Chemical engineering education

chemical engineaerig education

Some of the metals we mine

are more precious than told.

An ounce of cold steel can do Manganese, tungsten, silicon, No computers, or lightbulbs,

wonders for a warm smile.
But it must be a very special
steel. Strong, yet ductile. Hard,
yet smooth.
It must not rust or stain.
And it must remain unchanged
through ice-cold sodas and red-
hot pizzas.
At Union Carbide we mine or
process the alloying metals that
make possible this special steel
and hundreds of others.
We produce over 60 different
alloys and alloying metals.

chromium, vanadium.
Not exactly households words.
But - combined with iron, alu-
minum and other metals - they
have transformed the world we
live in.
If it weren't for alloys there
would be no high-strength steels
for buildings and bridges.
No jet engines or aircraft
bodies.
No sophisticated tools.
No electric motors for shavers,
typewriters or vacuum cleaners.

or television sets.
When you think of them this
way, our alloying metals become
very precious indeed.
Whether they're as far away
as a rocket on its way to the
moon. Or as close to your heart
as a brace shaping a beautiful
smile.

Today, something we do
will touch yourlife.

An Equal Opportunity Employer

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SUMMER 1975

Chemical Engineering Education
VOLUME IX NUMBER 3 SUMMER 1975

FEATURES
115 Self Instruction in Thermodynamics
Frank Tiller
118 Carberry's Ultimate Paper
Aris Rutherford
128 Pollution of the Environment-
Causes and Cures
M. Hawley, M. Chetrick and E. Shaheen

DEPARTMENTS
106 The Educator
Bob Reid of M.I.T.

110 Departments of Chemical Engineering
West Virginia University

102 Views and Opinions
Hot Lips, A Cold Heart and
Thermomometry
O. Levenspiel

Classroom
120 Transients in Plug Flow Systems
L. Fan and S. Lin

133 Use of a Continuous System Simulation
Language in Chemical Reaction Engi-
neering, R. Williams and D. Wolf

Laboratory
124 Experiments in Heterogeneous Catalysis
B. Gates and J. Sherman
138 Demonstrating Catalytic Reactor
Stability, R. Hudgins

Curriculum
144 Georgia Tech's Pulp and Paper Program
G. Lightsey

139, 143 Book Reviews

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The International Organization for Standarization has assigned the code US ISSN
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101

views and opinions I

HOT LIPS, A COLD HEART AND THERMOMOMETRY

OCTAVE LEVENSPIEL
Oregon State University
Corvallis, Oregon 97331

T HE ORIGIN OF THE THERMOMETER, a
device with some sort of scale for measuring
the hotness or coldness of objects, is obscure.
However, the climate in Europe in the beginning
1600's was hot for it, it had to be invented at that
time, and so it was . . . but by whom? In Italy
Galileo had his champions, and so had Santorio,
Professor of Medicine at Padua. Then there was
the Welsh doctor and religious nut Fludd; also
the gadgeteer, inventor, and perpetual-motion-
machine-maker, Drebbel of Holland. But who was
first? Since people in those days didn't much care
about getting into the Guinness Book of Records
we probably will never satisfactorily resolve this
question. It seems that this sort of immortality
was not the passion then that it is today.
In any case, by the middle of the 1600's the
thermometer was widely known in Europe, each
maker having his own scale of measurement. A
popular design started with "1" in the middle of
the device to represent everyday comfort. It then
indicated 8 degrees of coldness and 8 degrees of
hotness, each degree in turn divided into as many
as 60 minutes. Other makers were more descrip-
tive, viz
Extream Hott
Very Hott
Sultry
Hott
Warm
Temperate
Cold
Frost
Hard Frost
Great Frost
Extream Frost
Evenas late as the middle 1800's one could buy a
thermometer having 18 different marked scales.
The development of a standarized temperature
scale was a long and bumbling process. About 100
years after the invention of the thermometer enter
Daniel Gabriel Fahrenheit, Danzig born, Dutch

adopted, master instrument maker, and traveller.
While in Copenhagen in 1704 or 5 (or maybe 6)
he visited Ole R6mer, Danish astronomer, where
he observed him busily calibrating thermometers.
Struck by the elegant simplicity of Romer's choice
of calibration points . . . 71�/ for the ice-water
and 221/� for body temperature, Gabe immedi-
ately adopted these for his own. But since frac-
tions always bothered him he eventually multi-
plied everything by 4 to get rid of the two halves,
fudged upward a bit, and ended up with 320 and
960 for these calibration points. On this scale a
mixture of sea salt and ice melted at about 0� and

The temperature measures the "quantity of heat"
in a body, or in today's language, "thermal energy."
So "why not measure temperature directly."
Georgian, an American engineer, strongly
urges we adopt such a scale choosing
the ideal gas as measuring instrument.

water boiled somewhere between 2000 and 2400
(say 2120 as a good average). Because humans
are somewhat unreliable, some hot blooded, others
questionable, before long the freezing point (32�)
and the boiling point of water (212�) became the
accepted calibration points. Since Fahrenheit's
thermometers sold well this scale soon became
widely adopted.

PARTY PLEASER
T WAS QUITE A MARVEL in those days to
put ice and a liberal helping of salt in a pan,
insert a thermometer and see it zonk down to
0�F and stubbornly refuse to budge . .. even with
the pan on a hot stove! But in our age of TV
marvels we may have to dress up this experiment
to catch anyone's attention. Here is one way, best
done at a large party or gathering. Bet a par-
ticularly obnoxious fellow $10 that he cannot keep
his foot in a pan of salt and ice for 10 minutes.

CHEMICAL ENGINEERING EDUCATION

-I$

|

t~L~O(

Sit him down and while his foot is freezing solid
get hold of a hammer. After 10 minutes his pain
is gone and you are ready for the finale to this
demonstration. Remove his foot from the pan and
strike his big toe firmly with the hammer. The
brittle toe will snap off and fly across the room.
Accompanied by "ooohs" and "aaahs" retrieve this
toe and in a matter-of-fact way return it with $10
to the surprised owner. This spectacular ending
will guarantee that you and thermometers will be
the talk of the town for a long time to come.
To return to the thermometer, while Gabe's
came into wide use in England and Holland, the
French completely ignored this Northern develop-
ment. Their man was Reaumur who after 1731
vigorously championed a spirits of wine thermom-
eter . . . French wine, of course, and red for easy
reading. His scale went from 0� for ice water to
800 for boiling water. Unfortunately, however,
among other things Reaumur's insistence on a
one-point calibration and the fact that the quality
of French wine varied from year to year, led to
all sorts of complications. So although the French
gave this thermometer a good try for over a cen-
tury, they eventually gave it up; and drank their
wine instead.
While these developments were taking place in
warmer climes Swedish astronomer Anders Cel-
sius tramped his snowy land with 10 cold fingers
and 10 cold toes advocating a 100 division scale
(centigrade) by continually proclaiming "water
boils at 0�, water freezes at 1000, boils at 0�,

4-

Octave Levenspiel, professor at OSU, is primarily interested in
problems of chemical reactors. He has written a text on this subject,
and has won the ASEE Lectureship Award for his early visions in
this field.
His weakness for scientific curiosities has led to flirtations with
4-colorologers, 2nd law repealers, Fibonacciics, boomerologists, topo-
lographers, and other such. He is also 1975 president of the Northwest
Neothermo Society.

Vacuum

.Q. �

Boiling

point

Freezing
point

K )

Mercury Alcohol, toluene,
dilute H2S04,etc.
FIGURE 1.

Bead of
mercury

such as air

freezes at 100." By happenstance however, An-
ders' intimate friend, Linnaeus, the great botan-
ist, was left-handed. Because of this he kept
snatching the wrong end of the instrument and
using it upside down, and kept reading 0� for the
freezing point and 100 for the boiling point, and
thus recommended this scale.
To confuse the issue further there were other
strong claimants for the honor of inventing this
scale; nevertheless, in 1948 the 9th General Con-
ference of Weights and Measures decided that it
knew enough, it dismissed all the others, and
ruled that what had been known as oCentigrade
should henceforth and forever more be known as
"Celsius. And so Celsius' name will be with us
forever, and all because he chose his parents
wisely. Had Linnaeus' name been Clinnaeus we
might today be talking of �Clinnaeus instead of
degrees Celsius.

CALIBRATION CONFUSION
THERMOMETERS EVOLVED into three
broad types, as shown in Fig. 1, and as users
became fussier and demanded more precision all
sorts of problems cropped up. For example, should
melting ice or freezing water be one of the calibra-
tion points? In practice they differ! Should boil-
ing water or condensing steam be the other? The
zero point also slowly and continually changed
with time. In mercury thermometers it crept up-
ward, in alcohol thermometers it slid downward.

SUMMER 1975

2L.

SHOI ODjeci ' 1^,

to extract
some work
Direction Not so hot . ( / eat
of heat ---5 flows from
flow object to
:A bit cooler still object

etc.
FIGURE 2.

Was this due to the aging of glass, the slow de-
composition of the fluids, or what? And these
changes continued for 10, 20, 30 years!! Also,
how did these scientists explain the small periodic
variations according to season!! ?
Probably the most serious problem was that
when one type of thermometer read a temperature
halfway between calibration points the others did
not because of changing coefficients of expansion
of fluids. This is illustrated in Figure 1. In this
case which thermometer read the true midpoint
temperature-which to trust? Was the selection of
equal intervals of temperature an arbitrary mat-
ter, or was there a rational way for doing this?
These difficulties kept scientists out of mischief
for quite a while.
In the 1800's there was much concern about
developing a rational temperature scale. In 1847
Regnault pinpointed the problem by stating:
"We give the name thermometer to instruments in-
tended to measure the variation of the quantity of
heat in a body . . . A perfect thermometer would be
one whose indications are always proportional to the
quantity of heat absorbed, or, in other words, one in
which the addition of equal quantities of heat al-
ways produces equal expansions . . . Unfortunately
this is not so for real substances."
Just a year later William Thomson, later Lord
Kelvin, magically devised just such a temperature
scale based upon the concept of the ideal reversible
heat engine of Sadi Carnot. To illustrate its basis,
imagine a number of objects or heat reservoirs ar-
ranged from hot to cold as shown in Fig. 2, and
let heat flow from one to the other while doing as
much work as possible.
Suppose that 100 units of heat leave reservoir
1 for reservoir 2, and in the process are able to do
10 units of work in the most efficient engine con-
ceivable. Then 90 units of heat reach reservoir 2.
Suppose these 90 flow on, doing 10 more units of

work before reaching the next reservoir, and so
on.
Kelvin argued that we should choose a tem-
perature scale which is proportional to this heat
flow. Any proportionality would do, thus 100, 90,
800, etc. or 250, 225, 2000, etc., for the sketch
shown in Fig. 3. Scales such as these are now
called Absolute temperature scales.

Best of all
possible
work-extractors

R.7 Reservoir 1;;.

Heat flow
100 units/time

Ideal
engine

Htf

Work
extracted
10 units/time

Heat flow
90 units / time

K Reservoir 2:.:

Heat flow
90 units/ time

etc

Heat flow
10 units/time

iReservoir 9

Heat flow
10 units/time

Ideal Work
extracted
enge 10 units/ time

Zero
heat flow

, : Reservoir 10'

This reservoir is said to
be at a temperature of
absolute zero.
FIGURE 3.

CHEMICAL ENGINEERING EDUCATION

I

An interesting bonus to this argument of
Kelvin's is that since no heat enters the lowest
reservoir of Fig. 3 none can leave it to flow to an
even colder one. Thus this bottom reservoir in the
sketch must be the lowest imaginable of tempera-
tures, the ABSOLUTE ZERO of temperature.
What a jewel of an idea this turned out to be.
On this basis we now commonly use two scales;
the Kelvin scale corresponding to degrees Celcius
and the Rankine scale corresponding to degrees
Fahrenheit. These are sketched in Fig. 4.
Today, more than 100 years later, how pure do
we find his conclusions? Giant refrigeration ma-
chines fueled by Nobel prizes help us freeze our
way even closer to this "THOU SHALT NOT
TRESPASS" limit, yea, within a thousandth of a
degree, but Kelvin's limit still stands unshaken
and confident.
Finally Kelvin found that simple gases at very
low and constant pressures occupied volumes pro-
portional to their absolute temperature, and there-
fore provided a practical way for accurately cali-
brating thermometers.

TEMPERATURE TODAY

S O HERE IS HOW THINGS stand today. First
of all the lowest possible temperature imagin-
able, the absolute zero, has been invented. This is
where our temperature scales should start from,
and this is where our absolute scales ("Kelvin
and �Rankine) in fact do. Secondly, we have a
rational way for choosing equal intervals of tem-
perature.
We just have one question left. Starting from
this cold cold zero point, why pick our unit of
temperature the way we do? Why base it on 100
intervals or 180 intervals between the freezing
and boiling point of water? Why pick water, why
not googliox? Isn't there a more reasonable way
of selecting our unit of temperature?
As Regnault long ago pointed out, the tem-
perature measures the "quantity of heat" in a
body, or in today's language, its "thermal energy".
So why not measure temperature directly as
energy per unit quantity of material. Georgian,
an American engineer, strongly urges that we
adopt such a scale choosing the ideal gas as meas-
uring instrument. The reason for this is that the
energy of any ideal gas is proportional to its ab-
solute temperature. So measure its energy and
you've got its temperature.
The sketches in Fig. 5 compare various pos-
sible absolute temperature scales following this

3730Kt IO0�Ct ..- Boiling water ... t2120F t6720R

2730K

00�C .. Freezing water-... 32F J492�R

OOK -273oC ...

OC and OK
have the
same interval

Absolute zero- t-460F4 O�R

oF and �R
have the
same interval

FIGURE 4.
proposal. Because of its compatibility with the SI
units Georgian particularly favors the last of
these scales, or joules/kmol.
It may seem awkward and foreign to talk of
water freezing at 2270�X, boiling at 3100�X, and
of having a mild fever of 2600�X (where X would
then honor some famous scientist whose name
does not start with the letters C, F. K or R). How-
ever, you must admit that it would be a smashing
bit of one-upmanship to sprinkle one's talk this
way. But more seriously, with such a scale a num-
ber of simplifications occur naturally. In par-
ticular it would forever banish one conversion
(Continued on page 137.)

fo0
Kelvin
temperature
scale

22.4 i-atm 542 cal
mol -- mol

3.10x 106

2270ous 2.27x106 joules
mol kmol

to to to to

Various ideal-gas-energy
temperature scale
FIGURE 5.

SUMMER 1975

Educator

3of Reid

of M. I. T.

MICHAEL MODELL
Massachusetts Institute of Technology
Cambridge, Massachusetts 02139

U USUALLY, BOB REID IS IN class five
minutes before the hour to greet and chat
with early arrivals to his 9 a.m. graduate thermo-
dynamics course. This day, the students find in-
stead, coffee and doughnuts set up in the back
of the room. At the bell, Maria (Bob's secretary)
announces: "Unfortunately, Professor Reid

In spite of the fact that the graduate thermo
course is known to be the toughest,
most demanding course in the program,
Bob was chosen by the students
as the Outstanding Teacher in the
Department in 1973 and again in 1975.

couldn't make it today, but he has sent a guest
lecturer, J. Willard Gibbs." She proceeds to lead
in a decrepit old man, dressed in an academic
gown and made up in a wig, false nose and glasses.
Leaning heavily on a cane, he presents a fascinat-
ing, but incoherent lecture on the criteria of equi-
librium and stability. The contrast with one of
Bob's lectures, which are usually marked by
clarity and simplicity without any trace of
academic arrogance or pretension, couldn't be
greater. But it's all in fun, because the man in
the gown is Bob himself. Unexpected? Not really.
For those fortunate enough to know Bob Reid,
the unexpected often becomes the expected. The
Gibbs routine is pure RCR. It's just one of many
gestures Bob makes to develop a close rapport
with the students. Early in the term, for example,
he invites every entering graduate student to chat
with him for a half hour. "I try to show them
that the inside of my office is really not very
grotesque; once they've been in, the second time
is much easier." And they do come back, time and
again, to discuss their interests and problems,

and to seek his counsel. In spite of the fact that
the graduate thermo course is known to be the
toughest, most demanding course in the program,
Bob was chosen by the students as the Outstand-
ing Teacher in the department in 1973 (the
second year the award was given) and again
in 1975.
Bob's interest in chemistry, as well as his
classroom sense of humor, date back to his high
school days in Denver. He recalls his chemistry
teacher, who conducted a qualitative analysis lab.
"He used to give us all sorts of fascinating
samples. He was quite a joker. He'd give you
powdered concrete as an unknown. Your first re-
action was to see if it dissolved in water. It would
set up like a rock overnight; then he'd get the
biggest kick out of seeing your reaction the next
day. He was the kind of teacher a student could
relate to. He'd have a standing challenge that
any student who could beat him in shooting
baskets would automatically get an A, regardless
of how little chemistry the student knew."
QUESTIONABLE BACKGROUND
B OB'S COLLEGE EDUCATION could best be
described as sporadic. He entered Colorado
School of Mines in 1942, majoring in petroleum
refining because "I was offered a scholarship and
petroleum refining was the closest offering to
chemistry." But he didn't stay long: "In my
freshman year, I turned eighteen, quit school,
and joined the Army Air Corp as a cadet. After
eight months, I contracted rheumatic fever and
was given a medical discharge. I drove a truck,
worked in a steel mill, went back to school, and
then joined the Navy in 1943. The computers
weren't very good in those days; before I was
discharged in 1946, I think I was the only one in
the country with an active commission in the US
Navy and a medical discharge from the Army."
After the war, Bob returned to Colorado
School of Mines, where his candor and curiosity
almost led to several suspensions. "I used to
argue in class and most professors didn't like a

CHEMICAL ENGINEERING EDUCATION

pij~: �*
J;.�.. *�r*
~ls"'
1;,
,--.i� .

Unfortunately Prof. Reid couldn't make it today, but
he has sent a guest lecturer, J. Willard Gibbs.

student questioning their presentation. This is
why, even now, I feel very strongly that a student
should raise questions-on everything I say, on
everything I do."
After his junior year, he transferred to Pur-
due, where he obtained B.S. and M.S. degrees
in chemical engineering, and where he met Joe
M. Smith. "Joe really turned me on; he was the
first teacher who gave me problems I couldn't
solve. As a matter of fact, I'm still using some of
them. I had never met a professor who wanted to
know you as an individual. If I were working
in the lab late at night, he'd stop in, put his feet
up on the desk, and talk with me, not necessarily
about my thesis, but about almost anything."
"Warren K. Lewis was another teacher who
had a great impact on me. I'll never forget one of
my first classes with Doc after I entered M.I.T.
in 1951. He gave us a homework assignment and
I put in a lot of time on it; I thought I had it
cold. When he called on me to do the problem, I
breezed through my solution and knowledgeably
commented on it. Well, he stood there and looked
at me, horrified. Then he marched down the aisle,
poked that finger of his in the middle of my face,
and said in his inimitable fashion, 'Go-o-o-d
da-m-m-it, Reid, you don't re-a-a-a-lly believe
that!' Everybody in the class was staring at this
little character, scrunched up in his seat and
wondering what he'd say. You see, either you
were firmly convinced that you were right and
were willing to argue with him, or you had to

think of another answer awfully fast. I had the
right solution, and he knew it, but he forced his
students to develop confidence in their own con-
victions and to learn how to defend their posi-
tions. That was an experience I'll never forget,
and one I've tried to emulate."

