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CHEMICAL ENOIIIEERING DIVISION
T=E AMfiCAN lOCIT FOR ZNGCUNMNIG EDUCATION ----
CHEMICAL ENGINEERING EDUCATION
Chemical Engineering Division
American Society for Engineering Education
Computers in Chemical Engineering Education
by P.B. Lederman, B. Carnahan & G.B. Williams - - - 1
The Integrated Use of the Digital Computer in Chemical
by Paul T. Shannon -------------------- 11
The Use of Analog Computers in Teaching Process Control,
by James E. Stice and Bernet S. Swanson - - - - - 23
Chemical Engineering Division
American Society for Engineering Education
s (Colorado) Chairm
Martin (Michigan) Vice C
t (Oklahoma State) Secret
CHEMICAL ENGINEERING EDUCATION , Journal of the Chemical
Engineering Division, American Society for Engineering Education.
Published Quarterly in March, June, September and December, by
Albert H. Cooper, Editor.
Publication Office : University of Connecticut
P.O. Box 445, Storrs, Connecticut
Subscription Price, $2.00 per year.
J. B. Wesa
COMPUTERS IN CHEMICAL ENGINEERING EDUCATION
P. B. Lederman (1), B. Carnahan, & G. B. Williams
Department of Chemical and Metallurgical Engineering
University of Michigan
The advent of computers has enabled the engineer to broaden his horizons
with respect to the types of problems he may study and solve in a given amount
of time. As an educational tool, the computer also proves very useful in that
it takes over the routine calculations once an appropriate algorithm or proce-
dure has been established for the problem at hand.
Students can investigate problems using numerical methods which before
were not presented to them until they were able to solve them by compact ana-
lytical techniques. These methods are usually not presented in an undergrad-
uate curriculum. One must, however, choose problems carefully so that the
students avoid the numerous pitfalls present when numerical methods of solu-
tion are used.
Computers and Engineering Science
Considering the significant impact which the high speed electronic com-
puter will have on our future technological development, several questions
arise concerning the role of computers in engineering education. There seems
little doubt that a good fraction of today's engineering graduates (engineers
who may well be working as engineers in the year 2000) will have occasion to
use computers in their technical work. Considering his probable imminent in-
volvement with computers as part of his engineering work, the engineer must
know a great deal more about computers than he can learn from the "giant brain"
articles so prominent in the Sunday supplements. The question which comes to
mind first is, Where should he learn about them? On the job or in the engi-
Those who feel that on-the-job training is adequate, usually claim that
computer programming and computer-related work involves primarily techniques
rather than engineering principle. Those who feel that the engineering school
is a proper place for such training agree*that there is a significant amount
of technique (technique which will incidentally be useful in the student's future
engineering work) but that the primary justification for such training, parti-
cularly at the undergraduate level, is based on the computer as an educational
tool useful in the training of problem solvers. Viewed as an educational tool
the computer can be considered a language for communicating as well as a
machine for solving problems. A better understanding of principles can be at-
tained because of the rigor required when communicating with the computer.
This understanding is also reinforced because the student has a broader exper-
ience with solved problems.
Some features of a computer experience which seem to be related to the
educational aspect of problem solving are:
a. Precise Definition: The computer is a rather rigid task master which
requires precision in the statement of the problem and its method of solution.
Preparation of procedures for computer solution introduces the student to a
precise formal language (usually a mixture of English and algebraic notation).
Because of the nature of such languages, the students communication skill
should be enhanced, he should tend to be more accurate, and he should achieve
added understanding of mathematical notation and manipulation.
b. Logical Organization: Complex engineering problems require both an
analytical ability (to subdivide the overall problem into simpler ones which
can be handled) and an ability to synthesize (bring together solutions of in-
dividual parts as the solution of the whole). Preparing algorithms (problem
solving procedures, flow diagrams) for a computer requires just such analysis
and synthesis abilities.
c. Ilnimize Ambiguity: Because a computer solution requires the pre-
paration of an orderly and detailed step-by-step procedure, the approach to
the solution must be an unambiguous one (formal languages used by computers
allow no ambiguity). No gaps in the logic are permitted.
