except if no thermal

interactions (Joule)

Work and heat are not

equivalent even in

reversible changes

Work can be degraded

to heat, but not

vice versa

Objective

Proper # variables

for describing system

Replace boundary-crossing

quantities with changes

of system state properties

Conceptual properties and

their "natural" variables

Connections among

properties via

partial derivatives

Partial derivatives

as properties

Property evaluation from

integration of

partial derivatives

Atomic and

molecular "weights"

Heat, work, and

material interactions

Closed system

AE WAdiabatic

Q = AE- W

U = E EK -EP

Closed system

dS- 8QRev / T

T is integrating factor

(Born and Caratheodory)

dSGen a dS- 0

T

Equations

Mass balance

MIn MOut = MAccumulated

(#Ind) = (#Work) + (# Species) + 1

P = P(T,V,x)

V' = V(T,P,N') = N'V(T,P,x)

Energy balance

Ein(Work,Heat,Material)-

EOut(Work,Heat,Material) =

EAccumulated

Closed system

dE= TdS + WRev

Entropy balance

Sin(Heat,Material)-

SOut (Heat,Material)=

SAccumulated

Example Mechanisms and Equations

Determine total # variables; Count # equations

Difference is # independent variables =

# dependent (solved-for) variables is # equations

dUSys = 8Surroundings + WSurroundings

=dQRev +dWRev

= TSysdSSys PSysdVSys

H-U+PV G-=H-TS

dH=TdS+VdP dG= -SdT+VdP

Maxwell relations

(S / ap), = -(av / aT)p

Gibbs-Helmholtz relations

(G /T)/a(l/T)|p= H

T =_(aU / aS)V P = -(au / aV)S

Cp(T,P)=( QRev / dT)p = T(aS / aT)p = (aH / aT)p

AH = f(aH/aT)pdT + f(aH/aP)TdP

Path independent Path dependent

Path dependent

Table 3. Articulation

Chemical Engineering Education

Table 2b. Generalizations II

KNOWLEDGE STRUCTURE

Composition Variations

Amounts or fractions of

species affect system

Nt =[N]t

xi [x]i

n variables

n -1 variables

Independent variables

Extensive = n + 2

Intensive = n + I

Mass fractions, volume fractions,

molarity, molality, etc.

Chemical potential

gi(S,V,X) =aut /aNt

St ,V t,Nj

J*i

Fluid Mixtures

Gases

Compressibility factor

Residual properties

Fugacity and fugacity coefficient

dGi = RTd In fi (Fixed T)

Condensed Phase Solutions

Excess properties

Reference fugacities and

activity coefficients

Lewis-Randall (LR) reference

Henry's Law (HL) reference

Famous Fugacity Formulae (FFF)

Have P in various terms

Use Poynting correction

Connections of residual to

excess properties

Partial Molar Properties

Fi F / N P

F Ft/ T,P,Nt

Fi= YxiFi

Gibbs-Duhem equation shows how n+2 intensive

variables (Fi,T, P) are related by one equation

(aF /aT)p,x dT + (aF / aP)T, dP = xidFi

to give n+l independent variables

Partial Molar Gibbs Energy

GiaGtc'/aNI =gi(T,P,x)

TPNji

Nonidealities and Idealities

PV = zNtRT lim z=

IG

FR F- FIG

fi xiiP

lim G i = 1

IG

Real z, i from EOS

F(T,P,x) xiFio(T,P)+FE (T,P,x)

Ideal Solution FE = 0

fi (T,P,x) = xiifo Ideal Solution Yi =1

fio pure

-i

lim yi-l

xi-*l

fi=Hi lim i=l1

xi->0

#2 fi(T,P,x)=xiYi(T,P,x)fi(T,P)

#3fi(T,P,x)=xiYi(T,P,x)fio(T)exp[J( Vo/ RT)dP]

#4i(T,P,x)= i(Txxii(Tx)fi(T)exp[(Vi /RT)dP]

#5 fi(T,P,x)=xiYi(T,P,x)f(T)

FFF#2 f(T,P)= ?(T,P)P

Yi (T,P,x) = i (T,P,x) / (T, P)

Table 4b. Multicomponent systems II

efficient to parameter mixing rules

for PVTx equations of state (e.g.,

Heidemann and Kokals51).

By this point in the course, there

has been a tremendous amount of

abstractness and it is time to get to

applications which can be addressed

via change and equilibrium, as

shown in Tables 5a and 5b. This is

where the generalizations can be

made real with characterizations of

driving forces and entropy genera-

tion in interesting systems under-

going change as well as in equilib-

rium (and metastable!) cases. A key

is to make sure students overcome

the myth about entropy always be-

ing maximized.

The next section (Table 6) shows

the sets of relations that apply to

phase and reaction equilibria as well

as some of the physics of what Na-

ture can do when it settles down. I

use many plots of different variables

for different kinds of substances and

mixtures. The message is that "Na-

ture does all things easily; ain't Na-

ture grand!" I also insist that stu-

dents recognize that "for every equa-

tion there is a graph, and for every

graph there is an equation." If they

are not sure of what an equation re-

ally means, they should draw its

graph and vice versa.

At this point, the fundamentals are

done. It's time to use thermodynam-

ics. Table 7 shows the elemental

methodology. The ultimate goal is a

quantitative result that is reliable

Change

Driving forces for change

Heat flows from high to low temperature

Work flows from high to low "force"

(e.g., PV work from high to low P)

Material diffuses from high to low chemical potential fugacityy)

Reversible changes Equilibrium changes (S,. =_ 0)

Only differential differences in T, P, Gi

Spontaneous changes Real changes (Se. > 0)

Finite differences in T, P, Gi

SG. increases with property difference

Greatest for heat flow with T difference

Table 5a. Change

Spring 1993

Criteria for Stability-What is Observed

Systems Only in isolated systems is entropy maximized

All others-minimization of an energy function

e.g., Minimum G if T,P fixed while varying x, phase, reaction

(Entropy not minimized for ambient 2-liquid oil/water!)

Phases Differential criteria

Pure fluids-Proposed phase unstable if (aP / aV)T > 0

Mixtures-Proposed phase unstable if stability matrix of

aGi /IN T,,N t not positive definite

J *

SMetastability satisfies differential but not global criteria

Can occur in solids, microstructured fluids (polymer, bio,

surfactant, colloid)

Table 5b. Equilibrium

Table 4a. Multicomponent systems I

I

KAlflWI FflIE RTRIJCTURE

and appropriately accurate for the case at

hand. This requires organization of

thermodynamic knowledge and introduc-

tion of models at the proper stage. Since

with models "where there's a way, there's

a will," the latter requires decisions.

While students feel unprepared and/or

unmotivated to choose among the myriad

of options, "life's like that," so the practice

is good. Modeling consists of a math-

ematical relation used to connect certain

properties to measurables that will allow

calculation of values for unknown

measureables. Generalized thermo-

dynamic models contain parameters that

depend on the substances) of interest. The

kinds of choices are suggested in Table 7.

Teachers must make sure that students

are given the tools to make these deci-

sions, including the common choices and

the usual rules of thumb.

The final requirement is to solve a set of

nonlinear algebraic equations. With cur-

rent computers and model software, stu-

dents can now solve numerically more "re-

alistic" problems, though the "black box

syndrome" can arise if the only student

input consists of numbers and "run."

PEDAGOGY

This process can be formalized in differ-

ent ways; I prefer the concept of problem

solving.[6' Table 8 shows a method devel-

oped with Jim Haile (Clemson University)

called "PSALMS". It is a step-by-step tech-

nique that works well for typical chemical

engineering thermodynamic problems. The

two initial steps of "Problem" and "Sys-

tem" are the same as in essentially all

"PS" methodologies. The next uses the

power of thermodynamics that declares cer-

tain relations to be "ALways true" so us-

ers can initiate something valid and rel-

evant rather than stare at a blank piece of

paper or make an assumption too early.

The fourth step of "Model" is an essential

part of contemporary thermodynamics (the

table suggests some of the choices to be

made). The final step is "Solve and check,"

which is again a part of all PS methods.

By now this article has either lulled you

to sleep because all of this seems so

straightforward, or made you extremely

100

Phase Equilibrium Relations

Chemical Potentials

gi(T,P,x)=ii (T,P,x")=...

Fugacities

fi (T, P,x')= fi(T,P,x")...

Reaction Equilibrium Relations

Minimum Gibbs Energy

SvikGi =0 (Independent Reactions k)

Equilibrium Constant and Standard State (o)

Kk(T)= exp -vikG? / RT

= exp -vikAGO /RT

= [xiii(T,P,x)P] k (FFF#1)

Ref.()is pure IG at P=1

= I[fi(T,P,x)/fo(T) ik (FFF#3-5)

Ref.(o) is pure real (LR) or

hypothetical (HL) substance

Phase Diagrams

Pure P T

2-phase boundaries (S/V, L/V, S/L, S/S)

Fixed points (V/L, L/L critical; triple points)

Mixed multiphase systems

PTxy (multidimensional and projections)

Azeotropes, critical, 3- and 4-phases

Enthalpies ("Heats") of Vaporizing, Melting, Subliming

Related to P T 2-phase lines by Clapeyron equation

d i(PS) (H"-H')

d(/T) R -

d T) 2-phase -R z '

Clausius approximation for gases (") and liquids/solids (')

z =l>>z

Table 6. Phases and reactions

Organization of Information

Models and Data

Mathematical relations for

PROPERTIES (z, C GE, ) in terms of

MEASURABLES (T, P, x, V) for manipulation to get

ALL properties (e.g., conceptuals) (H, S, fi, etc.) needed for

SOLVING EQUATIONS for dependents (x, P, T, V, W, Q, etc) containing

PARAMETERS depending on molecular constitution

COMMON EXPRESSIONS requiring decisions

PVTx equations of state

GE = activity coefficients

Reference fugacities, f9

Mixing rules for pseudopure parameters of mixtures

Combining rules for unlike parameters from likes (often via kij)

Solve Nonlinear Algebraic Equations for

Intensive variables (T, P, x, etc.) in phases

Material flows (flash, etc.)

Phase existence and amounts

Table 7. Methods

Chemical Engineering Education

I\ I Q I EDGE STRUCTURE- -- --

KNOWLEDGE STRUCTURE

agitated because of how unrealistic it might seem to be. Cer-

tainly, it's not easy-but much of it is possible to achieve.

PSALMS

Problem Desired quantity, other variables

System Physical and chemical situation

Contents and constraints

Boundaries, work modes, species

Total variables, specified variables

ALways True Relevant generalized relations for specified system

Balances on mass, energy, entropy

Property differences

Fugacity, reaction equilibrium constant equations

Model Approximations to generalized relations

Choice of Famous Fugacity Formula

If FFF #1, EOS Type

Ideal, Virial, CSP, "Full"; P or V Independent

If FFF #2-5, Reference State, Pressure Effect

Specific choices, e.g.,

CSP parameterization; Cubic EOS;

fo values; GE correlation, group contribution method

Data (new or literature)

Solve and check Analytic, graphical, tabular, numerical

Table 8. A thermodynamics problem-solving strategy.

The Dilemmas of Beginners

There's a lot of material!

I've never done deduction before!

It's mostly abstract.

It's incredibly detailed!

It's a long way before real applications appear!

If I get started wrong, it takes a lot of work to get to the answer!

Table 9. How students respond to thermodynamics.

Suggestions to Keep Students Focussed

Stress procedure more than results, particularly in the beginning.

"Any fool, even a computer, can do a calculation."

Articulate that the goal is to quantitatively describe the richness of nature.

"Nature does all things and without any difficulty."

Emphasize exponential pattern of learning the subject.

"Hang in there. When things begin to click, you take off The question is

whether the end of the term happens first."

Connect equations to observable phenomena and pictures (graphs).

Student inexperience with natural behavior is pervasive and growing.

Insist upon precision of expression and thought, especially definitions.

"You gotta know what you're talking about!"

Minimize "understanding" and maximize "doing."

"I don't know what entropy andfugacity are, but I can tell you when to use them

and how they go."

Give practice problems involving only the setup steps (PSAL) of problem solving.

Assist students to develop their own PS style.

Have students read and report on the literature of physical properties.

"Hey guys! They actually use fugacity out there!"

Have students code a VLE program for real substances:

Forces decision-making and precision.

"Computers are unforgiving; they do all and only what they're told."

Undergraduates hard to teach fundamentals to; are not used to deduction, precision.

They want to "do" something immediately.

Hard to get graduates to unlearn old errors; they are reluctant to change old ways.

"They got me a B+!"

Table 10. Suggestions to keep students focused.

Spring 1993

Table 9 shows how I think the beginner in

this subject reacts. Of course, self-recogni-

tion is vital to making progress, so I confront

students with this soon after I begin to get

the "glazed-eyes syndrome" somewhere in the

multicomponent section. I also tell them that

I only became fully comfortable with thermo-

dynamics after the third time I taught it.

But that does not mean they can cop out-it

merely declares that progress is tough.

Finally, I have given in Table 10 a list of

some suggestions that seem to help keep us

on track. They are phrased as admonitions,

followed by salient quotes from instructors

and students.

My success as a teacher has fluctuated with

the class, my own distractions, the ions in

the air, and who knows what else. But it has

been tremendously satisfying when things

have clicked with students (the number in

class ranging from one to nearly all). Inter-

estingly, I think there is less a correlation

with intelligence than with commitment, at-

tentiveness, and willingness to move ahead

without being completely satisfied.

ACKNOWLEDGMENTS

In addition to those already mentioned,

many other stimulating individuals have in-

fluenced my pedagogy in thermodynamics.

They principally include Martin Fuller

(Pomona College), Bob Reid (MIT), John

Prausnitz (Cal-Berkeley), Tim Reed (Florida),

Grant Wilson (Wiltec), Aage Fredenslund and

Peter Rasmussen (DTH, Lyngby, Denmark),

Anneke Sengers (NIST), Ed Glandt (Penn),

and Herb Cabezas (Arizona). Also, Warren

K. Lewis (MIT), John Biery (Florida), and

Verna O'Connell (wherever I am) have been

tremendous inspirations.

REFERENCES

1. Truesdell, C., Rational Thermodynamics: A Course

of Lectures on Selected Topics, McGraw-Hill, New

York (1969)

2. Fenn, J.B., Engines, Energy and Entropy, W. H.

Freeman, New York (1982)

3. Van Ness, H.C., Understanding Thermodynamics,

Chap. 1, McGraw-Hill, New York (1969)

4. Abbott, M.M., personal communication, Rensselaer

Polytechnic Institute, Troy, New York (1978)

5. Heidemann, R.A., and S.L. Kokal, "Combined Ex-

cess Free Energy Models and Equations of State,"

Fluid Phase Equil., 56, 17 (1990)

6. Woods, D.R., ed., P.S. News, McMaster Univer-

sity, Hamilton, Ontario, Canada I

KNOWLEDGE STRUCTURE

THE BASIC CONCEPTS

IN TRANSPORT PHENOMENA

R. BYRON BIRD

University of Wisconsin-Madison

Madison, WI53706-1691

he transport phenomena can be described at

three scales: the molecular, the microscopic

(continuum), and the macroscopic. At each

scale the conservation laws for mass, momentum,

angular momentum, and energy play a key role.

Also, at each scale empiricisms have to be intro-

duced to complete the description of the systems: an

intermolecular potential expression at the molecu-

lar scale, the flux expressions (constitutive equa-

tions) at the microscopic scale, and the transfer co-

efficient correlations at the macroscopic scale. The

three scales are intimately connected, with the re-

sults for each scale contributing to the understand-

TABLE 1

The Equations of Change Based on Conservation Laws

(A) -pa = -(V pav)-(V ja)+ra a = 1,2,3...

(B) pv = -[V pvv]- [V ]+ paga

aat

(C) p p[rx v] + )= -V pv([rx v]+ [V ]

V. rx w'} + [rx pga] +XPata

T a a

(D) tp (1v2 + =-(V.v[v2 + ) (V q)

(V [. v])- ((pav +ja) ga)

a

p. = mass concentration of species a

p = density of fluid mixture

v = mass-average velocity

j = mass flux of a with respect to v

r = mass rate of production of a by chemical reaction

zT = (total) stress tensor

g. = external force per unit mass acting on a

r = position vector

L = internal angular momentum per unit mass

X = couple stress tensor

t = external torque per unit mass acting on a

U = internal energy per unit mass

q = heat flux vector

ing of the next larger scale.

At the microscopic scale, some information about

the constitutive equations can be obtained from the

thermodynamics of irreversible processes. This ap-

proach is particularly important in understanding

multicomponent diffusion and the "cross-effects" in

energy and mass transport.

For the most part, the notation and sign conven-

tions here will be those used in references 1, 2, 3, 4,

and 5, hereinafter referred to as TrPh, DPL1, DPL2,

STTP, and MTGL, respectively.

The Equations of Change

The basic equations of transport phenomena are

the equations of change for the conserved quantities

as shown in Table 1:

(A) Conservation of mass for each species

TrPh Eq. 18.3-4; MTGL 11.1-1

(B) Conservation of momentum

TrPh Eq. 18.3-2; MTGL 11.1-3; DPL1, 1.1-8

(C) Conservation of angular momentum

MTGL, p. 831, Problem 6

(D) Conservation of energy

TrPh Eq. 18.3-6; MTGL 11.1-4;DPL1, 1.1-12

These equations can be obtained by writing conser-

vation statements over

(a) a region fixed in space through which the fluid is

moving (DPL1, Chapter 1)

(b) a material element of fluid (i.e., a "dyed" blob of

fluid) moving through space.[61

"Bob" Bird retired in 1992 after forty years of

teaching-one year at Cornell and thirty-nine

years at Wisconsin. The book Transport Phe-

nomena, which he wrote with colleagues Warren

Stewart and Ed Lightfoot, was the first textbook

on the subject specifically prepared for under-

graduate chemical engineering students. He also

coauthored Dynamics of Polymeric Liquids, with

Bob Armstrong (MIT), Ole Hassager (DTH), and

Chuck Curtiss (UW).

Chemical Engineering Education

KNO WLEDGE STRUCTURE

The equations of change have been written in Table

1 in terms of the total stress tensor t which is

conventionally split into two parts: i = p5 + T

(where 8 is the unit tensor); p is the "thermody-

namic pressure"; and T is the "(extra) stress tensor"

which vanishes in the absence of velocity gradients.

No assumption has been made here that the stress

tensor be symmetric. Equations (A) through (D)

have to be supplemented with the thermal equa-

tion of state p = p(p,T,o,) and the caloric equation

of state U = U(p,T,o,)), where o. stands for the

mass fractions of all but one of the chemical

species a in the mixture.

By adding the equations in Eq. (A) over all spe-

cies, one gets the equation of continuity for the fluid

mixture (TrPh, Eq. 3.1-4]. By forming the cross prod-

uct of the position vector r with the equation of

motion, Eq. (B), one obtains Eq. (E); when the latter

is subtracted from Eq. (C) (the equation of conserva-

tion of total angular momentum), the equation for

internal angular momentum, Eq. (F), is obtained. 71

Similarly, by forming the dot product of the fluid

velocity v with the equation of motion, Eq. (B), one

obtains Eq. (G), the equation of change for the ki-

netic energy; when the latter is subtracted from Eq.

(D), the equation of change for the internal energy,

Eq. (H), is obtained. These various derived equa-

tions are tabulated in Table 2.

As pointed out in TrPh (page 314), the term

(nT:Vv) appears in Eq. (G) with a plus sign and in

Eq. (H) with a minus sign; it describes the

interconversion of mechanical and thermal energy.

Similarly, the term [e:'T] appears with a plus sign

in Eq. (E) and with a minus sign in Eq. (F), thus

TABLE 2

Equations of Change for Nonconserved Quantities

(E) -p[rxv]=-[V.pv[rxv]]- V. rxnrTT]

+ [rxpag ]+ [e:rrT]

a

(F) pL= -VpvLp-[Vk]]- [ pt- _e:,]

(G) 2 v(2)) -)

a

+(,T:v)((V.paga)

(H) apt=-(v pvt)-(V-q) ( T:vv)+^(v.pag a)

a

NOTE: On page 831 of MTGL, Eq. (E) is given for a

symmetric stress tensor, but [r x p] should be re-

placed by [r x p]T.

Spring 1993

describing the interconversion of external and inter-

nal angular momentum. In fluid dynamics textbooks,

it is usually assumed that the stress tensor is sym-

metric (i = eT), so that the external and internal

angular momentum are conserved separately, since

[E:'T] is then identically equal to zero. The so-called

"proofs" that the stress tensor is symmetric (such as

in Problem 3.L in TrPh, pages 114-115) tacitly as-

sume that there is no interconversion of external

and internal angular momentum, and that the ex-

ternal angular momentum is conserved in the fluid.

The kinetic theory of dilute monatomic gases yields

a symmetric stress tensor, as does the kinetic theory

for dilute solutions of flexible and rodlike polymers.

So far there is no experimental evidence that a

nonsymmetric stress tensor is needed.

When all species are subjected to the same exter-

nal forces (so that all gn equal g), and when it is

assumed that the stress tensor is symmetric, Eqs.

(B) and (D) simplify to Eqs. 3.2-8 and 10.1-9 in

TrPh. If all species are subjected to the same exter-

nal torques so that all t, are equal to t, a similar

simplification occurs in Eq. (C).

We emphasize that the equations in Table 1 are to

be considered the fundamental equations at the mi-

croscopic scale, whereas those in Table 2 are de-

rived from those in Table 1. As explained in TrPh,

the equations of change may be put into many alter-

native forms; for example, they may equally well be

written in terms of the "substantial" (or "material")

derivative operator D/Dt (TrPh Eq. 3.0-2). The en-

ergy equation has always been a special problem

because it can be written in so many different ways

(see TrPh, pages 322-323, 582, for useful tabular

summaries).

The Flux Expressions

(Also Called "Constitutive Equations")

In order to get solutions to the equations of change,

we need to have expressions for the fluxes j, T, and

q. The standard expressions for these are the "lin-

ear laws," in which the fluxes are proportional to

gradients, as shown in Table 3.

Equation (I) for the mass-flux vector is shown only

for the binary system A-B, and the thermal diffu-

sion, pressure diffusion, and forced diffusion terms

have been omitted (see Eq. (Z) for the complete ex-

pression). Equation (K) shows the conductive and

diffusive contributions to the heat-flux vector, but

the diffusion-thermo (Dufour) effect has been omit-

ted. In Eq. (J) we have included the two viscosity

coefficients I and K, although the latter is omitted

in most fluid dynamics texts since it is zero for mona-

103

KNOWLEDGE STRUCTURE

KIfTJL4I FflIF STRIIC~TIJRE

tomic gases (we know this from kinetic theory-see

MTGL, Chapter 7) and since for liquids incompress-

ibility is often assumed, so that div v = 0 and the

term containing K is zero anyway.

The flux expressions do not have the exalted sta-

tus accorded to the conservation laws in Table 1.

They are empirical statements, proposed as the sim-

plest possible linear forms; they also emerge from

the kinetic theory of gases when one works to the

lowest orders in the gradients of concentration, ve-

locity, and temperature (see MTGL, Chapter 7). It is

well known that Eq. (J) does not describe the me-

chanical responses of polymeric liquids (see DPL1,

Chapter 2); various nonlinear expressions, and in-

deed time-dependent expressions, arise from the ki-

netic theory of polymeric liquids (see DPL2, Chap-

ters 13-16, 19-20). Furthermore, for some complex

materials it is found that the thermal conductivity

and diffusivity are tensors rather than scalars, so

that the fluxes and forces are not collinear. In order

to use Eqs. (I,J,K), one needs numerical values for

the diffusivity, viscosity, and thermal conductivity;

these are preferably obtained from experiments, but

in the absence of experimental values kinetic theory

results can be used.

Once the flux expressions have been substituted

into the equations of change, we then have a set of

equations which, when solved, will give the concen-

tration, velocity, and temperature distributions as

functions of time. There are many ways in which

these important equations can be used:

Analytical solutions can be found (for simple, ideal-

ized problems, in which transport properties are

assumed to be constant)[''10

Approximate solutions can be found with perturba-

tion theories1'l

Numerical solutions can be foundl12"15

Boundary-layer solutions can be found116

Time smoothing can yield the turbulent transport

equations"17"9]

Volume smoothing leads to the equations for po-

rous media'20'

Flows with chemical reactions can be analyzedt211

Approximate solutions can be used for lubrication

flows['1

Mixing and chaos can be studied1221

Particulate motion, suspensions, and emulsions can

be described121

Interfacial transport equations can be established123'

Polymer fluid dynamics and transport phenomena

can be studied[DPL"1

This partial list of topics gives some idea as to the

breadth of the field of transport phenomena and the

extremely great importance of the equations of

change. All these topics are active research fields

in which chemical engineers are obligated to play

an important role.