FIRST OF MANY CHAPTERS
B OB BEGAN HIS TEACHING career as an
Instructor while finishing his Ph.D. disserta-
tion in 1954. He was teaching an undergraduate
thermo course with Tom Sherwood. At one point,
the two of them were trying to make out a re-
frigeration problem, involving a mixture of re-
frigerants. Bob recalls, "We couldn't find some
boiling points or critical pressures, and so Tom
turned to me in disgust and said, 'Reid, some-
body ought to write a book that tells you how to
estimate these things if they're not in the litera-
ture.' About a month later, Bob dropped a chapter
and an outline for a book on Tom's desk. Tom
was so shocked that he agreed to co-author the
book. Bob finished the manuscript while he was
Director of the School of Chemical Engineering
Practice at Oak Ridge. The rest is well-known
history. The first edition of Properties of Gases
and Liquids was printed in 1958, received rave
reviews, and has been an essential part of every
chemical engineer's library ever since. The
second edition was printed in 1966 and has since
been translated into Russian and Spanish. Bob
is currently working on the third edition.

The first edition of
Properties of Gases and Liquids
was printed in 1958, received rave reviews,
and has been an essential part of every
chemical engineer's library ever since.

Bob has also co-authored two other books:
Modelling Crystal Growth Rates from Solution
(with M. Ohara, 1974) and Thermodynamics and
its Applications (with M. Modell, 1974).
Bob joined the faculty at M.I.T. ostensibly to
finish Properties of Gases and Liquids. One thing
led to another, and Bob has been at the Institute
ever since. Although Bob considers himself to be
inbred, he has consistently been at the forefront
of movements for change and improvement: in
curricula, in graduate school policy, and in faculty

SUMMER 1975

Joe Smith really turned me on; he was the first teacher who gave me problems
I couldn't solve. As a matter of fact, I'm still using some of them ... I had never met
a professor who wanted to know you as an individual. Warren K. Lewis was
another teacher who had great impact on me ... he forced his students to develop
confidence in their own convictions and to learn how to defend their positions.

hiring policy. He has been opposed to M.I.T.'s
long-standing policy of hiring its own Ph.D.'s
as assistant professors. "For many years, in-
breeding worked in M.I.T.'s favor, but today there
are numerous first-rate chemical engineering de-
partments around the country, each with its own
style and qualities, and it's high-time we cross-
fertilized students and faculty with other schools.
I am pleased to see that we're making concrete
progress in that area."
In his most recent crusade, Bob assumed the
editorship of the ailing AICHE Journal in 1970.
In a short time, he introduced much needed re-
form and pioneered innovations in ways of dis-
seminating technical knowledge. To be a journal
editor, one must have patience and tact in dealing

with authors, many of whom have strong convic-
tions, and some of whom regard their manu-
scripts as sacred prose. The fact that he remains
on good terms with them, and is highly admired
by many of them, is a tribute to his skill and
finesse. He has managed to inspire confidence
once again in potential contributors, mostly by
reducing hold-up time for manuscripts, but also
by careful and fair attention to reviewer's com-
ments as well as the author's special wishes and
needs. His performance has earned him deep
respect from a large and increasing following. In
this capacity alone, he has probably contributed
more to our profession in just a few years than
many of us will be able to accomplish in a life-
time. D

CHEMICAL ENGINEERING EDUCATION

ACKNOWLEDGMENTS

The &llouiot o. . aaiel do.atead eid jo& J& the

"Wwot o4

CHEMICAL ENGINEERING EDUCATION
DURING 1975:

MONSANTO COMPANY

3M COMPANY

We aiea tlak tMe 133 Chemical Cneei bepadt-

meat w"4 ha"e co4twneated t&a e pp4Ol of GCC ig N

1975!

332 ofourpeople

left their jobs last year.

ofthatrecord.

Job hopping is something we encourage through our
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We happen to believe our most valuable corporate
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our Career Guide. SUN OIL COMPANY, Human
Resources Dept.CED, 1608 Walnut Street, Philadel-
phia, Pa. 19103. An equal opportunity employer m/f.

A Diversified Energy and Petrochemical Company

[INI department

ChE DEPARTMENT FACULTY
Il't(4 V'ir\-( ,iiii ,,i,'L, -'sitll
,Mlorniiiitri',,. \'(:est I'-fiii'il 26506

IN THE COAL-RICH mountains of West Vir-
ginia, the '70's will undoubtedly be remembered
as the decade of the energy crisis. The state's
abundant supply of coal brought it new promi-
nence as an energy supplier; but with that promi-
nence came questions. How could the coal be mined
cheaply without destroying the rugged beauty of
the state? How could its high sulfur content be
treated so that it could be burned without pollut-
ing the air?
The young men and women who are today's
chemical engineering students are eager to take
a hand in answering these and other questions;
yet when the time comes, that step out of the class-
room into a job is a big one. Recognizing the un-
certainty students are likely to experience making
that transition, West Virginia University's De-
partment of Chemical Engineering has developed
a program aimed at enabling students to apply
ChE concepts to complex real world problems.

Called PRIDE, the program combines indi-
vidualized instruction, increased emphasis on de-
sign courses, and programmed instruction to pro-
vide Professional Reasoning Integrated with De-
sign Experience.
The PRIDE concept was developed at WVU
over a number of years. Dr. H. P. Simons, former
department chairman, took the first step in the
early '60's when he introduced the Senior Block, a
10 credit course taken both semesters of the senior
year. The content of traditional fourth year stud-
ies were incorporated into the block's year-long
comprehensive design project.
Later, a unique course called "Guided Design"
was introduced for all freshmen engineering stu-
dents. Planned, controlled projects are emphasized
in this course aimed at developing the student's
ability in analysis, synthesis and evaluation.
The PRIDE program has four basic objec-
tives:

CHEMICAL ENGINEERING EDUCATION

* To present a coordinated, professional ChE curriculum
oriented more toward the education of practicing en-
gineers than research engineers.
* To involve the student in the team-effort approach to
solving engineering problems.
* To take advantage of faculty specialties in each area by
the use of team-teaching.
* To utilize programmed instruction and other innovative
educational techniques to achieve maximum efficiency in
the teaching of content subject matter.
Recognizing the importance of design pro-
ficency for the professional engineer, WVU's ChE
faculty resolved to introduce this complex activity
early and to give students frequent opportunity to
practice it.
In 1972 a grant was awarded by the Exxon
Education Foundation to fund the development of
this program in the sophomore and junior years.
Now, over three years later, most of the "bugs"
seem to have been worked out and the program is
operating smoothly.
Al Pappano directs the sophomore segment of
PRIDE, a two semester (two/credit/semester)
course. The Junior Block, supervised by Duane
Nichols and Dick Bailie, consists of two three-
credit courses taught back-to-back each semester,
allowing several uninterrupted hours of class time.
Faculty members guide the students to com-
plete the projects themselves. In these classes, the
student plays the role of a professional engineer
on a four-man team trying to solve a design proj-
ect problem.
Each design problem presented is carefully
chosen to require knowledge of the concepts which
make up the course content. Students learn sub-
jegt material based on a "need to know" in order
to complete the design project.

Dr. C. Y. Wen, Department Chairman, heads research
activities in coal/energy research.

The role of the instructor changes as the stu-
dents progress through the program. Moving
away from the traditional role of transmitter of
knowledge, the instructor becomes a consultant
who guides the student's decision-making activ-
ities.

*�_l

Senior Block group leaders look over plant model.

SENIOR DESIGN PROJECT
T HE SENIOR BLOCK, DIRECTED by Fred
Galli and John Sears, is the culmination of
this practice in decision-making and design work.
Planned to simulate as nearly as possible the
working environment of the practicing engineer,
the focus of the senior curriculum is a compre-
hensive design project. Students meet every week
in uninterrupted class periods to work on this
project.
Each fall the student chief engineer, who is
recommended for the job by the previous year's
graduating class, receives from the faculty a brief
description of the project to be undertaken. For
example, the recently graduated chief engineer,
David Daugherty, guided his class in an explora-
tion of the use of alcohol as a gasoline extender, a
topic particularly relevent in these days of high
fuel prices.
The project description specified the volume of
alcohol to be produced each day and identified the
particular processes to be used to produce ethanol
or methanol from wood or coal. The class divided
into five groups to investigate these processes and
to study the economics of each one. As their plan-
ning became more exact, the group considered en-
vironmental and safety concerns. They found that
some processes presented special problems. For
instance, all of the wood in Pennsylvania was
needed as a raw material for one of the processes.

SUMMER 1975

'*~~' 'p '~ i"'*

When the class reached agreement on the most
feasible process, a detailed design and economic
analysis was conducted to determine what effects
factors such as fluctuation in material costs or
changes in the nation's financial outlook would
have on the cost of production. Construction of a
plant model was the last step in completing the
project.

WVU ChE department is perhaps
the only place on campus
where students are
enthusiastic about examinations,
recognizing the learning opportunity
they present.

At the final presentation, each group leader
summarized the group's contribution to the proj-
ect and answered questions posed by faculty and
students. This occasion gives students a chance to
demonstrate their creativity and it becomes ap-
parent that the program isn't called PRIDE by
accident.
Students also have a chance to display their
expertise during another feature of the Senior
Block, the major examination. When a "major"
is scheduled, all senior ChE classes are cancelled
and students work individually for one or two
weeks on a process analysis project proposed by
the faculty. The project is designed to develop stu-
dent maturity-and judgment counts as heavily as
the student's performance on the "major." Crea-
tivity and judgment count as heavily as design
proficiency. Students present a written report of
their work and defend it orally before a faculty
panel. The oral presentation is particularly valu-
able because students get experience in presenting
and defending their ideas before a technically
trained group. The WVU ChE department is per-
haps the only place on campus where students are
enthusiastic about examinations, recognizing the
learning opportunity they present.

COMMUNICATIONS SKILLS
IN ADDITION TO DESIGN experience, good
communications skills will be important to
these students in their engineering careers. With
this need in mind, the grant from the Exxon Edu-
cation Foundation helped to develop another pro-

gram called "Communications Integrated Into En-
gineering Curriculum". Marian Jones, a journalist
with a background in ChE, conducts the program
to help each student develop oral and written com-
munications skills.
Beginning in the sophomore year, Mrs. Jones
schedules individual conferences with the students
as they are needed, and gives each one advice for
improving writing and speaking abilities. A video
tape system is available to allow students to evalu-
ate themselves in oral presentations. Students
gain experience in writing laboratory reports,
progress reports, memos, and the major design
examinations. In addition, they are given advice in
preparing resumes and job applications.
West Virginia's PRIDE program has not gone
unnoticed. Representatives from industry conduct-
ing job interviews on campus have commented on
the poise and self-confidence the students exhibit.
Although research is not emphasized in the
undergraduate curriculum, that is not to say it has
no place at WVU. When Dr. C. Y. Wen became de-
partment chairman in 1969, he brought to the job
an expertise in coal/energy research. Under his
direction, the department has become internation-
ally known for its work in energy and environ-
mental problems.

John Sears, faculty member, discusses performance
characteristics of an adsorption column.

CHEMICAL ENGINEERING EDUCATION

Continuing research programs in the area of
coal conversion technology have gone on for sev-
eral decades. Currently, one of these projects will
assess the potential of coal-based energy com-
plexes which produce either liquids, gases, power,
or combinations from coal. Research is presently

being conducted on processes for reducing air and
water pollution. These projects range from small
scale laboratory studies determining the feasibil-
ity of electrophoretic dewatering of chemically
stabilized emulsions to the design, constriction
and operation of a 60,000 gallon/day reverse

Integrated Content-Design Flowsheet for West Virginia University

S5

JU

* GRADUATION

MATERIALS -- EQUIPMENT DESIGN-- /
IN TRANSFER AREAS
4 LABORATORY
PROCESS HEAT AND with Integrated
CONTROL MASS TRANSFER Statistics

MAS TRANSFER ---CHEMICAL
REACTION
ENGINEERING
SENIOR YEAR

HEAT TRANSFER ---CHEMICAL
A REACTIONN
S / ENGINEERING
FLU MECHANICS

PHYSICAL AND
CHEMICAL EQULIBRIA

SECOND LAW OF
THERMODYNAMICS
A

EQUILIBRIUM
STAGE
.* OPERATIONS
INTRODUCTION TO INTRODUCTORY
COMPUTERS PHASE
EQUILIBRIA

INIOR YEAR

Thermochemisi

First Law of
Co mmication MATERIAL-ENERGY Thermodynami
Program begun, BALANCES
carried on
throughout the Chemical
senior year. Reaction
Balances

MATERIAL
BALANCES
Physical Bal.

COMPREHENSIVE PLAN
DESIGN

REACTOR UNIT
DESIGN

WATER DISTRIBUTION
SYSTEM FOR
FIRE-FIGHTING
IN A PLANT

ETHYLENE-ETHANE
SEPARATIONS DESIGN

COMPUTER DESIGN
IN DESALINATION
FOR WASHING SALT
FROM ICE

MEDICAL COLD PACK

CRYOGENIC
LIQUEFACTION OF
A METHANE-ETHANE
MIXTURE

NATURAL GAS USE
FOR POWER AND
OTHER PURPOSES

TREATMENT OF
EFFLUENT WASTES

try

cs

ances

T

Equipment Design
and Integration

Process Strategy
Economics

Alternative Process
Selection

Marketing

Process Strategy

t
Understanding the
Use of Operating
and Capital Costs

t
Process Strategy;
Integrate Thermo. and
Stage Operations

Extending Material
Balances to Require
Computer

Application of Principles
to other Fields

Process Trade-off
Concept for
Minimum Cost

Conservation of
Resources; Maximum
Profit Criteria

Recycling in
Environmental Action;
Minimum Cost Criteria

SOPHOMORE YEAR

Topic Benefits
CONTENT MAJOR DESIGNS

Simple laboratory experiments are introduced throughout the curriculum when appropriate. Content and design particulars may vary from year
to year. An advantage of the use of the flowsheet is that if more, or less, time is required for student comprehension of a concept of design, the
curriculum flow can be shifted. For example, Reactor Design may have a greater emphasis in the junior year for one class, for the next class it
may have more emphasis in the senior year.

SUMMER 1975

q

J

The PRIDE program combines
individualized instruction, increased
emphasis on design courses, and
programmed instruction to provide
Professional Reasoning with
Design Experience.

osmosis pilot plant to study the possibility of pro-
ducing potable water from acid mine drainage.
Extensive research is underway on novel sep-
aration processes. Joe Henry's research on dual
functional separations combines the interactions
of surface, electrokinetic, and diffusion phenom-
ena to develop novel separation techniques. The
relevance of these research projects is reflected by
the solicitation of Henry and Wen to teach courses
on New Separations and Heat Transfer in Fluid-
ized Beds for the AIChE Today Series.
Graduate students are encouraged to take an
active role in the department's research activities.
Besides the M.S. Ch. E., for students who have
earned a B.S. Degree in ChE, students who hold
a baccalaureate degree in ChE, in other fields of
engineering, or in the physical sciences may work
toward the M.S.E. in a broad interdisciplinary
program.
Some of the projects in which these students
are involved include fluidization, materials sci-
ence, separation processes, simulation, and op-
timization. Interdisciplinary research has also
been conducted in biomedical engineering.
For the past fiscal year, $1,200,000 in federal
funds have been awarded to the College of Engi-
neering for research in the coal/energy field. The
energy research program is diverse, e.g., projects
are underway on energy policy, energy farming,

A.F. GALLI GL BLACKSHAW J.D HENRY JR R.G BAILIE
JD HENRY JR J D. HENRY JR J.T SEARS AF GALLI
OG NICHOLS AW PAPPANO C.Y WEN CY WEN
C Y WEN C.Y WEN

DG NICHOLS
C Y WEN

Students in the PRIDE program work in laboratories
with faculty supervision. Here Dr. Duane Nichols is
shown with student.
to pursue their careers. Some go to work in cities
and towns in all parts of the country. Others stay
here to apply their technical skills to the develop-
ment and implementation of the potential of West
Virginia. O

ACKNOWLEDGEMENT
The faculty expresses its sincere thanks to
Susan S. Dotson for writing this article and
Marian W. Jones for her editorial work.

letters

Sir:
Since it is the only one of its kind, your readers may be
interested in learning of the publication of the book Com-
prehending Technical Japanese, written by E. Daub, R. B.
Bird and N. Inoue and published by the University of Wis-
consin Press. We hope it will be a useful teaching book and
research tool for engineers and scientists.
R. Byron Bird
University of Wisconsin

CHEMICAL ENGINEERING EDUCATION

and tertiary oil recovery in addition to coal con-
version. Almost half of these grants were admin-
istered by the ChE faculty. In addition, grants
have been received for research in such diverse
areas as dual functional separations, polymer
processing and biomedical engineering.
From the state's earliest days, West Virginia's
mountaineers have had a reputation for bold
thought and decisive action. These characteristics
are reflected in the innovative curriculum and far-
sighted research objectives developed by WVU's
Department of Chemical Engineering. Confident
of their preparation, students leave the university

'3'; 1 \ A '

SELF-INSTRUCTION IN THERMODYNAMICS

FRANK M. TILLER
University of Houston
Houston, Texas 77004

ALTHOUGH SUBSTANTIAL attention has been fo-
cused on self-paced instruction in engineering, the
majority of courses continue in the traditional form of
professorial lectures. A middle path can be followed in
which a portion of the material is presented in the form
of "written lectures" akin to, but different from SPI. In
the self-instruction (not self-paced) technique, standard
lectures can be intermixed with written lectures. Students
come to scheduled classes and read rather than listen. A
monitor is available to answer questions. With the two
lectures described in this article, there were few questions.
The students appeared to understand the material. None
were able to complete the entire assignment in the 1.5
hour (30 minutes) second period.
The self-instruction process represents a moderate step
away from classical procedures. The advantage is that
students continue to attend class and do not have to break
abruptly from accustomed practice. At the same time, part
of the responsibility for learning as in SPI is transferred
to their shoulders. If half of the lectures in a course were
given with the self-instruction system, one instructor and

LA-

Frank M. Tiller, M. D. Anderson professor of Chemical Engineering
and Director of International Affairs obtained his bachelor's degree
from the University of Louisville in 1937 and his PhD from the Uni-
versity of Cincinnati in 1946. In 1962 he was awarded a Doutor
Honoris Causa by the University of Brazil. He has been a staff mem-
ber at Cincinnati, Vanderbilt, Lamar Tech, and the Instituto de Oleos in
Rio de Janeiro. As consultant, adviser and coordinator, his services
have been rendered through a variety of organizations including the
Fulbright Commission, Organization of American States, and Agency
for International Development.

assistant could handle two sections with substantial sav-
ings in time of senior personnel.
The author decided to test the self-instruction technique
with fundamental and presumably difficult topics, (1) first
law of thermodynamic and (2) entropy. No statistical con-
trol evaluation was carried out. Informally it was learned
that good students developed excellent comprehension of
the subjects; and poor students performed about as ex-
pected.
The following material is exactly as presented to stu-
dents except for portions which were omitted for editorial
purposes.