(1) Present address: Esso Research Laboratories, Baton Rouge, Louisiana.
CHEMICAL ENGINEERING EDUCATION March 1963
d. Recognition of Assumptions: During preparation of organized detailed
procedures, assumptions which may be overlooked in a hand computation are fre-
quently brought to the forefront. Of course, a bad assumption in a computer
program has just as deleterious an effect as in a hand solution; however, be-
cause of the great computational speed, some assumptions necessary to permit
hand computation may be removed entirely.
e. Solution of the General Problem: Because of the nature of the dig-
ital computer, i.e., its ability to read parameter values as data, it is usu-
ally possible (with little extra effort) to produce a general program which
will solve a whole class of problems rather than a specific problem in a spe-
cific problem situation. This necessitates an essentially symbolic approach
to problem solving and is rather different from the customary solution tech-
niques involving mostly numbers. Such an approach requires a more abstract
analysis which focuses on problem structure, rather than on "slide rule" de-
f. Problem Complexity: Because of high computational speed, the com-
puter permits solution of significantly more complex (nd hence, frequently
more realistic) problems than can be "hand" solved. The drudgery of tedious
repetitive calculations is removed. Unfortunately, it is usually wise (essen-
tial) to work at least one example problem in detail by hand for checkout pur-
g. Numerical Solutions: The high speed computer solution permits nu-
merical approximation of problems which are intractable analytically.
h. Logical Non-Numeric Problems: Since the digital computer is in
fact a symbol manipulator rather than a mere number manipulator, it can solve
a large class of logical, essentially non-numeric problems.
Computers and Engineers in Industry
Computers, both digital and analog, have wide acceptance in production,
design and research. This trend, although still in its infancy, is making
rapid strides. For example, the high degree of sophistication in some appli-
cations is illustrated in a recent announcement that complete engineering draw-
ings fro roads are being turned out by computers. A recent survey for the Amer-
ican Petroleum Institute indicated that 86 of 127 responding refineries used
off line computers, and several larger refineries have several computers working
Today a large percentage 9f the "green light time" can be attributed to
accounting and scheduling type functions in those computers associated with pro-
duption units. More and more time is being used, however, by engineering
groups to do repetitive computations and optimization studies. Several on
line control computers are operating with some success. In a number of pro-
ceases, where the reaction scheme is complex, for example, co-polymerization,
there appears to be great incentive to use either open or closed loop compu-
In research organizations computers are widely used in a number of areas.
Although Esso Research Laboratories may not be typical because we are fortunate
to have access to a great variety of computers, it is not atypical with respect
to computer utilization. Therefore, we would like to take the liberty of using
this organization as a basis for discussing the needs of the engineer vis-a-vis
computers in industry.
A very brief look at the organization with particular emphasis on com-
puters, as shown in Pigurel, will help to orient the discussion. The Labora-
tory is one of the major development groups affiliated with Easo Research &
Engineering Co. and does bench scale exploratory work as well as operate small
and large pilot plants. To fulfill its mission it has several research groups,
an engineering group and an applied mathematics group. Three digital computers
are available, an IBM 1620 in the applied math group, an IBM 7074 in the Baton
Rouge Refinery, and an IBM 7090 in Florham Park accessible by transceiver.
The latter two installations are closed shop and the in-house facility is open
shop. FORTRAN and symbolic assembly programs are available for all machines.
Almost all of the professional employees are involved with computers to
some degree. Computers are used in two primary areas in our technical comput-
ing, data work-up and engineering studies. For the former some of the pilot
plants are tied to a data gathering system. The data tape is used, along with
data picked up from a daily analytical results tape, as input to any one of
several unit data work-up programs. Much of the logic for these operations
has been handled by experienced non-engineer programmers. The engineers must,
however, supply algorithms for the unit work-ups. The programmers in the ap-
plied mathematics group are available to program the algorithms. It is usually
more efficient, however, for the engineers to write and debug their own pro-
grams especially when, as is usually the case, program requirements change fre-
March 1963 CHEMICAL ENGINEERING EDUCATION 3
The engineering studies include process optimization, reactor stability,
control, reaction mechanism and similar studies which require the use of chem-
icel engineering and related sciences together with a knowledge of mathematics
and computer sense to bring them to a successful conclusion. This type of
problem hbs increased in importance and will continue to take a greater share
of the engineering talent and computer time in the future.