The Macroscopic Balances

The statements of the laws of conservation of mass,

momentum, angular momentum, and energy can be

written down for a typical macroscopic engineering

system, with one entry port ("1") and one exit port

("2"); heat can be added to the system at the rate Q,

and the system can do work on the surroundings at

a rate Wm by means of moving parts (such as pistons

or rotatory devices). These conservation statements

are given in Eqs. (L-O) in Table 4. It is assumed

there that the fluid velocities at the inlet and outlet

planes are parallel to the directions of flow n, and

n2. It is also assumed that the extra stress tensor

does not contribute to the work done on the system

at the entry and exit planes. It is further assumed

that there are no mass-transfer surfaces in the mac-

roscopic system; such surfaces are considered in

TrPh, Chapter 22, and in STTP, Chapter 1.

Of course, Eqs. (L-O) can also be obtained by inte-

grating the equations of change in Eqs. (A,B,E,D)

over the entire volume of the flow system; in doing

this we must take into account the fact that the

shape of the volume is changing with time because

of the moving parts.[24,25] The macroscopic mechani-

cal energy balance (also called the engineering Ber-

noulli equation) cannot be written down directly since

there is no conservation law for mechanical energy.

It can be derived by integrating Eq. (G) over the

macroscopic system as outlined in Table 5. For the

sake of simplicity, we take the external forces go to

be all the same (g = -6, where D is the potential

TABLE 3

The Flux Equations (or "Constitutive Equations")

(I) JA =-PDABVoA (binary system of A and B)

(J) T = -VV+(VV)T) + V)a

(K) q=-kVT +(H, /Ma)ja

DA = binary diffusivity

oA = pA/p = mass fraction of a

p = viscosity

K = dilatational viscosity

8 = unit tensor (with components 5.)

k = thermal conductivity

Ha = partial molar enthalpy of a

Chemical Engineering Education

K-A1W1 )Df-- STRCTUR

KNOWLEDGE STRUCTURE

TABLE 4

Macroscopic Balances

Assumptions:

no mass-transfer surfaces;

all species subject to same external forces and external torques;

7r contributions neglected at "1" and "2"

(L) mtot =wal-Wa2 +ra,tot

(M) Ptot 2 wi+PiSij wni ( 2 2+P2S2 -2 F+mtotg

(M) -tPtot= I f2

(N) -Mtot= )1 w+plS1 [rlxni]- w2+P2S2 [r2xn2]-T+[rcxmtotg]

dt (vl M2

()3 1 ____3) P

(0) (Ktot+ tot+Uto 2t) (V +il+1 W- 2 +2 W2 2+Q-Wm

(Q v3) 1 1 3 2 M2

(P) d(Ktot + _tot)= +1+ wl 21 v 2 + 2 -Ec-Ev -Wm

()2 (v)d 1w 2 M P2

(Q) dUtot=Uilwl-U2W2+Q+Ec+Ev

dt

mt = total mass in flow system

Pt = total momentum in flow system

Mt = total angular momentum in flow

system

Ktot= total kinetic energy in flow system

tot = total potential energy in flow system

Utt = total internal energy in flow system

() = averages over tube cross section at

entry and exit

n,n2 = unit vector in flow direction at entry

and exit

w l,w = mass rate of flow of a at entry and

exit

w,, w2 = mass rate of flow at entry

and exit

pl, p2 = thermodynamic pressure at

entry and exit

S,, S2 = cross-sectional areas of entry

and exit conduits

Q = heat added to system

through container walls

Wm = work done on surroundings

E,, Ev = quantities defined in Eq. (S)

rl,r2,r = location of the centers of the

entry and exit planes and

the center of mass of the

fluid in the system

energy per unit mass,

which is considered to be

independent of time). In

doing the integration, we

need to use the Gauss di-

vergence theorem (TrPh,

A.5-1) and the 3-dimen-

sional Leibniz formula

(TrPh, A.5-5).

This leads to Eq. (R), in

which S, and S2 are the

cross-sectional areas at

"1" and "2", Sf stands for

the fixed surfaces of the

system, and Sm stands for

the moving surfaces, by

means of which work can

be done on the surround-

ings. Since the velocity v

of the fluid equals the sur-

face velocity vs on the

fixed and moving sur-

faces, these surface inte-

grals contribute nothing

to the first term on the

right side. Also, since the

fluid velocity v is zero on

all fixed surfaces, the

fixed-surface contribution

to the second term on the

right side is zero; the in-

tegral over the moving

surfaces gives the work

transmitted via these sur-

faces, Wm, (sometimes

called the "shaft work").

The integrals of the extra

TABLE 5

Intermediate Steps in Deriving the Macroscopic Mechanical Energy Balance

(R) A J (lpv2+p )dV=_-J(n.(pv2+p()(v vs))dS-J(n.[(p6 +T)v])dS-Ec-Ev

V(t) S=S,+S,+s+S,(t) S=S,+S,+S,+S,(t)

(S) inwhich Ec=- fp(V.v)dV and E =- J(Tr:Vv)dV

V(t) V(t)

(T) -t (Ktot+(Dtot)= P 3l(v13S1-lp2 v3 2S2+Pl(vl(1SI -p2(v)2 2S2+Pl(V)lS1-p2(v)2S2-Ec-Ev-Wm

V(t) = volume of engineering flow system

S, = fixed surfaces of flow system

Sm = moving surfaces of flow system

v. = velocity of surface (equals zero on S,,S,,S,)

6 = potential energy per unit mass

n = outwardly directed unit normal on surface S

7 = (extra) stress tensor

Spring 1993 10O

KNOWLEDGE STRUCTURE

stress tensor T over S, and S2 are presumed

small and have been omitted here; they are

identically zero for laminar, Newtonian flow

when the fluid velocity vectors are parallel to

the walls of the entry and exit tubes. The inte-

grals labeled E, and E, are not evaluated; the

latter gives the rate at which mechanical en-

ergy is degraded into thermal energy. From

Eqs. (R) and (S) we get Eq. (T), which is easily

rearranged to give the mechanical energy bal-

ance in Eq. (P); the latter includes the two

special cases given in TrPh Eqs. 15.2-1 and 2.

Equation (P) is particularly convenient for in-

compressible fluids for which E, is exactly zero.

Equations (L)-(P) are easily generalized to sys-

tems with multiple inlet and outlet ports.

NOTE: In some textbooks it is stated that

the mechanical energy balance (Eq. P) is an

"alternative form" of the total energy balance

(Eq. O). Such a comment seems inappropriate

since Eq. (P) comes from the equation of con-

servation of momentum, whereas Eq. (0) has

its origins in the equation of conservation of

energy. In other textbooks some thermody-

namic "incantations" are offered to get from

Eq. (0) to Eq. (P). The arguments must essen-

tially involve Eq. (Q), obtained by subtracting

Eq. (P) from Eq. (0); of course, Eq. (Q) can also

be obtained from integrating Eq. (H)-which

is a consequence of the equations of energy

and motion-over the macroscopic flow sys-

tem. Certainly Eq. (Q) cannot be written down

directly, since there is no conservation law for

the internal energy in an open system with

dissipative processes. Furthermore, the ther-

modynamic arguments cannot yield the expres-

sions in Eq. (S), showing how E, and E, are

related to the velocities and stresses in the

system. Comments from textbook authors (and

others) on this point would be welcome; before

commenting, however, it would be advisable

to read Whitaker's historical essay.[6, pp 90-931

The Transfer Coefficients

Although the macroscopic balances can be

used, as shown in Table 4, it is often useful to

estimate some of the terms in them by using

dimensionless correlations:

F can be estimated by using friction factor

correlations

E, can be estimated by using friction loss

factor correlations

Q can be estimated by using heat-transfer

coefficient correlations

wa m can be estimated by using mass-transfer coefficient

correlations

These quantities are given in the form of dimensionless

correlations based on large amounts of experimental data;

they contain the transport properties and the density and

the heat capacity, as well as quantities describing the char-

acteristic length, velocity, temperature, etc.

For steady-state systems, the macroscopic balances form a

set of algebraic relations; for unsteady-systems they become

a set of differential equations, with time as the independent

variable. The macroscopic balances are the starting point for

calculations involving heat exchangers, separations equip-

ment, chemical reactors, and fluids-handling systems.

The Three Levels of Transport Phenomena

For many engineering applications, one starts with the

macroscopic balances in order to understand the overall

behavior of the system. One can often estimate some of

the quantities in the balances by using transfer coefficient

correlations, photographic or other visualization methods,

direct pressure, temperature, and density measurements

on the system, etc. Other quantities may be assigned by

crude methods.

In other problems, one needs to know more about the de-

tails of the pressure, velocity, temperature, and concentra-

tion distributions within the system. This calls for "moving

down" one level (see Table 6) and solving the equations of

change. Many analytical solutions are available, but there

are also modern computing techniques if numerical solu-

tions are needed (usually the case if pressure, temperature,

TABLE 6

The Three "Levels" of Transport Phenomena

Basic Empirical

Equations Expressions Results

Macroscopic Dimensionless Solve to get

Balances over correlations relations among

b engineering f, h, k,, inlet, outlet, and

system and e, transfer quantities

S J T dimensional analysis

S Equations of Flux Solve to get

8' change for + expressions concentration,

o 0 conserved for pressure, velocity,

S quantities j,, T, q and temperature

a

Equation for Intermolecular Solve to get

dg time evolution + force D^, Ki, and

S of phase-space expression kT in the flux

distribution function expressions

Chemical Engineering Education

KNOWLEDGE STRUCTURE

and concentration dependence of the physical prop-

erties have to be taken into account). Dimensional

analysis of the equations of change suggests the

form that the transport-coefficient correlations

should take, these being needed for the macroscopic

balances.

It should be recognized that there is still one scale

smaller than the macroscopic and microscopic scales,

namely the molecular scale. Although this part of

the subject normally lies in the domain of the theo-

retical physicist or the theoretical chemist, engineers

occasionally need some familiarity with the molecu-

lar aspects of transport phenomena. The basic equa-

tion at the molecular level is an equation for the

time evolution of a phase-space distribution func-

tion. One example of this is the Boltzmann equation

for dilute gases (MTGL, Chapter 7), and additional

examples may be found for dilute polymer solutions

and polymer melts in DPL2, Chapters 17-19.

From the differential equation for the phase-space

distribution function, one can obtain a "general equa-

tion of change," special cases of which are the usual

equations of change in Table 1; in developing these

equations, one makes use of the fundamental con-

r

Spring 1993

servation laws as applied to molecular collisions. As

a by-product of this derivation, formal expressions

are obtained for the fluxes in terms of the distribu-

tion function. In this way expressions are obtained

for the transport properties in terms of molecular

models.

Recently there has been an interesting develop-

ment in connection with the kinetic theory of dilute

gases and the Boltzmann equation. This famous

equation, although over one hundred years old, has

been found to be in error in that it cannot be ob-

tained by starting with the quantum Boltzmann

equation and letting Planck's constant vanish.26" The

new "Boltzmann-Curtiss equation" does not suffer

from this defect since it accounts properly for the

contributions associated with bound pairs of mol-

ecules; the added terms in the equation are appar-

ently important at low temperatures; as a result the

table in TrPh, page 746, will have to be modified.

It is seen in Table 5 that at each of the three

scales, use is made of the basic conservation laws.

Also, at each scale some kind of empiricism is intro-

duced. Each scale can be better understood by going

to the next smaller scale in order better to appreci-

ate the origins of the equations

Thermodynamics of Irrevers-

ible Processes

If into Eq. (H), the equation

of change for the internal en-

ergy, we insert the thermody-

namic relation Eq. (U) (see

Table 7) for a binary mixture,

we get (after using the equa-

tion of continuity) the result

in Eq. (V)-an equation of

change for the entropy. In this

equation we can identify an

entropy flux s as the sum of

two contributions, one associ-

ated with heat conduction and

one with diffusion; we can also

identify a rate of entropy pro-

duction o, which is given as a

sum of terms, each of which is

the product of a flux and a

force.

Then, according to the ther-

modynamics of irreversible

processes, every flux will de-

pend linearly on each of the

107

TABLE 7

Thermodynamics of Irreversible Processes (Binary Systems)

(U) dJU=TdS-pd(1/p)+ AdOA

(V) pS=-(v.pvS)-(V.s)+o

at

in which s=l(q-IjA)

c =-((q- jA)- 1VT)'-(jA -(V + (gB -gA)))- rAr- (T: Vv)

( ) JA =-11 vA+(B-gA))- a12- V

(X) q-RJA=-a21(Va +(gB-gA))-a22-VT

2 T2

(Y) q= a12 A 22 1 VT=HA HB -kVT

(Z) jA =-PAB(VOA +kTVinT+kpVenp)+kF(gB-gA)

S = entropy per unit mass

A = (GA/MA)-(GB/MB)

s = entropy flux

a = rate of entropy production

a. = phenomenological coefficients

q = Dufour effect contribution to heat flux

kT = thermal diffusion coefficient

k = pressure diffusion coefficient

kl = forced diffusion coefficient

and their limitat s.

KNOWLEDGE STRUCTURE

forces, with the restriction that fluxes must depend

on forces of the same tensorial order, or with order

differing by 2 (Curie's law). There is also the restric-

tion that the matrix of coefficients in the flux-force

relations be symmetric (Onsager-Casimir reciprocal

relations). This leads us to Eqs. (W) and (X), in

which a12 = a21. Then combination of Eqs. (W) and

(X) gives Eq. (Y) for the heat flux vector. In this

equation, the coefficient of -VT can be identified as

the thermal conductivity for the mixture. The other

term in Eq. (Y) leads to the second term on the right

side of Eq. (K), the diffusion term, plus one addi-

tional very small term associated with the Dufour

effect.

The term involving Vj in Eq. (W) can be expanded

by using the chain rule of partial differentiation

V= = (D / 3COA)Vw(A + ( 1/ T)VT + (/ / ap)Vp

The term in VT combines with the other VT term in

Eq. (W), and the final result is Eq. (Z); in this equa-

tion the coefficients kp and kF are completely deter-

mined from the thermodynamic properties of the

mixture, whereas the diffusivity DA and kw are two

phenomenological coefficients that have to be deter-

mined experimentally for each gas pair or estimated

by kinetic theory. As a result of the Onsager rela-

tions, the four phenomenological coefficients in Eqs.

(W) and (X) have been reduced to the three trans-

port properties: diffusivity, thermal diffusion ratio,

and thermal conductivity.

Equation (Z) shows clearly that a mass flux of

species "A" can result from a concentration gradient

(ordinary diffusion), a temperature gradient (ther-

mal diffusion), a pressure gradient (pressure diffu-

sion), and a difference of external forces (forced dif-

fusion) (TrPh, Chapter 18 and MTGL, Chapter 11).

A concise introduction to the thermodynamics of ir-

reversible processes has been given by Landau and

Lifshitz;'27' a more thorough discussion can be found

in the classic text by de Groot and Mazur.1281 The

thermodynamics of irreversible processes has been

found to be particularly useful in the systematiza-

tion of the flux expressions for multicomponent dif-

fusion as well as in linear viscoelasticity.[291 Although

this topic is not essential for undergraduate stu-

dents, perhaps graduate students can benefit from

the extra insight provided by the thermodynamic

approach.

CONCLUDING COMMENTS

It is essential that students of transport phenom-

ena recognize the central position occupied by the

conservation statements. The conservation laws for

108

mass, momentum, and energy applied to a large

engineering system through which a fluid is flowing

lead to the macroscopic balances; the two additional

balances for angular momentum and mechanical en-

ergy can be obtained from the integration of mo-

ments of the equation of motion. The utility of the

balances is enhanced by the use of empirical corre-

lations for the transfer coefficients. The five macro-

scopic balances are the starting point for many analy-

ses of unit operations and chemical reactors. They

are invaluable for making order-of-magnitude esti-

mates for engineering systems.

The conservation laws, when applied to a small

region of space through which a fluid is flowing,

lead to the equations of continuity, motion, and en-

ergy; the assumption of the symmetry of the stress

tensor is usually made, and this assumption makes

it unnecessary to deal with the interconversion of

external and internal angular momentum. The flux

expressions usually used in the equations of change

are the simplest possible relations that are linear in

the gradients. The vast literature dealing with solu-

tions of the equations of change should be familiar

to engineers, even though these solutions are for

idealized systems; they are, however, very useful for

making order-of-magnitude estimates and for check-

ing the computer programs used for obtaining nu-

merical solutions.

The conservation laws applied at the molecular

scale are used in kinetic theory developments. Ki-

netic theory provides expressions for the transport

properties in terms of intermolecular forces; these

expressions are highly developed for dilute mona-

tomic gases. In the last several decades the kinetic

theory of polymers has developed rapidly, so that

much more is now known about the transport prop-

erties of polymeric liquids.'301

The subject of transport phenomena can be useful

in many fields, including micrometeorology, zool-

ogy, analytical chemistry, nuclear engineering, tri-

bology, metallurgy, biomedical engineering, phar-

macology, and space science. Chemical engineering

departments are in a good position to provide gen-

eral service courses in transport phenomena for other

department on campus.

ACKNOWLEDGMENTS

The author wishes to thank Professors W.E.

Stewart and T. W. Root, and Mr. Peyman Pakdel of

the Department of Chemical Engineering at the Uni-

versity of Wisconsin, and Professor J.D. Schieber at

the University of Houston for valuable suggestions.

Chemical Engineering Education

KNOWLEDGE STRUCTURE ~-~`

REFERENCES

1. Bird, R.B., W.E. Stewart, and E.N. Lightfoot, Transport

Phenomena, Wiley, New York (1960)

2. Bird, R.B., R.C. Armstrong, and 0. Hassager, Dynamics of

Polymeric Liquids. Vol. 1: Fluid Mechanics, 2nd ed., Wiley,

New York (1987)

3. Bird, R.B., C.F. Curtiss, R.C. Armstrong, and 0. Hassager,

Dynamics of Polymeric Liquids. Vol. 2: Kinetic Theory, 2nd

ed., Wiley, New York (1987)

4. Bird, R.B., W.E. Stewart, and E.N. Lightfoot, Selected Top-

ics in Transport Phenomena, Chem. Eng. Prog. Symp. Se-

ries No. 58, Vol. 61, AIChE (1965)

5. Hirschfelder, J.O., C.F. Curtiss, and R.B. Bird, Molecular

Theory of Gases and Liquids, Corrected Printing with Added

Notes, Wiley, New York (1964)

6. Whitaker, S., in One Hundred Years of Chemical Engineer-

ing, ed. N.A. Peppas, Kluwer Academic Publ., Dordrecht,

pp. 47-109 (1989)

7. Dahler, J.S., and L.E. Scriven, Nature, 192,36-37 (1961)

8. Berker, R., "Integration des equations du movement d'un

fluide visqueux incompressible," in Enyclopedia of Physics,

ed. S. Fliigge, Springer, Berlin, pp. 1-384 (1968)

9. Carslaw, H.S., and J.C. Jaeger, Heat Conduction in Solids,

2nd ed., Oxford University Press (1959)

10. Crank, J., The Mathematics of Diffusion, Oxford University

Press (1956)

11. Leal, L.G., Laminar Flow and Convective Transport Pro-

cesses: Scaling Principles and Asymptotic Analysis,

Butterworth-Heinemann, Boston (1992)

12. Kim. S., and S.J. Karrila, Microhydrodynamics: Principles

and Selected Applications, Butterworth-Heinemann, Bos-

ton (1991)

KNOWLEDGE STRUCTURE

13. Finlayson, B.A., The Method of Weighted Residuals and

Variational Principles, Academic Press, New York (1972)

14. Finlayson, B.A., Nonlinear Analysis in Chemical Engineer-

ing, McGraw-Hill, New York (1980)

15. Finlayson, B.A., Numerical Methods for Problems with Mov-

ing Fronts, Ravenna Park, Seattle, WA (1992)

16. Schlichting, H., Boundary Layer Theory, 4th ed., McGraw-

Hill, New York (1960)

17. Hinze, J.O., Turbulence, 2nd ed., McGraw-Hill, New York

(1975)

18. Tennekes, H., and J.L. Lumley, A First Course in Turbu-

lence, MIT Press, Cambridge, MA (1972)

19. Speziale, C.G., in Ann. Rev. Fluid Mech., 23, 107-157 (1991)

20. Adler, P.M., Porous Media, Butterworth-Heinemann, Bos-

ton (1992)

21. Rosner, D.E., Transport Processes in Chemically Reacting

Flow Systems, Butterworth-Heinemann, Boston (1986)

22. Ottino, J.M., The Kinematics of Mixing: Stretching, Chaos,

and Transport, Cambridge University Press (1989)

23. Slattery, J.C., Interfacial Transport Phenomena, Springer,

Berlin (1990)

24. Bird, R.B., Chem. Engr. Sci., 6, 123 (1957)

25. Slattery, J.C., and R.A. Gaggioli, Chem. Engr. Sci., 17,893

(1962)

26. Curtiss, C.F., J. Chem. Phys., 97, 1416, 1420, 7679 (1992)

27. Landau, L., and E.M. Lifshitz, Fluid Mechanics, Chap. VI,

Addison-Wesley, Reading, PA (1959)

28. de Groot, S.R., and P. Mazur, Non-Equilibrium Thermody-

namics, North-Holland, Amsterdam (1962)

29. Kuiken, G.D.C., Thermodynamica van de Irreversibele

Processen, T.U. Delft, Netherlands (1992)

30. Bird, R.B., and H.C. Ottinger, in Ann. Rev. Phys. Chem.,

43, 371 (1992) 0

r M book review

NATURAL GAS ENGINEERING:

PRODUCTION AND STORAGE

by Donald L. Katz, Robert L. Lee

McGraw Hill, New York, NY 10020; 760 pages, $54.95

(1989)

Reviewed by

R. A. Greenkorn

Purdue University

This book covers most aspects of natural gas engi-

neering. It is a survey suitable for a short course to

introduce practicing engineers to the topic. The book

is descriptive and as such is much too broad to be

used as a textbook. The later half of the book is

essentially a monograph recording the senior author's

extensive experience in this area. Chapters 1-7 de-

scribe the material properties of the system, chap-

ters 8-13 contain the core of the material concerned

with the production and storage of natural gas, chap-

ters 14-15 mainly discuss operations, and chapters

16-17 contain miscellaneous topics.

Chapter 1 Natural Gas Technology and Earth

Spring 1993

Sciences. This chapter is a concise review of natural

gas engineering production and underground stor-

age of natural gas. Several subjects are covered,

e.g., the branches of petroleum industry, sources of

information for natural gas engineering, a brief dis-

cussion of geology and earth sciences, and earth

temperatures and pressures.

Chapter 2 Properties of Rocks. This chapter con-

tains some descriptions of the properties of rocks or

porous media, including a description of how these

properties are measured. The discussion is under-

standable and relatively clear-but very terse.

Chapter 3 Thermodynamics: Flow Equation,

Fluid Properties, Combustion. This chapter is basi-

cally descriptive. It is terse, explaining how the equa-

tions are derived and giving some limited informa-

tion on how to calculate combustion of natural gas.

Chapter 4 Physical Behavior of Natural Gas

Systems: Physical and Thermal Properties, Phase

Behavior, Analyses. The initial part of this chapter

is a review of pressure, volume, and temperature

relationships of pure fluids. The phase rule and the

behavior of complex mixtures are briefly discussed.

Continued on page 116.

KNOWLEDGE STRUCTURE

AN APPETIZING STRUCTURE OF

CHEMICAL REACTION ENGINEERING

FOR UNDERGRADUATES

H. SCOTT FOGLER

The University of Michigan

Ann Arbor, MI 48109

Chemical reaction engineering (CRE) is fun to

teach, not only because it has extremely in-

teresting subject matter and is one of the

few courses that sets chemical engineering apart

from other engineering disciplines, but also because

it has a very logical structure. The six basic pillars

that hold up what could be called the "Temple of

Chemical Reaction Engineering" are shown in Fig-

ure 1.11] The four on the left are usually covered in

the majority of undergraduate reaction engineering

courses.[2' But diffusion effects, which include mass

transfer limited reactions, effectiveness factors, and

the shrinking core model, are covered in only a small

number of courses. Contacting, which includes reac-

tor characterization (e.g., residence time distribu-

tion) and modeling non-ideal reactors, is normally

left to graduate-level courses.