FIRST LAW OF THERMODYNAMICS

THIS "LECTURE" IS PART of an experiment
to see if it is possible to present effectively a
portion of the material in EGR 234 in written
rather than oral form. The topics discussed in this
"lecture" are equivalent to those which would be
given by the lecturer. The material represents the
single most important principle in the course of
thermodynamics. It is a building block for all sci-
ence and engineering. It is essential that every stu-
dent has a thorough mastery and understanding of
the subject.
It is the object to present the underlying basis
for the first law of thermodynamics also known as
the law of conservation of energy. The concepts
which are necessary to an understanding are as
follows:

* Work and heat
* Properties and non-properties, point and path functions
* Tests for exact differentials in the form

aP aQ
a. dz = Pdx + Qdy is exact if ay - a

b. fc dz =0

Note: Line integrals formed a part of prior lectures.

BACKGROUND MATERIAL

The concept of work and quasiequilibrium
processes is important to the first law. (At this
point a reading assignment is given.) The authors

SUMMER 1975

(of the book assigned) imply that a quasiequilib-
rium process is inherently frictionless. That is
not true. A quasiequilibrium process can be car-
ried out with as well as without friction. A body
can be moved very slowly up a frictional plane. A
piston moving in a heat engine could work against
an internal friction generating device. Therefore,
the term quasiequilibrium as used by the authors
should always be accompanied by the adjective
frictionlesss". In general, thermodynamicists use
the term "reversible process" as equivalent to the
works frictionlesss, quasiequilibrium process". I
use the expression frictionall quasiequilibrium
process" to describe a large group of operations
which are not reversible.

WORK AND HEAT

T HE CONCEPTS OF WORK and heat are es-
sential to the development of the first law.
Heat is a transitory phenomenon which represents
the passage of "something" between bodies having
different temperatures. Work is similarly another
transitory phenomenon which results from me-
chanical, electrical, magnetic, or gravitational ef-
fects. After establishing the concept of "conserva-
tion" of the effects to be studied, work and heat
will be viewed as energy in transitory passage
from one body to another.
You should be clearly aware that d'W is a path
function. Written in the form for a frictionless,
quasiequilibrium process involving only work of
expansion, we have

d'W = pdv (1)
W is given by the area under a curve connecting
A to B. (Two paths connecting the same endpoints
are presented in a figure). As the areas under the
curves are different, W is a path function and not
a property of the system.
As we do not as yet have variables which give
Q in the form YdX, it is not so easy to show that
Q is a path function. However, if we resorted to
experiment we should discover that heat trans-
ferred depends upon the path.

HISTORY OF THE FIRST LAW

A HISTORICAL APPROACH to the first law is
helpful in an analysis of the fundamental un-
der-pinnings. Before work could be quantitized
and defined, the science of mechanics had to be
developed. That required an understanding of mo-
tion or the inter-relationships of mass, velocity,

and acceleration. Accurate clocks were essential to
measurement, and no serious progress was possi-
ble prior to the development of accurate measure-
ment of time. Sun dials were of no value, and
water clocks offer a dubious means to satisfactory
experimentation. The pendulum clock was one of

In the self-instruction (not self-paced) technique,
standard lectures can be intermixed with
written lectures. Students come to scheduled
classes and read rather than listen.
A monitor is available
to answer questions.

the first instruments to permit reasonably precise
measurement.
A study of falling bodies was one of the im-
portant first steps in modern mechanics with the
recognition of the difference between velocity and
acceleration. Out of the Gallileo experiments at
the Leaning Tower of Pisa came the basis for the
first form of the law of conservation of energy in
the form:

v = V2gz (2)
where v is the velocity and z the distance of fall
from rest. Equation (2) can be manipulated into
a more general form
V2 V12
2g 2g
Later Bernoulli modified Equation (3) for a
flowing fluid and arrived at
p v2 pi v12
w + 2g z = w + -+z (4)
where p is the pressure and w the specific weight.
Although different language was employed, Equa-
tion (4) represented the first law of the conserva-
tion of mechanical energy.
Simultaneously with development of mechan-
ics, experimental studies in heat were taking place.
Just as the clock was basic to mechanics, the
thermometer played a similar role in the science
of heat. Fahrenheit produced the first reliable
mercury thermometer in the early part of the
eighteenth century just as the steam engine and
industrial revolution began to emerge. The therm-
ometer permitted studies to be made in a variety
of areas including irreversible mixing of hot and
cold bodies. From such experiments came equa-
tions of the form

CHEMICAL ENGINEERING EDUCATION

mC, (T1 - T) = m,C, (T - T,) (5)

where T is the final temperature and T, and T2 are
the initial temperatures. Equation (5) represents
a form of conservation of heat energy.
The idea of "heat energy" is foreign to modern
thermodynamicists. As pointed out earlier, heat is
a transitory phenomenon and therefore not some-
thing which is indestructible and conserved.
Nevertheless, the caloric theory of heat evolved
upon the basis that heat was an imponderable (no
mass) fluid which could neither be created or
destroyed.
Thus, at the beginning of the nineteenth cen-
tury, there were two important theoretical prin-
ciples which might be referred to as:

* Conservation of mechanical energy
* Conservation of heat energy

During the first half of the nineteenth century, a
basis was laid for unifying the two principles
which at that time appeared to be irreconcilable
to many scientists.
The principle of conservation of energy was
developed on slim evidence. A highly specialized
case was extrapolated into a great law. The sec-
ond law of thermodynamics was established be-
fore the first law in Carnot's remarkable writings,
the numbering of the laws having nothing to do
with their chronological development.
A number of people contributed to the develop-
ment of the first law and to the demise of the
caloric theory. The problem of friction entered
heavily into the debate over the energy laws. It
was known that mechanical actions such as canon
boring produced large amounts of heat. It was
reasoned that an "imponderable" fluid was not a
reasonable hypothesis. Basically it was found that
the frictional work as measured by the number of
turns of a frictional device was proportional to the
increased length of a mercury column in a small
bore tube (as shown in a figure). The turns were
considered to be proportional to work and the
length of the mercury column (temperature) pro-
portional to heat absorbed by the cooling water.
Stated mathematically

d'W - J d'Q (6)
where the arrow indicates the work was converted
to heat but the process (by the second law) could
not be reversed. It was a one way frictional proc-
ess in which mechanical energy disappeared and
the cooling water became hotter.

It is interesting to note Equation (6) depends upon the
straightness of the line. If the data had yielded a curve,
say a parabola of the form W = KT2 instead of W = KT,
no one would have presumed there was a direct, linear re-
lation between Q and W. If water with dye had been used
as a thermometer, the results would have been drastic,
near 40C, where water has its maximum density. (A figure
demonstrates the minimum length of the water column and
the lack of linearity. The curve is double-valued). We can
philosophize over what might have happened if the length
of the mercury column had not been approximately pro-
portional to what we call "temperature" today. Even with
mercury, the expansion is not quite linear with tempera-
ture. There is no question but that the line shown would
not be straight for any carefully done experiment. Never-
theless, a true spark of genius led scientists to assume
Equation (6) was valid under all circumstances and to ad-
just the specific heat of various substances to force Equa-
tion,~(6) to remain valid. That has turned out to be a
truly monumental "fudge factor" methodology.
On performing the reverse process of adding
heat to a gas or vapor as in a steam engine, it was
discovered that the work was not all changed into

Nevertheless, a true spark of genius
led scientists to assume Equation 6 was
valid under all circumstances and to adjust
the specific heat of various substances
to remain valid. That has turned out to be
a truly monumental "fudge factor" methodology.

heat so that we may write
d'Q - d'W = dz (7)
where dz simply represents the difference between
the heat added d'Q and the work of expansion d'W,
both of which are inexact differentials. It would be
quite natural to inquire about the properties of z.
Is it an exact or inexact differential? If it is exact,
it is a property of the system. If it is inexact, it is
kin to Q and W in that it, is a path function.
If the process involved only reversible work of
expansion, d'W could be written as
d'W = pdV (8)
and (7) would become
dz = d'Q - pdV (9)
We do not know whether to write dz or d'z.
Before reading further, attempt to answer the
following questions. Spend no more than five min-
utes on the questions, and then turn the page and
read the commentary.
1) What is your opinion about the probability of dz being
(Continued on page 140.)

SUMMER 1975

CARBERRY'S ULTIMATE PAF

ARIS McPHERSON RUTHERFORD
University of Minnesota
Minneapolis, Minnesota 55455

WITH THE PROBLEM of a bloated literature
with us so much these days, it was encourag-
ing to learn recently [1] that one particularly pro-
lific contributor at least had written his last paper.
The announcement was made whilst the cardinal's
nephew was travelling incognito in Italy, but it is
confidently rumoured that he returned from Rus-
sia with such love that he is now lost in the deeper
anonymity of matrimony, thus putting a term to
his publication list-at least for a time.
While he is to be congratulated on his deter-
mination to add no more to that superabundance
of papers, concerning which it is frequently and
truly said "the burden of them is intolerable", it
would seem only proper to honor the imperishable
memory of so great a publisher by giving an ac-
count of his last work. After all, Carberry was
the founder and president of the Lucrezia Borgia
Society [2] and the only recipient of the University
of Minnesota's prestigious Wet Test-Meter (what-
ever that may be) Award. The reader should be
warned however that Carberry's work is neither
clear of form nor elementary of content and
though the present editor hopes that his long
friendship with the author will allow him to ex-
cogitate the main ideas, he is well aware that his
efforts are only preliminary and that the full ex-
egesis will give scope to not a few PhD students.
The manuscript which has come into the ed-
itor's hands is a palimpsest, a bundle of foliae
rescriptae. It is written in a crabbed script rem-
iniscent of the darkest Borgia period; the paper
itself, the underneath script, is indeed so illegible
that the editor is forced to adopt an almost nar-
rative style in this preliminary exposition. (The
upper script is an indescribable cursive and caused
the editor a great deal of confusion until he dis-
covered that it was the game plan for an Interhall
football foray, cribbed, if you please, from the
little known monograph "American football-a
guide for interested Scots" [3] published by the

Copyright 1975 Minneapolis Star and Tribune Company.
A. McPherson Rutherford was born 45 years ago in Strath Spey,
where he grew up with a natural bent for distillation and graduated
with distinction from the Glenlivet Institute later becoming chief tester
of the famous Strath Spey Distillation Company. Author of "Sampling
Techniques" (1957) and "Distillation Procedures" (1963), both pub-
lished by the Drambuie Press, he has lately turned his talents to
mediating the American sports scene to British readers in a series of
books "American X - a guide for interested Y" where X = (Football,
Baseball, Basketball) and Y = (Scots, Englishmen, Welshmen). Professor
Rutherford is listed in Who's Who in America.

Drambuie Press in 1960. Unfortunately this pro-
vides us with no clue for dating the paper.) The
text is in Italian (suggesting that it was com-
posed at that intermediate stage of inhibition at
which the language comes most naturally to him)
and parts are in terza rima to which the editor's
halting prose does less than justice. However the
authenticity is unquestionable since under a
broken-backed T-bone formation a colophon may
be discerned-apud laboratorium catalyticum
nostre damensis-a hybrid formula of doubtful
latinity but known to be used by clerks of that
institution.
The title, as before announced, is "Nth-order
adiabatic reaction in a plate and frame filter
press". The editor, innocent of such marvels as a
p. and f.f.p., was relieved to find that such carnal

CHEMICAL ENGINEERING EDUCATION

knowledge was unnecessary for the MS begins
"Let H be a plate and frame filter press in which
the reaction aA + bB -* j C takes place." At first
blush we feel that here is a mind of hyper-
Boudartian asceticism [4] at work, for not only
are the chemical species abstracted but the very
reactor itself has become generalized. However
there may be a Titchmarshian picturesqueness [5]
hidden in the symbols for reactants and their
stoicheiometric coefficients which are more than
likely to mean "an Ancient & bountiful Bourbon".
(An alternative interpretation, that relates A to
Antoinette, B to bread and C to cake, fits the ac-
tion of the filter but fails on historical and
linguistic grounds, since A, P and B would have
to be used and the attribution to Marie-A is
questionable [6]). It is to be noted that the
stoicheiometric coefficient of the product is posi-
tive since only an electrical engineer would be
guilty of the barbarism j2 =- 1. After this aus-
picious beginning the text degenerates rapidly
and it is difficult to discover what value or values
of N the author had in mind. It appears that a
cake gets plastered in or on II and rapidly builds
up to such a thickness that N becomes 1/2 (N + 1)
with dire consequences. The reaction is exothermic
so that the cake is baked in situ and in the experi-

The Short Happy Life
It pops up on page 2,672 of the current edition
of "Who's Who in America," a thirteen-line biog-
raphy set between those of James Merle Ruth
("food co. exec.") and David Ross Rutherford Jr.
("educator"). The luminary is Aris MacPherson
Rutherford, a Scottish-born professor who gradu-
ated from the "Strath Spey and Glenlivet Institute
of Distillation Engineering," is a trustee of the
"Scottish-Greek Friendship Foundation" and has
written a book called "American Football: A
Guide for Interested Scots."
Aris MacPherson Rutherford is also a phony.
For the first time in its 78-year history, "Who's
Who," that fusty arbiter of American celebrity,
has been victimized by a hoaxer. The confessed
perpetrator is Rutherford Aris, 45, a normally no-
nonsense professor of chemical engineering at the
University of Minnesota. A while back, Aris, who
was already listed in "Who's Who," received a
biographical form from the reference book's pub-
lisher addressed to "Aris Rutherford." Aris as-
sumed correctly that the name transposition was
a computer error and let it pass, but a rather
pompously insistent follow-up letter convinced

mental section there is a record of one run (an
assistant K. Alfred was in charge) which ran
away to such high temperatures that II was ruined
and had to be thrown out. Carberry evidently be-
lieves that gamma radiation will fix this-or at
least fix Alfred.
There are several other esoteric effects that
Carberry considers in his terse and lapidary style
and it is with mingled emotions that we recall
that this is to be his last paper. It is perhaps proof
of the proof of the reactants that he finally lumps
together many of these-diffusional intrusions,
monoliths, filter cloths, something called naptha-
lene, inverse kinetics, carbon monoxide and much
more-and uses his poet's license to dismiss them.:
Non ragioniam di lor, ma guard, e pass.
(Let us not speak of them, but look and
pass on). O

REFERENCES
1. Chem. Eng. Educ. 8, 2 (1974).
2. Chemtech. Feb. 1974, p. 124.
3. Who's Who. 1974-75 Edn. 2, 2672.
4. Boudart, M. Kinetics of chemical processes. Prentice-
Hall. 1968. p.v.
5. Titchmarsh, E. C. Introduction to the theory of Fourier
integrals. Clarendon Press. 1937. p.v.
6. Oxford Dictionary of Quotations. 2nd Edn. 329:18.

of Aris Rutherford*
him that "Who's Who" was "begging to have its
leg pulled." Since Aris Rutherford sounded Scot-
tish, the professor meshed the fictional specialty
of "distillation engineering" with the name of
Glenlivet, a label familiar to lovers of unblended
malt whisky.
This is not the first time that the 70,000-odd
entries in "Who's Who" have included a fake. In
order to discover those who use "Who's Who" as
a source for mailing lists, the book's Chicago-
based publishing firm occasionally inserts bogus
biographies using employees' home addresses.
"But I know of no other instance," sighs Kenneth
Petchenick, the firm's president, "where a made-
up biography has gotten in from the outside."
After The Minneapolis Star exposed the hoax,
Aris sent an apologetic letter to Petchenick, al-
though he had already submitted an update on
Rutherford's record to include the title of his
latest book: "American Baseball: A Guide for
Interested Englishmen."

*Copright 1975 by Newsweek, Inc. All right reserved.
Reprinted by permission.

SUMMER 1975

l classroom

Metkhd oa Caatdeadticd

TRANSIENTS IN PLUG FLOW SYSTEMS

L. T. FAN and S. H. LIN
Kansas State University
Manhattan, Kansas 66506

T HE PLUG FLOW MODEL, along with the
completely stirred tank model, may be one
of the most basic or elementary flow models in
chemical engineering. This is hardly surprising
because of the tubular nature of many of the
equipment employed in a variety of continuous
chemical systems and processes such as chemical
reactors, heat exchangers, gas adsorption, extrac-
tion, and adsorption. Many steady state design
equations for these processes are based on the
plug flow model (e.g. see Perry and Chilton, 1973).

S. H. Lin was born in Kaohsiung, Formosa on September 7, 1940.
He received the B. S. degree from Chung Yuan College in 1965, the
M. S. degree from National Taiwan University in 1968 and the Ph. D.
degree from Kansas State University in 1974.
From 1968 to 1970 he was an instructor at the Department of
Chemical Engineering, Chung Yuan College. He is currently a lecturer
in the Department of ChE., University of Melbourne, Australia par-
ticipating in research and teaching activities in water pollution control
and biochemical engineering.

L. T. Fan was born in Formosa on August 7, 1929. He received the
BS degree in ChE. from the National Taiwan University in 1951, the
MS degree in ChE. from Kansas State University in 1954, and PhD'de-
gree in Chfifrom West Virginia University, Morgantown, in 1958. In
that same year he joined the faculty of Kansas State University, where
he is now Professor and Head of Chemical Engineering, and Director
of the Institute for Systems Design and Optimization. He has published
two books and numerous technical papers in chemical reaction engi-
neering, environmental pollution control, energy resource conversion,
systems engineering, fluidization, and related fields.

These processes as well as other chemical pro-
cesses, are often operated under transient or un-
steady conditions during start-up and shut-down.
They are also constantly subject to environmental
disturbances and changes in feed conditions.
It appears that, in spite of its importance, the
elementary analysis of transient characteristics
of processes represented by the plug flow model
has seen only limited coverage in undergraduate
textbooks in process dynamics and control, reac-
tion engineering, transport phenomena, and pro-
cess design. This contrasts sharply to the situa-
tion for processes described by the completely
stirred tank model.
The deterministic mathematical representa-
tion of a plug flow process under transient condi-
tions is a first order, one-dimensional partial
differential equation (hyperbolic PDE) or a set
of such equations. This note contains tutorial ma-
terial for solution of a first order partial differen-
tial equation by means of a well-known technique,
namely the method of characteristics (Abbott,
1966; Acrivos, 1956; Aris and Amundson, 1973;
Courant, 1962; Lapidus, 1962; Liu, Aris, and
Amundson, 1962), which is suitable for presen-
tation to undergraduate classes.