The demands on the engineer using computers in industry are many even
though specialized help is usually close at hand. To maximize the information
obtained froi extensive pilot plant operations he must decide when computer
data reduction with or without automatic data gathering is warranted, keeping
in mind programrnnng time required and computer cost. It is helpful if he can
write and test his own programs because this cuts down lead time, often one of
the greatest costs of research, and allows him to make any changes with the
This class of problems does not usually require extensive application of
advanced mathematical techniques. It does demand a degree of rigor which we
as chemical engineers were not able to exhibit before the computer era. Often
the algorithms for this class of problems are simplified by use of simple ma-
Engineering studies are becoming much more sophisticated and more encom-
passing in their scope. Engineers today should have a better understanding of
the advanced methemntical techniques used to solve partial differential equa-
tions. In this area the computer is a great help, and at the same time its own
worst enemy. "lany engineers are not aware of the pitfalls which round off er-
rors and non-convergence present. In addition to learning sound problem analy-
sis and efficient algorithm construction, it is important that the engineer be
made aware of the pitfalls involved in numerical methods and approximations so
often used in digital computation.
A third area where the chemical engineer and the computer have found com-
mon cause is in scheduling and economic optimization. This, of course, re-
quires a knowledge of linear (or, in general, mathematical) programming. Today
there is a need to develop a logic which can be used for ultimate design opti-
mization by welding together and exercising supervisory control over independ-
ent routines representing a series of interdependent moduli or operations.
Here again there is a need for a sound foundation in logic.
The use of computers by engineers in an industrial organization would
not be complete without discussing communication between man and the computer.
This has been very much simplified in the past few years at Michigan because
of an excellent executive routine and a very versatile ilgol language, MAD,
with superb diagnostics. Due to the multiplicity of demands on most large in-
dustrial computers -- they do payrolls, accounting and complex engineering cal-
culations -- and the limitations of the smaller computers such as the IBM 1620,
communication is usually not quite as simple. This means that precompilation
debugging should be more thorough. More important, it is most helpful if the
engineer has some knowledge of computer operation or logic so that he can eas-
ily adapt to different computers, programming systems and methods of searching
The use of computers in engineering calculations and their introduction
into the engineering sciences curricula is of great benefit to the young en-
gineer. It forces him to be more analytical and rigorous in his approach to
problems. It is important that along with the use of computers, numerical
analysis, logic and some basic concepts of computer operation be introduced so
that the engineer can make wise and efficient use of this powerful tool in an
COMPUTERS IN AN INDUSTRIAL RESEARCH ORGANIZATION
Development Section Engineering Secto
Praces D.evel pment* Design
--- Exploratory Work 1 ,Instrumentation* .... ata Gat hiering
Ap.plied SoOC Ocap
Programing Computer Services Special Studies
IBM 7074 Refinery
IBM 7090 Transceiver
..... Program Route & Consul.at-on
Education With Computers
At Michigan there has been some contact with computers for the past 10
years. At first this was rather limited but since 1956 when an IBM 650 became
available on an open-shop basis, the use of computers in the chemical engineer-
ing science curricula has been ever increasing. At first only limited use was
made of the computer in graduate courses because access was rather difficult.
With the arrival of a large computer, an IBM 704, and problem oriented languages
such as FORTRAN and MAD, the computer became relatively accessible to under-
A question which arose is where and how the student should be introduced
to the computer. If he is to gain a real computer proficiency, it appears that
an introduction to computer organization and computer language should come ear-
ly enough in his training to allow opportunity for extensive use of the machine
in solving some engineering problems. Since it seems impractical (and probably
unwise) to remove engineering course material to allow insertion of computer
work into engineering courses, it would appear that the student should have an
independent introductory course which gives him thorough training in the lan-
guage and a general understanding of computing procedures. If he is not to be
lost in the hopeless mire of detail there seems little doubt that the selected
computer language should be of the problem-oriented rather than the machine-
oriented type. If engineering classroom time is not to be wasted, then he
must be trained well enough in the first course to eliminate the need for later
retraining in the engineering classroom. The solution to this problem at The
University of Michigan has been the introduction of a required one-hour course
at the sophomore level which trains the student in the use of a problem-oriented
language (MAD) and introduces him to some of the elementary numerical techniques.