The pillar structure shown in the figure allows

one to develop a few basic concepts and then to

arrange the parameters (equations) associated with

each concept in a variety of ways. Without such a

structure, one is

faced with the possi-

bility of choosing, or

perhaps memorizing,

the correct equation

from a multitude of

equations that can

arise for a variety of

different reactions,

reactors, and sets of

conditions. We draw

a loose analogy with

dining at a Swedish

smorgasbord where it

is difficult to choose

H. Scott Fogler is the Ame and Catherine

Vennema distinguished professor of chemical

engineering at the University of Michigan. His

teaching interests are in the areas of reaction

engineering and problem solving. His research

interests are in the areas of colloid stability and

flow and reaction in porous media, in which he

has over one hundred research publications.

from a multitude of dishes in order to end up with a

satisfying, well-balanced meal that fits together. In

CRE, consider the number of equations that arise in

calculating the conversion in CSTRs, batch, plug

flow, and semibatch reactor-for zero, first, second,

and third order reactions-for both liquid and gas

phase systems-with and without pressure drop. The

number of equations (dishes) from all the above pos-

sible combinations which we must choose (memo-

rize) is then 4 x 4 x 3 = 48. If we also consider

catalyst decay with either first, second, or third or-

der decay laws, the number of dishes increases to

192. IfLangmuir-Hinshelwood kinetics are included,

the number of equations, or dishes (i.e., equations in

isothermal reactor design) increases to well over

1,000. Finally, if we add non-isothermal effects, the

MULTIPLE REACTIONS

MASS TRANSFER OPERATIONS

INONISOTHERMAL OPERATION, MULTIPLE STEADY STATES

MODELING REAL REACTORS, RTD, DISPERSION. SEGREGATION

ANALYSIS OF RATE DATA, LABORATORY REACTORS, LEAST-SQUARES ANALYSIS

DESIGN OF CHEMICAL REACTORS, PFR, CSTR, BATCH, SEMIBATCH, PACKED BEDS)

M R

E I

B L

A A

L W

A S

C

S

S E D

T e I

I R F

C G U

H Y S

O B 0

M A N

E L

T A

R N

Y C

C

10

N

T

A

C

T

N

G

number of dishes in-

creases to such an ex-

tent that choosing the

right dish, or dishes,

becomes a task of un-

believable gastronomi-

cal proportions. The

challenge is to put ev-

erything in an orderly

and logical fashion so

that we can proceed to

arrive at the correct

equation (dishes that fit

together) for a given

situation.

Copyright ChE Division ofASEE 1993

Chemical Engineering Education

Figure 1. Pillars of the Temple of Chemical Reaction Engineering.

KNOWLEDGESTRUCTUR

KNOWLEDGE STRUCTURE

Fortunately, by structuring CRE using an

algorithm analogous to a fixed-price menu in

a fine French restaurant, we can eliminate

virtually all memorization (see Figures 2 and

4) and proceed in a logical manner to de-

velop the reaction engineering equation nec-

essary to describe the given situation. The

lower price (220 FF) menu corresponds to

isothermal reactor design, while the higher

price menu (280 FF) corresponds to non-iso-

thermal design.

Here we start by choosing one dish from

the appetizers listed. The analog is to choose

the mole balance from one of four reactor

types shown. Next, we choose our main course

from one of four entries: the main course

analog in CRE is to choose the appropriate

rate law. Continuing with our meal, we

choose cheese or dessert; the analogy in CRE

is stating whether the reaction is liquid or

gas phase in order to use the appropriate

equation for concentration.

The main difference between CRE and

ordering and eating a fine French meal as

we have just done is that in CRE we com-

bine everything together at the end; such

a mixing of the courses on a single plate

before eating a wonderful French meal would

be a disaster! The application of this struc-

ture to a first order gas phase reaction car-

Le Cataliste Flambi

344 Champs Elysees

AMenu 4 220TT

appetizer

fatd de Canard (supplement 15F7)

Coquifessaint-5acques

Potage Crime de Cresson

Escargots & La Bouguine (supplment

1577F)

Entrie

Cassoutet

Ragnons de Veau

Coq au 1in

'Boeufd a provenpale

(Tous nos plats sontgarnis)

Dessert

Brie on Crime Anglais

1/2 bouteilfe

e vin b6anc ou vin rouge

Mole Balance

sBatch Pactor

CMzIR

Semibatcht actor

Rate Law

Power Law (e.g.)

Ist Order

2nd Order

N9n-Integer Order

Stoichiometry

Gas orLiquid

Combine

Mix together and digest with

1/2 bouteiife of PoLyMr'1

Service Compris

Figure 2. French Menu I: Isothermal reactor design

Spring 1993

ried out in a PFR (with a change in the total number of

moles) is shown in Figure 3. As an example, we will follow

the dark lines as we proceed through our algorithm. The

dashed lines represent possible pathways for other situa-

tions. Here we choose

1. the mole balance on species A for PFR,

2. the rate law for an irreversible first order reaction,

3. the equation for the concentration of A in the gas phase, and

then

4. combine to evaluate the volume necessary to achieve a given

conversion or the conversion that can be achieved in a

specified reaction volume.

For the case of isothermal operation with no pressure drop,

we were able to obtain an analytical solution. In the majority

of situations, however, analytical solutions of the resulting

ordinary differential equations appearing in the combine

step are not possible. Consequently, we include POLY-MATH131

in our menu. POLYMATH is analogous to vin blanc ou rouge

in that it makes obtaining solutions to the differential equa-

tions much more palatable.

1. MOLE BALANCES

PFR CSTR BATCH

dX V FAnX X =-rAV

dV FA -A dt NAO

2. RATE LAWS

-rA= kCA -rA -C-A

1+KA A A CA

3. STOICHIOMETRY

FLOW BATCH

CA

FA = FAO(1-X) NA =NAO(-X)

A

LIQUID GAS GAS LIQUID OR GAS

constant flowrate variable flow rate variable volume constant volume

PT. P T

S= o = ol( +sX)V-'- = Vo(l +X)- V=Vo

CA=CAO(I-X) CA= C(l-XPL C C"n(l-X)P], CCAo(1-X)

S(+X) P T (1+X) T

4. COMBINE (1st order Gas Phase Reaction in a PFR)

From mole balance Ifrom rate law from stoichiometry

dX -rA kC k C

dV FFA FA = AO (+eX)P. T

=- where y = (A)

Integrating for the case of constant temperature and pressure

Vi 3 li +EX)nISrea rsX

Figure 3. Algorithm for ISOTHERMAL reactors

KNOWLEDGE STRUCTURE

HEAT EFFECTS

Studying non-isothermal reactor design is analo-

gous to ordering from a more expensive (280 FF)

French menu (see Figure 4) in which we have an

extra category from which to make a selection. In

CRE this corresponds to choosing which form of the

energy balance to use (e.g., PFR, CSTR) and which

terms to eliminate (e.g., Q=0 for adiabatic opera-

tion). The structure introduced to study these reac-

tors builds on the isothermal algorithm by introduc-

ing the Arrhenius Equation, k = A e-E/RT in the rate

law step, which results in one equation with two

unknowns, X and T, when we finish with the com-

bine step. The students realize the necessity of per-

forming an energy balance on the reactor to obtain a

second equation relating X and T. For example, us-

ing again the PFR mole balance and conditions in

Figure 3 (Eq. A), we have, for constant pressure

dX Ae-E/RT (-X)(T) A)

dV vo (1+ X) ()

An energy balance on a PFR with heat exchange

yields the second equation we need relating our in-

dependent variables X and T

dT [UA (T T) + (rA)(AHR)] (

dV FAOCPA

Le Cataliste Flamb6

344 Champs Elyses

Menu tt28OrP

appetizer

Pati de Canard

CoquiffesSaint-acques

Pouge Crime de Crsson

'Ecargots A La Bourguine

Entrie

Bouifabaisse

I

hroutruue qanmi

oufsBourauat ona

Tous nospfatssontgarnis)

Assiette de Fromge

Dessert

Emvaroi a range

souffia u Cuoto at

fdtuaua eL Crps a [a "inarmi

Petit Tour _

revenz so me,

Mole Balance

Batch

Semibathd

RatLa w kt-sAe

Power Law

Langmuvir.-nshduwood

Midichae-Menten

Stoichiometry

qas or Liquid

LEnerqg Bafancx-fm

Adiabatic

Combine

5u(# Steadyj tats

Service Compris

Figure 4. French Menu II: Non-isothermal reactor design

With the emergence of extremely user-friendly

software packages, we can now allow students to

explore the problem much more effectively, to

develop an intuitive feeling for the

reactor/reaction behavior,...

1111111111Ei-: l

Figure 5. Paradigm shifts in chemical engineering education.

These simultaneous differential equations can be

readily solved with an ODE solver, as discussed

below.

A PARADIGM SHIFT

With the emergence of extremely user-friendly soft-

ware packages (see Figure 5), we can now allow

students to explore the problem much more effec-

tively, to develop an intuitive feeling for the reac-

tor/reaction behavior, and to obtain more practice in

creative problem solving.

To illustrate this point, consider an exothermic

reaction carried out in a plug flow reactor with heat

exchange. Obtaining the temperature and concen-

tration profiles requires the solution of two coupled

non-linear differential equations such as those given

by Eqs. (A) and (B). In the past, it would have been

necessary to spend a significant amount of time

choosing an integration scheme and then writing

and developing a computer program before any re-

sults could be obtained. Now, with the available

software programs (especially POLYMATH), it rarely

takes more than ten minutes to type in the equa-

tions and obtain a solution."31 As a result, the major-

ity of the time on the exercise can be spent explor-

ing the problem through parameter variation and

analysis of the corresponding observations. For ex-

ample, in the above exothermic reaction in a PFR

with heat exchange, the students can vary such pa-

rameters as the ambient and entering temperatures,

the flow rates, and the heat transfer coefficient, and

look for conditions where the reaction will "ignite"

and conditions for which it will "run away." By try-

ing their own different combinations and schemes,

the students are able to carry out open-ended exer-

cises which allow them to practice their creativity

and better understand the physical characteristics

of the system.

Chemical Engineering Education

KNOWLEDGE STRUCTURE

VARIATIONS ON A THEME

As a result of the paradigm shift in the ease of

computation using ODE solvers, the study of a

wide variety of chemical reaction engineering sys-

tems just becomes a variation on our main theme

(menu?). Once the concepts of the four left-most pil-

lars are mastered, many important extensions can

be viewed as minor variations on the four basic

steps in our isothermal reaction design algorithm.

Table 1 shows the basic algorithm for solving

CRE problems (including the energy balance), along

with the steps that need to be examined to handle

the individual variation.

To reinforce how many different CRE problems

are minor extensions of the basic algorithm, we shall

discuss three in greater detail below.

Pressure Drop

If pressure drop is not accounted for in gas phase

reactions, significant under-design of the reactor size

can result. This variation is handled in the stoichi-

ometry step, where concentration is expressed as a

function of conversion, temperature, and total pres-

sure. The change in total pressure is given by the

Ergun equation'"

I Variations

MOLE BALANCE

Reactive Distillation

Membrane Reactors

."

RATE LAW

STOICHIOMETRY

--

--

Catalyst Decay

Catalysis/CVD

Pressure Drop

Multiple Reactions

Membrane Reactors

COMBINE

ENERGY BALANCE

ADIABATIC

NON ADIABATIC

Multiple Steady States

PARAMETER

EVALUATION

ODE SOLVER

What if...??

I '-------

Table 1. Variations on the basic algorithm

Spring 1993

dP_ G(1-0) 150(1-0)p .75G (C)

dL pgcDp3 Dp

This equation can be rearranged by lumping the

constant parameters to arrive at the following equa-

tion, giving the variation of the pressure ratio (y=P/

Po) with either reactor volume

dy al(l+eX) (D)

dV 2y

or catalyst weight

dy_ 2 (1+eX) (E)

dW 2y

Either of these equations can be coupled with the

combined mole balance, rate law, and stoichiometry

and solved numerically (e.g., with an ODE Solver).

For example, for isothermal conditions, Eq. (E) would

be coupled with Eq. (A) adopted to an isothermal

PBR

dX k(1-X)

dW vo(l+eX)y (F)

Catalyst Decay

For the case of separable kinetics, we simply in-

clude a catalyst decay law in the rate law step of our

algorithm. For example, for a straight through trans-

port reactor (STTR), the rate law might be given by

kCA

-rA =a(t) ACA (G)

1+KACA

where the catalyst activity, a(t), is

a(t)= 1 (H)

The algorithm for studying a catalytic reaction in a

straight through transport reactor is shown in Fig-

ure 6.

STRAIGHT THROUGH TRANSPORT REACTOR

MOLE BALANCE dX = -

dV FAO

RATE LAW -rA a(t)CA

1+KACA

1

DECAY LAW a(t)= 1+

STOICHIOMETRY CA = CA(1 X)

COMBINE dX k (1-X) 1

dV u(1+KACAo(1-X)) (1+3t1/2

O.D.E. SOLVER

Figure 6. Variations on a theme: Catalyst decay in a STTR

KNOWLEDGE STRUCTURE

Membrane Reactors

The only trick in studying membrane reactors is

to make sure to write the equations in terms of

molar flow rates rather than conversion, and to ac-

count for the products that are leaving the reactor

through the sides of the membrane reactor in our

mole balance step. Consider the reaction

A->B+C

taking place in a membrane reactor

$C

A- ) A, B, C

For the product that exits through the side of the

membrane reactor, C, the mole balance and stoichi-

ometry steps are

=-rA-kcCc

dV

c _Fi

V=v~o-=V FAO+FB

Fo ( FTO

After writing a mole balance on A and B, tl

ing set of non-linear ODEs is solved numer

sample POLYMATH solution is

shown in Figure 7.

MULTIPLE REACTIONS

The steps that are varied when

multiple reactions occur are rate

law and stoichiometry. As with

membrane reactors, we work in

terms of the number of moles or

molar flow rates of each species

rather than concentration or con-

version. Figure 8 shows the appli-

cation of the algorithm to a sample

reaction problem.

MECHANISMS / RATE

LIMITING STEPS

One of the primary pedagogical

advantages of developing mecha-

nisms and rate limiting steps in

heterogeneous catalysis is that it

provides insight into how to ana-

lyze and plot the data in order to

evaluate the rate law parameters.

Most schools spend one-and-a-half

to two weeks on heterogeneous ca-

talysis. Once the basic concepts of

114

ie result-

rically. A

adsorption, surface reaction, and desorption are in-

troduced in conjunction with the idea of a rate limit-

ing step, one can derive many possible rate laws by

varying the mechanism and rate limiting step. For

example, consider the following dual site isomeriza-

tion mechanism

A+ S= A*S

A.S+So B-S+S

B-So B+S

One can write the rate laws for each step in this

mechanism and then show that if the catalytic reac-

tion (A B) in this example is surface reaction

19 *99

B *

6.9

4 *9

0.00 2.00 4.90 6.00 8.90 I19B.

r (Vi/o)

Figure 7. Composition profiles in a membrane reaction

MULTIPLE REACTIONS

STOICHIOMETRY

A-4-B -rAl= kAICA

A--C+D -rA2=kA2CA Ci=

V

B+D-4E -rB3 = kB3CBCD

RATE LAWS

rA =A1 +rA2 =-kA1CA kA2C

rB = rB1 +rB3 = kACA -kB3CBCD

rc = rc2 = kA2C

rD = rD2 +D3 = kA2C -kB3CBCD

E = rE3 = kB3CBCD

MOLE BALANCES

dNAA =-kA NA-kA2 V2

=Adt V=-2 V

dNE NBND

dNE = rE = kB3 V

USE O.D.E. SOLVER

IT'S ONLY A MATTER OF BOOKKEEPING!

Figure 8. Variation on a theme: Multiple reactions

Chemical Engineering Education

KNO WL EDfF STRUC~TIIRF

limited, a plot of the initial rate data in the form of

'o

H-rAo

versus PAo should yield a straight line, as shown in

Figure 9. By formulating different mechanisms

and rate limiting steps, a variety of rate laws can

be developed which provide a number of options

on how to interpret the data and evaluate the rate

law parameters.

Currently, there is an added incentive to study

mechanisms in heterogeneous catalysis because of

the emergence of chemical vapor deposition (CVD).

CVD is widely used in the microelectronics indus-

try, and the mechanisms for CVD are very similar

to the mechanisms analyzed in heterogeneous ca-

talysis. By developing fundamental laws and

principles such as those in heterogeneous catalysis,

the students will be prepared to analyze chemical

reaction engineering problems in engineering tech-

nologies, e.g., CVD.

Other mechanisms and rate laws that can be eas-

ily incorporated into the original algorithm include:

* Enzyme kinetics (e.g., the Michaelis-Menten equations)

pCs

rs = 1+KCs

PAO

Figure 9. Gaining insight into how to

analyze the data.

Bioreactors (e.g., the Monod equation for bacteria

growth; see Figure 10)

r ^-C

^ T+KCs.CB

g = B

Pseudo Steady-State-Hypothesis

Reaction

A->B

Mechanism

A+A<>A* +A

A* B

-r =0

Anet

klCA

-rA -j

-A 1+k2CA

Polymerization (long chain approximation)

In studying these topics, rules are put forth to

guide the student in the development of the under-

lying mechanism and of the rate law. Once the rate

law(s) is formulated by analyzing the particular re-

action mechanism, one can then use it (them) in

step 2 of the algorithm (menu) to study the particu-

lar system of interest.

THINGS TO COME

Discussion of future directions in CRE with col-

leagues at Michigan and elsewhere is the same as

discussion on other academic issues. Where n fac-

ulty members are gathered to express an opinion on

an issue, there will be 1.5 n opinions. But my feeling

is that in the immediate future we will continue to

focus on developing problems that exploit software

packages such as POLYMATH, Maple, and

Mathematica. We will see materials processing, en-

vironmental reaction modeling, reaction pathways

and more applications on safety, batch processing,

mixing, ecology (see Figure 11), and novel reactors

(membrane batch reactors?) along with stochastic

approaches for analyzing reacting systems.

Finally, in the not-too-distant future I see a greater

emphasis on predicting the reactivity of different

species, first perhaps by using empirical means but

u Time

Figure 10. Phases of bacteria cell growth

Spring 1993

0 z

Figure 11. Using wetlands to degrade toxic wastesil4

I

KNOWLEDGE STRUCTURE Vm mI

KNOWLEDGE STRUCTURE

later on from first principles. This direction will

lead us into what I would call molecular chemical

reaction engineering. These and other topics not men-

tioned here may first be covered (and in some cases

are currently covered) at the graduate level, but

they will filter down to the undergraduate level.

This filtering will occur much more rapidly than

have analogous topics in the past.

SUMMARY

By arranging the teaching of chemical reaction

engineering in a structure analogous to a French

menu, we can study a multitude of reaction systems

with very little effort. This structure is extremely

compatible with a number of user-friendly ordinary

differential equation (ODE) solvers. Using ODE solv-

ers such as POLYMATH, the student is able to fo-

cus on exploring reaction engineering problems

rather than on crunching numbers. Thus, one is

able to assign problems that are more open-ended

and to give students practice at developing their

own creativity. Practicing creativity is extremely

important, not only in CRE but also in every course

in the curriculum, if our students are to compete in

the world arena and succeed in solving the relevant

problems that they will be faced with in the future.

REFERENCES

1. Fogler, H.S., The Elements of Chemical Reaction Engineer-

ing, 2nd ed., Prentice Hall, Englewood Cliffs, NJ (1992)

2. Eisen, E.O., "The Teaching of Undergraduate Kinetics/Re-

actor Design," paper presented at the AIChE Annual Meet-

ing, Los Angeles, CA, November 14 (1991)

3. Shacham, M., and M.B. Cutlip, "Applications of a Micro-

computer Computation Package in Chemical Engineering,"

Chem. Eng. Ed., 121), 18 (1988)

4. Kadlec, R.H., "Hydrologic Factors in Wetland Treatment,"

Proc. Int. Conf. on Constructed Wetlands, Chattanooga, TN,

Lewis Pub., Chelsea, MI (1989)

NOMENCLATURE

a catalyst activity

A frequency factor, appropriate units

Ac cross sectional area, m2

Ci concentration of species i (i = A,B,C,D), mol/dm3

C heat capacity of species i, J/g/K

D, particle diameter, m

E activation energy, J/mol

F. entering molar flow rate of species i, mol/s

G superficial gas velocity g/m2/s

ge conversion factor

k specific reaction rate (constant), appropriate units

Ke equilibrium constant, appropriate units

L length down the reactor, m

N. number of moles of species i, mol

P pressure, kPa

ri rate of formation of species i per unit volume,

mol/s/dm3

r' rate of formation of species i per unit mass of

catalyst, mol/s/g

t time, s

T temperature, K

U overall heat transfer coefficient, J/dm3.sK

V volume, dm3

W catalyst weight, g

X conversion

y pressure drop parameter, (P/Po)

yA mole fraction of A

Subscripts

A refers to species A

0 entering or initial condition

Greek

a

AHR

CL

V

V

pressure drop parameter, g'1

catalyst decay parameter, s12

heat of reaction, J/mole A

change in the total number of moles per mole of A

reacted

volume change parameter = yA08

porosity

viscosity, cp

density, g/dm3

volumetric flow rate, dm3/s

REVIEW: Natural Gas Engineering

Continued from page 109

There is a discussion of the compressibility of natu-

ral gases with an explanation of the various correla-

tions that have been used, including the effects of

nitrogen, carbon dioxide, and hydrogen sulfide. There

are a few examples that show how to use these

particular charts.

Chapter 5 Gas Hydrates and Their Prevention.

The formation of hydrates is an important issue

associated with the production of natural gas, espe-

cially in colder circumstances. The discussion is quite

complete.

116

Chapter 6 Applications of Flow Equations: Pres-

sure Drop, Compression, Metering. The material in

this chapter is relatively standard on fluid flow.

However, the emphasis is on problems of natural

gas flow and two-phase flow. The problems associ-

ated with calculating vertical and horizontal flow

are useful-especially the hints on how to calculate

flow in such systems.

Chapter 7 Drilling and Completion of Wells.

Chapter 7 is an overview containing relatively con-

cise descriptions of gas fracturing and acidizing op-

erations. The discussion of well logging is a review

of most of the various kinds of logs that are used.

Chemical Engineering Education

Chapter 8 Flow in Reservoir and Adjacent Aqui-

fer. This is a strong chapter. It presents a discussion

of the flow of gas in reservoirs. The pressure, (pres-

sure)2, and pseudopressure methods of general flow

are discussed. The unsteady state solution for the

constant terminal rate case and for the steady-state

drainage radius case are discussed. In addition, there

is a good discussion of the skin effect, the effect of

high-velocity flow, and the well storage effects.

Chapter 9 Gas Well-Testing. Another strong chap-

ter, it begins with a good discussion of deliverability

tests. The second part discusses tests for determin-

ing reservoir parameters. Examples are given of how

to calculate the actual pressures. Tests for deter-

mining reservoir parameters include drawdown tests,

multi-rate tests, two-rate tests, and build up tests.

The discussion, though concise, is complete, and there

are several examples that show how to use these

particular tests to determine reservoir properties.

Chapter 10 Reservoir Engineering Applied to

Gas, Gas / Condensate, and Gas / Oil Fields. This sur-

vey chapter discusses determining initial estimates

of oil and gas reserves using either volumetric cal-

culations or early production history. The mecha-

nisms of oil recovery are discussed in very general

terms. The solution of the material balance equa-

tion for a reservoir is shown.

Chapter 11 Simulation: Field and Reservoir Per-

formance. This chapter and its first three sections

discuss the implicit, explicit, and Crank-Nicolson

numerical methods for solving the partial differen-

tial equations that approximate the flow in a reser-

voir. The discussion is concise and includes an ex-

ample of the one-dimensional situation. There is

also a brief discussion of the inverse problem.

Chapter 12 Conversion of Depleted Gas, Gas/

Condensate Fields to Gas Storage Reservoirs. The

gas storage problem is discussed at a survey level in

this chapter. There is a good description of why

storage is needed and how gas is stored. A detailed

case study is presented.

Chapter 13 Gas Storage in Aquifers. This is an

excellent chapter-the strongest in the book. It be-

gins with procedural steps in locating and develop-

ing an aquifer storage reservoir. The discussion of

locating such a reservoir is detailed, and there is a

series of discussions of the measurements that are

required. Predictions on the rate of bubble develop-

ment or water pushback are discussed. There is a

general discussion of the various studies of aquifers.

Chapter 14 Monitoring, Inventory Verification,

Deliverability Assurance, and Safety in Storage Op-

erations. This chapter surveys what must be done to

Spring 1993

run a gas storage operation and represents the tre-

mendous experience of the senior author. This chap-

ter and the previous one are condensed from Under-

ground Storage of Fluids, by Katz and Coats (1968).

Chapter 15 Natural Gas Liquid Recovery and

Gas for the Fuel Market. Natural gas liquids (ethane,

propane, butanes, and pentanes) are recovered by

refrigeration adsorption stripping or cryogenic ex-

pansion/compression.

Chapter 16 Storage in Salt Cavities and Mined

Caverns. The description in this chapter is narra-

tive, explaining the attributes of such caverns and

how one develops caverns. Also, there is a discus-

sion of creating cavities by dissolving materials or

leaching out the materials.