BASIC PRINCIPLE

T HE GENERAL EXPRESSION for a first-
order, one-dimensional partial differential
equation can be written as

A(T, t, x) T + B(T, t, x) R(T, t, x) (1)

subject to
T = To(x) att = 0, x > 0 (2)
T = Ti(t) att > 0, x =0 (3)
in which T denotes the dependent variable, t the
time variable, x the space variable, and R (T, t, x)
the source or sink term. A (T, t, x) and B (T, t, x)
represent arbitrary functions of T, t and x or a
constant,
As indicated by Eq. (1), the solution for T
can be expressed in terms of t and x; hence, the
total differential of T can be written as

CHEMICAL ENGINEERING EDUCATION

dt + dx = dT (4)
-t ax
Since the solution of Eq. (1) should also satisfy
Eq. (4), there exists a parameter a such that
A(T,t,x) = adt, B(T,t,x) = adx, R(T,t,x) -
adT or

dt dx dT 1
A(T,t,x) - B(T,t,x) - R(T,t,x) - a

Equation (5) can be rewritten as

dx B (T, t, x)
dt - A(T,t,x)

dT R (T, t, x) (
dt - A(T,t,x)

Equations (6) and (7) should satisfy the condi-
tions given by Eqs. (2) and (3).
The original partial differential equation, Eq.
(1), now is transformed into two ordinary
differential equations, Eqs. (6) and (7). The first,
Eq. (6), represents the so-called characteristic
lines along which the second, Eq. (7), is integrat-
ed. Both Eqs. (6) and (7) can be integrated
either analytically or numerically. It should be
noted that a set of these two equations is not an
approximation to the original partial differential
equation. However, approximate or exact solu-
tions can be obtained for these two equations de-
pending on their complexities.
The integration of Eqs. (6) and (7) subject
to the appropriate conditions can be graphically
interpreted by Fig. 1. In this figure, the indepen-
dent variables, t and x, are chosen as two co-
ordinates, and the magnitude of T, if shown, will
appear as a line segment perpendicular to the
(t - x) plane. The curves, i.e., characteristic
lines, originating from the t-axis or the x-axis
represent the (t - x) relation determined by
integrating Eq. (6). The characteristic line
passing through the origin divides the (t - x)
plane into two regions: the upper left region, and
the lower right region. In the upper left region
the dependent variable, T, can be obtained by in-
tegrating Eq. (7) and by using the condition
given by Eq. (3). Therefore, starting from a cer-
tain point on the t-axis, the values T can be deter-
mined for every point along the corresponding
characteristic line. Similarly the values of T on
the lower right region can be obtained by inte-
grating Eq. (7) with the condition given by Eq.
(2). Note that there exists a discontinuity in the

AX
0 T=To(x); t=0, x-O
FIGURE 1. Representation of the characteristic lines in the (t-x) plane.

values of T along the characteristic line passing
the origin if T1 (0) f To (0).
The characteristic lines shown in Fig. 1 are
projections down from the three-dimensional
space. They are plotted parallel to each other in
this figure for clarity. In reality, the characteristic
lines may not be so simple especially when A and
B are strongly nonlinear functions of T, t, and x.
They may become twisted as the value of T
changes, and projections of them down from the
three dimensional space to the (t - x) plane may
lead to their crossing.

EXAMPLES
T WO EXAMPLES ARE GIVEN here for illus-
tration. Consider the linear partial differen-
tion equation
C + a = -kC (8)
at ax
subject to

C =0 at t 0, x> 0
C = C at t > 0, x = 0

(9)
(10)

Equation (8) represents the start-up of an iso-
thermal plug flow reactor, with a first order
chemical reaction. The reactor contains no reac-
tant initially and is then fed with a reactant with
a fixed concentration of Co. In reality, per-
formance equations of numerous processes such as
ion exchange, gas adsorption and heat transfer
which take place in a long tubular system can be

SUMMER 1975

0 0.5 1.0 15 2.0 2.5
T
FIGURE 2. Concentration vs. distance for the first example.

transformed into the form represented by Eq.
(8) by simple linear transformation.
For simplicity, the following dimensionless
groups* are introduced:
C xk
e = co, 0 = kt, T =

Then Eqs. (8), (9) and (10) can be rewritten

q = 1 at 0 > 0, 7 = 0 (18)
Integration of Eqs. (15) and (16) yields, respec-
tively,

7= 0 + AO
- = Ae-'

(19)
(20)

where AO and A are integration constants to be
determined.
For the condition of 0 = 0 and r > 0 which
appears in Eq. (17), Eq. (19) gives

AO > 0

which implies that

because T=O + A6. Therefore, the solution ob-
tained by using the condition of Eq. (17) is ap-
plicable when > 0 . Thus from Eq. (20), one
obtains A = 0 and

r = 0, 7 2 0
Similarly, for the condition of 0
7 = 0, which appears in Eq. (18), Eq.
AO <0

(21)
> 0 and
(19) gives

Z)0_ -ar7

subject to
=0 at = 0, 7> 0
? = at0 > 0, 7= 0
According to Eq. (5), one can write
dO dr d
1 1 - =1)

(11)

(12)
(13)

(14)

This expression can be rewritten into the follow-
ing two parts;

d-
= 1 with 0 , 7 > 0
d -

di-

C x
SCo ,0 = kt, I =l-

with

= 0 at = 0, 7 2 0

*The dimensionless groups used here are not necessarily
unique. For example, the following dimensionless groups
can also be employed in many cases.

FIGURE 3. Three-dimensional concentration plot for the first example.

CHEMICAL ENGINEERING EDUCATION

2.5
m.-. *I

(15)

(16)

(17)

which is equivalent to
T<0
because 7 = 0 + A0. Hence, the solution obtained
by using the condition, Eq. (18), is valid in the
region 7 < 0. The solution obtained by applying
Eq. (18) to Eq. (20) is
-? = e-l, 7 < 0 (22)

8=25

Equations (21) and (22) constitute the com-
plete solution of Eq. (11) subject to Eqs. (12)
and (13).
Figures 2 and 3, respectively, show the two-
and three-dimensional concentration distributions.
It can be seen in Fig. 3 that there is a discon-
tinuity in the concentration surface along the
characteristic line passing the origin.
Consider a second example which is governed
by the same partial differential equation, Eq. (11),
but subject to the following conditions;
C = Co at t = 0, x > 0, or - = 1 at 0 = 0, 7 > 0
(23)
C = Co at t > 0, x = 0, or - = 1 at 0 > 0, 7 = 0
(24)
These conditions imply that the reactor is
originally filled with a reactant having the con-
centration of the feed. Obviously, Eqs. (19) and
(20) are still applicable.
From Eqs. (19), (20) and (23), one has
r> 0

05 10 1 5

FIGURE 4. Concentration vs. distance for the second example.

1 = A e-"
(Continued on page 148.)

ARE YOU APPLICATIONS ORIENTED?

At Fluor Engineers and Constructors, Inc. our 4
billion dollar plus backlog offers all kinds of practical
applications opportunities for chemical engineers to
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At Fluor Engineers and Constructors, Inc. we de-
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industry-oil refineries, gas processing plants, and
petrochemical installations. We are very active in
liquefied natural gas, methyl fuel, coal conversion, and
nuclear fuel processing.

If you want to find out about opportunities, loca-
tions you can work in (world wide) and why Fluor is
the best place to apply what you have learned, meet
with the Fluor recruiter when he comes to your campus
or contact the College Relations Department directly.

Fluor Engineers and Constructors, Inc.
1001 East Ball Road
Anaheim, CA 92805

L U d I ENGINEERS AND
* rFLUOR CONSTRUCTORS, INC.

SUMMER 1975

(25)

__ ~

Sn N laboratory

EXPERIMENTS IN HETEROGENEOUS CATALYSIS:

Kinetics of Alcohol Dehydration Reactions

B. C. GATES
University of Delaware
Newark, Delaware 19711
J. D. SHERMAN
Union Carbide Corporation
Tarrytown, New York 10591

IN MANY INDUSTRIAL chemical processes,
the reactions are catalytic, taking place on
internal surfaces of high-area porous solids. The
chemical nature of surface catalytic sites is dif-
ficult to determine, and consequently an industrial
catalyst is chosen not from understanding of re-
action mechanism, but from results of trial-and-
error experiments designed to determine the solid
having the best combination of catalytic activity
(measured by reaction rate), selectivity (meas-
ured by product distribution), and stability
(measured by rate of decay of activity and selec-
tivity during operation). Potential catalysts are
often evaluated in continuous flow reactors at
conditions approximating those of industrial op-
eration. Products flowing from test reactors can
be analyzed efficiently by such methods as gas
chromatography or mass spectrometry, and tests
may be designed to establish from product ana-
lyses the influence of temperature, pressure, and
reactant composition on catalyst activity, selec-
tivity, and stability.
Before the development of analytical methods
like gas chromatography allowed efficient evalua-
tion of catalyst performance, there was little
quantitative data available. Early researchers in
catalysis recognized the advantages of experi-
ments that could be interpreted without the need
for frequent product analyses, and consequently
some of the most thorough investigations con-
cerned reactions of model compounds which give
gaseous products and allow rates of reaction to be
measured as rates of gas evolution. For example,
the following decomposition reactions have been

studied extensively to characterize catalysis by
solid acids and by metals [1, 2, 3]:

metal - H2 + CO0
"H -. g Ni
solid a id H 0 + CO
o'.g. A1203

solid acid
e.g. si02/A12 0

3CH3

0
�H-mC2 + H20
c\ 2

H2C=CH-CH +

solid acid + HOCH
e.g. ion-exchange 2 + O- -
resin 2H5

Reactions in this class are no longer objects
.of much research, but they retain their value as
easily accessible means for study of heterogene-
ous catalysis, a practically important subject
which is usually neglected in undergraduate lab-
oratories. Our objective is to point out a hetero-
geneously catalyzed reaction, the dehydration of
t-butyl alcohol to give isobutene, which can be in-
vestigated in a simple, inexpensive, and safe ex-
periment; yielding thorough kinetic data in a
short time. One of the recommended catalysts is
an ion-exchange resin, which is applied industri-
ally to catalyze the hydration of propylene to give
isoproply alcohol [4].

EXPERIMENTAL METHODS
TERTIARY-BUTYL ALCOHOL at its boiling
point (82.50C) undergoes no decomposition
reaction, but in the presence of an acid such as a
sulfonated copolymer of styrene and divinylben-
zene (an ion-exchange resin),

CHEMICAL ENGINEERING EDUCATION

..-CH2 - CH . --CH ..

SO3H ...-CH-CH2...

a decomposition reaction proceeds rapidly, giving
water and isobutene gas [5]. The rate of isobutene
evolution can be measured easily with a soap-
film flow meter or a wet-test flow meter. When
this rate is measured with the equipment shown
in Figure 1, the reaction rate can be measured as
a function of alcohol concentration in solution
with methylcyclohexane (expected to be an inert
diluent) and as a function of alcohol concentration
in solution with water (a reaction inhibitor).
Methylcyclohexane and water have been chosen
because each forms an azeotrope with t-butyl
alcohol at about 78�C; a range of solution com-
positions, all boiling at nearly the same tempera-
ture, can therefore be studied-and the reactants
themselves provide a thermostat.
In the suggested experiment, a series of
methylcyclohexane-t-butyl alcohol solutions is pre-
pared, and each is stored over particles of ac-
tivated Linde 4A Molecular Sieve to remove im-
purity water. In a kinetics experiment, 200 ml of
solution are charged to the reaction flask and
brought to a boil. A weighed sample of ion-ex-
change resin catalyst beads (Amberlyst 15, Rohm
and Haas) is tranfserred rapidly to the reactor
from a vaccum oven at 120�C, where it has been

FIGURE 1. Apparatus for Measurement of t-Butyl Alcohol Dehydration
Kinetics.

2.00

1.80

w J 1.60

Z 0 1.40
-o

1
02 1.20
>--

a 2

*3ian
Z00 1.00

0w 0.12
oiS

o M

-INITIAL SOLUTION COMPOSITION: 1-BUTYL ALCOHOL,
> 5.05 MOLES/LITER
>METHYLCYCLOHEXANE,
- �3.62 MOLES/LITER
-*-

- ".'s
**"

-'

INITIAL SOLUTION COMPOSITION: t-BUTYL ALCOHOL,
5.90 MOLES/LITER
0
WATER, 23.8 MOLES/LITER
- ---- 0-0- 0
o o o o oo o

0 0 0
0
o o o
o
1 5 10 15 2
10-2 x TIME, SEC

FIGURE 2. Rates of t-Butyl Alcohol Dehydration (8).

dried overnight. The rate of evolution of isobutene
is then measured periodically, about once per min-
ute, for half an hour. Typical results (Figure 2)
indicate a rapidly increasing rate of evolution as
the solution becomes saturated with isobutene.
After saturation, the rate of evolution becomes
equal to the rate of reaction, which decreases with
time as water accumulates in the reactor and in-
hibits reaction. The reaction rate characteristic of
the initial solution composition is determined by
extrapolation of the reaction rate data to zero time
(Figure 2). Rate is determined for various stir-
ring speeds and amounts of catalyst in the reactor,
and when there is no effect of either variable on
rate per equivalent of catalyst -SO, groups, de-
termined by titration (ref. 6, pp. 91-92), the re-
action is free of the influence of mass transfer in
the liquid phase, and intrinsic chemical kinetics
are determined [7].
Data for water-alcohol solutions are obtained
in a similar way; the procedure is simpler when
the water concentration is high. Then as il-
lustrated by the data of Figure 2, the solution
becomes saturated rapidly with isobutene, and
after data are collected for a few minutes, a
known amount of water is added to the reactor
and the procedure is repeated for the new solution
composition.

RESULTS

A SET OF RATE DATA is shown in Figure 3
L [8]. These results demonstrate kinetics com-
mon to many reactions catalyzed by surfaces and

SUMMER 1975

enzymes: The data represented by the dashed line
show that the reaction is approximately first
order in reactant concentration at the lowest
values, approaching zero order at high values as
the catalytic sites sulfonicc acid groups) become
saturated with reactant. The data represented by
the solid line show that water present at the low-
est concentrations is a strong inhibitor, compet-
ing with alcohol for the catalytic sites. When
water is present in high concentrations, it is no
longer an inhibitor (inset, Figure 3); the resin
becomes strongly hydrated and similar to an aque-
ous solution of dissociated acid; the reaction is
catalyzed by hydronium ions and is first order in
reactant concentration.
An interpretation of the catalyst structure
and reaction mechanism is given elsewhere with
an empirical rate equation [8]. Determination of a
non-linear rate equation to fit the data is easily ac-
complished with the least-squares algorithm of
Marquardt [9], which is a standard program avail-
able at many computer centers.

EXTENSIONS OF THE EXPERIMENT

T HE ADVANTAGES OF THIS experiment are
the ease of production of kinetic data and the
many possibilities for modification and extension.
Most of the modifications suggested in the follow-
ing paragraphs have been investigated by students
in freshman research seminars at the University
of Delaware and Massachusetts Institute of Tech-
nology.

Catalysts-The resin catalyst can be modified
easily by ion exchange, as sulfonic acid groups
are replaced by their salts.* Replacement of acid
groups markedly reduces catalytic activity [10].
The reaction is also catalyzed by many other in-
soluble acids, including commercial zeolite crack-

Our objective is to point out a reaction,
the dehydration of t-butyl alcohol,
to give isobutene, which can be investigated
in a simple, inexpensive and safe
experiment; yielding thorough
kinetic data for a
heterogeneously catalyzed reaction.

*The process of ion exchange is widely applied in water
purification, and this application of the resins is industrially
much more important than catalytic applications [9].

CONCENTRATION OF WATER, MOLES/LITER
15 50 40 30 20
S 00I
1 -BUTYL ALCOHOL- o
0 10- WATER MIXTURES 0 0
0
g
I 005
_o
0 C O0 II I I I I
0 1 2 3 4 5 6 7
o3
> -

S 1t-BUTYL ALCOHOL- , "
METHYLCYCLOHEXANE
S MIXTURES
2

/- -

C

- BUTYL ALCOHOL-WATER MIXTURES

0
0 I 2 3 4 5 6 7 8 9 10
CONCENTRATION OF !-BUTYL ALCOHOL, MOLES/LITER
FIGURE 3. Kinetics of t-Butyl Alcohol Dehydration Catalyzed by Sul-
fonic Acid Ion-Exchange Resin at 80�20C (8).

ing catalysts (used in gasoline manufacture) and
the zeolite H-mordenite [11]. The zeolites have
only about 1% of the activity of the sulfonic acid
resin per unit mass of catalyst. Soluble acids such
as p-toluenesulfonic acid** and polystyrenesul-
fonic acid (analogs of the resin) can also be used.

Reactions-Other alcohols, e.g. s-butyl alcohol,
undergo dehydration reactions to give olefins in
the presence of the resin catalyst. Reaction of
s-butyl alcohol at its normal boiling point
(99.5�C) proceeds at only about 0.2% of the rate
observed for t-butyl alcohol at its normal boiling
point.
Decomposition reactions giving carbon mon-
oxide from formic acid and from methyl and
ethyl formates have also been investigated with
the resin catalyst [13].

Reactor Design-A modified glass reactor
shown in Figure 4 (a Schwab reactor) has been
used for determining rates of reaction occurring
as vapor-phase reactants flow at steady state
through a bed of catalyst particles. Analysis of
the reactor performance has been described by

**The anhydrous acid can be prepared from the com-
mercially available monohydrate by drying under high
vacuum at 400C for 130 hours [12].

CHEMICAL ENGINEERING EDUCATION

Weisz and Prater [2]. This reactor has a sep-
arately heated catalyst section, allowing study of
reaction at various temperatures.
The reactor is suited to all the reactants and
catalysts mentioned in the preceding paragraphs.
If s-butyl alcohol is used as the reactant, then the
gas produced in the resin-catalyzed reaction is
butene-1 plus cis- and trans-2-butenes; the selec-
tivity can therefore be studied as a function of
temperature and alcohol and water partial pres-
sures [14], provided an instrument such as a gas
chromatograph is available for product analysis.
Since the resin catalyst undergoes desulfona-
tion and loss of catalytic activity during operation
at temperatures higher than about 130�C, this
reactor also provides an opportunity for evalua-
tion of catalyst stability.

Mass Transfer-Mass transfer effects in cat-
alyst particles have been observed with ion-
exchange resins like Dowex 50W-X12. This. is a
nonporous gel-form resin distinct from Amber-
lyst 15, which is a porous solid with a high in-
ternal surface area, and the interior acid groups
of the gel are inaccessible to reactant alcohol

MIXTURE OF
CATALYST

ELECTRIC
HEATING

TAPE

THERMOMETER

CONDENSER

TO GAS
FLOW METER

HEATING
MANTLE-

FIGURE 4. Schwab Reactor for Measurement of Reaction Rates with
Vapor-Phase Reactants flowing through a Bed of Solid
Catalyst Particles.

Bruce Gates has degrees in ChE from Berkeley and the University
of Washington. He worked on petroleum process development at
Chevron Research Company, and since 1969 he has been at the Uni-
versity of Delaware. His research in applied catalysis is focused on
hydroprocessing of fossil fuels and on the design and characterization
of polymeric catalysts incorporating acidic, basic, and metal groups.
John Sherman studied ChE at RPI and MIT and was a member of
the MIT faculty from 1962 until 1966. He later worked on develop-
ment of catalyst carriers and zeolites for the Norton Company in
Worcester, Massachusetts. Since 1969 he has been with the Linde
Division of Union Carbide in Tarrytown, New York, where, as a
supervisor in the Molecular Sieve Department, he is involved in de-
veloping new products for adsorption and ion exchange.

until water is present to hydrate and swell the
resin and allow passage of alcohol molecules be-
tween the polymer strands. The performance of
gel-form catalysts depends strongly on particle
size, crosslinking (divinylbenzene content), and
water content, and the effects can be measured
with the apparatus shown in Figure 1 [6].
The operation of each reactor can also be mod-
ified by inclusion of a dessicant such as Linde 4A
Molecular Sieve, which selectively adsorbs water
produced in reaction and reduces the product in-
hibition as reaction proceeds. O

REFERENCES

1. Mars, P., Scholten, J. J. F., and Zwietering, P., Advan.
Catal. 14, 35 (1963).
2. Weisz, P. B., and Prater, C. D., Advan. Catal. 6, 143
(1954).
3. Gruber, P. E., and Noller, H., Z. Phys. Chem. (Frank-
furt), 41, 353 (1964).
4. Neier, W., and Woellner, J., Chem. Technol., 95, Feb-
ruary, 1973.
5. Frilette, V. J., Mower, E. B., and Rubin, M. K., J.
Catal. 3, 25 (1964).
6. Helfferich, F., "Ion Exchange," McGraw-Hill, New
York, 1962.
7. Heath, H. W., Jr., and Gates, B. C., Amer. Inst. Chem.
Eng. J. 18, 321 (1972).
8. Gates, B. C., and Rodriguez, W., J. Catal. 31, 27
(1973).
9. Marquardt, D. W., J. Soc. Ind. Appl. Math. 11, 431
(1963).
10. Gates, B. C., Wisnouskas, J. S., and Heath, H. W.,
Jr., J. Catal. 24, 320 (1972).
11. Ignace, J. W., and Gates, B. C., J. Catal. 29, 292
(1973).
12. Zundel, G., "Hydration and Intermolecular Interac-
tion. Infrared Investigations with Polyelectrolyte Mem-
branes," p. 129, Academic Press, New York, 1969.
13. Knizinger, E., and Noller, H., Z. Phys. Chem. (Frank-
furt), 79, 66 (1972).
14. Thornton, R., and Gates, B. C., J. Catal., in press.