At the present time at least one problem whose solution is best obtained
with the aid of a high speed computer is presented in most every course in chem-
ical engineering science. As can be seen in Figure 2 this means that students
are exposed to computer methods from the beginning of their sophomore year. By
applying the techniques learned in the course "Elementary Computer Techniques"
immediately we find that students get a better appreciation of computer tech-
niques. In each succeeding course one or more computer oriented problems are
presented to the students. These problems, chosen by the individual instructor,
are coordinated so that they illustrate many facets of computer programming and
Problems which arise in the assignment of computer problems as part of
the engineering coursework homework load include timing. While there seems lit-
tle doubt that a project-type assignment involving a time period of perhaps two
weeks or more causes no significant difficulty, homework assignments done on a
day-to-day basis do present some problems. Because of the nature of computer
languages, i.e., the necessity for very precise grammar and punctuation, It is
unusual for an undergraduate student to solve completely correctly an engineer-
ing problem on the first approach to the computer. The average may be three or
four tries before success. The turn-around time, i.e., the elapsed time between
submission of a program to the computer and its return for checking and possible
resubmission in case of error, must consequently be fairly short if problems are
to be completed between class meetings.
If computer integration into engineering classrooms is to be successful,
the student's overall computer ability is certainly a major factor. The in-
structor's ability is probably even more important, particularly for undergrad-
uate training. The selection of appropriate problems and the illustration (by
example) of good computer habits (pointing out inadequacies or places where the
computer should probably not be used, as well as where it should be) is essen-
In an attempt to help develop a better appreciation of the computer and
computer techniques, a set of problems for use in an undergraduate chemical
engineering curriculum is described in the Appendix. It is expected that the
student will have had prior to or concurrently with the first of these problems
a basic course in programming, as tpo much time taken from course content would
be required to learn basic programming techniques.
It is not wise to attempt to justify the use of a computer as a time
saving device when one deals with a single problem operation, common to intro-
ductory educational endeavors. It is much better to look at the computer and
program as a method of introcuding a tool which will enable the student, after
some experience, to solve complex problems and will force the student into hab-
its of careful, detailed problem analysis and logical solution methods. If ex-
posure to computers and computer programming does nothing else it will be well
worth the time and effort required if our students think more logically and
CHEMICAL ENGINEERING EDUCATION
C C astIR flQSS.
LMTUY C (4)
OCIAL SC. (1II
MoS. SCIEanna ____
6 CHEMICAL ENGINEERING EDUCATION March 1963
It is true that this is a relatively new area in our curricula, but a
v e7 essential one. At this stage we have and should raise more questions than
we can answer but by proper choice of problems the advantages of the computer
will be well demonstrated. The student will gain new insight into many more
problems and will become quite at home with the computer, a valuable tool for
The authors appreciate the support of their colleagues in the Department
of Chemical and Metallurgical Engineering at the University of Michigan and at
Esso Research L'boratories for the many helpful discussions about their exper-
iences. We are especially grateful to Professor D.L. Katz for his many helpful
suggestions and Mr. E.A. McCracken for reviewing the original manuscript.
A SERIES OF GRADED CHEMICAL ENGINEERING COMPUTER PROBLEMS
This series of computer problems is typical of those used during the
past four years in the chemical engineering curricula at the University of
Michigan. No attempt has been made to be all inclusive as this set, it is
hoped, will merely serve as a guide. Complete solutions for many of these
problems -- mainly written in MAD -- may be found in the various reports is-
sued by the Ford Foundation Project on Computers in Engineering Education (2).
PROBLEM FOR A FIRST COURSE IN STOICHIOMETRY
A typical first problem after some basic programming experience might be
a detailed mass balance as follows:
A countercurrent multiple-contact extraction system is to treat 100 tons
per hour of tailings with fresh water as a solvent. The composition of the
tailings fed to the extration unit is
Component Mass Fraction
The strong solution leaving the system is to contain 0.15 mass fraction salt.