Chapter 17 Miscellaneous Topics. This chapter

opens with a narrative of compressed air energy

storage for electric power peaking cycles. Much of

the chapter discusses the design of a storage facil-

ity. It also contains calculations associated with

transcontinental pipelines, geochemical identifica-

tion of natural gas, superheat limit vapor explosion,

and the phase behavior associated with it.

Six appendices contain data on computer programs

for calculating flow, derivations of gas flow equa-

tions in reservoirs, a detailed discussion of the Peng-

Robinson equation of state, equilibrium constants,

and nomenclature. n

book review

MASS TRANSFER

by J. A. Wesselingh, R. Krishna

Ellis Horwood Ltd., Market Cross House, Cooper St.,

Chichester, West Sussex, P019 1EB England; 243

pages, $69.95 (1991)

Reviewed by

Phillip C. Wankat

Purdue University

This is an extremely interesting (but in many ways

frustrating) short book on the use of the Maxwell-

Stefan (M-S) approach for solving complicated mass

transfer problems. Since the authors assume con-

siderable familiarity with Fickian diffusion and with

various separation methods, this book is appropri-

ate for graduate students. A finite difference ap-

proximation to the differential equations is used

throughout the book, and the calculations required

are well within the capabilities of graduate students.

After an introductory chapter, Chapter 2 explores

Continued on page 126.

re, curriculum

-- .--------------

ON LETTING THE INMATES

RUN THE ASYLUM

ALVA D. BAER

University of Utah

Salt Lake City, UT 84112

Please accept my apology for the deceptiveness

of the title of this paper. It should read "What

About Telling Students How and Why We

Run Engineering Colleges the Way We Do," or some-

thing like that-but that would really be too

long to be useful. The deception was designed to

attract your attention. (Besides, we professors do

let the inmates run the asylum by permitting

anonymous students' comments to affect RPT deci-

sions in the universities!)

Many engineering students consider an engineer-

ing college to be simply a super high school which

has as its main purpose subjecting them to a cur-

riculum of difficult and unrelated courses, or worse.

Such a belief is, of course, incorrect-but it is sel-

dom that anyone attempts to change the perception.

James Wei wrote a paper entitled "The Reju-

venation of Chemical Engineering" (first presented

in 1979 as a Phillips Petroleum Lecture at Okla-

homa State University and later given wider distri-

bution in CHEMTECIH1) that included an excellent

discussion of the rationale for most chemical engi-

neering curricula. This discussion was, and is, an

effective means of explaining to students the nature

of their progress toward an engineering degree. I

have given a one-page synopsis of the lecture to

undergraduate students for some time now, and the

perceptive students greatly appreciate Professor

Wei's observations.

One thing that is not obvious to students (or even

Copyright ChE Division ofASEE 1993

to some young faculty!) is the manner in which prob-

lem solving pervades the whole of engineering study

and practice. Although the list of successive courses

in the curricula bears titles of chemical engineering

topics, the nature of the problems treated in each

course is more complex than those that were en-

countered in the prerequisite classes. Table 1 at-

tempts to outline how problems change throughout

the education and career of an engineer.

This table is, for the most part, self-explanatory.

The word "paths" was used as a shortened term

to indicate strategies or approaches, and "practitio-

ner" is used in a broad sense to include students at

all levels. Also, the term "technician" implies the

semi-professional or industrial technician-operator.

The number of levels corresponds to about the nor-

mal yearly educational breaks in engineering edu-

cation and was selected to avoid any religious or

political implications.

The fact that such a progression is deliberate and

proceeds in an ordered fashion is something that

students need to know and to appreciate. When this

table is given to serious students who then take

the time to ponder its information, their acceptance

and understanding of the engineering approach to

problem solving becomes easier. Perhaps the

faculty is no longer seen as just being "difficult"

when they require more demanding and complex

assignments. Note also that it is here implied that

the introduction of truly "open-ended" problems is

later in the course of study than is normally sug-

gested by ABET requirements. However, it appears

that the undergraduate's later encounter with such

difficult problems corresponds to current engineer-

ing education practice.

Table 1 is not an outline for a problem-solving

algorithm. The manner in which complexity is in-

troduced into the problem solving process of very

quantitative disciplines is illustrated. The method

for introducing complexity into more qualitative

fields would be much different than the process

shown in the table. This is just one of the more

obvious differences between problem solving in en-

Chemical Engineering Education

Alva Baer has taught chemical engineering at

the University of Utah since earning his PhD

from that school in 1969. His academic and

industrial research efforts have been in support

of the areas of propulsion and combustion. He

has now reached the age where it is easier to

write short papers than it is to read long ones.

TABLE 1

Possible Levels of Engineering-Type Problem-Solution Methods

NOTE: Each level is based on the lower-level method

Level Number of

Steps and Concepts

'Information

Source

Characteristics of Solution Method

1 1 or 2 Given only the

data needed

2 2 or 3 May change units

of data

3 4 or 5

May be given

extraneous data

4 several Must find some

needed data

5 many Must decide on and

find needed data

in published

sources

6 many

Must evaluate

conflicting data, the

data are incomplete,

and needed accuracy

depends on how the

data enter the problem.

7 many Measurement of data

paths by standard methods

may be required

8 most paths Measurement of

fail needed data may

require new techniques

or be impossible.

Numbers are inserted into a given equation

Numbers are inserted into given, combined, or

rearranged equations

Final relationships must be developed; the problem

has an exact answer; and one may work toward

a given solution

The problem has one unique solution and one may

work toward a known answer. At this point, trial-

and-error and iterative methods may be introduced.

Computer solution methods become practical.

The problem has a unique solution, but the answer

is not given. A method is required to verify the

solution. Progress is now based on personal efforts

mainly by learning from one's own mistakes.

The problem may have several possible solutions,

but there may be an optimum answer. Usually

approximations must be made. Time-critical

answers are required. Economic factors are

important.

The type of problem may never have been solved

before. Economics must be considered at all

stages. Safety and environmental considerations

maybe important. The starting and ending points

are not obvious.

The problem selection is critical, but the selection is

usually by the practitioner. Often, the final

answer may not be recognized. Likely, an

acceptable solution is not possible.

High school students

and technicians

First-year science and

engineering students;

technicians

Second-year science and

engineering students;

advanced technicians

Second- and third-year

engineering students

Third-year engineering

students

Fourth-year engineering

students; graduate

students; design engineers

Graduate students; design

engineers; research

engineers

Researchers; creative

engineers

gineering and activities in less mathematical fields.

A result of this difference is that it is not likely

that a general problem-solving algorithm exists for

the range of human endeavors, and this fact is too

often missed by engineers. People with quantita-

tive training too often get into difficulties by

attempting to attach numbers to truly quali-

tative activities such as in the arts and humani-

ties, or for supervision and evaluation of other

people, etc. Engineering students should be made

aware of the limitations of their quantitative edu-

cation. Anyone who disagrees with this suggestion

should consider attaching a number to indicate the

affection of their dog.

Spring 1993

Finally, it should be noted that the details in Table

1 represent my observations and biases. Others

might organize the information in a different order

or with different emphasis. The important point,

however, is that there is a continuous progression in

complexity leading to the goal of efficiently solving

real-world problems. The table represents an origi-

nal effort, but if this notion or the information ap-

pears elsewhere the omission of a reference is the

result of ignorance, not perfidy.

REFERENCES

1. Wei, James, "The Rejuvenation of Chemical Engineering,"

CHEMTECH, 15, 655, November (1985) 0

Practitioners

O classroom

~l~sssmomJ

WHAT WORKS

A Quick Guide to Learning Principles

PHILLIP C. WANKAT

Purdue University

West Lafayette, IN 47907

Great teachers may be born that way, but the

vast majority of professors have to work to

improve their teaching. Fortunately, a re-

search base now exists that shows which teaching

methods work in a variety of situations. In this pa-

per, ten of the procedures which are known to work

will be briefly presented and applied to chemical

engineering education. More details and a variety of

earlier references are given by Wankat and

Oreovicz.[11

TEN LEARNING PRINCIPLES

1. Develop a structured hierarchy of content

and guide the learner.

Content is king (or queen). The professor should

be sure that the content of his subject is both impor-

tant and up-to-date. Some structure should be evi-

dent to the students, and they should be guided in

their learning. Tell the students where they are go-

ing and why it is worth their effort to get there. For

example, thermodynamics is both beautiful and ex-

tremely useful, but many professors act as if the

beauty of thermodynamics alone should be suffi-

cient to hold their students' attention, and they ne-

glect to tell the students what they will be able to do

once they have mastered the subject. Be sure that

the students know what the objectives of the course

are. Actually developing some of the structure of

knowledge themselves helps students learn the ma-

terial; thus, an overly rigid structure should be

avoided. A good homework assignment is requiring

the students to prepare a "key relations chart" which

lists everything the student wants to know to solve

problems or for a test. Obviously, first-year students

...thermodynamics is both beautiful

and extremely useful, but many professors act

as if the beauty of thermodynamics alone should

be sufficient to hold their students' attention ...

Copyright ChE Division ofASEE 1993

need considerably more structure than graduate stu-

dents, and courses should be designed accordingly.

Since problem solving is a major part of chemical

engineering, both the structure and the method of

problem solving should be part of the course.1'"21 Much

of the structuring of content and guiding the stu-

dent can be done in lectures, although other teach-

ing methods work just as well if not better.

2. Develop images and use visual modes of

learning.

Most people prefer visual learning and remember

visual images much longer than words, but most

college instruction is auditory (e.g., see Felder and

Silverman[31). The McCabe-Thiele diagram has been

a successful teaching method for decades simply be-

cause it provides the student with a visual image.

Modern computer graphics and plotting calculators

can also be used to provide visual images-they are

particularly useful for three-dimensional plots and

for showing motion. Most students better under-

stand equations when they are plotted for a variety

of circumstances rather than simply looking at the

symbolic form. The professor should require that

the students develop their own visual images.

3. Make the students actively learn.

People learn best by actively grappling with infor-

mation; thus, some sort of classroom activity is re-

quired.[4] This activity can be external (such as dis-

cussing a question, solving a problem, developing a

structured flowsheet of knowledge, brainstorming,

or working in a group) or internal (such as reading,

questioning by oneself, pondering, etc.). Lecturing

without student interaction is active only for the

Chemical Engineering Education

Phil Wankat received his BSChE from Purdue

and his PhD from Princeton. He is currently a

professor of chemical engineering at Purdue Uni-

versity. He is interested in teaching and counsel-

ing, has won several teaching awards at Purdue,

and is Head of Freshman Engineering. His re-

search interests are in the area of separation

processes with particular emphasis on cyclic sepa-

rations, adsorption, preparative chromatography,

simultaneous fermentation and separation.

professor-which is one reason why professors often

feel they have learned more than anyone else in the

class. Most students will initially resist active in-

volvement in the classroom since it is not safe and

they have been trained to passively take notes. But

once the students become familiar with classroom

activity, they usually grow to like it-and most stu-

dents certainly benefit from it.

4. Practice and feedback.

The professor should provide the students with an

opportunity to practice what they learn while they

are still in a supportive environment. A variety of

different problems and questions should be tackled,

and it is important to have some (but not excessive)

repetition to increase both speed and accuracy. A

series of regular assignments with frequent feed-

back will elicit more work and higher levels of com-

mitment to the class than will one long assignment.151

Following this principle, a long design project can

be broken into several smaller parts with various

assigned due dates. Students should have feedback

during, or shortly after, their first practice so that

they do not keep practicing incorrect methods.12' Feed-

back a month later is not useful. The students should

have the opportunity to practice again-after they

have received the feedback. For instance, after

a laboratory or design report has been returned to

the student with the usual excessive amount of red

ink, it is most effective to require the student to

produce a final, corrected, clean copy. With the aid

of word processors, preparing a clean copy is much

less work than it used to be. Computer-aided in-

struction can provide very useful practice, particu-

larly if it is interactive.

5. Positive expectations and student success.

Studies have shown that when a teacher expects

students to do well, they usually respond by doing

well."41 When someone important believes in the

student, his or her expectations can be a major in-

fluence in the student's success. A very interesting

and accessible report on this topic, pertaining to

families, is given by Caplan, et al.16' Success is a

strong motivation in itself, and it leads to additional

success. When a student does not have the proper

educational background, he or she will be probably

be unsuccessful; so one useful activity is to pro-

vide background material for those students, and

then to make sure that they use it. For instance, a

lack of skill in algebraic manipulation will cer-

tainly sink a student in a mass and energy balance

course-extra help in algebra can be much more

effective in advancing that student than tutoring in

mass and energy balances. Many capable students

Spring 1993

The professor should provide the students

with an opportunity to practice what they learn

while they are still in a supportive environment.

A variety of different problems and

questions should be tackled...

leave engineering due to a lack of encouragement or

a lack of success."71

6. Develop a cooperative class with students

teaching each other.

Most students learn better in a cooperative envi-

ronment where a significant amount of the work is

done in groups.l41 Since modern engineering practice

usually involves groups of engineers, group classwork

can be good training for the students' professional

careers. Many students who leave engineering cite

the overly competitive atmosphere as a major rea-

son for leaving."' A number of successful programs

involving group work with engineering students have

been reported.1'2] A recent study at Harvard Univer-

sity found that the students who grow most aca-

demically and who are happiest structure their time

to include intense interpersonal interactions with

faculty or other students."5' In large classes the pro-

fessor may not have time to meet individually with

every student, but he or she can and should encour-

age group work both in and out of class. Study groups

should be set up with the understanding that each

group member must do the reading or problem as-

signments before coming to the study group. Opti-

mum group size appears to be from four to six stu-

dents. Competitive grading procedures using "the

curve" do not encourage cooperation; other proce-

dures, such as grading against an absolute standard

or mastery testing, will encourage more cooperation

with the professor and between the students them-

selves."11 One advantage of working in groups is that

students have an opportunity to informally teach

other students (which helps both of the students

learn better). Formal approaches to encouraging stu-

dents to teach other students (such as tutoring or

serving as the expert on a laboratory experiment)

also increase student learning. It is important to

note that teaching others should not be reserved for

only the best students.

7. Be enthusiastic-care about teaching.

Students respond to enthusiasm. It is important

that the professor cares about what he or she is

teaching. Those professors who put teaching on "au-

tomatic" cannot possibly do a good job. There is no

excuse for reading a book to the students in lec-

Continued on page 127.

jg 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.

CZOCHRALSKI

CRYSTAL GROWTH MODELING

A Demonstrative Energy Transport Problem

DAVID C. VENERUS

Illinois Institute of Technology

Chicago, IL 60616

he development of new and interesting trans-

port phenomena examples and problems that

can be solved using relatively simple math-

ematical tools can be a challenge. This is especially

true when teaching an undergraduate course in

transport phenomena where the students have little

or no experience solving partial differential equa-

tions. There are, unfortunately, a finite number of

physically meaningful problems one can formulate

that lead to linear, ordinary differential equations

(even with three coordinate systems and several

types of boundary conditions to choose from).

This paper presents an energy transport problem

that is both instructive and interesting; it can be

used to demonstrate

the use of dimensional analysis

the quasi-steady state approximation

the fin approximation

As the example progresses, students see an "intimi-

David C. Venerus is an assistant professor of

chemical engineering at Illinois Institute of Tech-

nology. He received his BS degree from the Uni-

versity of Rhode Island and his MS and PhD

degrees from Penn State University He has been

at IIT since 1989 and conducts research in the

areas of polymer theology and processing. He

has taught courses in material and energy bal-

ances, unit operation, transport phenomena, and

polymer processing, and is faculty advisor to the

AIChE student chapter.

Copyright ChE Division ofASEE 1993

dating" PDE transformed into an innocent ODE

through the introduction of several physically rea-

sonable assumptions. The novelty of the example

arises from the fact that it applies to a technology

not traditionally associated with chemical engineers,

although it is one that virtually all engineers use.

INTRODUCTION

The example arises from an energy transport

analysis of a process widely used in the semiconduc-

tor device industry. The process, known as

Czochralski Crystal Growth (CZCG), is used to

produce single-crystal, defect-free ingots of Si (and

similar materials) which are subsequently sliced

into thin disks (or "wafers"), polished, and used

as substrates in the fabrication of microelectronic

devices, or "computer chips." The example or prob-

lem might be introduced by giving a short descrip-

tion of the process.

CZCG is a batch process initiated when a seed

crystal is dipped into a melt of the same material so

that the liquid wets the seed crystal. As solidifica-

tion occurs, the seed is slowly withdrawn from the

melt so that a neck and shoulder are grown. Once

the desired radius is achieved, a nearly cylindrical

crystal is grown by manipulation of the pull rate

and/or melt temperature.

It should be noted that even for the simplified

description of CZCG given above, a high level of

complexity is required to develop detailed transport

models. The presence of a number of free bound-

Chemical Engineering Education

aries (at the crystal-melt, crystal-ambient, and melt-

ambient interfaces), radiative heat transfer, and tem-

perature-dependent physical properties all make the

problem highly non-linear. Detailed transport mod-

els which account for these phenomena require nu-

merical solution on large computers. An excellent

review of the CZCG and other crystal growth pro-

cesses along with discussions on the importance of

various transport processes can be found elsewhere.11

PROBLEM FORMULATION AND ANALYSIS

Before they are presented with this example, stu-

dents should have been exposed to the appropriate

energy transport phenomena fundamentals: conser-

vation laws (either by the shell balance[2] or Reynolds

Transport Theorem"" approach), constitutive equa-

tions, and boundary conditions.

For the example, we will consider a relatively

simple model of the CZCG process that describes

energy transport within the cylindrical crystal. A

schematic diagram of the process in shown in Fig-

ure 1, which indicates the position of the coordinate

system. Results from this analysis could be used to

estimate thermoelastic stresses (due to temperature

gradients), which can lead to crystal defects, or used

to find relationships between crystal length, growth

rate, and melt temperature. The assumptions to be

used in the development of the model are

1. Axial symmetry in the crystal.

2. All physical properties are isotropic and indepen-

dent of temperature.

3. Heat transfer between the crystal and the ambient

V

Crystal

TR

T-a L T

Ambient

z

Tm

Melt

Figure 1. Schematic diagram of Czochralski Crystal

Growth (CZCG) process.

Spring 1993

can be described by a convective heat transfer law

to an ambient temperature that is independent of

time and position.

4. Heat transfer between the crystal and the melt can

be described by a convective heat transfer law to a

melt temperature that is independent of position.

5. The velocity of the crystal (pull rate) is constant.

6. The crystal-melt interface is planar and fixed at

the origin of the coordinate system.

Assumptions 1 to 6 lead to the following for the

thermal energy equation and boundary conditions:

_T 1T -1 aT a2 T]

at +Vz =ar ar =i (1)

T(r,z,0)= Tf 0

T(r,0,t)= Tf 0 r 0 (3)

-kzT(r,L(t),t) =ha[T(r,L(t),t)-Ta] 0 r0 (4)

az

-k (R,z,t)=ha [T(R,z,t)-Ta ] 00 (5)

where a = k / pCp. The (jump) energy balance at the

crystal-melt interface gives

-k ( (r,0,t))= hm[Tm (t)- Tf ]+ pVAHf t>0 (6)

where ( ) indicates a radially averaged quantity.

A list of the dimensional variables that appear

in this set of equations can be found at the end of

this paper.

Equations (1) to (5) define the linear boundary

value problem (BVP) for T(r,z,t). The boundary con-

ditions given by Eqs. (4) and (5) simply relate the

conductive and convective energy fluxes at the crys-

tal-ambient interfaces according to assumption 3.

Equation (6) is an energy balance for the crystal-

melt interface that must be satisfied so that a con-

stant radius crystal is grown by manipulation of the

melt temperature, Tm(t). If Tm is made constant,

then the crystal velocity V, rather than the melt

temperature, is manipulated to maintain a con-

stant radius crystal. In this case, Eq. (6) would be

solved for the crystal velocity which would be a func-

tion of the temperature gradient at z = 0 rather

than a constant. Hence, Eqs. (1) to (6) would consti-

tute a non-linear BVP since Eq. (1) would be non-

linear (due to the convective term) and because the

moving boundary L(t) would be a function of the

dependent variable rather than some external influ-

ence. In this case, assumptions 4 and 5 would, of

course, be modified.

Although the problem defined by Eqs. (1) through

(6) can be solved analytically, we will try to find

123

ways to simplify it using several additional assump-

tions. To begin, we first put the equations in dimen-

sionless form using

Sr z t T-Ta

R =R R2 Tf-Ta

Substitution of the above definitions into Eq. (1)

gives

ao ao i a + 8 ao2

T+ ePe 1 (7)

where Pe is a dimensionless group

VR

Pe = VR Peclet No.

The problem at hand would be much simpler if it

were a steady-state problem, but unfortunately no

steady-state exists because the length of the crystal

is a function of time: V = dL(t)/dt. Suppose, how-

ever, that we could neglect the unsteady term in Eq.

(7) but still allow the length of the crystal to change.

Under what conditions would this be a good as-

sumption? To answer, let us consider the time scale

for energy transfer (tE) and the time scale associated

with a change in the length of the crystal (tL). If

t << tL, i.e., conduction along the length of the crys-

tal is instantaneous compared to the time required

for the length to change, then neglecting the un-

steady term in Eq. (7) would seem reasonable. Of

course, what we are saying is that the quasi-steady

state approximation (QSSA) would be valid. If we

let tE = L2/a and tL = L/V, then we have

tE = VL

tL Oa

L
L < < V

For CZCG growth of Si, a ~ 101 cm2/sec and

V ~ 103 cm/sec, so that the QSSA will be valid if

L < -100 cm. We will later see the QSSA will also

be valid for much greater crystal lengths. Thus we

will add the following assumption to our list:

7. The quasi-steady state approximation is valid.

The complete problem in dimensionless form is

now given by

P e +_ 1 a ( 2 (8)

(4, 0) =1 0 <1 (9)

-o (,A)+Bia (I,A)=0 050 <1 (10)

(1,)+Bia(1,)=0 0

(, ))+ Bi[-l1]= PeSt (12)

which includes the following dimensionless groups:

A = L Aspect Ratio

R

Bii = Biot No. for ambient (i=a) or melt (i=m)

St = CpAHf Stefan No.

Tf Ta

The solution to Eqs. (8) through (11) can now be

found by the separation of variables method for

#((,0), and Eq. (12) can be evaluated for the dimen-

sionless melt temperature, m,. For the case when

Pe -- 0, one might have the students find the solu-

tion in the literature.[41

Let us see if there are other physical arguments

that will further simplify our CZCG model. For stages

of the process when the crystal is long (A > > 1), it

would seem reasonable to expect the temperature

variation in the z-direction to be much greater than

in the r-direction. Does this mean that neglecting

the radial conduction term in Eq. (8) would be a

good assumption? While this seems like a good idea

at first glance, we remind the students that in doing

so we are in effect saying that the cylindrical sur-

face of the crystal is insulated and no energy is

transferred across it. For large A, this surface is

much larger (2A times) than the surface of the top of

the crystal and neglecting the heat transfer from it

would be a poor assumption.

Our original argument, however, still seems valid,

and it would be nice if we could find some way of

simplifying the radial conduction term. Since the

variation of T in the r-direction is probably small,

suppose we use an average radial temperature to

represent it? This approach is, of course, the "fin

approximation" which is frequently used to describe

finned heated transfer surfaces. In terms of dimen-

sional variables, the definition for average tempera-

ture we use is

2n R

fJ T(r,z)rdrd6 R

(T(z))= 0 0 =2 J T(r,z)rdr

21c R R2 (-0

J Jrdrd6

0o o0

or, in dimensionless form

1

<((())= 2\ $(,0))d (13)

0

Since A can be large (-102) in a typical CZCG

process, we will pursue this approach and add the

following assumption:

8. The fin approximation is valid.

Of course, the fin approximation can also be incor-

porated into the governing equations by the shell

Chemical Engineering Education

balance approach.2'

Integration of Eq. (8) according to Eq. (13) gives

Pe =2 (1, ) + 2 (14)

ao a4 ao

and substitution of the boundary condition given by

Eq. (11) in Eq. (14) leads to

a(4) a2()

Pe =-2 Bia(,o)+ a2

which, since (1,ao) =< 0(o) >, can be written as

d2(o) d(e)

dG2 Pe d -2 Bia() = 0 (15)

Equations (9), (10), and (12), in terms of the radially

1.00

0.80

0.60

0.40

0.20

0.2o

0.00

0.00 0.20 0.40 0.60 0.80 1.00

a/A

Figure 2. Dimensionless axial temperature distribution

from Eq. (19) for the indicated values of Bio.

Solid lines: Pe = 0; dashed lines: Pe = 0.1.

1

Bi.*0.2

0.05

/ ^-----_--___

0.1 06.02

0.01

0 1 2 3 4 5 6 7 8 9 10

A

Figure 3. Dimensionless temperature gradient at the crys-

tal-melt interface from Eq. (20) versus crystal length for

the indicated values of Bi..