SUMMER 1975

An Coiwaonmenti l Gaae 7o4 o a- eo- nickel StadetUs

POLLUTION OF THE ENVIRONMENT-

CAUSES AND CURES

MARTIN C. HAWLEY, M. H. CHETRICK
Michigan State University
East Lansing, Michigan 48823
and
E. I. SHAHEEN
Institute of Gas Technology
Chicago, Illinois

DURING THE FALL of 1972 the Chemical En-
gineering Faculty at Michigan State Uni-
versity (MSU) deliberated on the idea of offering
a course to the general university student body.
These considerations were motivated to some ex-
tent by discussions by College of Engineering ad-
ministrators at Michigan State University of the
desirability and the challenge related to such an
undertaking. These two factors, in turn, were
based primarily on cost accounting methods used
by the university and an opportunity to partici-
pate in general education. Courses were beginning
to be offered by various departments and colleges
on ecology and other topics related to environ-
mental issues. We asked ourselves at that time
questions such as:
"What unique subjects related to the environment
could the Chemical Engineering faculty offer to the
University?" and "Should we really try to develop a
course of general interest?"
During this same period Dr. Hawley was working
with Dr. R. J. Forest of Catholic University on
the development of a session for the Chemical En-
gineering Division program of the 1973 Annual
Meeting of ASEE at Iowa State University on the
subject of "Courses by ChE Faculty for Non-En-
gineering Students." Dr. Forest had developed
and taught a course on pollution for the general
student body and provided us with valuable as-
sistance and encouragement during this early
planning period. Finally, late in the Fall of 1972,
the ChE faculty at MSU decided it was qualified to
teach a general course on pollution of the environ-

ment. It was our observation that many environ-
mental courses on a number of campuses were
treating, to a large extent, only the effects of pollu-
tion on the environment and were not dealing with
the total picture as related to the causes and cures
of pollution. We recognized that offering such a
course to the university community represented an
expansion of the scope of ChE and engineering
education at MSU. This matter was discussed with
Dean L. W. Von Tersch, and he encouraged the
ChE Department to develop the course. Finally,
normal channels were pursued to obtain course ap-
proval.
An outline for a course entitled "Pollution of
the Environment-Causes and Cures" was quickly
developed by Dr. C. M. Cooper, approved by the
ChE faculty, and submitted to the College of En-
gineering Curriculum Committee on November 21,
1972. It was here that this new course met its first
major roadblock. The primary issue was that each
of the other departments questioned whether ChE
was truly qualified to teach this pollution course;

It was our observation that many
environmental courses . .. were treating, to
a large extent, only effects of pollution ...
and were not dealing with the total picture
as related to the causes and cures of
pollution . . . Offering such a course ... represented
an expansion qf the scope of ChE at MSU.

when in fact chemical engineers, with their proc-
essing and chemical background, are truly
"naturals" for teaching and handling environ-
mental problems.
After considerable delay, the course was finally
approved on October 11, 1973, nearly one year
after submission. It is apparent, in retrospect, that
we had failed to communicate to the Curriculum

CHEMICAL ENGINEERING EDUCATION

Committee that this was a general course for non-
engineering students and did not really infringe
on other departmental provinces. We were en-
couraged by the Provost's Office to continue to
pursue course approval at the university level, and
within a short period of time this new course was
approved by both the special university Ad Hoc
Committee on Environmental Courses and the
university Curriculum Committee. After approval
by all parties concerned, the real work of course
planning and organizing began in order to offer
"Pollution of the Environment-Causes and
Cures" to MSU students during Spring term 1974.
We began to make decisions immediately and to
work on course format, assignment of lecture
topics, specific course schedule, publicity, adver-
tisements, et cetera.

COURSE OBJECTIVES
OUR PRIMARY OBJECTIVE in offering this
course was to contribute in a significant man-
ner, based on unique faculty expertise, to the en-
vironmental education program at MSU so that
the decision-makers of the future will be more
widely informed in their roles of solving complex
energy and environmental problems. Topics on
energy were included since energy conversion,
consumption, and availability are all directly re-
lated to pollution and environmental degradation.
It is the feeling of the ChE faculty at MSU that
ChE faculty, in general, have both the educational
background and experience required to effectively
deal with environmental and energy problems;
and hence, must interact with other sectors of our
society involved in decision-making.
It was decided to treat the subject of "Pollu-
tion of the Environment-Causes and Cures" in a
descriptive, but objective, fashion so that students
would be familiar with the nature of causes of and
approaches to solving environmental problems.
Thus, it was necessary to provide students with
factual information on the several sources of pol-
lution and environmental degradation followed by
a description and an objective assessment (includ-
ing economics) of the alternative solutions. In
this manner we were able to define the role of
technology in solving problems of the environ-
ment. In order to give balance to the course, it was
decided to invite speakers with various back-
grounds to describe the roles of other important
decision-making groups in solving problems of
the environment. Arrangements were made to
have prominent off-campus lecturers present their

views and knowledge of the roles of the public,
government, and industry in combating problems
of the environment.
It can be seen in the course outline, Table 1,
that the general theme of the role of technology is
implicit in the sense that the course was offered by

Our primary objective .. . was to
contribute ... based on unique faculty ex-
pertise, to the environmental education pro-
gram at MSU so the decision-makers of the
future will be more informed ... in solving
complex energy and environmental problems.

the ChE Department and taught to a large extent
by our faculty. The course focused on causes and
cures of environmental and energy problems and
included talks on the roles of industry, govern-
ment, and the public in solving such problems.

PUBLICIZING THE COURSE
CONSIDERABLE EFFORT and long-range
planning were required to insure the success
of this new course. Further, we recognized it
would be necessary to present this course to a
large number of students in order to make this
endeavor really worthwhile. The nature of the
course concept was such that a large lecture ap-
proach could be effective if lectures were ade-
quately organized for content and interest. We
knew organization and development of general
lectures would be a major task since, traditionally,
ChE faculty are accustomed to small classroom,
problem solving formats. Development of a good
publicity program was essential to attract a large
number of students. Thus, over the Christmas
holiday period, the top priority items were to line
up a few nationally known individuals for lectures
and to develop appropriate publicity material for
newspapers, radio, and mail campaigns. Students
at MSU pre-enroll for courses during the term
previous to that in which they actually take
courses. We timed newspaper releases and ad-
vertising to occur during the two weeks previous
to this pre-enrollment period.
The publicity campaign involved mailings of
course announcements and descriptions to stu-
dents enrolled in other environmental courses and
to student counselors. Course announcements and
descriptions were posted on bulletin boards

SUMMER 1975

throughout the campus. Approximately 4,000 of
these flyers were mailed and circulated on our
campus of 40,000 students. About ten special dis-
plays announcing this course were designed by
our Instructional Media Center and placed in the
University Library, Engineering Building Lobby,
and other conspicuous places on campus. Advertis-

The main features of the publicity program
which quite likely influenced many students
were the apparent comprehensive course
organization and the announcement that
two nationally recognized speakers,
Ralph Nader and a top oil company executive
were... to present lectures.

ing in the student newspaper and on campus radio
was done during the two week period prior to and
during the week of pre-enrollment. This publicity
campaign was quite successful in that approxi-
mately 400 students enrolled for this new course
during the pre-enrollment period.
The main features of the publicity program,
which quite likely influenced many students, were
the apparent comprehensive course organization,
and the announcement that two nationally rec-
ognized speakers, Ralph Nader and a top oil com-
pany executive, were scheduled to present lectures.
As can be seen on the course schedule, the course
was well organized in a thematic fashion and fea-
tured lectures by ChE faculty and off-campus
speakers such as Ralph Nader on "The Role of
the Public in Solving Problems of the Environ-
ment"; C. Howard Hardesty, Jr. Executive Vice-
President of CONOCO on "The Role of Industry
in Combatting Problems of the Environment";
Raymond Smit of the Michigan House of Repre-
sentatives on "The Role of Government in Solving
Problems of the Environment"; Dean Hadcock,
Vice-President of General Foods Company on
"Adulteration of Foods," and R. Nelson of Shell
Oil Company.

CLASS FORMAT

THE COURSE WAS OFFERED for three
credits (MSU is on a quarter system) to the
general student body with no prerequisite require-
ments. The class was scheduled to meet twice per
week on Monday and Wednesday evenings from
7:00 to 8:20 P.M. The evening period was selected
to minimize possible conflicts with other courses
and to make the course available to people in the

TABLE 1
Topics for "Pollution of the Environment"
Introduction of Faculty; Organization of Course; Grading
Procedures
Introduction to Course-Pollution, Energy, and Economics
Air Pollutants: Effects on Human Health, Animals, and
Plants
Air Pollution Control, Part I: Source and Control Methods
Air Pollut:on Control, Part II: Source and Control Methods
"The Role of the Public in Combating Problems in the
Environment"
Causes of Water Pollution: Source of Indentification of
Industrial Pollutants Source and Identification of Do-
mestic and Agricultural Pollutants
Water Pollution Cures: Control Methods
Pollution by Oil: Impact and Abatement
General Question and Answer Session
Mid-Term Examination
Solid Waste: Causes and Cures-Methods of Disposal &
Recycling
Noise
Technology Assessment as Related to Pollution
Adulteration of Foods
"The Role of Government in Solving Problems of Envirotf-
ment"
"The Role of Industry in Solving Problems of Environment
Advanced Energy Systems: Overall Energy Picture
Energy: Petroleum and Oil Shale; Coal; Nuclear Energy:
Solar Energy & Others
General Question and Answer Session
Final Examination
greater Lansing community. Class periods were
utilized in most cases with fifty minutes for
formal presentation of material, ten minutes for
break, and twenty minutes for questions and an-
swers. There were some modifications to this
format, especially for the distinguished off-campus
lecturers. The question and answer period was
handled by asking students to write out questions
which were collected during the break and were
then answered and discussed during the final
twenty minutes of the period.
The class, except for two occasions, met in a
large lecture hall which seated approximately 500
students and was equipped with a public address
system connected to a tape recording system. All
lectures were taped and filed in the library so that
students could review lectures or listen to those
they may have missed. Most lecturers used well
prepared slides or overhead transparencies along
with the detailed handouts, containing an outline
of the lecture and specific factual material.
Ralph Nader's lecture was held in the main
University Auditorium and was open to university
community. C. Howard Hardesty's lecture was
presented in a large lecture room containing sev-
eral hundred students and faculty and was broad-

CHEMICAL ENGINEERING EDUCATION

cast via closed circuit television to the university
community. Both the Nader and Hardesty lec-
tures were scheduled jointly with the university
seminar series entitled "Perspectives In Energy."
Six class sessions were handled by off-campus
lecturers, three lectures were presented by MSU
non-chemical engineering faculty, and the remain-
ing ten sessions were handled by ChE faculty. All
faculty- members in the ChE Department par-
ticipated in the teaching of this course.
Grading was based on multiple choice mid-
term and final examinations. Two general in-
formal question and answer sessions were con-
ducted by the ChE faculty just prior to the mid-
term and final examinations. MSU Evaluation
Services provided assistance at no direct cost to
the ChE Department on exam question editing,
typing, and administering of examinations, and
computer scoring and evaluation. The exams cov-
ered material from both lectures and the text book
[1] with approximately fifty percent (50%) of
the questions from each source.

CLASS COMPOSITION

T HERE WERE 365 STUDENTS who actually
finished the course and received final grades.
The composition of the class was as follows: Arts
majors 8%, Natural Science majors 13%, Social

M. C. Hawley is Professor of Chemical Engineering at Michigan
State University and has been on the faculty since 1964. Dr. Hawley's
researches are in areas of chemical kinetics and reactor design,
chemical separations, and energy. He teaches courses on applied
mathematics, chemical kinetics, process design and economics, and
serves as a consultant to industry on matters related to process
modeling and design and new business ventures. Dr. Hawley re-
ceived his B.S. and Ph.D. degrees in Chemical Engineering from Mich-
igan State University in 1961 and 1964, respectively. (LEFT)
Esber I. Shaheen is Manager of Education Services at the Institute
of Gas Technology (IGT) and is responsible for the preparation of
educational materials for IGT's graduate and undergraduate program
for the training of LNG Engineers in Algeria. Dr. Shaheen's record as

Science majors 18%, Human Medicine majors 2%,
Agriculture and Natural Resource majors 17%,
Business majors 7%, Engineering majors 19%,
Human ecology 3%, Education 3% and those with
no preference 10%. It is interesting to note that
the largest numbers of students were either fresh-
men or seniors. This non-homogeneity provided a
major in course presentation. This course was
taken by most students as a general elective.

STUDENT REACTION AND EVALUATION

STUDENT REACTION and input was sought
both at mid- and end-of-term via question-
naires. Over fifty percent (50%) of the students
had not taken an environmental course previously.
Students were requested to provide written com-
ments at mid-term relevant to improvement of the
course. Most comments pertained to improvement
of visual aids and to the style of lecturing. As a
result, care was taken in subsequent lectures to be
certain that visual aids could be read from all
parts of the classroom and to have the lecture
presentations become more informal. Also, most
faculty prepared handouts, containing important
information which was projected so that students
could spend their time during the lecture fathom-
ing the subject rather than writing notes. These
were all definite course improvements.

rA -

a Chemical Engineer comprises experience in both industry and educa-
tion and has authored various articles and books in the environmental
field. He received his Ph.D. in Chemical Engineering from the Uni-
versity of Tennessee in 1967. (CENTER)
M. H. Chetrick is Professor and Chairman of the Department of
Chemical Engineering at Michigan State University. He was associated
with the University of Louisville and the University of North Dakota
before coming to Michigan State University in 1963. His industrial
experience includes work with Shell Oil Company, Monsanto Company,
and Battelle Memorial Institute, as well as consulting for various
organizations. He received his B.S. from the University of Alabama and
his M.S. and Ph.D. from Ohio State University. (RIGHT)

SUMMER 1975

The Term-End Student Instructional Rating
Form indicated was generally quite favorable.
There are three other environmental courses
offered at MSU on the subjects of "Resource
Ecology and Man," "Environmental Systems,"
and "The Politics of Ecology." As part of a stu-
dent research activity, Mr. James Rye reviewed
our course relative to the other environmental
courses. [2] Mr. Rye attended all of the environ-
mental courses on a regular basis, collected hand-
outs, and interacted with faculty and students in-
volved in the courses. The following is an excerpt
from Rye's report pertaining to our course:
Chem. Engr. 222 is a very informative class. It is
basically awareness oriented, and does not venture
into developing problem solving abilities within the
student.

ASSESSMENT OF COSTS
B ASED ON STUDENT INTEREST, educa-
tional benefit to students and faculty, and
course enrollment (365 students and 1095 student
credit hours) this course appears to have been
highly successful. However, it is important to note
that there were major costs associated with the de-
velopment and operation of the course. These costs
fall into three categories: (a) Direct Expendi-
tures, (b) On-Campus Manpower, and (c) Off-
Campus Contributions of Manpower and Travel.
Estimates of these costs are summarized as fol-
lows:

$ PER STU-
COST ($) DENT QHR
Direct University Expenses $ 5,648.17 $ 5.16
On-Campus Manpower Costs 24,925.00 22.76
Off-Campus Contributions 3,968.16 3.62
Total Cost - --. - - $34,541.33 $31.54

On-campus manpower costs were determined
from estimates of time spent by each faculty
member involved on course development, lecture,
preparation, class attendance, and course admin-
istration. It is anticipated that when this course
is offered again this Spring, manpower require-
ments will be reduced for lecture preparation and
class attendance which accounted for approxi-
mately forty percent of the on-campus manpower
costs during the first offering. Course organiza-
tion, development, and administration costs would
likely continue to be about the same in order to
insure a high quality course with attractive fea-
tures to a large number of students.

The off-campus speakers were a major asset
to this course. The expenses and honorariums for
Nader and Shaheen were paid with university
funds as Direct Expenses. Lecturers Hardesty,
Nelson, Hadock, and Smit all contributed their
time and effort to this course and travel expenses
for each were covered by their respective employ-
ers, i.e., Continental Oil Company, Shell Oil Com-
pany, General Foods Company, and the State of
Michigan. In order to account for this off-campus
participation we estimated the value of the off-
campus contributions in a highly conservative
fashion.
Based on these actual expenses and estimates
of manpower and other costs, it can be seen that
for this first time offering, the course was rela-
tively expensive. In addition to these itemized
costs, during the development and operation of the
course all ChE faculty worked "overtime" on such
activities as research, proposal writing, paper
writing, and personal time to accommodate the
large time demands for this pollution course.
These would be real costs in the long-term if the
course were offered each year.
From the College of Engineering and the De-
partment of Chemical Engineering points-of-view
this course generated 1095 student credit hours.
From the university standpoint there was simply
a new course available with the associated added
benefits and costs.

SUMMARY

T HE ChE FACULTY at MSU have demon-
strated the scope of ChE education can be ex-
panded successfully to include meeting the general
education requirements of university students and
interested people in the community. If such an ef-
fort is to be undertaken at any university, it is
important to recognize the costs associated with
this expansion in scope. However, it is recognized
that such a course provides a very useful and valu-
able service to society. O

REFERENCES
1. E. I. Shaheen, Environmental Pollution: Awareness
and Control (Mahomet, Illinois: Engineering Tech-
nology Incorporated, 1974).
2. James A. Rye, "Environmental Education at Michigan
State University: A Student Reviews His Research
With Environmental Courses and The Center for En-
vironmental Quality" (Intra-Michigan State University
Communication, Center for Environmental Quality,
June 6, 1974).

CHEMICAL ENGINEERING EDUCATION

MOTO classroom --

USE OF A CONTINUOUS SYSTEM SIMULATION

LANGUAGE IN CHEMICAL REACTION ENGINEERING

R. D. WILLIAMS and D. WOLF*
University of Arizona
Tucson, Arizona 85721

M ANY PROBLEMS IN ENGINEERING, and
this is especially true in chemical kinetics
and reaction engineering, are dynamic in nature
and as such are described by differential equa-
tion. In the past, simulation of some of the more
interesting of these problems for instructional
purposes has been hampered by the lack of easy
to use solution techniques. Often the student would
become so embroiled in the method of solution that
he would not obtain the desired experience with
the physics of the problem. For example, setting
up nonlinear or high ordered linear problems on
an analog computer would involve considerable
experience with the particular computer being
used. If a digital solution was sought the student
might be involved in a nontrivial exercise in
numerical analysis. While these experiences are
not in themselves bad they do tend to detract from
the main point of the problem. The end result has
been that often these more difficult problems have
been avoided by the professor who feels he has a
time constraint to cover some given amount of
material.
User oriented Continuous System Simulation
Languages (CSSL) have been developed to the
point of practical use by undergraduate students
in the study of such advanced dynamic systems.
Experience with analog simulation and numerical
techniques may be covered more specifically in
other courses if desired, however, the availability
of powerful CSSL will be such that they will be
extensively used in industry, justifying their in-
clusion in the curriculum.
This paper is intended to briefly discuss the

*Permanent address: Weizmann Institute of Science
Rehovot, Israel and The University of the Negev Beer
Sheva,Israel

E71 ii,
David Wolf is a graduate of the Technion-lsrael Instittue of Tech-
nology, Haifa, Israel, where he received his BSc, MSc and DSc degrees
in Chemical Engineering. In 1963 he spent a year doing postdoctoral
work at Carnegie-Mellon University and from 1964 to 1966 he was
Assistant Professor of Chemical Engineering at McGill University in
Montreal. Since 1966 he has served as Associate Professor and Head
of the Isotope Separation Plant at the Weizmann Institute of Science
in Rehovot, Israel. He is also presently a Professor of Chemical En-
gineering at the Ben-Gurion University of the Negev in Beer Sheva,
Israel. During the 1972-73 academic year, he spent a sabbatical leave
at the University of Arizona. (LEFT)
Dick Williams received his undergraduate degree at Texas Tech
University and his doctorate at Princeton University, all in Chemical
Engineering. He has been at the University of Arizona since 1968
where his research has been involved primarily with chemical re-
action engineering. Current research projects include the develop-
ment of a hydrogen generator for automotive fuel applications and
a study of the hydrometallurgical leach recovery of minerals from
their ores with emphasis on characterization of the underlying mechan-
isms involved. (RIGHT)
philosophy behind such software packages and to
illustrate their successful implementation in teach-
ing an undergraduate course in chemical kinetics
and reactor engineering in the Department of
Chemical Engineering at the University of Ari-
zona. The specific simulation language used in this
course is DARE IIIB (Differential Analyzer Re-
placement, Version IIIB) which was developed
for CDC 6000 series computers by the Depart-
ment of Electrical Engineering at the University
of Arizona.

SUMMER 1975

CSSL PHILOSOPHY

A CSSL IS DESIGNED with one purpose in
mind, to solve differential equations. It con-
sists of one or several numerical integration
algorithms conveniently programmed to allow the
user to devote his attention to the problem physics
rather than the solution technique. The develop-
ment of such programs is a result of the logical
extension of the concept of analog computer simu-
lation. As digital computation speed and availa-
bility have increased they have been increasingly
used to simulate the operation of analog computers
but with much more accuracy and without the
problems involved in scaling of analog computers.
Early digital simulation languages were de-
veloped with the analog computer user in mind in
order to make his transition an easy one. Analog
signal flow diagrams were prepared as usual.
Each element of the analog computer program had
an equivalent element in the digital program. The
"connections" were then made by supplying to the
digital computer, in tabular form, the inputs and
outputs to the various elements of the model as
well as the initial conditions and problem param-
eters. More modern simulation languages are
statement oriented and users need not know any-
thing of analog computers to use them, only a
minimal knowledge of FORTRAN and differential
equations is required.

0o.4

-- - a rrot L t .

0 10 0 40 5 7
FIGURE 1: Concentration history for Example 1.

The user of DARE IIIB supplies the se-
quence of differential equations to be solved in
FORTRAN form, in any order. In addition, initial
conditions and problem parameters are specified
as is the integration algorithm to be used (cur-
rently from a selection of eight) and the integra-
tion parameters (default values are automatically
selected if the user does not specify these). Logic

FIGURE 2: Concentration history for reactive intermedi-
ate for Example 1.
control may be exercised for iterative boundary
valued problems, optimization problems and the
like. Output options include lineprinter listings
and plots, and Cal-Comp plotter displays. DARE
IIIB can handle problems with 100 parameters,
200 state variables, and 350 output variables
which is more than sufficient for most problems
of interest in the instruction of undergraduates.
More specific information on this simulation
package is available elsewhere [1, 2, 3].*

CSSL APPLICATIONS
TPHE APPLICATION EXAMPLES illustrated
are taken from a course in chemical kinetics
and reactor engineering and though specific to
chemical engineering they are typical of the larger
class of dynamic problems common to all engi-
neering and scientific disciplines. These applica-
tions are (1) the use of the pseudo steady state
hypothesis in formulating chemical reaction ki-
netic rate expressions and (2) the transient analy-
sis of Continuous Stirred Tank Reactors (CSTR).
Solution to problems of this type have been re-
ported in the literature, often obtained with great
effort. The purpose of this paper is to illustrate
the ease with which they may be analyzed in de-
tail by use of a CSSL such as DARE IIIB, making
their detailed analysis in an undergraduate course
more justifiable.

Example 1-Pseudo steady state hypothesis
When a sequence of chemical reactions occurs
which involves a very reactive intermediate, the
reaction rate expression may be considerably

*For information on obtaining this simulation package
write Dr. J. V. Wait, Dept. of Electrical Engineering, Uni-
versity of Arizona, Tucson, Az. 85721.

CHEMICAL ENGINEERING EDUCATION

simplified by assuming that since the concentra-
tion of this reactive intermediate is very small as
compared to the stable compounds, its time rate of
change in the system will be negligible, except for
a brief induction period. This assumption is
termed the pseudo steady state hypothesis. Con-
sider for example the following hypothetical chem-
ical reaction sequence.

1
A2 + B AB + A
2
3
B + A * AB
In this sequence A2, B, and AB are stable com-
pounds and A is a reactive intermediate. If these
reactions occur isothermally in a closed constant
volume reactor, species continuity requires that
Equations la-ld hold.

d [A2]
dt = - k[A2] [B] + k2[AB][A] (la)

dt

dAl = kl[A2][B] - k2[AB][A] - k3[B][A] (1c)
dt

d[AB] = ki[A2][B] - k2[AB][A] + k3[B][A] (Id)
dt

In these equations t is time, the k's are reaction
rate constants and brakes symbolize molar con-
centrations of the species enclosed. Initial condi-
tions are that [A2(0)] = [A2]o, [B(0)] = [B]o, [A
(0)] = [AB (0)] = 0. This set of coupled equations
may be simplified by making the pseudo steady
state assumption [4] for reactive intermediate, A.
This assumption requires that d[A]/dt = 0 for all
time. Equation lc then reduces to Equation 2.

[A] kl[A2]] (2)
k2[AB] + k3[B]

Replacing Equation Ic with this result then gives
a sequence of differential equations containing
concentrations only of measurable chemical
species, a desirable outcome, and the dimension-
ality is reduced by one.
Confusion in the use of this approximation
arises not from the mathematical mechanics but
from the justification for its use, i.e., it is not
intuitively obvious to the student that the approxi-
mation is a good one or under which conditions it
may be. This is where DARE IIIB comes in. Solu-

LFN = INPUT
$D1
A2. = -C11*A2*B + C12*AB*AST
AST = CII*A2*B/(C12*AB + C21*B)
B. = -C11*A2*B + C12*AB*AST - C21*AST*B
AB. = CI *A2*B - C12*AB*AST + C21*AST*B
TOTA = 2.*A2 + AST + AB
TOTB = B + AB
A21. = -C11*A21*B1 + C12*AB1*ASTI
ASTI. = C11*A21*BI - C12*ABI*AST1 - C21*AST1*B1
81. = -C1I*A21*B1+C12*AB1*ASTI-C21*AST1*81
ABI. = Cli*A21*BI-C12*AB1*AST +C21*AST1*BI
TOTAL = 2.*A21+AST1+AB1
TOTBI = 81+AB1
7/8/9
7/8/9
$SYSTEM TMAX = 100.O,NPOINT = 51$
$ST1 A2 = 1.0,B = 1.0, AB=0.0, A21 1.0,B =1.0,AST1 =0.0,
ABI =0.0$
$UND C11 = 0.1,C12 = .05,C21=1.0$
7/8/9
LIST,A2,B,AST,AB,TOTA,TOTB
LIST,A21,B1,ASTI,ABI, TOTAL,TOTB1
PLOT, A2,A21,B,B1,AB,AB1
PLOT,AST,AST1
7/8/9
7/8/9
7/8/9
6/7/8/9

FIGURE 3: Program used in solving Example 1.

tions to Equations 1 for various values of the re-
action rate constants may be easily obtained and
compared to solutions of the equations when the
approximation is made. In doing this, values of
rate constants or rate constant ratios may be ob-
tained for which the approximation is appropri-
ate. Table 1 gives the lineprinter concentration
history for the rigorous case when [A (0)] = [B
(0)] = 1 and k, = 0.1, k - = 0.05, and k3 = 1.0.
Lineprinter plots of the state variables are given
in Figures 1 and 2. In Figure 1 concentrations of
stable compounds are plotted against time for the
rigorous case (solid lines) and with the steady
state approximation (dashed line). It may be
seen that the approximate concentration histories
for these compounds are in good agreement with
the exact values. Figure 2 gives the same com-
parison for unstable intermediate, A. The
descrepancy in this case results from the non-
zero initial value of [A(0)] as given by Equation
2 when the approximation is used.
This exercise provides a better understanding
of the implications of making the pseudo steady
state assumption, but without the agony of a com-
plicated analysis. Figure 3 gives the entire pro-
gram supplied in obtaining these results.

SUMMER 1975

Example 2-Unsteady state CSTR and
steady state multiplicity

An important area of chemical reactor engi-
neering is the transient response of continuous
stirred tank reactors, especially when multiple
steady states are possible for a given set of op-
erating conditions. The possibility of multiple
steady states and stability is a new concept to
students in the reactor engineering course, but
lend themselves readily to student investigation
using a CSSL. The differential equations to be
solved in this case, with the usual assumptions [5],
are:

qpC (T -T) + US(T -T) + i(-AHr)V VpC dT
a. dt

(3a)
q. (CiF-Ci) + riV = V dC (3b)
IF dt (3b)

The kinetic rate expression, ri, is left implicit in
these equations and is specified in a separate
algebraic statement for ease in adapting the pro-
gram to investigate the effect of various types of
kinetics. For simplicity a first order irreversible

Sdt
- \

Pur Conuitiirs
(See Nomenclature for units)
S1.0 TF 300.
C = 1.0 CF .005
q = 6.0 k = 7.86 x 01
= 2000. E = 22,500.
US 1.356 T = 30E.
HR = 104 a -

Run Conditions
(See Nomenclature for units)
= 1.0 TF = 300.
S1.02
CiF .005
q 8.0 k = 7.86 x 102
S2000. F 22,500.
US = 1.356 T 305.
R = 104 a .

- stadly sta
x 1niti l Conditi I

- - state varla' trajectory

S- nasl: lane separatri
I I i I

T, �F

FIGURE 5: Phase plane plot for CSTR
steady states.

I , I

PnI 11 320 330 340 350 360

with multiple

rate expression may be used with Arrhenius tem-
perature dependence.

r. = -k C.

Sexp(-E/RT)
k = k exp (-E/RT)
0

(4a)

(4b)

/ .The differential equations may now be solved sub-
ject to an appropriate set of initial conditions,
Ci(0) and T(O).
S \Reactor conditions (adapted from Bilous and
SA Amundson [6]) which will give single and multiple
,\ \steady states are given in Figures 6 and 7.
dT _ Steady state values of reactant concentration and
t temperature in the reactor are found by setting
their derivatives equal to zero in Equations 3 and
y s solving the two resulting algebraic equations. A
S steady state lineprinter plot of these equations for conditions
x initial condition resulting in multiple steady states is given in

-- state variable trajeotor, Figure 4. The three intersection points correspond
dy state o.ns.tio. qat to the possible steady states for the conditions im-
- - steady stite conservation equations - ~- - ,
I I posed.
a0 310 1 0 330 30 0 360 A typical lineprinter phase plane trajectory is
300 310 120 330 340 350 360
, �F given in Figure 5. The existence of multiple steady
states is readily confirmed for the second set of
RE 4: Phase plane plot for CSTR with a single states is readily confirmed for the second set of
A . -.& reactor conditions. Reactor sensitivity to variables

CHEMICAL ENGINEERING EDUCATION

- 15

10

5

0

FIGUI

I I I I I

I

-

sea y sae.

other than flow rate may also be easily investi-
gated.

CONCLUSION

OBVIOUSLY MANY OTHER applications of
CSSL may be envisioned, not only in kinetics
and reactor engineering, but in other areas of
chemical engineering and other engineering and
scientific disciplines as well. These languages
should be used as instructional aids in the investi-
gation of advanced dynamic systems on the under-
graduate level. They allow considerable ease of
analysis such that the student may devote his at-
tention to a detailed study of system mechanics.
This does not constitute much of a compromise in
LFN = INPUT
$D1
CI = Q/v
C2 = -DHRXN/(RO*AA*CP)
C3 = US/(V*RO*CP)
RA = -RKO*EXP (-E/(R*TEMP))*CA
CA. = C1* (CAO-CA) +RA
CB = CAO-CA
TEMP. = CI*(TF-TEMP) + C2*RA+C3* (TC-TEMP)
7/8/9
7/8/9
$SYSTEM TMAX = 5000., DT = 0.01, DIMIN=0.01, POINT =
51$
$ST1 CA = 0.002, TEMP = 318.5$
$UND RO=1., CP=1., Q=8.0, V=2000., US = 1.356, DHRXN
= -10000., TF = 300., CAO = 0.005, RKO=7.86E+12, R=
1.9872, TC=305., AA =-1.$, E=22500.$
7/8/9
LIST, CA, CB, TEMP
PLOTXY, TEMP, CA
PLOT, CA, CB
PLOT, TEMP
7/8/9
6/7/8/9

FIGURE 6: Program used in solving Example 2.

the education process since the details of nu-
merical analysis are normally covered in other,
more basic, applied math courses. Digital simula-
tion is fast replacing analog simulation and the
modern CSSL represents an extremely high level,
user oriented simulation package. DO

REFERENCES

1. Trevor, A. B., "DARE IIIB, A Digital Simulation Sys-
tem", MS Thesis, University of Arizona, Tucson, 1971.
2. Trevor, A. B. and Wait, J. V., DARE IIIB User's
Manual, CSRL MEMO 221, University of Arizona, De-
partment of Electrical Engineering, Tucson, July 1971.
3. Trevor, A. B., and Wait, J. V., "DARE IIIB-A
CSSL-type batch-mode simulation language for CDC
6000-Series Computers", Simulation, June 1972, p. 215.

4. Benson, S. W., The Foundations of Chemical Kinetics,
McGraw-Hill Book Co., New York, 1960, pp. 50-54.
5. Smith, J. M., Chemical Engineering Kinetics, McGraw-
Hill Book Co., New York, 1970, p. 184 and 236.
6. Bilous, D. and Amundson, N. R., "Chemical Reactor
Stability and Sensitivity , A.I.Ch.E. Jour., 1, De-
cember 1955, p. 513.

NOMENCLATURE

a, Stoichiometric coefficient, dimensionless.
Ci, CiF Reactant concentration in reactor and reactor feed
respectively, moles/cc.
CP Reacting fluid heat capacity, cal./ (gm.) (OC.).
E Activation energy, cal./mole.
AHR Energy of reaction, cal./mole.
k,ko First order reaction rate constant and pre-ex-
ponential factor respectively, sec-1.
k1, k,, k3 Second order reaction rate constants, liter/ (mole)
(sec.).
q Volumetric flow rate, cc./sec.
ri Reaction rate, mole/(cc.) (sec.).
R Gas law constant, cal./ (mole) (oK).
S Heat exchange surface area, cm.2.
t Time, sec.
T,TF,Te Temperature in reactor, reactor feed, and to heat
exchange coil respectively, OC.
U Overall heat transfer coefficient, cal./ (cm.2) (oC.)
(sec.).
V Reactor volume, cc.
p Reacting fluid density, gm./cc.
[] Denote molar concentration of enclosed species.

THERMOMOMETRY: Levenspiel
Continued from page 105.
factor from our lives (all thermo students would
cheer this), that miserable gas constant. Thus,
for a mole of ideal gas

pV = RT would become pV = T
Cp - Cv = R would become C, - C, = 1,

for one mole of any substance

C, and S would be dimensionless
and the gas constant R, the Boltzman constant k,
and Avogadro's number A would be related as
follows:
k 1
R 1=1 or k= A

Imagine, the letter R would be free forever more
to play new roles. In fact so would the Boltzman
constant k. With all the new concepts of science
crying for symbols what a boon this would be.
I wonder whether a change to so pure and
rational a temperature scale could receive serious
consideration today, or is science too big, with too
much inertia? We'll see. El

SUMMER 1975

N a laboratory

DEMONSTRATING CATALYTIC

REACTOR STABILITY

R. R. HUDGINS
University of Waterloo
Waterloo, Ontario, Canada

T HE PURPOSE OF THIS communication is to
bring to the attention of the chemical engi-
neering community an example of a catalytic re-
action that among other things, can be used to
demonstrate reactor stability. The demonstration
uses very simple and inexpensive equipment, is
easy to assemble (taking less than an hour), and
is highly portable.
The reaction itself is the catalytic oxidation
of ammonia. As an example of catalysis, this re-
action is well known in various forms in the
literature on chemical demonstrations [1, 2]. How-
ever, the published accounts of it fail to appreciate
not only that the reaction is controlled by film heat
transfer, but also that the experiment can be used
for a demonstration of catalytic reactor stability.
The apparatus used in the demonstration con-
sists of:
1 200 ml erlenmeyer flask
1 pair of tongs
3 5-cm lengths of glass rod (3 mm diameter)
1 bottle of concentrated ammonium hydroxide solution
1 propane torch or bunsen burner
Several 30-cm lengths of copper wire of varying di-
ameters (AWG Nos. 12, 18, 24; see Diameters in
Table 1).
We shall first illustrate the phenomenon of
control of reaction by heat transfer across the gas
film. First, add about a 1-cm depth of ammonium
hydroxide solution to the bottom of the flask.
Then, using the No. 18 copper wire, fashion a
helix of about 3 or 4 turns 11/2 cm in diameter at
one end of the wire, and wind a turn or two
around a glass rod such that the helix can hang
inside the flask within 1/2 cm of the surface of the
ammonia solution. A schematic diagram of this
configuration is shown in Figure 1. Grasping the
wire and glass rod with the tongs, heat the copper
helix in the torch flame to incandescence (yellow-
orange). Then quickly place the wire in the flask.

FIGURE 1. Diagram of the Apparatus.
Legend: 1 - erlenmeyer flask (200 ml), 2 - copper wire, 3 - concen-
trated ammonium hydroxide solution, 4 - glass rod.
The wire will continue to glow for some time (per-
haps 10 to 15 min. or until the ammonia coming
off the solution becomes too weak to support a
reasonable rate of oxidation).
The experiment may be repeated using the No.
24 copper wire. The wire will reach yellow heat
and melt. With No. 12 wire, however, the tem-
perature will slowly decline during which the
yellow-orange glow turns dull red and is finally
extinguished. These various observations demon-
strate the control of a catalytic reaction by heat
transfer across the gas film.
Using the No. 18 copper wire, we can now il-
lustrate the phenomenon of reactor stability. With
the helix glowing in the flask, withdraw it fairly
abruptly above the mouth of the flask. The glow
should start to fade to a bright red. Immediately
replace the wire in the flask. The glow should
slowly return to the original yellow-orange colour.
If the coil is once again withdrawn, but this time
allowed to fade to dark red, and replaced in the
flask again, the glow will not return. Rather, the
glow will continue to be extinguished. This il-
lustrates the phenomenon of reactor stability.
Similar observations can be made with the No. 24
wire, except that the response time is much
smaller. Also, some practice may be required to
avoid melting the wire. With the No. 12 wire, a
demonstration of stability is not possible, since
the glow gradually declines after insertion in the
flask. Perturbing the temperature by removing the
wire from the flask simply hastens the decline.
Typical stability results are offered in Table 1.