Solid lines: Pe = 0; dashed lines: Pe = 0.1.

Spring 1993

averaged temperature, < (oc) >, can be written as

()(0) = 1 (16)

do (A)+ Bia()(A) = 0 (17)

d(~)

d (O) + Bi [m 1] = Pe St (18)

Hence, utilization of the quasi-steady state and

fin approximations has transformed the original

problem (Eqs. 1-6) to the problem given by Eqs. (15)

through (18), which the typical junior or senior

chemical engineering student can solve.

SOLUTION AND APPLICATIONS

For the sake of space, we present only the solution

to the last model, Eqs. (15) through (17), which is

given by

cosh[X(A-)]+ + 2 sinh (A-a )

(0(Y)) = exp[ (Y] P2. 2

((I)) exp[] cosh [A]+ +2 Bia sinh A]

(19)

where X= -Pe2 + Bia. The gradient at the crystal-

melt interface is given by

d(o)

J0- (0)-

-Bia cosh[ A]+ Bia(Pe-4) sinh[ A]

cosh[A]+ Pe+2 Bi sinh[A]

2 X 2

which can be used in Eq. (18) to find 0.

This solution can be used to demonstrate various

aspects of the heat transfer processes in CZCG. Stu-

dents can see how the temperature distribution and

pull rate depend on the dimensionless groups that

arise in the model, which always provides physical

insight into their meaning. The temperature distri-

bution predicted by Eq. (19) is shown in Figure 2 for

typical values of Bia and Pe. One might also point

out that a crystal length A, can be found beyond

which the crystal has an effectively infinite length.

For A > A&, we can infer that tL -- so that the

QSSA will be valid for long crystals as was men-

tioned earlier. A, can be estimated by plotting the

interfacial temperature gradient 3 from Eq. (20) as

a function of crystal length A, as shown in Figure 3.

Another interesting exercise is to have students

find the range of Bia for which the fin approximation

is valid (this turns out to be Bia -0.2). This can be

done by comparing P from Eq. (20) to the radial

average of the crystal-melt temperature gradient

determined from the two-dimensional model, which

125

can be given in class or derived from results found

in the literature.[41

The simple model and its solution that have been

presented in this paper are most appropriate for an

undergraduate-level transport phenomena course.

When used in a lecture, it is a compact example that

demonstrates the use of two important engineering

approximations. At the graduate level, the two-di-

mensional models (both unsteady and steady) could

provide the basis for a good homework or exam prob-

lem. The validity of the QSSA can be determined by

comparing results from the transient and quasi-

steady models. A more realistic transient model could

be developed by allowing the crystal-melt interface

to move according to a mass balance on a melt of

finite volume. In this case, the crystal pull rate and

crystal velocity will not be the same.

This type of problem can also be useful to demon-

strate techniques for boundary immobilization. There

are, of course, many other ways to look at or use

this example; they are left for the reader to ponder.

ACKNOWLEDGMENT

The author is grateful to Daniel White, Jr., for

bringing the CZCG modeling problem to his atten-

tion during an excellent course Dr. White taught at

Penn State University in the fall of 1986.

NOMENCLATURE

C specific heat capacity of crystal

h convective heat transfer coefficient to ambient

h convective heat transfer coefficient to melt

AHf specific enthalpy of fusion

k thermal conductivity of crystal

L crystal length

r radial position

R crystal radius

t time

T crystal temperature distribution

Ta ambient temperature

T, melting temperature of crystal

Tm melt temperature

V crystal velocity or pull rate

z axial position

a thermal diffusivity of crystal

p density of crystal

REFERENCES

1. Brown, R.A., "Theory of Transport Processes in Single Crys-

tal Growth from the Melt," AIChE J., 34, 881 (1988)

2. Bird, R.B., W.E. Stewart, and E.N. Lightfoot, Transport

Phenomena, John Wiley and Sons, Chap. 9 (1960)

3. Slattery, J.C., Momentum, Energy and Mass Transfer in

Continue, McGraw Hill, New York, Chap 5 (1972)

4. Carslaw, H.S., and J.C. Jaeger, Conduction of Heat in Sol-

ids, 2nd ed., Oxford University Press, Chap. 8 (1959) O

REVIEW: Mass Transfer

Continued from page 117

some problems in using Fickian theories of diffusion

when more than two species are present. Chapters 3

and 4 start formulating the M-S theory, but with

little mention of it by name. Chapter 3 discusses

driving forces for mass transfer, while Chapter 4

considers friction effects. The idea of a "bootstrap"

relationship to provide an absolute level of velocity

in the M-S equations is introduced in Chapter 4 and

is explained with examples in Chapters 5 and 6.

Chapter 5 shows several binary ideal solution ex-

amples and notes that the M-S theory gives the

same results as Fickian diffusion and is no more

difficult to use. Ternary examples are the subject of

Chapter 6. The example for distillation is a particu-

larly clear explanation of how the Murphree effi-

ciency can be infinite or negative.

Chapter 7, on combined mass and heat balances,

suffers from the need for a more complete descrip-

tion of the energy balance. Chapter 8, on

nonidealities, has an interesting example on etha-

nol water distillation, but the reasons for lack of

agreement with the exact solution are not spelled

out. This chapter also contains the first detailed

comparison between the M-S and Fickian ap-

proaches. Moving parts of this comparison to a place

much earlier in the book would help many readers.

Chapter 9 briefly presents theories for determin-

ing the M-S diffusivities. Driving forces other than

activity gradients are the topic of Chapter 10. These

include pressure gradients, centrifugal force, sup-

port forces (from solid matrices), and electrical forces.

With these additional forces, Chapter 11 can look at

the diffusion of ions in electrolytes. The end of Chap-

ter 11 is a natural break in the book since the fun-

damental ideas have all been presented.

The second part of the book briefly covers a vari-

ety of separation processes. Chapter 12 is an over-

view of various membrane separation processes,

while individual processes are covered in detail in

the following chapters: gas permeation (13), dialysis

and pervaporation (14), electrodialysis (15), and re-

verse osmosis and ultrafiltration (16). There is very

little detail on the nature of the membrane itself,

and statements such as "We shall treat the mem-

brane as homogeneous," (p. 125, referring to reverse

osmosis) could easily be misinterpreted. Supplemen-

tation of these sections with a book such as R.E.

Kesting, Synthetic Polymeric Membranes: A Struc-

tural Perspective (2nd ed., Wiley, New York, 1985) is

Continued on page 149

Chemical Engineering Education

Guide to Learning Principles

Continued from page 121

ture-it is boring and shows a tremendous lack of

respect for both the students and the material. En-

thusiasm and caring (both for the students and for

the material) are so important that they are suffi-

cient to help cover a variety of other teaching sins.

One advantage of professors teaching courses in their

research areas is that most of them are naturally

enthusiastic and caring about their subject. Of

course, someone still has to teach the beginning

courses, and it is vitally important to also show a

love of learning in them. Small classes can be a

big advantage since it is easier for professors to

show enthusiasm and caring when there are fewer

students. Small classes almost force personal inter-

action between students and faculty. It has been

shown that students who took small classes early in

their careers were much more likely to become en-

gaged in academics."5

8. Challenge the students-

ask thought-provoking questions.

Many students leave engineering because they see

it as boring!"7 To offset this, the professor should

find ways to provide some measure of challenge to

each of the students. One method is to ask ques-

tions which "stretch" the students, requiring that

they use their fundamental knowledge in new

ways to answer questions about real phenomena.

For example, ask what the temperature will be in a

car sitting on the street if the wind chill is -10C but

the ambient temperature is 200C-then ask the stu-

dent to explain what "wind chill" is. It is often a

good idea to leave a question unanswered during

class and to challenge the students to obtain an

answer within their study groups. The challenges

should be arranged so that each student can shine

once in a while.

9. Individualize the learning environment.

Since students have very different learning

styles,"['3 it is useful to employ a variety of teaching

styles throughout the course. In that way each stu-

dent will be able to use his or her favorite style at

some time during the course. The professor should

use both inductive and deductive approaches to teach

the material, although an inductive approach is usu-

ally more effective the first time through the mate-

rial. Use a variety of different exercises-when brain-

storming is one exercise and analysis is a second

exercise, you will often be able to observe that dif-

ferent students shine in the different exercises. Rich

Spring 1993

Felder's column, "Random Thoughts" in CEE, has

contained many examples of individual learning

styles and methods to individualize instruction in

chemical engineering.

10. Ifpossible,

separate teaching and evaluation.

Evaluation gets in the way of teaching since the

evaluator tends to be seen as the "enemy," particu-

larly if grading is done on the curve. The professor

who separates teaching and evaluation can then be-

come a coach who is there with the sole purpose of

helping the students learn. Someone else should do

the evaluation, or a mastery style course where ev-

ery student can succeed should be used. For ex-

ample, in a large multisection course with several

professors, one of the professors could write and be

in charge of scoring all tests and quizzes while the

other professors do the teaching. In a design course,

an industrial evaluation of the designs may well be

appropriate-it is certainly realistic.

CONCLUDING REMARKS

These learning principles are certainly not inclu-

sive, but they do present a good start for improving

teaching and avoiding disastrous classes. Note that

most of the focus of these principles is on the stu-

dents. It is the students, not the professor, who have

to learn in order for the course to be a success.

ACKNOWLEDGMENT

This article was written while the author was en-

joying the hospitality of the Department of Chemi-

cal Engineering at the University of Florida while

on sabbatical there. The work was partially sup-

ported by NSF grant USE-8953587.

REFERENCES

1. Wankat, P.C., and F.S. Oreovicz, Teaching Engineering,

McGraw-Hill, New York; (1993)

2. Hewitt, G.G., "Chemical Engineering in the British Isles:

The Academic Sector," Chem. Eng. Res. Des., 69 (Al), 79,

Jan. (1991)

3. Felder, R.M., and L.K. Silverman, "Learning and Teaching

Styles in Engineering Education," Eng. Ed., 78 (7), 674

(1988)

4. Chickering, A.W., and Z.F. Gamson, "Seven Principles for

Good Practice in Undergraduate Education," American As-

sociation for Higher Education Bulletin, 3, March (1987)

5. Light, R.J., "The Harvard Assessment Seminars", Second

Report, Harvard University, Cambridge, MA (1992) [Free

copies of this report can be obtained by writing to: School of

Education Office, Harvard Graduate School of Education,

Larsen Hall, Cambridge, MA 02138]

6. Caplan, N., M.H. Choy, and J.K. Whitmore, "Indochinese

Refugee Families and Academic Achievement," Sci. Amer.,

266 (2), 36, Feb. (1992)

7. Hewitt, N.M., and E. Seymour, "A Long Discouraging

Climb," ASEE Prism, 1(6), 24, Feb. (1992) O

127

Random Thoughts...

SPEAKING OF EDUCATION

RICHARD M. FIELDER

North Carolina State University

Raleigh, NC 27695

What all great teachers appear to have in common is love of their subject, an obvious

satisfaction in arousing this love in their students, and an ability to convince them that

what they are being taught is deadly serious. (Joseph Epstein)

The only rational way of educating is to be an example-if one can't help it, a warning

example. (Albert Einstein)

Teaching is not a lost art, but the regard for it is a lost tradition. (Jacques Barzun)

A good education is not so much one which prepares a man to succeed in the world, as

one which enables him to sustain failure. (Bernard Iddings Bell)

If we desire to form individuals capable of inventive thought and of helping the society of

tomorrow to achieve progress, then it is clear that an education which is an active dis-

covery of reality is superior to one that consists merely in providing the young with

ready-made truths. (Jean Piaget)

The Romans taught their children nothing that was to be learned sitting. (Seneca)

There is nothing on earth intended for innocent people so horrible as a school. To begin

with, it is a prison. But it is in some respects more cruel than a prison. In a prison, for

instance, you are not forced to read books written by the wardens and the governor.

(George Bernard Shaw)

+ "We must remember," said a Harvard Classics professor at a meeting, "that professors

are the ones nobody wanted to dance with in high school." (Patricia Nelson Limerick)

I try not to let my schooling interfere with my education. (Mark Twain)

I learned three important things in college-to use a library, to memorize quickly and

visually, and to drop asleep at any time given a horizontal surface and fifteen minutes.

(Agnes de Mille)

It can be said unequivocally that good teaching is far more complex, difficult, and de-

manding than mediocre research, which may explain why professors try so hard to avoid

it. (Page Smith)

128 Chemical Engineering Education

+ Do not try to make the brilliant pupil a replica of yourself (Gilbert Highet)

At present the universities are as uncongenial to teaching as the Mojave Desert to a clutch

of Druid priests. If you want to restore a Druid priesthood you cannot do it by offering

prizes for Druid-of-the-year. If you want Druids, you must grow forests. (William

Arrowsmith)

Examinations are formidable even to the best-prepared; for the greatest fool may ask more

than the wisest man can answer. (Charles Colton)

If you are given an open-book exam you will forget your book. If you are given a take-home

exam you will forget where you live. (Variant of Murphy's Law)

One of the great marvels of creation is the infinite capacity of the human brain to with-

stand the introduction of knowledge. (Theodore Roosevelt)

+ Universities are full of knowledge; the freshmen bring a little in and the seniors take none

away, and knowledge accumulates. (Abbott Lowell)

Ifyou want a track team to win the high jump, you find one person who can jump seven

feet, not seven people who can jump one foot. (Anonymous)

The best way to get a good idea is to get a lot of ideas. (Linus Pauling)

A first principle not formally recognized by scientific methodologists-when you run onto

something interesting, drop everything else and study it. (B. F. Skinner)

If you hear the word "Impossible!" spoken as an expletive, followed by laughter, you will

know that someone's orderly research plan is coming along nicely. (Lewis Thomas)

Four to six weeks in the lab can save you an hour in the library. (G. C. Quarderer)

Experience is not what happens to you; it is what you do with what happens to you.

(Aldous Huxley)

Believe those who are seeking the truth; doubt those who find it. (Andr6 Gide)

I arise in the morning torn between a desire to improve the world and a desire to enjoy the

world. This makes it hard to plan the day. (E. B. White)

We know that the most advanced computer in the world does not have a brain as sophisti-

cated as that of an ant. True, we could say that of many of our relatives but we only have to

put up with them at weddings or special occasions. (Woody Allen)

+ The only thing God didn't do to Job was give him a computer. (I. F. Stone)

Why, a four-year-old child could understand this. Someone get me a four-year-old child.

(Groucho Marx) C

Spring 1993

laboratory

INTRODUCING STATISTICAL CONCEPTS

IN THE

UNDERGRADUATE LABORATORY

Linking Theory and Practice

ANNETTE L. BURKE, ALOKE PHATAK,

PARK M. REILLY, ROBERT R. HUDGINS

University of Waterloo

Waterloo, Ontario, Canada N2L 3G1

Laboratory experiments are an integral part of

the chemical engineering curriculum because

they serve several purposes. Their primary

purpose is to reinforce key chemical engineering

concepts, but they are also supposed to teach stu-

dents about model development and how to obtain

reliable data in the presence of experimental error.

With the present-day emphasis on quality control

in chemical industries and manufacturing, these

skills are needed by every chemical engineer who

will collect and analyze data, and they are espe-

cially important for engineers involved in process

modeling and development.

Unfortunately, with the exception of one course

in statistics, we do very little to teach under-

graduates about data collection and analysis. At Wa-

terloo, an introductory course in statistics is given

in the second year, and topics include an introduc-

tion to probability distributions, properties of means

and variances, estimation, confidence intervals, sig-

nificance tests, and linear regression. These tools

provide a background in collecting and analyzing

data-but students forget most of the material be-

cause they never get a chance to apply it. As a

result, they complete their undergraduate training

without really grasping the connection between sta-

tistics and experimentation.

In the students' defense, most laboratory experi-

ments are not designed using the same principles

that we teach in class. For example, in a statistics

course we might emphasize the importance of re-

porting confidence intervals for a parameter that we

have estimated, but laboratory experiments are

rarely designed to allow students to do just that.

Copyright ChE Division ofASEE 1993

Annette Burke obtained her BASc in chemical engineering from the

University of Waterloo in 1990. She is working on the development of

improved methods for designing sequential model discrimination experi-

ments. Her research interests include a variety of issues related to process

modeling and experimental design.

Aloke Phatak obtained his BASc and MASc in chemical engineering from

the University of Waterloo. After working as a research scientist in the field

of rocket propellants for three years, he returned to UW for his doctorate.

He is currently working on applications of multivariate statistics in ChE.

Bob Hudgins holds degrees from the University of Toronto and Princeton

University. He teaches reaction engineering, staged operations and labo-

ratories that go with them. His research interests lie in periodic operation of

catalytic reactors and in the improvement of gravity clarifiers.

Park Reilly graduated from the University of Toronto in 1943 and worked

in industry until 1967 when he joined the faculty at the University of

Waterloo. He studied statistics at the University of London and received a

PhD in Statistics in 1962. His research and publications are in the area of

applied statistics.

Consequently, they are left wondering about the

practical "real-world" value of statistical techniques.

To bring statistics down from the blackboard and

onto the lab bench, therefore, we must include sta-

tistical concepts in undergraduate laboratory experi-

ments. If we do not reinforce this link between the

theory and the practice of statistics, we will be do-

ing a disservice to our students who, as practicing

engineers, will have to deal with measurement

error on a daily basis.

OBJECTIVES

The purpose of this paper is to show that it is

possible to incorporate statistical ideas within exist-

ing experiments, while still respecting the need to

illustrate chemical engineering concepts. We have

made changes in two second-year physical chemis-

try experiments. These experiments are particularly

appropriate, not only because they are a part of

physical chemistry courses in many departments,

but also because here at Waterloo they are carried

out in the term following the introductory statistics

course. Thus, students begin applying statistical tools

very early in the curriculum. We hope that through

this early exposure they will come to view sound

Chemical Engineering Education

statistical analysis as a necessary part of all experi-

mentation. Our long-term objective is to incorporate

more advanced concepts, such as design of experi-

ments and response surface methodology, into all

laboratory courses-especially into the unit opera-

tions laboratories in the third and fourth years.

In the following paragraphs we outline the old

procedures, the changes we have made, and the sta-

tistical concepts that have been introduced. We be-

lieve that the new procedures are better, but we

also suggest additional modifications which could be

made to further improve the didactic value of the

experiments. Complete laboratory procedures, which

include laboratory questions and supplementary ma-

terial, can be obtained from the authors.

EXPERIMENT 1

Determination of the Molecular Weight of

Polystyrene by Viscometry

In this experiment, students determine the viscos-

ity-average molecular weight (My) of a sample of

polystyrene by dilute solution viscometry. Some of

the concepts introduced in this experiment (the rheo-

logy of suspensions, for example) are also discussed

in the physical chemistry course and in a fluid me-

chanics course. In addition, the students learn a

little bit about polymers and polymer-solvent inter-

actions. The standard experimental procedure for

determining My is described by Smith and Stires."'

It is quite commonly used in both industrial and

research laboratories.

In dilute solution viscometry, the idea is to relate

My to the viscosity of a very dilute solution of poly-

mer and solvent. The viscosity of a polymer solution

increases with both the concentration and the mo-

lecular weight of the polymer. By measuring the

viscosity of a polymer solution at several concentra-

tions, however, and then extrapolating to zero con-

centration, the effect of molecular weight can be

isolated, thereby allowing us to estimate My.

The viscosity-average molecular weight of a poly-

mer is related to the intrinsic viscosity of a polymer

by the Mark-Houwink-Sakurada (MHS) equation[21

[ ]= KMa (1)

Here, [il] is the intrinsic viscosity, and K and a are

constants which depend upon the polymer, solvent,

and solution temperature. The intrinsic viscosity,

sometimes known as the limiting viscosity number,

is defined in terms of the Newtonian viscosity of a

polymer-solvent solution of concentration, c, as the

concentration approaches zero, e.g.,

[TI] = lim (T( / 11o 1) (2)

[J= im (2)

Spring 1993

Spring 1993

where Tr is the viscosity of the polymer-solvent

solution of concentration c, and io is the viscosity

of the solvent alone. Once we know the intrinsic

viscosity of a polymer in a given solvent and the

MHS constants K and a, we can calculate its viscos-

ity average molecular weight by solving Eq. (1) for

My. But how can we determine the intrinsic vis-

cosity in the first place?

The Newtonian viscosity of a polymer-solvent so-

lution depends on the concentration of the polymer.

For very dilute solutions this concentration depen-

dence can be described by the Huggins equation,"

which is written as

( /i -1) [l] + kH [l]2c (3)

where the constant kH is known as the Huggins

constant. Thus, to determine the intrinsic viscosity,

we first measure the viscosity of the solvent as well

as the viscosities of at least two polymer solutions of

known concentration. Then, assuming that the

Huggins equation is correct, we can use linear re-

gression to estimate [il] in Eq. (3).

In the experiment, however, 1" and rn are never

actually measured. In the viscometer used, the time

required for the polymer solution to flow through a

marked length of glass tubing is measured. It turns

out that in such a viscometer, the flow time is pro-

portional to the viscosity of the solution and in-

versely proportional to its density. However, because

the different polymer solutions used are very dilute,

their density is roughly the same, and flow time

depends on the viscosity of the solution only. Thus,

we can write i/To = t/to, where t is the flow time for a

polymer solution and to is the flow time for the pure

solvent. As a result, Eq. (3) can be written in terms

of flow times instead of viscosities, e.g.,

(t/t- 1) = []+kH[n]2c (4)

and we can carry out a linear regression as outlined

above to estimate [i].

Old Procedure: A 50-ml solution consisting of

0.5 g of polymer in solvent (toluene, for example) is

prepared and left for a day to allow the polymer to

dissolve. A 10-ml aliquot of pure solvent is then

placed in a Cannon-Ubbelohde viscometer, and the

flow time is measured three times. These measure-

ments are then averaged. All flow times are deter-

mined in this way since uncertainty in these mea-

surements is the major source of error in this ex-

periment. The solvent is removed and the viscom-

eter cleaned. Next, 10 ml of polymer solution is placed

in the viscometer and the flow time is measured.

The solution is diluted by the successive addition of

131

2, 5, 5, 10, and finally 20 ml of solvent. After each

addition the solution is mixed and the flow time

measured. Then, the data are plotted using the

Huggins equation, and by using linear regression,

[1i] is estimated. Figure 1 is a plot of typical data.

Once [il] has been determined, Mv can be calcu-

lated using the Mark-Houwink-Sakurada equation.

Students are supplied with appropriate values of

the constants K and a from the Polymer Handbook. 4

0.__ Why is such a

design inherently

0.48 flawed? Reilly, et

6 al.,[51 pointed out

that as more and

-0.44 more solvent is

o added to the ini-

0.42 tial polymer so-

0.40 lution, the error

in measuring flow

0.38 times increases,

o.36 as does the un-

0.0 0.2 0.4 0.6 0.8 1.0 certainty in the

c (g/mL) concentration. As

Figure 1. Huggins plot of viscosity a result, the error

data generated using the old ex- in the quantity

perimental procedure. The polymer (q/Tio 1)/c in-

system is polystyrene in toluene at creases as con-

300C. centration de-

creases, and making a large number of measure-

ments at low concentrations decreases the precision

with which we can determine [Tn]. Our objective in

modifying this experiment, therefore, was to imple-

ment an improved procedure suggested by Reilly, et

al.,-one which yields more precise estimates of [qr]

and My and which, more importantly, allows

students to construct confidence intervals for these

two quantities.

New Procedure: How many polymer-solvent so-

lutions should we run through the viscometer to

estimate the intrinsic viscosity with the greatest

precision? The answer, according to Reilly, et al.,51

is only two! The first solution has a concentration

given by c1, and the second a concentration of c1/2,

which we denote by c,2. Once the flow times of these

solutions and of the pure solvent have been mea-

sured, the problem of estimating [r] by regressing

(t/to 1)/c on c reduces to fitting a straight line

between two points. After a little bit of algebra, it is

easy to show that the intercept of this line, the

intrinsic viscosity, is given by

-t +4 tl/2 -3 t (5)

cito

Here, to denotes the average flow time of pure sol-

132

vent, while t, and t/2 are the average flow times of

the solutions of concentration cl and c,2, respectively.

In the modified procedure, c, corresponds to an ini-

tial solution of 0.35 g polymer in 50-ml solvent. Two

solvents are used: toluene and 80/20 by volume mix-

ture of toluene and methanol. Thus, in all, students

measure the average flow times of six solutions,

where each average has been calculated from three

measurements. This allows them to estimate the

variance of the flow measurements as

S2- = 1 n[ k-i)] (6)-

n(k -1) i=1 (6)

where ti is the jth replicate measurement of the ith

solution, ii is the average of k(= 3) replicate mea-

surements of solution i, and n(= 6) is the total num-

ber of solutions. Our practice is to combine the

data from two groups of students to get a more

reliable estimate of the variance based on n = 12

solutions.