CHEMICAL ENGINEERING EDUCATION

---~-~-~I

Some variation in these observations will occur
depending upon the precise geometry of the copper
coils, the proximity to the ammonia solution, and
the concentration of the solution. The observations
in Table 1 refer to fresh solution.
By now, an observer will have noticed a num-
ber of local changes in temperature on the surface
of the copper coils. These take the form of the
occasional flickering of the colour of the surface,
sometimes in response to movement of the coil, at
other times apparently in response to convection
within the flask. Without pursuing the exact cause
of these fluctuations, one may observe that the
temperature colour changes are fairly large, and
that they occur swiftly across the surface of the
catalyst wire, despite its thermal inertia. This ob-
servation illustrates that transient temperatures
are easily produced in catalyst particles with ex-
othermic reactions.
Finally, questions that should be asked of stu-
dents watching this demonstration include:
* What observations make it clear that the
(pseudo) steady state reaction is heat transfer
rather than mass transfer controlled?
* Estimate from the colour of the wire (or its
melting point) a temperature difference across
the gas film.
" Why does the thinner No. 24 wire become hotter
than the thicker No. 18 wire? In your answer
include the effects of radiation as well as con-
duction along the wire.
* Is conduction responsible for the gradual loss of

Robert R. Hudgins is a professor in the Department of Chemical
Engineering, University of Waterloo, Waterloo, Ontario, Canada. He
received his B.A.Sc. and M.A.Sc. degrees from the University of
Toronto and his Ph.D. from Princeton University (1964). His research
interests are the influence of diluent gases on rates of heterogeneous
catalytic reactions, catalytic reactors with oscillating inputs, and wet
air oxidation. The experiment described here was developed in 1972
during sabbatical leave at Universite de Sherbrooke, Sherbrooke,
Quebec, Canada.

TABLE 1
Typical Stability Observations
Wire gauge Diameter
No. (AWG) (in.) (cm.) Observations
12 0.081 0.21 Bright glow on entering
flask gradually fades to
extinction. Stability dem-
onstration not possible.
18 0.040 0.10 Glow readily stabilizes
at bright yellow-orange;
when small temperature
perturbation is introduced,
glow slowly recovers to
original colour; large per-
turbation of temperature
extinguishes glow.

24 0.020 0.051

Glow can increase to yel-
low heat, melting wire.
Observations similar to
No. 18 wire, but with more
rapid responses.

glow in No. 12 wire? An experimental answer
may be easiest here by cutting the helix off the
No. 12 wire sample, and holding it by a thin
wire (say No. 22 copper), heating to incan-
descence, and placing it in the flask.
*Explain by means of a diagram the return of
the wire to its former temperature after with-
drawal from and replacement in the flask. E
REFERENCES
1. G. Fowles, Lecture Experiments in Chemistry, 6th
Ed., p. 178, G. Bell and Sons Ltd., London 1963.
2. N. Nechamkin and J. J. McClarnon, p. 169, 1960 Re-
print Edition of "Tested Demonstrations", J. Chemn,
Educ., H. N. Alyea, (editor).

book reviews

Introduction to Control Systems
By D. K. Anand
Pergamon Press, Inc. 1974
Reviewed by Doug Wilde, Stanford University
This text is interchangeable with many other
books on elementary linear control theory, all of
which are good for electrical and mechanical en-
gineers, and none of which deal with chemical en-
gineering systems. There are books much more
suitable for courses taught exclusively to chemical
engineering students. Still other books would be
better for a general control course mixing chem-
ical with mechanical and electrical engineering
students. This book would be appropriate only for
a general control course not catering to chemical
engineering students at all, and it is little different
from earlier texts written for the same purpose. D

SUMMER 1975

SELF-TAUGHT THERMO: Tiller
Continued from page 117.
exact or inexact? A logical approach would revolve around
the fact that both d'W and d'Q are inexact. Work with two
inexact differentials like the following:
d'u =ydx + dy
d'v = dx + 2dy
Substract one from the other to obtain some idea of the
possibility of the difference leading to an exact or inexact
differential.
2) Test Equation (9) for exactness (if you can) by using
the relation ap/ay = SQ/ax for an exact differential of the
form dz = pdx + Qdy.
Work on these two questions before looking at the
answers that follow.
ANSWERS
1) It is demonstrated that no linear combination of certain
inexact differentials can be made exact and the following
comment added:
It would be judicious (but not necessarily correct) to
think that dz in Equation (9) was inexact.
2) Equation (9) is restricted to a reversible, quasiequilib-
rium process. Therefore, any conclusions drawn from Equa-
tion (9) will apply only to those restrictions.
Writing the equation in the form
dx = d'Q - pdV (10)
We might say the coefficients could be derived from
dz = Md'Q + NdV (11)
and apply the rule
(a ) (aN- ) (12)

Such a mathematical process would imply that Q is a state
variable, i.e., Q=f(p,V). However, Q is a path function;
and the operations used with properties like p,v,T cannot
be used with Q and Q. For example, writing
dz = d'Q - d'W (13)
it could be argued dz is exact because
a a
w (1) = 0 and (-1) = 0 (14)
Thus Equation (14) does not have the same status as
dz = dx - dy (15)
where it is obvious z = x - y.
We conclude it is impossible to apply the ap/ay = 3Q/
ax test.

INTERNAL-ENERGY
THERE IS NO PURELY mathematical method
to demonstrate the exactness or inexactness of
dz. It is necessary to resort to experiment, because
the first law rests upon the basis of factual evi-
dence. Place Equation (9) in integrated form

fc dz = c d'Q

fc d'W

(16)

in which the circuit integral starts and stops at
the same point. From the "half" law of thermo-

dynamics*, we assume there are two independent
variables, say p, T, or p, V over which the circuit
integral must be performed. In working with d'Q,
there will be portions of the cycle when Q and W
are positive or negative. Let us call the sum of all
the heat transferred to the system Q1 and all
transferred from the system Q, where both quan-
tities are considered as positive numbers. Then

fcd'Q= Q - Q = .et

(17)

where Q,,t represents the net heat transferred to
the system. With a similar situation for W, Equa-
tion (16) becomes

(18)

cdz= Qnet - Wnet

Overwhelming experimental evidence points to-

ward Q,,et = Wet and f c dz = 0. This is the es-

sential point of The Law of Conservation of
Energy: The Heart of the Subject.
The quantity z now possesses special interest
as it is a property of the system. It deserves a
name. Thermodynamicists generally call it in-
ternal energy. It represents the storage of heat or
work as they are transferred to the system. It is
frequently given the symbol U, I, or E. In accord
with the textbook, we shall choose U and rewrite
Equation (18) in the form

dU = d'Q - d'W
The integrated form is
AU = U- - U1 = Q - W

(19)

(20)

For a frictionless, quasiequilibrium process in
which there is only work of expansion
dU = d'Q - dpV (21)
Various examples involving the First Law follow.

ENTROPY
IN THERMODYNAMICS, it is frequently use-
ful to define certain quantities which appeal to
the senses like pressure and temperature or may
be conceptualized as voltage, current, and re-
sistance. In this exercise, a powerful but abstract

*In a previous lecture, students were introduced to the
zeroth law and the "half law". The latter which lies be-
tween the zeroth and first laws states that Boyle (or Mar-

riot) and Charles showed that fc dv=0 when p and T were

changed and, therefore, that v=f(p,T).

CHEMICAL ENGINEERING EDUCATION

concept which arises out of application of an inte-
grating factor to d'Q will be developed.
Our task is to seek a generalized displacement
which yields heat transferred in a reversible proc-
ess. Concepts necessary to this "lecture" are:
* First Law of Thermodynamics
* Integrating factors which turn inexact into exact dif-
ferentials

GENERALIZED DISPLACEMENT FOR
HEAT TRANSFERRED
In general, work is given by
d'W = �- XdY (1)
where X is a generalized force and Y is a gen-
eralized displacement.
X and Y are both properties, and they possess
exact differentials. W, is not a property, and its
differential is inexact. We know from the study
of differentials an inexact differential multiplied
by an integrating factor yields an exact differ-
ential. From Equation 1 we can see (1/X) serves
as an integrating factor for d'W because dY is
exact. Various kinds of generalized quantities are
shown in Table 1 along with a description of the
type of work involved.
TABLE 1

PROCESS

Fluid expansion
Elastic solid
Electric
Surface charge
Heat transfer
Mass transfer
Potential energy

GENERALIZED
FORCE

Pressure P
Force F
Voltage E
Surface tension
Temperature T
unknown X*
weight (-mg)

GEN-
ERAL-
IZED
DIS-
PLACE-
MENT

volume V
length L
charge Q
s area A
unknown Y*
mass m
distance z

PdV
FdL
-EdQ
-sdA
+ TdY
�+Xdm
-mg dz

In Table 1, it is apparent there are two missing
quantities marked by * which have not been previ-
ously encountered in non-thermodynamics courses.
If we accept Equation (1) as valid for expressing
work done in general terms, there must be a gen-
eralized displacement Y for transfer of heat. We
assume temperature is the generalized force which
causes heat to flow. That is not the only assump-
tion which could be made. From elementary ki-
netic theory, we know that temperature is pro-
portional to the kinetic energy of the molecules.
We might assume the generalized force was the
square of the velocity or the velocity of the mole-
cules. Such assumptions would lead to a somewhat

different if equivalent conclusion. To simplify the
problem, we shall assume T is the generalized
force for heat transfer.
When a crystal dissolves in a liquid, there is
necessarily a transfer of energy. In fact, any time
there is a transfer of mass from one phase to an-
other, there will be an energy transfer. Thus if a
differential mass, dm, passed from one phase to a
second, there would be an energy transfer of the
type Xdm.
Previous knowledge from non-thermodynamic
sources does not provide us with definitions of the
generalized quantities needed for heat and mass
transfer. We shall seek an answer for heat trans-
fer at this time but will postpone seeking a solu-
tion for mass transfer until we study multicom-
ponent systems and define new thermodynamic
functions such as Gibbs free energy and the work
function.
There is no general formula for finding new
thermodynamic functions. There is some contro-
versy among thermodynamicists about rigorous
methods for defining our Y in the equation
d'Q = � TdY (2)
The method which will be followed is not rigorous.
It will apply only to a specialized case of an ideal
gas in a frictionless, quasiequilibrium, non-flow
process. Thus the method applies to a highly-re-
stricted, non-existent situation. Nevertheless, the
method will produce the same answer which can
be obtained from more rigorous (and contro-
versial) methods.
We shall give the name of entropy to our gen-
eralized displacement Y before we find it. Our
method will involve integrating factors. The proc-
ess we are about to consider was commented on by
Clausius in an appendix of his book on the me-
chanical theory of heat. He recognized the lack of
rigor at that time (close to 1850).
Concepts that are needed to understand this
development include (1) integrating factors and
(2) internal energy of an ideal gas.
QUESTIONS
Take the function
z = xy + x2 (3)
and find its differential. Then divide the differential by x
to obtain a new differential du. Show du is inexact by
*The generalized forces are generally, but not always,
intensive quantities. Pressure, surface tension, and electric
potential are examples of intensive variables. The general-
ized displacements are extensive variables in that they are
dependent on length, area, volume, mass, or charge. Gravi-
tational force mg is an example of a force which is ex-
tensive rather than intensive.

SUMMER 1975

means of the 3P/ay = 3Q/Ix test. Then assume there is an
integrating factor X(x) which is a function of x alone and
find A. Attempt to find another integrating factor which is
a function of y alone.
Answer
The differential
du = (z + y/x)dx + dy (4)
is shown to be exact. Assuming X is an integrating factor,
it is demonstrated that X(x) = x and that no integrating
factor which is a function of y exists.

INTERNAL ENERGY AND ENTROPY

A N IDEAL GAS CONSISTS of point masses
having no gravitational, electrical, or mag-
netic interaction. Therefore an ideal gas can only
have translational kinetic energy. From kinetic
theory, it can be shown that

3 ( 2

Mu2 )

where u is the square root of the average velocity
of the molecules. Thus the molar kinetic energy is
directly related to the ideal gas temperature. In
fact
RT = (2/3) (molar K.E.). (6)
In deriving (5) all but translational kinetic en-
ergy has been neglected. The molecules are as-
sumed to be incapable of having rotational, vibra-
tional, gravitational, magnetic or electrical energy.
Therefore, the internal energy of an ideal gas de-
pends only on its temperature. We can write

( u
which states that
which states that

u =u(T)

(8)

The first law for a non-flow, frictionless, quasi-
equilibrium process can be written as
d'Q=dU + pdV (9)
The generalized specific heat is defined by
d'Q NCdT (10)
where C is the molar specific heat. For a constant
volume process, combining (9) and (10) yields
d'Q = NC,.dT = dU (11)
Integration gives
Q = AU = NCAT = NC,.T + U (12)
At this point, a number of examples involving
specific heats and ideal gases are presented.

SEARCHING FOR ENTROPY
WE ARE LOOKING for the generalized dis-
placement in the equation

1

* Find an integrating factor which is a function of T.
Do this work before continuing. The answer is on the next
sheet.
NOTE: Basically the student develops the concept of
entropy in this example by himself. By providing him the
appropriate catalyst, a situation is produced in which
entropy naturally falls out of the process of finding an
integrating factor for d'Q. To the equation
NRT
d'Q = NCdT + PdV = NCdT + - dV (15)
an integrating factor X(T) is applied. Then applying the
rule for exactness

(ANC,), = 0 ( NRT (16)

The product XT must be constant, and . = 1/T. Therefore,
T =dY=NC, dT +NR V (17)
T T V
It can be seen that dY is exact. We shall call it entropy and
use the letter S.

SIGNIFICANCE OF ENTROPY
IT HAS BEEN SHOWN that 1/T is an integrat-
ing factor for d'Q. Therefore, the quantity dS
= d'Q/T must be an exact differential. It fulfills
our search for a dY to satisfy the relation d'Q -
+ XdY. The question of sign has been settled; a
plus is used. Further as Q is proportional to mass
(lbs. or lb-moles), it can be written as Q = Nq.
Then

dS d'Q Nd'q Nds
T T -

(18)

and we see entropy is an extensive variable which
is proportional to mass. (In the accompanying
figure (Three graphs show x (generalized force)
vs Y (generalized displacement), P vs V, T vs S))
we see that the heat transferred is given by the
area under the T-S curve in accord with

Q =fT dS (19)
There is a direct correlation between the area

CHEMICAL ENGINEERING EDUCATION

d'Q = � TdY (13)
Basically we want to find a function which is an
integrating factor of d'Q. We do not know if T it-
self will turn out to be the function we are look-
ing for. However, we shall experiment and see
what results.
You are to do the following:
* Write the first law for a general non-flow process and
solve for d'Q.
* Assume that work is restricted to a frictionless, quasi-
equilibrium expansion process.
* Assume the gas is ideal and replace dU by NC,.dT.
* Eliminate P by means of PV = NRT.
* Place the differential of Q in the form
d'Q = AdT + B dv (14)

uP u
Dp)T =0

under the X-Y, P-V, and T-S curves. Each area
corresponds to some kind of work.
There are an infinite number of integrating
factors for d'Q. Each one would lead to an exact
differential with a new X and Y. As an example,
vk-1 where k = c,/cy is an integrating factor for
the case of an ideal gas. Thus
vk-' d'Q = dY (20)
or
d'Q = vl-k dY (21)
There is no special value attached to this XY com-
bination. Further, 1/T has general application to
all processes, although the present development
has been restricted to ideal gases. There may be
some useful integrating factors other than 1/T,
but we shall not search for them.
WHAT DO WE HAVE?

W E HAVE FOUND a function, entropy, which
is a property of the system. We shall be able
to show that entropy plays a very useful role in
thermodynamics. But that comes later. We now
ask, what do we have? Usually when a physical
quantity is defined, there is some material concept
involved which appeals to our senses. In the case
of the other generalized displacements in Table 1,
it is simple to visualize distance, area, and volume.
The concept of electric charge is not difficult to
imagine. In the case of magnetic quantities, we
have to use a little more imagination. The gen-
eralized forces can be understood in terms of
measuring instruments. Everyone thinks of a
mercury column in glass as signifying tempera-

U I-book reviews

INTRODUCTION TO PROCESS ECONOMICS
F. A. Holland, F. A. Watson and J. K. Wilkinson,
John Wiley & Sons, 290 pages.
Reviewed by James H. Black, University of Ala-
bama, University, Alabama
This book is intended as an undergraduate text
for the process engineering disciplines, such as
chemical, metallurgical, and mineral engineering.
It would also give an excellent introduction to
process economics for the practicing engineer or
serve him as an excellent reference book. It is, as
the title states, a book covering process economics;
but some wider aspects, such as some of the man-
agement sciences, are also presented.

ture. A dial on a voltmeter gives a direct reading
of voltage.
If we went deeply into measurement in a so-
phisticated manner, we would find the simple
concepts must be examined with much more care.
We would discover temperature is difficult to de-
fine precisely. In the end, we would be asking how
can we measure the variables and how can we as-
sure reproducibility and comparative accuracy.
Entropy suffers in comparison with other
physical quantities, because we have no en-
tropometer from which we can read values of
entropy. However, if we can show how to measure
entropy, that should enable us to form an intel-
lectual if not a physical notion of what it is.
Returning to the equation for an ideal gas, we
have on a unit mass basis

ds = d'q/T = C,

dv
+R
V

This equation can be integrated to give
s = C, In T + Rln v + So

As = C, In T/To + R In v/vo

(22)

(23)

(24)

These equations tell us how to measure s orAs for
an ideal gas. However, we must make measure-
ments of T and v and then calculate s. We could
develop an instrument which would translate (24)
into something which could be visibly seen. Such
an instrument would not be very useful.
We must be satisfied with a mathematical and
intellectual rather than a familiar physical con-
cept of entropy. D

The organization of the book is excellent. It is
divided, logically, into two parts: the elements of
profitability assessment and the elements of de-
cision making. Thus, the reader first gets a com-
plete treatment of time value of money calcula-
tions, followed by chapters on profitability esti-
mates, uncertainties in profitability estimates, cap-
ital cost estimates, and manufacturing cost esti-
mates. The second part of the book covers such de-
cision making tools and techniques as statistical
analysis, curve fitting and trend analysis, linear
programming, financial and cost accounting, price
and cost trends, value engineering, marketing, and
some material on risk and insurance.
This is a good book, well worth the cost. It
would be of particular interest and value to those
who found use in the recent series of articles on
engineering economics, by the same authors, in
Chemical Engineering magazine.