Having determined s2, it is relatively straightfor-

ward to estimate the variance of [T1] by applying

standard formulas for the variance of the quotient

of random variables to Eq. (5). If we do so, it turns

out that

2

s2V

var []- tll 2 (7)

where V is a factor that depends on the number of

replicates of flow time measurements, el, and the

estimate of [rl] obtained by using Eq. (5). Then, con-

fidence intervals for [in] and Mv can be constructed

in the usual way.

Discussion; The new procedure is better in two

important respects: 1) the estimate of [i], and hence

of Mv, is more reliable, and 2) the students can now

construct confidence intervals based on an estimate

of the variance that is independent of the regression

that is carried out to estimate [rn]. In addition, we

also briefly discuss the old procedure so that the

students can understand why its design is flawed

and why the new procedure yields a more precise

estimate of intrinsic viscosity.

How could we further improve the didactic value

of the experiment? One way would be to explain to

the students why a design in which only two concen-

trations are used is optimal. In addition, we could

also make them derive Eq. (7), including the exact

value of the factor V. However, we have to strike the

right balance between illustrating statistical con-

cepts and illustrating physical principles. Although

we are convinced of the value of introducing statisti-

cal ideas into these experiments, we do not want to

Chemical Engineering Education

do so at the expense of the chemical engineering

concepts being illustrated. Thus, we leave it up to

the instructor to decide whether or not to incorpo-

rate the additions mentioned above.

EXPERIMENT 2

Adsorption of Acetic Acid on Charcoal

This experiment illustrates the discussion of

adsorption from solution that is presented in the

second-year physical chemistry course. Like dis-

tillation, adsorption can also be thought of as a

chemical engineering unit operation.'61 Two expres-

sions-the Freundlich isotherm and the Langmuir

isotherm-are used to describe the adsorption of

acetic acid onto activated charcoal. Each isotherm

is based on different assumptions about the nature

of adsorption, and they apply under different condi-

tions. The Freundlich isotherm"7' is a purely em-

pirical model which works well at low solute con-

centration. It relates the mass of solute adsorbed (x)

on the adsorbent to the equilibrium concentration of

solute (C), e.g.,

_x = kC" (8)

m

where m is the mass of adsorbent, and k and n are

empirical constants. The Langmuir isotherm,'71 how-

ever, was derived assuming an explicit adsorption

mechanism. It may be written as

x (x / m)o KC

m 1+KC (9)

where K is the equilibrium constant, and (x/m)O is

the mass ratio required for monolayer coverage of

the surface of the adsorbent. Equations (8) and (9)

are nonlinear, and they are usually used in their

linearized form, e.g.,

n- = in k + n nC (10)

m

for the Freundlich isotherm, and

1 1 1 1 (11)

x/m K(x/m)0 C (x/m)0

for the Langmuir isotherm.

After measuring x/m for several different concen-

trations of acetic acid, the students are asked to

comment on the fit of Eqs. (10) and (11) to the data.

The procedure used in the past is based on the ex-

periment described by Ellis and Mills;1"' it is not

well designed to allow the students to quantitatively

assess which of the two isotherms better describes

adsorption of acetic acid onto charcoal. Furthermore,

note that the linearized forms of the equations are

used. Also, as we will see from the procedure below,

x and C are not statistically independent.

Old Procedure: Two grams of activated charcoal

Spring 1993

are placed in each of six flasks. Starting with 0.5 M

acetic acid, six 100-ml lots of acetic acid with con-

centrations ranging from 0.5 to 0.025 M are pre-

pared. The acetic acid solutions are added to the

charcoal, mixed, and left to stand overnight to

reach equilibrium. The solutions are then suction

filtered. Filtrate samples are titrated with 0.2 M

NaOH to determine the equilibrium concentrations.

Finally, the amount of acetic acid adsorbed onto the

charcoal is calculated.

Students then plot the data using Eqs. (10) and

(11). The correlation coefficient for the Freundlich

isotherm is typically 0.99, and for the Langmuir

isotherm it is typically 0.70. Figures 2(a) and 2(b)

show plots of representative data. Students notice

the curvature in the plot of the Langmuir isotherm

and then conclude that it is not due to chance alone,

but to systematic departure from the fitted model.

Unfortunately,

3.0 they rarely real-

2.8 ize that the ob-

2.6 served curvature

2.4 provides informa-

22 tion which is dif-

\2. ferent from that

12. provided by a low

1.8 correlation coeffi-

1.6 cient. As a result,

1.4 they often pro-

1.2 ceed in later

1.0 .5 years to rely

0.0 0.5 1.0 1.5 2.0 2.5 C30 3.5 4.0 4.5 5.0 heavily on the

1n (C)

Figure 2(a). Acetic acid adsorption correlation coeffi-

data generated using the old pro- cient as a mea-

cedure and plotted according to sure of model-fit

Freundlich isotherm. and sometimes

even neglect to

20 plot data. Our

s1 purpose in modi-

16 fying this experi-

14 i ment, therefore,

is to emphasize

12 the limitations of

10 the correlation co-

8 o efficient and to

6D give the students

4 experience in us-

2 ing other mea-

0 sures of model fit.

0 20 40 60 80 100 120 140 160 New Proce-

1/cdure: The proce-

Figure 2(b). Acetic acid adsorption dure: The proce-

data generated using the old proce- dure is un-

dure and plotted according to changed except

Langmuir isotherm, for the number of

133

solutions used. Instead of preparing six solutions of

different concentration, three independent replicates

of four different concentrations are prepared. The

concentrations used are between 0.5 and 0.025 M.

For each replicate, charcoal is weighed out and ace-

tic acid solution is prepared separately to ensure

independence. The twelve samples are left overnight

to reach equilibrium and are then suction filtered;

the filtrate from each is again titrated using 0.2 M

NaOH. It is tempting here to titrate a set of three

replicates sequentially, but this would invalidate

the estimate of the error variance. Filtrate samples

must be titrated in random order so that the corre-

lation between any two measurements is constant,

and the data may be treated as independent. Fi-

nally, students perform least-squares regression to

fit Eqs. (10) and (11) to the data, calculate the corre-

lation coefficients, plot the residuals, and perform

the lack-of-fit test described below. Figures 3(a) and

3(b) show typical results using Eqs. (10) and (11).

The lack-of-fit test is an extension of analysis of

variance in linear regression, which students learn

in their introductory statistics course. It is described

in standard texts such as Draper and Smith."19 If a

model is a good representation of the data, the re-

siduals, or prediction error, should reflect only ran-

dom error. If a model is a poor representation of the

data there is additional variation caused by lack-of-

fit, which manifests itself as a systematic departure

from the fitted line. This is evident when the data

from this experiment are plotted using the Langmuir

isotherm, but in the original experiment there is no

way to estimate random error independently of the

model or to confirm lack-of-fit quantitatively.

The introduction of replication allows us to esti-

mate the random error, or pure error, independently

3.0

2.8

2.6

2.4

2.2

2.0

1.8

1.6

1.4

1.2

1.0

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0

In(C)

Figure 3(a). Acetic acid adsorption

data generated using the new proce-

dure and plotted according to

Freundlich isotherm.

134

20

18

14

12

m 10

6

2

of the model that is postulated. The model predic-

tion errors can then be divided into random error

and lack-of-fit error. Comparison of the lack-of-fit

sum of squares to the pure error sum of squares

using an F-test serves as a quantitative measure of

the fit of the model.

The calculations for the lack-of-fit test are straight-

forward. Let yij, i = 1,2,...,k, j = 1,2,...,n, be the jth

measurement on the 'dependent' variable at the ith

concentration. In the modified procedure outlined

above, three replicates (ni = 3, Vi) are performed at

each of four (k = 4) different concentrations. Recall

that because we are using the linearized forms of

the Freundlich and Langmuir isotherms, y = ln(x/m)

for Eq. (10) and y = 1/(x/m) for Eq. (11).

The random, or pure, error can be estimated by

k ni 2

I I (Yij-Y)

2 i=l j=l

n-k

k

n= Yni

i=l

where yi is the average of the ni measurements at

the ith concentration. In much the same way, the

lack-of-fit sum of squares (LFSS) is estimated as

LFSS= ni(yi-i)2 (13)

i=1

where yi is the value predicted by the model (Eqs.

10 or 11) at the ith concentration. Once we have

fitted the Freundlich and Langmuir isotherms and

calculated the corresponding values of s2 and LFSS,

we can construct an F-statistic and compare it to

the critical F-value at the desired confidence level,

e.g.,

SLFSS/(k- 2)

2 Fk-_2,n-k (14)

If the calculated value is larger than the critical F

value, then lack-of-fit error is signifi-

cant at the chosen confidence level, and

o the model does not describe the data

adequately. Using such an F-test, stu-

dents find significant lack-of-fit for the

Langmuir isotherm, which provides

quantitative reinforcement of the con-

clusions they draw by simply observ-

ing the curvature in Figure 3(b).

DISCUSSION

The changes we have made to the

experimental procedure are minor; the

benefits reaped by the students, how-

ever, will be substantial. First, the stu-

dents will be introduced to replication,

which is essential in estimating ran-

Chemical Engineering Education

A4

0 20 40 60 80 100 120 140 160

1/C

Figure 3(b). Acetic acid adsorption

data generated using the new proce-

dure and plotted according to

Langm uir isotherm.

dom error and in identifying problems such as non-

constant variance. More important, we hope that

students will realize just what experimental error

really is when they carry out repeat measurements

which do not yield the same results. Second, the

introduction of the lack-of-fit test and the analysis

of residual plots encourages students to use tools

other than the correlation coefficient in discriminat-

ing between competing models. Finally, students are

forced to review least-squares regression and analy-

sis of variance in order to understand the lack-of-fit

test and to interpret the residual plots.

We recognize, however, that some flaws which are

present in the old procedure remain in the modified

one. First, linearized forms of the original expres-

sions are still fitted, which may change the error

structure. Second, the amount of solute adsorbed is

determined from the change in solution concentra-

tion, which causes the variables x and C to be statis-

tically dependent. Finally, we can see in Figure

3(a) that the variance of the data, plotted according

to the Freundlich isotherm, increases as the con-

centration, C, increases. This violates one of the

assumptions of least-squares regression-that of

constant variance.

How can we remedy these deficiencies? One way

of doing so is to express the models in terms of the

actual quantities measured: the initial acetic acid

concentration, the equilibrium concentration, and

the mass of charcoal. Since the resulting model

will be nonlinear with error in all the variables, an

analysis using the error-in-variables method""l would

be most appropriate. It would be unrealistic, how-

ever, to expect second-year students to carry out

such an analysis. Here, we face a question that we

will no doubt encounter when trying to incorporate

statistical concepts into other experiments: how can

we adopt the best, "statistically correct" analysis of

a poorly designed experiment without burdening

our second-year students with statistical methodol-

ogy that would tax even a competent researcher?

Our solution here is a compromise-we have incor-

porated changes that we think are better, but we

also recognize the remaining deficiencies and en-

courage the students to think about and discuss

other ways of analyzing the data and why they

might be more appropriate. In this way we hope

that they will be able to recognize how the design of

an experiment can affect the statistical analysis of

data derived from it.

CLOSING REMARKS

Our objective in modifying these two experiments

was to introduce statistical concepts into the under-

Spring 1993

graduate laboratory. The changes to the procedures

themselves are minor, but by modifying the analy-

sis of the data it is possible to include a wealth of

ideas which reinforce the connection between statis-

tics and experimentation. By introducing replica-

tion, we force the students to confront experimental

error-they see that measurement uncertainty is an

unavoidable fact of life. By showing them the means

to quantify this error, we show them a rational ba-

sis for dealing with it.

In the long term, our objective is not only to make

notions like replication and interval estimates an

essential element of all undergraduate laboratories

but also to include advanced concepts such as facto-

rial designs, especially in upper-year unit opera-

tions laboratories. As we saw with the analysis of

Experiment 2, however, it is sometimes difficult to

incorporate statistical concepts into existing proce-

dures that are poorly designed to begin with. Short

of redesigning all undergraduate experiments or in-

troducing students to advanced statistical techniques

which they may not be able to appreciate, our solu-

tion has been to incorporate statistical techniques,

but at the same time point out deficiencies where

they exist and encourage the students to discuss

alternative methods of data analysis. However we

choose to do it, it is clear that we must incorporate

statistical concepts into the undergraduate labora-

tory. By doing so as early as possible in the chemical

engineering curriculum, we hope to remove the mis-

taken notion of statistics as something complex and

mysterious when it is really fundamental to the

engineer's craft.

REFERENCES

1. Smith, J.L., and A. Stires (Eds.), Experimental Physical

Chemistry, 7th Ed., McGraw-Hill, New York (1970)

2. Rudin, A., The Elements of Polymer Science and Engineer-

ing, Academic Press, New York (1982)

3. Huggins, M.L., "The Viscosity of Dilute Solutions of Long-

Chain Molecules. IV. Dependence on Concentration," J. Am.

Chem. Soc., 64, 2716 (1942)

4. Brandrup, J., and E.H. Immergut (Eds.), Polymer Hand-

book, Wiley-Interscience, New York (1975)

5. Reilly, P.M., B.M.E. Van der Hoff, and M. Ziogas, "Statisti-

cal Study of the Application of the Huggins Equation to

Measure Intrinsic Viscosity," J. Appl. Polym. Sci., 24, 2087

(1979)

6. Mantell, C.L., Adsorption, 2nd Ed., McGraw-Hill, New York

(1951)

7. Castellan, G.W., Physical Chemistry, 3rd Ed., Addison-

Wesley, Reading, MA (1983)

8. Ellis, R.B., and A.P. Mills, Laboratory Manual in Physical

Chemistry, McGraw-Hill, New York (1953)

9. Draper, N.R., and H. Smith, Applied Regression Analysis,

2nd Ed., John Wiley & Sons, New York (1981)

10. Reilly, P.M., and H. Patino-Leal, "A Bayesian Study of the

Errors-in-Variables Model," Technometrics, 23, 221 (1981)

0

1 laboratory

PURDUE-INDUSTRY

COMPUTER SIMULATION MODULES

2. The Eastman Chemical Reactive Distillation Process*

S. JAYAKUMAR, R.G. SQUIRES, G.V. REKLAITIS,

P.K. ANDERSEN, L.R. PARTIN

Purdue University

West Lafayette, IN 47907

As described in previous papers,"1'21 a series of

computer modules for use in the chemical en-

gineering senior laboratory is being devel-

oped at Purdue University. The modules are meant

to supplement, not to replace, traditional laboratory

experiments. In our laboratory, for example, only

one of three month-long experiments may be the

use of a computer module. Computer simulated ex-

periments have a number of advantages over tradi-

tional experiments:

Processes that are too large, complex, or hazardous for the

university laboratory can be simulated with ease on the

computer.

Realistic time and budget constraints can be built into the

simulation, giving the students a taste of "real world" engi-

neering problems.

The emphasis of the laboratory can be shifted from the

details of operating a particular piece of laboratory equip-

ment to more general considerations of proper experimental

design and data analysis.

Computer simulation is relatively inexpensive compared to

the cost of building and maintaining complex experimental

equipment.

Simulated experiments take up no laboratory space and are

able to serve large classes because the same computer can

run many different simulations.

EASTMAN CHEMICAL

REACTIVE DISTILLATION PROCESS

The Eastman Chemical Reactive Distillation Pro-

cess is part of a series of steps for obtaining acetic

anhydride from coal. Acetic anhydride is an impor-

tant chemical intermediate used in the production

of cellulose acetate, which itself is used in the manu-

* The first paper in this series, "Purdue-Industry Computer

Simulation Modules: The Amoco Resid Hydrotreater Process,"

appeared in CEE, 25, 98 (1991).

S. Jayakumar is a post-doctoral research fellow in the School of Chemi-

cal Engineering at Purdue University. He received a B.Tech from Indian

Institute of Technology (1985), and his MS and PhD from Purdue Univer-

sity (1988, 1992). His research interests include process design, simula-

tion, optimization, and plant layout

R. G. Squires is a professor of chemical engineering at Purdue Univer-

sity. He received his BS from Rensselaer Polytechnic Institute (1957),

and his MS and PhD from the University of Michigan (1958, 1963). His

current research interests center on the educational applications of com-

puter simulation.

G. V. Reklaitis is Head of the School of Chemical Engineering at Purdue

University. He earned his BS from Illinois Institute of Technology (1965),

and his MS and PhD from Stanford University (1969). His research

interests include process systems engineering, process scheduling meth-

odology, and the design and analysis of batch processes.

P. K. Andersen is an assistant professor in the Department of Freshman

Engineering at Purdue University. He earned his BS from Brigham Young

University (1981) and his PhD from UC Berkeley (1987), both in chemical

engineering. His research has dealt with transport in multiphase flows and

the educational applications of computer simulation.

L. R. Partin is a Research Associate with Eastman Chemical Company in

Kingsport, Tennessee. He received his BS in chemical engineering from

the University of Kentucky in 1976 and his MS in chemical engineering

from Purdue University in 1977.

facture of photographic film base, fibers, plastics,

and other products.

Each day the plant converts 900 tons of coal to

acetic anhydride. Using conventional methodology,

the chemicals produced would require the annual

equivalent of one million barrels of oil. A brief de-

scription of the process is: synthesis gas produced

from coal is used for methanol production; methanol

(MeOH) is reacted with recycled acetic acid (HOAc)

to produce methyl acetate (MeOAc) and then acetic

anhydride; and finally, acetic anhydride is reacted

with cellulose to form cellulose acetate. The process

for formation of MeOAc was developed at the

Eastman Chemical Company3' and patented. The

reader is also referred to a paper by Agreda, Pond,

and Zoeller[41 for more details.

The formation of MeOAc is the focus of this project.

In this process, methanol reacts with recycled acetic

Copyright ChE Division ofASEE 1993

Chemical Engineering Education

This part of the project involves analyzing trays of the column. Students do not run a

tray to "obtain data," unlike the batch reactor or the equilibrium cell. Instead, they input the kinetic and

phase equilibrium parameters to observe tray performance and use the results of the simulation to

calculate the tray efficiency. In addition, for the same feed (vapor and liquid), they

are asked to predict the conversion that will be obtained in a CSTR.

acid in the presence of sulfuric acid catalyst to form

methyl acetate and water:

CH3COOH + CH3OH => CH3COOCH3 + H20 (1)

The reaction rate is given by

rMeOAc = koA exp(-E / RT){ CHOAcCMeOH

where

ko = preexponential factor

CMeOAcCH20 ()

K1 (2)

A = catalyst acidity function (0 < A < 1)

T = temperature

E = activation energy

and the equilibrium constant is

K = MeOAcCH20 (3)

e CHOAc MeOH

Clearly, the maximum conversion of the reactants is

equilibrium limited.

This Reactive Distillation Process relies on the

fact that MeOAc is more volatile than water or the

reactants. Thus, if the reaction mixture is distilled

simultaneously, a significant amount of MeOAc prod-

uct will vaporize, forcing the reaction to shift to the

right and thereby allowing a much higher conver-

sion than would be possible in the absence of dis-

tillation (conventional process). An additional con-

sequence and advantage is that high purity MeOAc

(> 99.5 wt%) is produced as the overhead product.

THE COMPUTER PROGRAM

The program is written entirely in the C language

and uses some IMSL routines for solving systems of

linear, non-linear, and ordinary differential equa-

tions. It can simulate

A batch reactor

An equilibrium cell

A tray in the distillation column

The program can run on any machine that sup-

ports the X Window System. At Purdue, it runs on

Sun Sparc workstations with 12 MB of memory.

Each module uses less than 10 MB of disk space.

An important feature of the program is its menu-

Spring 1993

TABLE 1

Expenses*

BATCH REACTOR Cleanup $700

Sample analysis $50 / sample

EQUILIBRIUM CELL Cleanup $500

CONSULTATION $500

All expenses are to be multiplied by 1.5 and 2 for Saturday and Sunday runs

respectively.

driven graphical user interface. This enables any-

one to use it, regardless of his or her knowledge of

computers. An on-line help facility is provided to

further assist the user in navigating through the

program. The user can exit the program at any time.

STUDENT ASSIGNMENTS

Budget and Experiments

In the first part of the Eastman project, the stu-

dents are required to determine the following:

1. Activation energy

2. Preexponential factor

3. Catalyst activity function

4. Wilson parameters for liquid activity coefficients

To determine these quantities, the students simu-

late a batch reactor and an equilibrium pressure

cell, both described below. Also, a requirement that

the students work within a budget of $30,000 con-

tributes a sense of realism to the module. Table 1

shows costs associated with operating the reactor

and cell.

Laboratory Batch Reactor A batch reactor is

available for the students to study reaction kinetics

for the determination of items 1-3 above: activation

energy, preexponential factor, and the catalyst ac-

tivity function. As seen in Eq. (2), the reaction is

first order in the concentrations of each of the reac-

tants and products. Preliminary data obtained us-

ing laboratory batch apparatus suggest that in the

range of conditions used in the Eastman column,

the equilibrium constant is independent of tempera-

ture and catalyst concentration. The catalyst acidity

137

function, A, depends on the sulfuric acid concentra-

tion, as shown in Figure 1.

The students are to design experiments to deter-

mine the activation energy E, the preexponential

factor ko, and establish the functional dependence of

A on the catalyst concentration. The equilibrium

constant, Ke is known.

Equilibrium Cell The purpose of this appara-

tus is to determine liquid phase activity coefficients

in two-component systems. The cell is simply a closed

vessel with a pressure gauge and a temperature

sensor. Temperature control is provided, so isother-

mal runs can be made. The user can charge it with

two components and record the equilibrium pres-

sure. For all practical purposes, equilibrium can be

assumed to have been established in four hours.

There is no facility to measure or monitor the vapor

or liquid phase mole fractions. However, since the

vapor volume is very small compared to the volume

of the liquid, it can be assumed that the concentra-

tions of the components in the liquid phase at equi-

librium are equal to the corresponding concentra-

tions of the liquid charged into the cell. Note that

there are five components of interest: the reactants,

the products, and the catalyst, H2SO4.

When the critical region is not approached (as in

this case), we can assume that the liquid phase

activity coefficients and standard fugacities are in-

dependent of pressure. If the standard fugacity is

taken in the sense of the Lewis-Randall rule, we

have for each component i

y *
where for component i,*

y = liquid phase activity coefficient

PO = vapor pressure

P = equilibrium pressure of the system

x = liquid phase mole fraction

yi = vapor phase mole fraction

0i, 0o = fugacity coefficients ofi, the latter calculated

at the saturation vapor pressure.

Quite often, however, 4, and 4o are nearly equal,

and Eq. (4) simplifies to

Yi P = xi y, P (5)

Since the total pressure equals the sum of the

partial pressures of the components, adding Eq. (5)

for each component results in

P = x,1P +X22 P (6)

The vapor pressures, Pi, of the pure components

138

Catalyst Acidity Function

Figure 1. The catalyst activity function

Figure 1. The catalyst activity function

may be calculated from the Antoine equation:

nP=A iB (7)

fn po = Ai (7)

i T+C(

where the Antoine constants, A,, Bi, C, are known

from the literature, and T is the temperature.

At low to moderate pressures, the Wilson equa-

tion[5'6' may be used to predict the activity coeffi-

cients as a function of temperature and composition

for a variety of liquid solutions comprising diverse

chemical species. The Wilson equation for compo-

nent i is

nT = 1-'n (xGij)- G(8)

The summations are over all components present

in the mixture. For an ij pair, there are two tem-

perature-dependent parameters, Gij and Gji. For

i = j, Gj = 1. Over the narrow temperature range of

interest, the temperature dependence of the param-

eters is weak enough to be ignored. The Wilson pa-

rameters for all of the component pairs except

MeOH MeOAc have been previously estimated and

are known. The assignment given to students is to

design a series of runs in the equilibrium cell to

determine the two Wilson parameters for the

MeOH MeOAc pair. It should be noted that acetic

acid was not chosen as a component in the binary

pair since it exhibits vapor phase association and

the simplification for Eq. (5) does not apply.

Application Problem-Tray Simulation

This part of the project involves analyzing trays of

Chemical Engineering Education

[~7~17~17 ~~7-rT1-TT~-~1Tr7

i i I i ~

j

the column. Students do not run a tray to "obtain

data," unlike the batch reactor or the equilibrium

cell. Instead, they input the kinetic and phase equi-

librium parameters to observe tray performance and

use the results of the simulation to calculate the

tray efficiency. In addition, for the same feed (vapor

and liquid), they are asked to predict the conversion

that will be obtained in a CSTR. It is to be observed

that the tray is actually a CSTR with an additional

operation, e.g., distillation. It is instructive to see

that the conversion obtained in a tray is much higher

(for the current process) than in a simple CSTR.

This is an important observation since the basic

idea in carrying out the methyl acetate process in a

distillation column was to increase the conversion.

Two representative trays, one in the upper portion

of the column and the other in the lower portion, are

simulated. The students must run both.

For the purpose of the current simulation, the

tray is assumed to operate isothermally at a known

temperature. Thus, material balance and equilib-

rium relationships are used to model the tray. A

tray efficiency is incorporated in the model. Given

the input flow rates of the vapor (from the bottom

tray), the liquid (from the upper tray), the composi-

tion of the input streams, the pressure, tempera-

ture, tray efficiency, and the kinetic and phase equi-

librium parameters, the model predicts the flow rates

and compositions of the output liquid and vapor

streams of the tray.

The tray model does not explicitly account for the

dependence of the acidity function on the acid con-

centration. For the steady state, it suffices to pro-

vide the simulator with the acidity value corre-

sponding to the steady-state acid concentration in

the liquid phase (output). This value, however, is

not known since the output acid concentration in

the liquid phase is not known. The student must

therefore resort to an iterative procedure. He must

guess a value of the acid composition in the output

liquid stream, calculate the value of A from his

catalyst acidity function, and input this value to

the simulator. The model solves the problem using

this value of A and predicts the output liquid-phase

acid concentration. This procedure must be repeated

until the entered acidity function value agrees

with the predicted acid concentration according to

the student's function.

In the event that students are unable to evaluate

the kinetic and phase equilibrium parameters within

the assigned time, or that they come up with im-

practical values or cannot establish the acidity func-

tion curve, they have the option of using the

Spring 1993

instructor's data (with the permission of the instruc-

tor, of course). In this case, the students do not have

to input the kinetic and phase equilibrium param-

eters; furthermore, the acidity function dependence

is implicitly taken into account in the model, so that

iteration is not required.

CONCLUSION

Our experience with the Eastman module has been

very positive. The module presents a challenging

problem that helps prepare students for the kinds of

problems they are likely to encounter in industry.

The simulated budget is especially effective in mak-

ing the project more true-to-life than conventional

lab experiments. Although the Eastman problem is

challenging, students report that the software itself

is very user-friendly.

One advantage of computer simulations is their

flexibility. The Eastman module was originally de-

veloped for the chemical engineering laboratory; how-

ever, it would also be useful in courses in thermody-

namics, chemical kinetics, and separations.

AVAILABILITY OF THE MODULES

The Purdue-Industry ChE Simulation Modules are

being made available for educational use by the

CACHE Corporation. Anyone interested in obtain-

ing more information should contact Professor

Squires.

ACKNOWLEDGMENTS

This work has been supported by the National

Science Foundation (Grant No. USE-888554614), the

Eastman Chemical Company, and the CACHE Cor-

poration.

REFERENCES

1. Squires, R.G., G.V. Reklaitis, N.C. Yeh, J.F. Mosby, I.A.

Karimi, and P.K. Andersen, "Purdue-Industry Computer

Simulation Modules: The Amoco Resid Hydrotreater Pro-

cess," Chem. Eng. Ed., 25(2), 98 (1991)

2. Squires, R.G., P.K. Andersen, G.V. Reklaitis, S.

Jayakumar, and D.S. Carmichael, "Multi-Media Based

Educational Applications of Computer Simulations of

Chemical Engineering Processes," Comp. Appns. Engr.

Ed., 1(1), 25 (1992)

3. Agreda, V.H., and L.R. Partin, U.S. Patent 4,435,595,

March 1984 (Assigned to Eastman Kodak Co.)

4. Agreda, V.H., D.M. Pond, and J.R. Zoeller, "From Coal to

Acetic Anhydride," Chemtech, 172 (1992)

5. Sander, S.I., Chemical and Engineering Thermodynam-

ics, John Wiley & Sons, New York, NY (1989)

6. Wilson, G.M., "Vapor Liquid Equilibrium. XI: A New

Expression for the Excess Free Energy of Mixing," J.

Am. Chem. Soc., 86, 127 (1964) 0

laboratory

AN INEXPENSIVE AND QUICK

FLUID MECHANICS EXPERIMENT

J.T. RYAN, R.K. WOOD, P.J. CRICKMORE

University ofAlberta

Edmonton, Alberta, Canada T6G 2G6

he first laboratory course in chemical engi-

neering at the University of Alberta is taught

to about seventy students in the first term of

their junior year, and its primary objective is to

improve and develop the students' writing skills.

They are required to write three reports. The first

two reports are each about ten pages in length and

deal with technical material which is familiar to the

student. Each of the first two experiments is per-

formed and the reports written within a period of

two weeks, and the corrected reports are returned

to the students within another two weeks. The En-

glish construction and the presentation of the re-

ports are brutally criticized by the academic staff

responsible for the course. The students then do a

standard engineering experiment and write their

third (hopefully readable) report.

The key to this approach is to present simple and

short experiments. Typically, the first two experi-

ments should each take less than ten minutes to

complete. Quick experiments have the advantage of

conveying to the students that even though the tech-

nical aspects are easy, describing them in clear, un-

derstandable English is often very difficult.

For the last six years the first experiment we have

used has been a computer simulation of a simple

concept that the students should be able to under-

stand. Usually, the simulated experiment is based

on a fundamental principle that was taught to the

students in the previous semester, i.e., the vapor

pressure of water as a function of temperature. The

students run the program, specifying the tempera-

ture, with the simulator returning a slightly inaccu-

rate value of the vapor pressure. The students are

asked to compare the simulated vapor pressures

with those in the steam tables and those calculated

Copyright ChE Division ofASEE 1993

from a published correlation of vapor pressure and

temperature. They then write a report about the

simulated experiment.

Experience has taught us that both of the short

experiments should not be simulations since, if they

are, the students will write a simulated second re-

port. Their attitude seems to be, "If you don't take

the experiment seriously, why should we take the

report seriously?" Clearly, this is not the objective of

the course. So, we make the second experiment a

real experiment-but still quick.

One experiment that is simple and fast is the

filling and blowdown of a tank of air. In spite of

its simplicity, this experiment is surprisingly rich in

its technical content, involving ideal gas ther-

modynamics, unsteady state material balances, and

simple fluid mechanics. All of these subjects have

been covered in the preceding term or are being

taken concurrently with this course. A further

advantage is that the complexity of the data analy-

sis can be adjusted to accommodate the technical

skills of the students.

EXPERIMENTAL EQUIPMENT AND PROCEDURE

The experiment consists of two stages: 1) filling

the tank with air at about 90 psig and 70'F, and 2)

emptying the tank by venting the compressed air to

the atmosphere. The equipment (shown in Figure 1)

J.T. Ryan is a professor and registered engineer. He has taught thermo-

dynamics, fluid mechanics, and process design for more than twenty-five

years.

R. K. Wood is professor of chemical engineering at the University of

Alberta. His recent teaching responsibilities, in addition to the introduc-

tory laboratory course, have involved process analysis, optimization,

dynamic modeling, and simulation. His research is concerned with digital

simulation of the dynamic and control behavior of process systems and

the computer control of distillation columns.

P. J. Crickmore is an associate professor of chemical engineering at the

University of Alberta. He received his BSc (Chemical Engineering), MSc

(Mathematics), and PhD (Chemical Engineering) degrees from Queen's

University, Kingston. Research areas include oil sands, coal and envi-

ronmental sampling, and remediation.

Chemical Engineering Education

I ChE

consists of a modified 30-pound propane bottle and

a manifold mounted at the top of the bottle. The

manifold has four nozzles, each of which is isolated

with a quick-acting ball valve. Standard 1/2-inch

copper tube and fittings are used for the manifold.

The nozzles are brass plugs which have holes drilled

to diameters ranging from 1/16 to 7/64 inch. These

plugs are soldered into the outlet of 1/2-inch unions

which are located above each of the ball valves.

While it is not required because of the limited air

supply pressure, a relief valve is installed on the

tank for educational purposes. A cheaper alterna-

tive would be to incorporate the relief valve in the

manifold. High-pressure air is supplied from the

building service air through a flexible hose. Another

quick-acting ball valve is installed on the tank at

the hose connection.

The instrumentation consists of a fast response

thermocouple, a pressure transducer, and associ-

ated signal conditioning equipment. The thermo-

couple is installed through the tank wall. Since one

of the objectives of the experiment is to finish the

experiment quickly, the data-logging was done with

a microcomputer using an OPTO 22 interface.

The experimental procedure is straightforward:

With the pressure in the tank at atmospheric, close

valves (VI V4). Start logging the pressure and tem-

perature using a one-second sampling time. Open V5.

r*

Figure 1.

Spring 1993

The tank will reach the supply pressure in about ten

seconds. Close V5 and open one or more valves in the

manifold. The pressure in the tank will reduce to

near atmospheric in about one minute, depending on

which valves) is opened. At this time the data-log-

ging can be stopped or the experiment repeated.

The cost of the equipment is small (less than $100,

not counting the instrumentation and microcom-

puter), and the total shop time required for machin-

ing and welding is less than two hours. Our advice

is to purchase a new propane bottle and have the

propane relief valve removed upon purchase since

this valve is extremely difficult to remove. An entire

class can perform the experiment in about two days

by using scheduled 15-minute time slots, so the in-

strumentation and data-logging computer can usu-

ally be borrowed.

FILLING THE TANK

This part of the experiment focuses primarily on

thermodynamics. As it is usually presented in ther-

modynamics texts, the theory for filling a tank with

an ideal gas is correct-but the major assumption is

wrong. The standard assumption is that the process

is adiabatic. When the experiment is actually per-

formed, however, the dominant influence is the heat

transfer, not the thermodynamics. But, the students

believe the textbooks and their professors-who also

believe the textbooks!

Van Wylen and Sonntag"1 give the following equa-

tion as the appropriate form of the first law of ther-

modynamics over a control volume for a uniform

state, uniform flow process:

Qcv + mi{hi +( )v2+gZi

=-me{he +( )v2 +gZe+Wcv +m2{h2 +() +gZ2

S -m 2 h 1+( +)gZ1 (1)

When we apply this equation to the filling of a tank,

neglecting the heat transfer, work, potential energy

changes, and all kinetic energy terms except for the

input, we get

mi hi+ ()v2Jm2u2-miul (2)

When it is combined with the definitions ofh and u

for an ideal gas, this equation can be used to solve

all the cases appropriate to this experiment. The

simplest case occurs if the incoming kinetic energy

and the initial mass of the system is neglected. Then

hi = u2 (3)

If we assume constant heat capacities, then

T2 kTi (4)

where k Cp / Cv.

A better approximation of the final temperature

can be made, a priori, by correcting for the initial

mass of air in the tank. A further refinement can be

made, after the experiment, by including an esti-

mate of the incoming kinetic energy. Supposedly,

the theory can be expanded or refined-however,

our objective is to introduce the students to a simple

laboratory experiment and to the difficulty of writ-

ing a technical report on such a simple experiment.

Table 1 shows a comparison of the measured final

temperature and those calculated from Eq. (2),

corrected for both the initial mass and kinetic en-

ergy of the incoming air but still assuming no heat

transfer. The point to be made from this table is

that all of the calculations are simply wrong and

differ from the measurement by a minimum of ap-

proximately 200F.

As soon as the students see the difference between

the theory taught in thermodynamics lectures and

the results of the experiment, they question the ex-

periment. There is sufficient time to do multiple

runs, but they find that the repeated experiments

produce virtually the same results. The students

are faced with an experiment which has precision

but, in their minds, is of dubious accuracy. To ex-

plain the difference between the experiment and

the temperature calculated from Eq. (4), many stu-

dents do all the corrections indicated in Table 1.

They work hard to prove that the theory is right and

the experiment is wrong. Ultimately, they realize

Eqs. (2) and (4) are simply not true and are based on

a bad assumption, and finally they conclude that

the process is not adiabatic and that the heat trans-

fer is the dominant effect. A typical value of the

heat transfer is 14 18 Btu/cycle.

VENTING THE TANK

At this point the students are convinced that ex-

periments are worthwhile, but they are somewhat

skeptical of theory. Venting of the tank is designed

to resolve this conflict for them. The venting of air

illustrates the polytropic decompression of an ideal

gas and an unsteady state material balance.

The relationship between the temperature and the

pressure of air in the tank, as it empties, must be

established before the material balance is attempted.

Analysis of the data is relatively simple and is cov-

ered in most introductory courses in engineering

thermodynamics. The decompression of the air in

the tank is taken to be a polytropic process. The

appropriate equation in terms of the measured vari-

ables is

TABLE 1

Comparison of Experimental and Calculated

Adiabatic, Final Air Temperatures

Method of Approximate Final

Determination Air Temperature

Experiment 100F

Equation 4 315F

Equation 2 (corrected for initial mass) 305F

Equation 2 355F

T (n-1)/n (5)

T0- P0

If the decompression is isothermal, n is equal to

one. The process is isentropic when n = k. The value

of n is found from the slope of the line through the

measured pressure and temperature data when plot-

ted on log-log paper. Many students use a regres-

sion program to estimate n from their data; how-

ever, we require the T versus P plot for educational

reasons. Using the equipment and procedure de-

scribed earlier, the typical experimental value of n

was 1.04 0.005. Even though the temperature of

the air in the tank drops by approximately 850F, the

students conclude that the decompression process is

better approximated by an isothermal process than

by an isentropic one. This conclusion simplifies the

mathematics of the material balance. A more accu-

rate analysis is possible but is not worthwhile given

the intent of the course.

After the students have established that the de-

compression process is approximately isothermal,

the unsteady state material balance equation fol-

lows easily

dm -= (6)

dt mN

Since the volume of the system is constant and the

temperature is nearly constant, the material equa-

tion for the air in the tank is

dm Vv dP 7

dt RT dt

The mass flow rate of air through the nozzle(s) is

rN = PN AN VN (8)

Provided that the air pressure in the tank is above

the critical pressure required for sonic velocity, the

velocity of the air through the nozzle is equal to

VN =(kRTN)12 (9)

The differential equation for the unsteady state ma-

terial balance reduces to

V dP (kRT)112

T dt -PN A (RTN)I (10)

The trick is to convert, in a simple way, the ther-

modynamic variables evaluated at nozzle conditions

Chemical Engineering Education

to those measured in the tank. The theory required

for this transformation is fully developed in most

mechanical engineering thermodynamics texts,

though not in many chemical engineering texts. Our

students do not deal with compressible flow in lec-

ture courses until after the experiment. This prob-

lem is solved by simply stating that the thermody-

namic variables at the nozzle can be evaluated at

tank conditions by applying a correction factor. Stu-

dents seem to like correction factors. The two rela-

tionships, shown below, are derived by Holman.[21

T=T 2 (11)

I k I

PN=P( 2k l- (12)\

k+ (12)

When the change in mass inventory is equated to

the mass flow rate out of the nozzle(s), the differen-

tial equation for the pressure in the tank is

A k k+1 l

dP AN (kRT) /2( 2 2(k-i)p (13)

dt V\v Ik+)I k ))

Since the students previously established that the

absolute temperature in the tank is approximately

a constant, they can now write this differential equa-

tion in a short form as

dPt

d--KlP (14)

where K, is the constant term in Eq. (13). The solu-

1.0

0.9

0.8 Theory K1 = 0.027

0.7 Empirical K2 = 0.028

0.6 *\

P

Po

0 10 20 30 40 50 60 70

Time (sec)

Figure 2.

Spring 1993

tion, shown below, is simple; however, it is valid

only until the critical pressure ratio is reached.

in a -Kt (15)

Another tack would be to regard this equation

merely as the basis of a correlating equation. The

equation would be the same as Eq. (15) but have a

leading coefficient of K2, as

In(- =--K2t (16)

The students are required to plot the ratio of the

measured pressure to the maximum pressure ver-

sus time on semi-logarithmic paper. They then com-

pare the slope of the line determined by the data

and Eq. (14) and that predicted by Eq. (13).

A typical set of data taken by the staff, a regres-

sion line based on Eq. (16), and the theoretical pre-

diction from the solution of Eq. (15) are shown in

Figure 2. A nozzle with an internal diameter of 3/

32-inch was used. The empirical value of K2 was

found to be 0.028 based on ten runs with a total of

462 data points. The value of K, predicted by theory,

at the average temperature, was 0.027.

About 90% of the students find that the difference

in the slope of the lines between theory and data is

5% or less. This difference is not statistically signifi-

cant given the inaccuracies in measurement of the

nozzle diameters and the volume of the tank and

manifold. Surprisingly, the other 10% of students,

who predict differences of up to 200%, make the

mistake of using the wrong nozzle(s) or recording

the nozzle diameter(s) incorrectly. None of the stu-

dents have difficulty with the mathematics, though

some think that Eqs. (14) and (16) apply even when

the velocity in the nozzle is subsonic.

CONCLUSION

The experiment described in this paper is ideal

when the experiment requirements are a quick turn-

around time, inexpensive equipment, and flexible

technical content.

NOMENCLATURE

A = Area; ft2

h = enthalpy; Btu/lb

Ki = constant; defined by Eq. (14)

KI = constant; defined by Eq. (16)

ke = kinetic energy; Btu/lb

m = mass flow rate; lb/s

m = mass of system; lb

n = polytropic exponent

P = pressure; psia

Q = rate of heat transfer; BTU/cycle

Continued on page 149.

classroom

HELPING STUDENTS COMMUNICATE

TECHNICAL MATERIAL

WILLIAM R. ERNST

Georgia Institute of Technology

Atlanta, GA 30332-0100

GREGORY G. COLOMB

University of Illinois at Urbana-Champaign

Urbana, IL 61801

Communication skills are important to engi-

neers and to their employers, but the commu-

nication skills of graduates in engineering are

seldom as good as their technical skills.l1"3 In most

engineering curricula, laboratory and design reports

provide an opportunity to help students learn

how to communicate technical material.[4-8 We

miss that chance, however, if we evaluate the tech-

nical merit of students' reports but ignore how

well they are written.

The least we can do is to identify those places

where the reports communicate poorly, require that

the students rewrite them, and hope for improve-

ment. The best we can do is to show students why

their reports communicate poorly and how to make

the required improvements. This article will outline

a method of showing students how to write clearly

and will explain the principles behind that method.

BAD WRITING, GOOD ADVICE

Some writing problems are easy to spot and easy

to fix: errors in spelling, grammer, and punctuation;

problems in literature references; tables and figures

that lack legends or are not discussed in the text;

etc. Though important, these problems alone may

not determine how well a report communicates. By

focusing only on them, we do not help students to

master a skill crucial to employers and working en-

gineers-the ability to communicate technical infor-

mation in words as well as in numbers.

One key to effective communication is style-the

sentence forms in which students express technical

information. But when it comes to problems of style,

William R. Ernst is Professor of Chemical Engi-

neering at Georgia Institute of Technology and

has taught technical economics and the capstone

design course to seniors for the past twenty years.

His principal technical interests are kinetics and

reaction engineering. He is also interested in pipe-

line issues and has developed science and engi-

neering modules for pre-college education.

Gregory G. Colomb is Associate Professor of

English and Director of Business and Technical

Writing at the University of Illinois. With others,

he created the "Writing Across the Curriculum"

(WAC) program at the University of Chicago

and has conducted WAC faculty workshops at

more than fifty institutions. He has published on

writing theory, WAC pedagogy, and the relation-

ship between writing and critical thinking.

some of us have little to say. We might tell students

that their writing is unclear, indirect, abstract,

convoluted, flowery, awkward, etc., and advise

them to be "clear and direct" or to "write as you

speak." While such comments may be accurate,

they are far too general to be of much use. In order

to improve as writers, students need to know

both what causes their writing to be unclear or

convoluted and what they must change in order to

make it clear and direct.

Writing researchers have recently developed bet-

ter and more useful methods of responding to stu-

dents' writing-methods based on research on how

people process and understand what they read. Much

of that work can be found in the book Style, [9 which

presents a simple, but powerful, method of teaching

style. The research base of the book can be found in

Colomb and Williams,[o10 and the methodology de-

veloped by those authors is summarized and ap-

plied to scientific writing by Gopen and Swan."] In

this paper we will describe its most useful tools and

show how they can be used by teachers to help stu-

dents improve their communication skills.

Copyright ChE Division ofASEE 1993

Chemical Engineering Education

The First Principle

of Readable Writing

Express important actions as verbs, and the characters

associated with those actions as the subjects

of those verbs.

Consider the following "Conclusions and Recom-

mendations" section of a senior design report that is

technically sound but poorly written in typical ways.

From the study done regarding this process a fairly firm

conclusion may be stated affirming the feasibility of Case 1

in which only the n-butane rail imports are replaced. Be-

cause no modifications are made to the gas concentration

unit itself the specifications predicted may be obtained with

very little error....

For Case 2, in which all of the butane rail imports are to

be replaced, a feasible plan, which involves the purification

of the excess n-butane entering with the required amount of

isobutane in the NGL, has been developed. The introduction

of the NGL stream was made into the feed to the butane

splitter. The desired quantity of isobutane from the top of

the column was achieved by this method. The bottoms from

the butane splitter would then be sent to a packed column

which has been designed to separate pure n-butane which

meets industry specs. The bottoms from the new column

would then be returned to the blending butane product stream

which would then be producing an extra 10,000 Bbl/yr.

The style of this passage is typified by the sen-

tence

la. The introduction of the NGL stream was made

into the feed to the butane splitter.

In order to see the distinctive features of the sen-

tence la, compare the following three variations on

a theme:

2a. The heating of the reaction mixture occurred

after the introduction of the catalyst.

2b. The reaction mixture was heated after the cata-

lyst was introduced.

2c. She heated the reaction mixture after she intro-

duced the catalyst.

Sentences 2a-c tell roughly the same story, but

most readers find 2a less clear and readable than

either 2b or 2c. Between 2b and 2c, most readers

find 2c slightly more readable, but readers with tech-

nical backgrounds are perfectly comfortable with 2b.

Note that 2a is most similar in feel to la.

These reactions are uniform among readers be-

cause these examples demonstrate key features of

the way we understand sentences. Sentences, even

the most technical ones, tell stories. With rare ex-

ceptions, sentences have two necessary elements:

subjects and verbs. Similarly, stories have two nec-

essary elements: characters and actions. Readers

Spring 1993

Writing researchers have recently

developed better and more useful methods of

responding to students' writing-methods based

on research on how people process and

understand what they read.

find that sentences are clearer, more direct, less

abstract, less complex-in short, more readable-

when the story elements line up with the sentence

elements: characters as subjects and actions as verbs.

In 2b and 2c, key actions are expressed as verbs:

was heated was introduced and heated .

introduced. Subjects are characters: reaction mix-

ture ... catalyst and She ... she. In 2c the character

is a person, while 2b treats the experimental mate-

rials reaction mixture and catalyst as characters.

Although sentences are usually clearer when the

subject/character is a person (preferably the agent

or "doer" of the action) readers with technical back-

grounds are accustomed to stories about such things

as reaction mixtures and catalysts, and they gener-

ally prefer not to have their stories focus on the

persons who do the heating and introducing.

In both la and 2a, however, the actions are ex-

pressed not as verbs, but as nouns. As a result,

readers must struggle through the grammar in or-

der to unpack the story. The la and 2a sentences

are built around nouns made from verbs (often by

adding a suffix: -tion, -ness, -ence, -ity, or -ing). These

nouns, called nominalizations, are usually a prob-

lem because they steal important action from the

verb, forcing writers to use a weak or empty verb.

Students tend to overuse nominalizations, and they

need our feedback in order to distinguish between

those that are necessary technical terms and those

that steal action from the verb.

So now, for sentences la and 2a we can

locate the problem

explain to the writer what caused the sen-

tences to seem to us unclear, indirect, and

difficult

tell the writer how to make them more read-

able:

"Sentences la and 2a are unclear because the ac-

tions in the sentences are expressed as nouns rather

than verbs. As a result, the key sentence elements-

subject and verb--do not correspond to the key story

elements-character and action. You can make the

sentences more readable if you change the nouns

expressing actions into verbs (e.g., introduction into

introduce) so that the subjects express characters

and the verbs express actions."

The Second Principle

of Readable Writing

Keep subjects as short as possible

so that sentences move quickly from a short,

specific subject to an action verb.

Once again, we begin with sentences that tell

roughly the same story:

3a. The mixture, because it was vigorously stirred

and the temperature was maintained above 200

Deg. C, reacted rapidly.

3b. The mixture reacted rapidly because it was vig-

orously stirred and the temperature was main-

tained above 200 Deg. C.

While neither sentence is unreadable, most read-

ers find 3b more readable than 3a, and all readers

begin to struggle in passages with lots of sentences

like 3a. In this case, the story elements (character

and action) do line up with the sentence elements

(subject and verb). But in 3a the story in the main

clause, The mixture reacted rapidly, is inter-

rupted by all the rest of the sentence. Readers must

process all of the intervening information before they

achieve the subject-verb closure that holds the story

together. In 3b, the subject-verb/character-action

pairs are all joined, so that we are able to process

the story in three discrete chunks connected by logi-

cal markers (because and and).