SUMMER 1975

Icij curriculum

GEORGIA TECH'S PULP AND PAPER

ENGINEERING PROGRAM

GEORGE R. LIGHTSEY
Georgia Institute of Technology
Atlanta, Georgia 30332

A program of technical electives in pulp and
paper engineering was established in the fall of
1974 at Georgia Tech to help meet the need of the
pulp and paper industry for engineers both well
grounded in engineering fundamentals and also
knowledgeable of the special problems of the pulp
and paper industry.
The pulp and paper engineering (PPE) pro-
gram, while centered in the Chemical Engineering
School, is multidisciplinary in nature. Five tech-
nical electives in PPE have been approved for ad-
dition to the curriculum. Three of these are offered
in the Chemical Engineering School and deal with
the basic processes required for conversion of
wood to pulp. The other two courses, a survey
course and a course dealing with paper prepara-
tion and properties, is team taught by personnel
from Ch.E. and Textile Engineering and is co-
listed in both schools.
A committee composed of faculty from the
Schools of Chemical, Textile, Mechanical, and
Ceramic Engineering and the School of Architec-
ture directs the program. An Industry Advisory
Committee made up of pulp and paper industry
leaders has been formed to help guide the develop-
ment of the PPE Program.
Georgia Tech does not plan to develop a pulp
and paper engineering degree program. The goal
of the PPE Program is an engineer completely
competent in the basic engineering fundamentals
and who also possesses special training in pulp
and paper engineering.

PULP AND PAPER MANUFACTURING is
one of the major industries in the U.S. with
manpower needs of up to 3000 new B.S. technical
graduates each year. A large number of these B.S.
graduates are employed in Georgia which is the

leading state in the production of paper products
with 20 pulp and paper manufacturing plants.
A survey in 1970 by the Technical Association
of the Pulp and Paper Industry (TAPPI) found
that about 80% of the new B.S. graduates hired
by the pulp and paper industry had no special
training in pulp and paper engineering. Conse-
quently, most pulp and paper manufacturers must
devote the first 3 to 12 months of a new engineer's
employment to on-the-job training in the basics
of pulp and paper engineering. This often results
in low productivity for an extended period of time
for the company and a feeling of futility by the
new engineer.
An interesting result revealed by the TAPPI
survey was that many pulp and paper companies
felt that graduates from pulp and paper degree
programs who were trained in pulp and paper
technology were lacking in engineering funda-
mentals. The pulp and paper industry, the survey
showed, wanted engineers (usually Ch.E.) both
well grounded in engineering fundamentals and
also knowledgeable of the special problems of the

The pulp and paper engineering
program is centered in the Ch.E.
school and offers five technical
electives for addition to the
curriculum.

pulp and paper industry. A program of technical
electives in pulp and paper engineering was estab-
lished in the fall of 1973 at Georgia Tech to help
meet this industry need.

COURSES TAUGHT

THE PULP AND PAPER engineering (PPE)
program, while centered in the Ch.E. school, is

CHEMICAL ENGINEERING EDUCATION

engineering school with the mechanical engineer-
ing school providing guest lectures on forestry
operations. The steps in the kraft process required
to convert wood into pulp are covered. Also, the
kraft chemical recovery process is outlined. A de-
scription of the common bleaching steps in a kraft
mill completes the course. Since most pulp mills in
the Southeast use the kraft process an entire
course was devoted to a detailed description of it.
The third course in the series, "Pulp and Paper

George R. Lightsey earned a B.S. in ChE. from Mississippi State
University in 1965 followed by a Ph.D. in ChE. in 1969 from Louisiana
State University. Following a 21 month tour of duty in the U.S. Army,
during which he was assigned to NASA-Lewis Research Center, Cleve-
land, Ohio, he was employed by Buckeye Cellulose Corp. in Memphis,
Tenn. In Sept., 1973, he came to Georgia Tech as an assistant profes-
sor in ChE. He is currently chairman of the multi-disciplinary Pulp and
Paper Engineering Committee.

multidisciplinary in nature so that students from
any engineering discipline may participate. A
committee is composed of faculty from the schools
of Chemical, Textile, Mechanical, and Ceramic
Engineering and the School of Architecture di-
rects the program. Five technical electives in PPE
have been approved for addition to the curriculum
(Table I). The first of these, "Survey of Pulp and
Paper Technology", is a course dealing with all
aspects of pulp and paper manufacturing. It is
team taught by personnel from Chemical and
Textile Engineering and is co-listed in both
schools. This course is designed for students who
may not have a strong interest in pulp and paper,
but want a general understanding of the industry.
The first half of the course is taught by chemical
engineering faculty and includes an introduction
to the chemical and physical properties of wood.
The major pulping and bleaching processes are
also described. The second half of the course is
taught by textile engineering faculty. The funda-
mentals of paper making are covered with em-
phasis on the physical and chemical methods of
fiber modification. The operation of a paper ma-
chine is described. Methods for testing paper and
uses of paper products completes the course. The
text for this and all the PPE courses is Handbook
of Pulp and Paper Technology by K. W. Britt.
Another course, "Pulp and Paper Processes I",
describes in detail the operation of a modern kraft
pulp mill. The course is offered in the chemical

TABLE I
Courses Taught in Pulp and Paper
Engineering Program

COURSE
Survey of Pulp and Paper
Technology

Pulp and Paper Processes I

Pulp and Paper Processes II

Paper Formation and
Properties

Pulp and Paper Mill
Emission Control

DESCRIPTION
A survey is made of the
chemistry of pulp prepara-
tion, additives, and mechan-
ical systems used in pulp and
paper manufacturing.
A study is made of the vari-
ous processes in a Kraft pulp
and paper mill necessary to
convert raw material into
pulp. The chemical and me-
chanical characteristics of
Kraft pulping, bleaching, and
chemical recovery processes
are examined in detail.
The major pulping processes
other than Kraft pulping are
examined to establish a gen-
eral knowledge of the vari-
ous factors affecting each
pulping process. The unique
advantages and disadvan-
tages of each of the pulping
processes is stressed.
The processes involved in the
fabrication of paper and
paper products from pulp are
examined. The effects on
paper properties of Chemical
and mechanical pretreatment
of pulp are demonstrated in
the laboratory.
The methods available for
control of gaseous, liquid, and
solid wastes from pulp and
paper mill operations are
surveyed. Major biological,
chemical, and physical meth-
ods for treatment of waste
streams and in-plant changes
to prevent waste generation
and increase waste by-prod-
ucts utilization are described.

SUMMER 1975

Processes II", includes the major pulping proc-
esses other than kraft. The properties of soft-
woods, hardwoods, non-wood fiber sources, and
secondary fibers used in these processes are de-
scribed. The sulfite, both acid and neutral, semi-
chemical, and mechanical pulping processes are
outlined. A brief description of some of the more
important non-sulfur pulping processes such as
oxygen pulping concludes the course.
Following the courses dealing with the pulping
of wood, "Paper Formation and Properties",
which describes the processes involved in the
fabrication of paper and paper products, is of-
fered. The steps in pretreatment of the pulp prior
to the paper machine are explained. The func-
tions of the various operations in a paper machine
are then described. Considerable emphasis is
placed on the mechanism for coating paper and
the resulting paper properties. Testing of paper
and the properties and uses of paper are also cov-
ered. Guest lectures are given by faculty from
textile, ceramic engineering, and architecture in
the areas of pulp additives, clay coatings, and
uses of paper in structures respectively.
The last course in the series is "Pulp and
Paper Mill Emission Control". Several courses in
water and air pollution control are offered at
Georgia Tech. However, pulp and paper mills
have many unique pollution control problems. The
course begins with a discussion of some of the
regulatory and economic constraints that limit the
options in control of emissions from pulp and
paper mills. A guest lecturer from the federal or
state EPA Office is asked to lead the discussion.
All three types of emissions-gases, liquids, and
solids-are considered. While methods of treating
these wastes are described, emphasis is placed on
process changes that reduce or eliminate the
wastes.

STUDENT OPTIONS

THE PPE PROGRAM has been structured to
meet the needs of three types of students (Fig-
ure 1). The students who only need a general
knowledge of the pulp and paper industry are en-
couraged to take the survey course. Many textile
engineering students have elected to take this op-
tion. For students whose main interest is environ-
mental engineering we recommend the survey and
the emission control courses. This option has ap-
peal primarily to civil and mechanical engineer-
ing students.
The main thrust of our program is directed at

CHE, TEXT 453 GENERAL INTRODUCTION
SURVY OF PULP AO TO PULP AND PAPER
PAPER TECHNOLOGY ENGINEERING

MIIOPUP A ONTROL IN ENVIRONMENTAL PROBLEMS

CHE 4S01 , . ,
PROCESSES I ANO II
PROFICIENCY IN PULP
ANo PAPER ENGIEINEERING
PAPER FORMATION
AN. PROPERTIES

FIGURE 1. Study Programs in Pulp and Paper Engineering.

engineering students who wish to become pro-
ficient in all areas of pulp and paper engineering,
with the goal being a career in the pulp and paper
industry. For these students we suggest the four
advanced PPE courses. If a student working
toward an advanced degree (M.S. or Ph.D.)
successfully completes the four advanced PPE
courses and also completes an independent pulp
and paper related research project, he or she is
awarded a certificate of proficiency in pulp and
paper engineering.

TEACHING AIDS

SEVERAL TEACHING AIDS are used in the
PPE courses (Table II). The introduction of
each PPE course usually consists of a brief his-
tory of the topic covered by the course and an

TABLE II
Teaching Aids used in Pulp and Paper
Engineering Courses with Student Evaluation
Educational films 2.6
Guest lectures from industry, government, and Geor-
gia Tech. Faculty. 2.2
Plant trips to pulp and paper mills 2.4
Term paper dealing with current industry problem 1.8
Laboratory demonstrations of pulping and paper mak-
ing processes. 2.6
Use of visual aids such as samples of raw materials,
intermediate and finished products, wastes, etc. and a
scale model of a pulp and paper mill. 2.4

KEY:
3.0 significantly improved quality of course
2.0 moderately improved quality of course
1.0 no improvement in quality of course
0 detracted from quality of course

CHEMICAL ENGINEERING EDUCATION

educational film dealing with the pulp and paper
industry. Normally one or two guest lectures
from experts in various areas of pulp and paper
are included in each course. For example, in "Pulp
and Paper Processes I", an M.E. professor lec-
tures on forest operations and usually an industry
expert on some phase of kraft pulping. A plant
trip is also offered to students if sufficient interest
is shown. A term paper dealing with a current
problem in the pulp and paper industry is re-
quired in all PPE courses except the survey
course.
Other teaching aids used to make the PPE
courses interesting as well as educational are lab-
oratory demonstrations of pulping and paper mak-
ing processes and visual aids such as samples of
raw materials, intermediate and finished products,

dustry leaders has been formed. The initial meet-
ing of the advisory committee and Georgia Tech
faculty was held at Georgia Tech in September,
1974. Many useful suggestions were made by the
advisory committee which have resulted in im-
provements to the PPE program. Perhaps the
most important development to come out of the
meeting was the decision to limit the PPE pro-
gram to a series of technical electives to supple-
ment the traditional engineering training given
in the various engineering schools rather than at-
tempt to develop a formal dgree program.
Other recommendations of the industry ad-
visory included:
* Equipment for a small pu:p and paper laboratory for in-
structional and research needs should be obtained. How-
ever, no formal PPE laboratory courses should be in-

The PPE program is structured to meet the needs of three types
of students: those needing a general knowledge of the industry; those
wishing to apply environmental engineering to the industry; and those having
a professional interest in the industry.

wastes etc., and a scale model of a pulp and paper
mill.
At the conclusion of each of the three PPE
courses that were first taught the students were
asked to complete a questionnaire evaluating the
courses as a whole and the effectiveness of the
teaching aids discussed above. Table II shows the
student's evaluation of the teaching aids used in
the PPE courses. The use of educational films,
laboratory demonstrations, and visual aids re-
ceived the most favorable student response. The
students were slightly less favorably impressed
with the guest lectures. The lower rating of the
guest lectures resulted primarily from the low
scores given one guest lecturer who misunder-
stood the topic on which he was to speak. The
lowest student rating was given to the term paper
requirement. Despite the relatively unfavorable
student reaction, the term paper requirement will
remain. It should be noted that three students,
two Ch.E. and one M.E., have used the ideas gen-
erated during preparation of their term papers as
the basis for graduate research.

INDUSTRY ADVISORY COMMITTEE

T O HELP EVALUATE and strengthen Georgia
Tech's Pulp and Paper Engineering Program,
an Industry Advisory Committee composed of in-

eluded in the PPE program.
* "Real-life" problems of the pulp and paper industry
should be given the students in the PPE courses for
term papers, special problems, etc. These problems
would be supplied by industry (no shortages antici-
pated).
* A continuing education program, developed in coopera-
tion with TAPPI and other groups serving the pulp and
paper industry, should be developed.

CONCLUSIONS
The pulp and paper engineering program at
Georgia Tech is and will continue to be flexible.
Modifications of the program will be made as
needed to fit the changing needs of our students
and of the pulp and paper industry. The one con-
stant in our program is the goal of an engineer
completely competent in the basic engineering
fundamentals who also possesses special training
in pulp and paper engineering. O

REFERENCES
Academic Advisory Group, Technical Association of the
Pulp and Paper Industry, "The Effectiveness of Pulp
and Paper Schools", TAPPI, Vol. 55, No. 8, 1164 (Au-
gust, 1972).
Folger, J. K., "Future Demand for Graduate Manpower:
Is Wood Science and Technology Facing a Crisis?" Pre-
sented at Annual Meeting of Society of Wood Science
and Technology, Dallas, Texas, June 18, 1972.

SUMMER 1975

I-I

a I

PLUG-FLOW TRANSIENTS: Fan, Lin
Continued from page 123.

FIGURE 5. Three-dimensional concentration plot for the second
example.
Elimination of A from Eqs. (20) and (25) leads

e7 = e-c (") = e-, r> 0
Similarly, application of Eq. (24) to
and (20) yields
Tr<6

(26)
Eqs. (19)

1 =A eO= A
Hence,
r = e-', 7 < 0 (27)
The concentration distributions represented by
Eqs. (26) and (27) are graphically shown in
Figs. 4 and 5. In all the figures, the numerical
values are given up to an arbitrary dimension-
less time and length of 2.5.

CONCLUDING REMARKS
IT CAN BE SEEN THAT for relatively simple
linear systems, the solution procedure by
means of the method of characteristics is straight-

forward, and the graphical interpretation of the
numerical results can be very instructive. If the
original first order partial differential equation is
nonlinear, or if one has a set of simultaneous first
order partial differential equations in hand, the
analytical solution as illustrated by the two simple
examples may become impossible, and more often
than not, one must resort to numerical solution.
Even under such a situation, numerical integra-
tion of the ordinary differential equations result-
ing from the application of the method of
characteristics, i.e., Eqs. (6) and (7), may be
more desirable than direct numerical solution of
the original partial differential equation. There
are two reasons for this. The first is that most
of the undergraduates are sufficiently familiar
only with the solution of ordinary differential
operations. The second is that the numerical
solutions of ordinary differential equations can
always be made stable in contrast to those of
partial differential equations. Many easily ac-
cessible packaged computer subroutines, e.g.
CSMP, are available for the numerical solution
of ordinary differential equations.
Those who are interested in the mathematical
foundation and other applications of the method
of characteristics should consult the references
cited. O

ACKNOWLEDGMENT
T HE AUTHORS WISH TO EXPRESS their
appreciation to many of their departmental
colleagues and to Prof. R. Aris of the University
of Minnesota and Prof. L. Lapidus of Princeton
University for reviewing the original manuscript
of this paper.

REFERENCES
Abbott, M.B., An Introduction to the Method of Charac-
teristics, Thames and Hudson, London (1966).
Acrivos, A., "Method of Characteristics Technique,"
I&EC 48, 703-710 (1956).
Aris, R. and Amundson, N.R., "Mathematical Methods in
Chemical Engineering," Vol. 2, First-Order Partial
Differential Equations with Applications, Prentice-
Hall, New York (1973).
Courant, R., "Methods of Mathematical Physics," Vol. 2,
Partial Differential Equations, Wiley-Interscience,
New York (1962).
Lapidus, L. "Digital Computation for Chemical Engineers:,
McGraw-Hill, New York (1962).
Liu, S.L., Aris, R. and Amundson, N.R., "Stability of Non-
adiabatic Packed-Bed Reactors," I&EC Funda-
mentals, 2, 12-20 (1962).
Perry, R.H. and Chilton, C.H., Chemical Engineers' Hand-
book, 4th ed., McGraw-Hill, New York (1973).

CHEMICAL ENGINEERING EDUCATION

'mI(

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

0 DOW CHEMICAL U.S.A.

*Trademark of The Dow Chemical Company
Dow is an equal opportunity employer-male/female

440*10?

f;;: (.. S~T$E~;r~idB]

u~s~;��. �-
�;

�: * .- '
41W

FR"~!~.P

In the energy field, there aren't

any easy answers

which is one very good reason for
considering Atlantic Richfield for your career.

It's energy that has created and maintains the fabric
of today's civilization. That's basic.
But providing energy in vast amounts today-and
preparing for the greater needs of tomorrow-is a
tougher and more challenging problem than ever
before.
Now, new answers must be found to developing and
utilizing energy-and its by-products-if we are to
maintain our energy-based standards of living.
We want the best brains we can find to help us arrive
at these answers. We want people sensitive to the
human and natural environment-and realistic enough

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to know that preserving both must come from tough,
intelligent, dedicated work ... backed by outstanding
resources in capital, research and experience,
such as those of Atlantic Richfield.
If tackling such large-scale, significant problems is
one of your criteria in selecting a job, join us. We can
offer you a career rich in challenge, rich in meaningful
work, rich in personal reward.
See our representative on campus or your Placement
Director. Should that not be convenient, write
J. T. Thornton, Atlantic Richfield Company
515 South Flowers Street, Los Angeles, CA.
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AtlanticRichfieldCompany 0
An equal opportunity employer, M/F.

.. . ...; .. .�.
.'xf''' �~7~~~i~~c~ V:~

' r

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t^BsssrI� .'8

	Front Cover
	Table of Contents
	Hot lips, a cold heart and...
	Bob Reid of M.I.T.
	West Virginia University
	Self-instruction in thermodyna...
	Carberry's ultimate paper
	Transients in plug flow system...
	Experiments in heterogeneous catalysis:...
	Pollution of the environment -...
	Use of a continuous system simulation...
	Demonstrating catalytic reactor...
	Book reviews
	Georgia Tech's pulp and paper engineering...
	Back Cover

MILLISECOND	CLASS.METHOD	MESSAGE
0	sobekcm_page_globals.constructor
0	sobekcm_page_globals.constructor	Application State validated or built
0	sobekcm_database.verify_item_lookup_object
0	sobekcm_page_globals.constructor	Navigation Object created from URI query string
0	sobekcm_database.verify_item_lookup_object
0	sobekcm_page_globals.display_item	Retrieving item or group information
0	sobekcm_page_globals.get_entire_collection_hierarchy	Retrieving hierarchy information
0	sobekcm_assistant.get_entire_collection_hierarchy
0	cached_data_manager.retrieve_item_aggregation
0	cached_data_manager.retrieve_item_aggregation	Found item aggregation on local cache
0	item_aggregation_builder.get_item_aggregation	Found 'all' item aggregation in cache
0	system.web.ui.page.page_load (ufdc.page_load)
0	sobekcm_page_globals.constructor.on_page_load
0	html_echo_mainwriter.add_style_references	Adding style references to HTML
0	html_echo_mainwriter.add_text_to_page	Reading the text from the file and echoing back to the output stream
48	html_echo_mainwriter.add_text_to_page	Finished reading and writing the file


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