Technical writers are particularly prone to write

sentences with long, complex subjects or with infor-

mation intervening between subject and verb. Since

they so often use passive verbs in order not to focus

on the persons who perform the actions, technical

writers often push the verb toward the end of the

sentence. Here is an instance from our long example:

4a. For case 2, in which all of the butane rail imports

are to be replaced, a feasible plan which involves

the purification of the excess n-butane entering

with the required amount of isobutane in the NGL,

has been developed.

In this sentence, readers are forced to process quite

a lot of information before they attain subject-verb

closure.

Here too, the method allows us to locate the prob-

lem, explain to the writer what caused the sentences

to seem to us unclear, indirect, and difficult, and tell

the writer how to make them more readable:

"Sentence 4a is unclear because its subject is long

and complex. As a result, readers have to process

too much information before they can connect the

key sentence elements, subject and verb. You can

make the sentence more readable if you move quickly

from a short, specific subject to an action verb."

146

The Third Principle

of Readable Writing

Sentences should begin with old information

and end with new information.

It is not enough that our students write sen-

tences that are individually clear. The sentences

also have to "flow" together into a story that is

coherent as a whole. Sentences flow together be-

cause readers use the information they have al-

ready read and remembered to look forward to the

next sentence. If the next sentence surprises them

by beginning with something they did not expect,

they feel a little jolt of disorientation. If the sen-

tences in a passage consistently surprise readers,

their feeling of disorientation builds until it be-

comes hard to follow the story.

In order not to surprise readers, sentences should

begin with something that places them in the

context of the discussion: they should begin

with information that readers will already have

read and remembered. This familiar infor-

mation can be something in the immediately

previous sentence or any information that is as-

sumable or expectable, given what has come be-

fore. In short, sentences should begin with old

information.

Once again, we find an instance in our long ex-

ample:

5a. The introduction of the NGL stream was made

into the feed to the butane splitter. The desired

quantity of isobutane from the top of the column

was achieved by this method.

These sentences do not "flow." They feel dis-

jointed, even after we eliminate the nominalization

from the first sentence and connect the subject

and verb in the second sentence:

5a'. The NGL stream was introduced into the feed

to the butane splitter. The desired quantity of

isobutane was achieved from the top of the col-

umn by this method.

Few readers of the first sentence in 5a or 5a'

would expect the second sentence to begin with

"The desired quantity ofisobutane." Isobutane had

been mentioned earlier, but not in a way that

readers would expect it to return. In the second

sentence, the phrase that most strongly refers

backward is "this method." Although "method" has

not occurred before, it is nevertheless old informa-

tion, because the whole passage has been describ-

ing the method.

The old-before-new principle has even greater

Chemical Engineering Education

effect in longer passages, as in these examples:

6a. We should consider employing multiple reactors in

parallel before we finalize our design. If one reactor

shuts down, the other reactors can operate. For this

reason, the parallel arrangement is flexible. Identical

controllers can be used on all the reactors, thus mak-

ing the parallel arrangement easier to control than a

series arrangement. Plant operators have more diffi-

culty in understanding series operation than parallel

operation.

6b. Before we finalize our design, we should consider

employing multiple reactors in parallel. The parallel

arrangement is highly flexible; if one reactor shuts

down, the others can continue to operate. Parallel re-

actors are easier to control than reactors in series be-

cause all of the parallel reactors utilize identical con-

trollers. Parallel operation can be understood by the

plant operators more easily than series operation.

7a. We should consider employing multiple reactors in

series before we finalize our design. More control

equipment but less volume at a given conversion are

required for a series of reactors as compared to a

single reactor. Three reactors in series would save us

about $1,000,000 in fixed capital, at our required con-

version of 90 percent. Higher quality separators could

be purchased with the saved capital.

7b. Before we finalize our design, we should consider

employing multiple reactors in series. A series re-

quires more control equipment than a single reactor

but requires less volume for the same conversion. At

our required conversion of 90 percent, three reactors

in series would save us about $1,000,000 in fixed

capital. These savings could be invested in higher qual-

ity separators.

In both pairs, the second passage feels "tighter"

and more organized because each new sentence be-

gins in a way we expect. In 6b, each sentence re-

turns to the same idea ("parallel"). In 7b, the sen-

tences begin differently, but with an idea from the

immediately previous sentence. Both arrangements

create an organized flow through the passage.

RESPONDING TO STUDENTS' WRITINGS

Thus far, we have described the methodology in

terms of an interrelated set of principles. Once teach-

ers understand the principles, the methodology can

be implemented through a series of simple decision

procedures. These procedures focus on the first five

or six words of the sentence, because the three prin-

ciples work together to put the key elements there.

If the first several words of a sentence include a

subject that names a character, a verb that expresses

a key action, and some old information, then that

sentence is likely to be in a readable style.

Spring 1993

What follows is a method of responding to the

style of student writing before you require a revi-

sion. (It is equally useful as a way to edit our own

work.) At first the method might feel counter-

intuitive-especially if you usually start reading,

red pen in hand, marking as you go. In the long

run, however, the method allows us to mark those

problems that matter most and to give students

useful feedback.

* Read once, very quickly, for an overview. If the

report is long, skim just the major sections. The

goal of this step is to determine the overall story

line and to run a first check on the technical

merit of the report. Do this quickly, without mak-

ing any marks on the page.

* Check that the report has the right sections and

the right results in the right places. If data tables

or figures are especially important to the results,

check them now. Comment on any problems.

* Read through the report. Let the "feel" of the

prose, more than your understanding, be your

guide. (Because you know the material so well,

you can often understand even poorly written pas-

sages, supplying from your knowledge the infor-

mation and connections that students leave out

or misstate.) Whenever you feel that you are be-

ginning to work too hard to read a passage, slow

down and give it the six-word test.

* The six-word test: Check the first four to six words

of each sentence (ignore short introductory

phrases). The first several words should include

a short, specific subject naming a character

a verb expressing a key action

old information that sets a context for the rest

of the sentence

If a sentence fails the test, especially if it begins

with a nominalization that is not used as a term

of art, the sentence is very likely to violate the

principles.

* Comment on passages or sentences that violate

the principles. Don't mark up the page too much;

if there are many problems, comment only on the

most important ones. Your comments can take

any form that makes you comfortable, but it is

generally best to give the student something to

do: 1) analyze a portion of a problem passage on

the page, and then direct the student to use the

six-word test to check the rest for him- or herself;

or 2) pick out the problem element in a sentence

or passage and suggest a specific kind of change

(e.g., "Make this word a verb" or "Make sure your

sentences begin with old information"). If you don't

147

trust the student to be able to make the change

and you have the time, you can edit the sentence

or passage and comment on the change you made

(e.g., "This is clearer with X as a verb").

If you have the time and energy to spare and you

have not already made many comments, you can

check grammar, punctuation, spelling, etc. Un-

less students have very serious problems, these

comments will be less important in helping them

to communicate effectively. Yet correctness does

count, and some teachers believe that students

ought to be held to industry standards. It is gen-

erally better to pick out a problem and require

the student to fix it rather than to fix it yourself.

HOW STUDENTS RESPOND

One of the authors (Ernst) introduces the above

principles and report writing in general in a techni-

cal economics course, a prerequisite to the senior

capstone design course. The students are required

to submit a one- to three-page report every other

week, usually in the form of a letter discussing in

detail an assigned homework problem-its solution

and the implications of the solution. Each report is

graded on how well the student communicates the

information. If the report is poorly written, the writ-

ing style is checked and appropriate comments are

written in the margin as described above. Students

are given a chance to revise unsuccessful reports.

We have been pleased with the results of this

process for two reasons: 1) when it is applied to

reports assigned early in a quarter, most students

who initially submit poor reports produce well-writ-

ten reports after only one revision, and 2) toward

the end of the quarter, most students routinely sub-

mit reports that do not need revising.

For one assignment, students were asked to revise

a report previously written by another student-in

this case the "Conclusions and Recommendations"

section which we discussed earlier. Here is one of

the best revisions:

In Case 1, only the n-butane rail imports are to be

replaced by NGL. We have developed a feasible plan,

under which NGL would be transferred directly to

the blending butane product stream, yielding a com-

bined product which meets specification ....

In Case 2, all of the butane rail imports are to be

replaced by NGL. We have developed a feasible plan,

under which the NGL would be fed to the butane

splitter, where iso-butane would be removed as over-

head at the desired rate. The splitter bottoms would

be fed to a new packed column, designed to produce

148

a pure n-butane overhead stream which meets in-

dustry specs. The column bottoms would be returned

to the blending butane product stream at a rate that

would increase production by 10,000 Bbl lyr.

Often, students find it necessary to add informa-

tion as they revise the original work, which illus-

trates an additional feature of these principles: they

serve as a mental discipline that improves the qual-

ity of students' thinking. While any well-designed

writing assignment can help students consolidate

and improve their knowledge, students get an addi-

tional boost by writing and revising in accord with

these principles. Because the principles focus stu-

dents on the key elements of the story they have to

tell, they help students to think through those sto-

ries and discover missing information or gaps in

their logic. When students adhere to the principles,

they are encouraged to be complete, precise, and

logical. When teachers adhere to the principles and

follow three easy steps (locate the problem, explain

what caused it, explain how students can fix it), the

students' gain is threefold: they understand their

own research and its results more fully, they com-

municate their results to us more effectively, and

most of all, they learn how to do better next time.

REFERENCES

1. Cranch, E.T., and G.M. Nordby, "Engineering Education:

At the Crossroads Without a Compass," Eng. Ed., 76(8),

742 (1986)

2. Bennett, A.,W., and D. McAuliff, "Integrating Communica-

tions Skills into the Engineering Curriculum," ASEE-IEEE

Frontiers in Ed. Conf. Proc., Vol 2, 693, November (1987)

3. Friday, C., "An Evaluation of Graduating Engineers' Writ-

ing Proficiency," Eng. Ed., 77(2), 114 (1986)

4. Frank, C.W., G.M. Homsy, and C.R. Robertson, "The Devel-

opment of Communications Skills Through a Laboratory

Course, Chem. Eng. Ed., 16(3), 122 (1982)

5. Bakos, Jr., J.D., "A Departmental Policy for Developing

Communication Skills of Undergraduate Engineers," Eng.

Ed., 77(2), 101 (1986)

6. Sullivan, R.M., "Teaching Technical Communication to Un-

dergraduates: A Matter of Chemical Engineering," Chem.

Eng. Ed., 20(1), 32 (1986)

7. Hudgins, R.R., "Tips on Teaching Report Writing," Chem.

Eng. Ed., 21(3), 130 (1987)

8. Hanzevack, E.L., and R.A. McKean, "Teaching Effective

Oral Presentations as Part of the Senior Design Course,"

Chem. Eng. Ed., 25(1), 28 (1991)

9. Williams, J.M., and G.G. Colomb, Style: Toward Clarity

and Grace, University of Chicago, Chicago (1990). Also pre-

vious editions of this book: Williams, J.M., Style: Ten Les-

sons in Clarity and Grace, 1st and 3rd eds., Scott Foresman,

Glenview, IL (1981)

10. Colomb, G.G., and J.M. Williams, "Perceiving Structure in

Professional Prose: A Multiply Determined Experience," in

Writing in Academic Settings, edited by L. Odell and D.

Goswami, Guilford, NY (1986)

11. Gopen, G.D., and J.A. Swan, "The Science of Scientific Writ-

ing," Amer. Sci., 78, 550, Nov-Dec (1990) C

Chemical Engineering Education

Fluid Mechanics Experiment

Continued from page 143.

R = gas constant; Btu/lb(R)

t = time; s

u = internal energy; Btu/lb

v = velocity; ft/s

V = volume; ft3

W = power input; BTU/cycle

p = density; lb/ft3

Subscripts

cv = control volume

e = exiting air

i = incoming air

N = nozzle

0 = time zero valve opening

1 = initial state

2 = final state

REFERENCES

1. Van Wylen and Sonntag, Fundamentals of Classical Ther-

modynamics, 3rd ed., SI Version, John Wiley, New York

(1985)

2. Holman, J.P., Thermodynamics, 4th ed., McGraw-Hill, New

York (1988) 0

REVIEW: Mass Transfer

Continued from page 126

strongly recommended.

Chapter 17, on sorption processes, discusses fixed

bed adsorption and ion exchange. The presentation

on why loading and elution in ion exchange are not

symmetrical is particularly clear and easy to under-

stand. In general, the authors assume that the reader

is familiar with these separation processes. Readers

who are not (particularly electrodialysis) will find

these chapters difficult, but readers familiar with

the processes will gain deeper insight.

A third part of the book starts with Chapter 18,

which compares the M-S, Fickian, and irreversible

thermodynamics approaches to mass transfer. This

is a very enlightening chapter, and sophisticated

readers should read it following Chapter 2 or 3.

Chapter 19 cites references. A rather complete list

of symbols starts on page 160. I found myself refer-

ring to this list often and wish it were in a more

prominent location.

The fourth part of the book consists of thirty-six

worked exercises (pages 163 to 238) which consider

some very interesting and challenging problems. Al-

though the solutions are not polished, they are cer-

tainly sufficient to show how to attack the problems.

A major problem with this book is highlighted in

the Guidelines to the Reader on page 11: "This text

was written to accompany overhead transparencies

Spring 1993

The 1993 (maroon) revised printing of the

CHEMICAL REACTOR OMNIBOOK

is now out,

and it still costs $24.

Order at your bookstore,

or FAX your order and card number to

OSU Bookstores, Corvallis, OR at 503-737-3398

in a course on multicomponent mass transfer. So

the Figures are quite important." Unfortunately,

many readers will not pay enough attention to this

section and will find reading the book difficult until

they have learned the proper way to read it. Also,

since the figures are hand drawn, the reader needs

to learn how to decipher the authors' script. The

inclusion of equation numbers would be useful. Some

of the examples are confusing since the problem

statements are not clear (e.g., Figure 6.2) and data

or formulas are slipped into the solutions with little

explanation (e.g., Figures 3.7 and 5.5). Statements

such as "Qualitatively the reasoning should be clear,"

(page 91) will unintentionally demotivate readers

who are struggling, and they should be removed.

The basic ideas of the M-S approach are not sum-

marized until pages 64 and 65. A much earlier expo-

sition of this would help many readers. Also, since

the authors assume considerable familiarity with

mass transfer, Chapter 18 could appear earlier in

the text. If a second edition is planned, the authors

could aid readers by correcting these problems. One

hopes that the authors will make this effort since

the book presents a very important topic in a way

which will be accessible to most readers.

Where can this book be used in the curriculum?

The book is a curious mix of sophistication (M-S

theory and challenging problems) and of approxima-

tions (difference solutions and overly simplified ther-

modynamics). Because of the subject matter and the

assumed high degree of knowledge in mass transfer

and separations, this text is appropriate at the gradu-

ate level. However, the approximations and some

lack of rigor may cause difficulties. It book would be

a very useful supplement in a graduate-level course,

particularly if journal articles are used in most of

the course. It is also a very good source of problems

and examples for a graduate-level course.

Finally, for practicing professionals who missed

the M-S theory in their formal education, this book

would be very useful for self study. Wesselingh and

Krishna will stimulate and frustrate, but the reader

will never be bored. )

re. laboratory

AN INTERESTING AND INEXPENSIVE

MODELING EXPERIMENT

W.D. HOLLAND, JOHN C. MCGEE

Tennessee Technological University

Cookeville, TN 38505

In the search for new laboratory experiments, a

simple experiment that works well is always

welcome. In this paper we describe an inexpen-

sive apparatus, using simple and widely available

components, that will help student understanding

of process modeling. The equipment can be arranged

in a variety of configurations to allow study of dif-

ferent models. Many chemical engineering depart-

ments carry out mixed-tank experiments, some with

computer interfaces for data collection, that can be

rearranged and modified to include the models sug-

gested in this article.

THEORY

In a text by Levenspiel1' several models are pre-

sented for long time scale behavior of real stirred

tanks. The models examined here are Levenspiel's

model L (which is described in more detail by Bischoff

and Dedrick121) and a modification of that model.

In these models, shown in Figure 1, flow enters a

perfectly mixed tank of volume aV, is interchanged

at a rate by with a second perfectly mixed tank of

William D. Holland is a professor of chemical

engineering at Tennessee Technological Univer-

sity. He has taught chemical engineering for

twenty-five years and has served as a consultant

at Oak Ridge National Laboratory in nuclear fuel

reprocessing.

John C. McGee is a professor of chemical engi-

neering at Tennessee Technological University,

where he served as the first chairman of the

department for twenty years. He holds BS and

MS degrees from West Virginia University and a

PhD from North Carolina State University. He has

had industrial experience with Dupont.

@ Copyright ChE Division ofASEE 1993

Syphon tubes

tubes

PumpLL- L Notched weir

overflow

Rotameter Tank 2

Tank 1

Water

supply

Figure 1. Stirred tank model (Levenspiel's Model L)

volume (1-a)V, and is discharged from the first tank.

Nomenclature used here is consistent, where pos-

sible, with that used by Levenspiel. The total vol-

ume of the system is V.

In Levenspiel's model L, a unit impulse is imposed

in the feed to tank 1. If the concentration in tank 1

is C1 and the concentration in tank 2 is C2, the

material balances on the two tanks, assuming per-

fect mixing, yield for tank 1

v6(t)+ bvC2 bvC1 ClV1 = (1)

and for tank 2

d[(1- a)VC2]

Cbv -C2bv = dt 2)

Initial conditions for each tank reflect no tracer in

either tank with the initial condition in tank 1 a

formal property assigned to the Dirac delta function

as indicated by Churchill13"

C(0)= 0 and C2(0)= 0 (3)

These equations yield to rather simple Laplace trans-

form solution. The transformed equations are

1+bC2(s) (4)

1C( as +(1+b)

bCl(s)

C2 (s) =E e Ed) (5)

(1- a)lts +b

Chemical Engineering Education

where t=V/v. Inverse transformation of these equations yields

the solutions in dimensionless time, 0, given by Levenspiel for

the two tanks

Ee=C1 1 [mi-am +b]em-(m-am2 +b)em20 (6)

a(1-a)(m1 -m2)

and

O2 b [emle (7m2)

a(1-a)(mi-m2)

where

= 1-a+b 1- 4ab(1-a)

ml,m2 =- a -1+ 1

2a(1-a) ( (1-a+b)2

The discussion in Levenspiel is necessarily brief, and stud

need to be sure they understand the equations describing

model, Eqs. (6) and (7) above, and the procedures to reduce

data to a similar form (or to change the equation for the m

to the data form). Fogler[41 also shows the development ol

equations for Levenspiel's model L.

Most of the long time scale models presented by Leveni

could be examined in the experimental apparatus with a ]

equipment rearrangement. A variation which has been trie

students in our laboratories is a modification of Levensy

model L in which the tracer or unit impulse is imposed in

"stagnant" compartment. The solution to this model as wo

out with Jones15' gives the following expressions:

Ee =Co a(1-a)(mlm2)1em-em2 ]

C2 am2)[(am +b+ 1)eml -(am2 +b+ 1)em2]

EQUIPMENT

The stirred tanks for this experiment were one 5-gE

aquarium and one 10-gallon aquarium placed end-to-en,

schematic diagram of the apparatus is shown in Figure 2 a

photograph of the apparatus is shown in Figure 3. Water

fed to the larger aquarium through a small rotameter,

water was discharged from the larger tank via four syp

tubes into a small notched-weir overflow tank and then tc

drain. Flow from the larger tank to the smaller tank was

enabled by using four syphon tubes. Return flow from the sm;

tank to the larger tank was accomplished by using a sii

aquarium pump/filter device without the filter.* The fil

intake was positioned in the smaller tank and the dischE

which was adjustable with an integral valve, was made to

larger tank. The filter used in this case included a one-

hold-up tank which was filled with inert materials to elimi:

a possible third mixed tank in the apparatus. Tracer selec

could be dye, salt, or any tracer with detection capabil

available. In this work, the tracer selected for the quantity

work was sodium chloride because a YSI Scientific Mode

* In this case a Model 2 Secondnature Whisper Power Filter: catalog No. 6(

Willinger Bros., Inc., Wright Way, Oakland, NJ (201-337-0001).

Spring 1993

C1, aV

2, (1-a)V

Figure 2. Schematic diagram of apparatus

rked -

Figure 3. The experimental apparatus

(9) conductance meter was available. This

meter allowed for either a continuous record

(10) of conductance when used with a millivolt

potentiometric recorder or an instantaneous

reading. Total equipment cost excluding the

conductance meter, rotameter, and stirrers

illon was $85.00.

d. A

nd a PROCEDURE

was Both tanks were initially filled with wa-

and ter. Then water flow at a rate of 3.1 liters/

)hon minute was initiated through the rotame-

the ter into the larger tank, and flow from the

also larger tank through the two syphon sys-

aller teams was started. Flow rates are typical

mple and, of course, may be set at any reason-

ter's able level. Stirrers, placed in both tanks,

Large, were activated. Flow through the pump/

the filter was started and measured using the

liter bucket-and-watch method on the outflow

nate of the power filter after a period of time to

.tion allow steady-state flow. A return water flow

cities rate to the larger tank of 4.8 liters/minute

Live was measured. At steady-state the volume

S35 of liquid in tank 1 was 36.2 liters, and the

)02, volume in tank 2 was 16.5 liters. The above

tank volumes and flow rates gave model

151

parameters of 0.678 for a and 1.55 for b. A one-

molar solution of sodium chloride was prepared for

use as tracer, and a calibration curve for the con-

ductivity meter was prepared. Before an experimen-

tal run was made using the salt tracer, a run was

made using dye as the tracer-this demonstrated

the flow patterns in the system and gave some in-

sight into the perfectly mixed tank assumptions.

Dye, instead of salt, has also been used in separate

experiments to monitor the tracer concentration.

When flows were properly established and steady-

state conditions were obtained, one liter of the 1 M

salt tracer was rapidly poured into the center of

the larger tank over a short period of time to

approximately replace the regular water flow in a

pulse-shaped input. The concentration of the mate-

rial in each tank was monitored alternately with

the single conductivity probe, with the probe rein-

serted into the tanks in approximately the same

location each time. Sampling was halted after ap-

proximately 37 minutes.

RESULTS AND DISCUSSION OF RESULTS

The experimental results are shown in Figure 4.

The response of Model L to a unit impulse input was

also determined by solving the equations numeri-

cally; these results are compared to the experimen-

tal results in Figure 4. The expected characteristic

shapes were obtained and agreement between

the experimental results and'the model were

within seven percent for tank 1 and within eleven

percent for tank 2. The maximum concentration in

tank 2 was eleven percent below the model and

about two minutes late. No attempt was made to

adjust model parameters.

Many variations of the experiment demonstrated

here could be studied including other models, effect

of tracer injection method, effect of adjusting the

model parameters, and effect of mixing. Because of

the flexibility derived from the ease of rearranging

the system, individual laboratory participants or

groups could study a number of different models or

a few models in depth.

SUMMARY AND CONCLUSIONS

An interesting and inexpensive process-modeling

experiment was demonstrated with qualitative and

quantitative results. Other models could be exam-

ined by simple modifications to the experimental

apparatus. The work integrates studies in chemical

reaction engineering courses with process modeling

and control courses and provides the students with

some insight into problems in modeling systems.

152

0 5 10 15 20 25 30 35 40

Time, minutes

Figure 4. Comparison of model with experiment

ACKNOWLEDGMENTS

The authors gratefully acknowledge helpful criti-

cism by the referees of this paper.

NOMENCLATURE

a = model parameter, fraction of total volume in feed

tank

b = model parameter, fraction of feed volume flowing

to "stagnant" region

C, = tracer concentration in tank 1

C2 = tracer concentration in tank 2

Ce1 = C-curve for tank 1 based on 6, C1 = Eg = tC1

C02 = C-curve for tank 2 based on 9, C02 = tC2

E, = exit age distribution for tank 1 in dimensionless

time

t = mean residence time, V/v

V = total system volume

v = volumetric feed rate

8(t) = Dirac delta function for unit impulse

8 = dimensionless time t /

REFERENCES

1. Levenspiel, Octave, Chemical Reaction Engineering, 2nd

ed., Wiley, New York (1972)

2. Bischoff, KB., and R.L. Dedrick, J. Theor. Biol., 29, 63

(1970)

3. Churchill, Ruel V., Operations Mathematics, 2nd ed.,

McGraw-Hill, New York (1958)

4. Fogler, H. Scott, Elements of Chemical Reaction Engineer-

ing, 2nd ed., Prentice Hall, Englewood Cliffs, NJ (1992)

5. Jones, S., private communication (1990) 01

Chemical Engineering Education

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