A 99 per cent recovery of the salt is anticipated. Calculate the number of
equilibrium stages required as a function of the solution retained by the gangue.
This problem may be solved by a number of methods, including the method
of linear differences. The basic material stage-wise balance method of solu-
tion is discussed in detail by Brown (1) and a computer solution for a similar
problem may be found in the First Annual Report of the Project on the Use of
Computers in Engineering Education sponsored by the Ford Foundation at the
University of Michigan. (2)
Basically, the solution requires that an overall balance around the ex-
traction be made and then stage-wise calculations be made until the raffinate
from the last stage meets the required concentration specifications. Once the
basic program is written, it may be easily enlarged to include either variable
solution retention (as a function of the solution composition) or a series of
solution retention values.
The problem is not difficult to program but does require the use of sub-
scripts. Students have programmed a similar problem in 15 steps and with rel-
atively little expenditure of time. It has the added advantage of illustrating
the effect of solution carry-over.
March 1963 CHEMICAL ENGINEERING EDUCATION 7
A SECOND PROBLEM IN STOICHIOMETRY OR A FIRST PROBLEM IN THERMODYNAMICS
A second problem in Stoichiometry which could also serve as a first
problem in Thermodynamics is the computation of the adiabatic flame tempera-
ture as a function of the fuel and fuel to air or oxygen ratio.
The solution to this problem requires writing a material balance for the
components involved and then making a thermal balance assuming a flame temper-
ature. If the amount of sensible heat out equals heat of combustion plus the
sensible heat in the correct flame temperature has been established. If the
heat in and out do not balance, a new flame temperature must be chosen; the
Newton-Raphson (3) method for estimating the successive values for the flame
temperature will allow for quick convergence on the correct answer.
This problem is quite simple to program for a given fuel and fuel to air
ratio and should require even less time than the problem discussed above. If
it is desired to investigate the effect of fuel to air ratio or type of fuel,
a little more thought is required to successfully program the problem. It is
still a reasonable problem for people with a minimum of computer experience.
A PROBLEM IN THERMODYNAMICS
A number of thermodynamic calculations lend themselves readily to solu-
tion by the computer. The study of non-ideality and physical equilibria are
probably two of the areas which are often neglected in beginning courses and
which with the aid of the computer may be studied quantitatively. A typical
request of students might be to require them to determine the degree of non-
ideality and the per cent vaporization of a ternary mixture of hydrocarbons as
a function of pressure and temperature.
The instructor must supply an equation of state which is to be used to
compute the properties of the non-ideal gases. This equation should be used
to obtain densities and fugacities as a function of pressure and temperature.
Once this hcs been programmed successfully, the students nay use the equation
of state in subroutine form.
The information, fugacity and density of the pure components and mixtures,
obtained from the equation of state subroutine, may now be used in a larger pro-
gram which actually calls on the subroutine when required. '.s may be eval-
uated as a function of the fugacity and estimated composition and these 'nay then
bh used in a flash-vaporization comiput-ti on to colcuite the degree of vaporiza-
tion of a inixture. In aidi tion CF phase densities may be checked ai inst ideal
densities to determine coaipressibili ties factor values, 9 measure of non-ilpl-
This program would i be foi rly advanced and it a7y be les rable to 1'ist
compute the degree of vaporization based on Raoultts Law, that is, ushn- v;'por
pressures obtained from a Clapyron reletionship. This pro r"n would be 'ulte
simple to write and would serve as a good introduction to tie aenerol prc"'e-s
of physical equilibr'i.
PROBLEM In RA.TE PROC eSSE
In the area of rate processes, the computer can greatly benefit -nd en-
hance the subject matter discussed in a beginning course. many of the probles-
involving rates of heat or mass transfer involve partial differential equations
which may be reduced to difference equations for numerical solution on the con-
puter. A good elementary discussion of these methods may be found in "r:umeri-
cal Methods for Science and Engineering" by Ralph G: Stanton.
The first problem in this area which is very suitable for computer solu-
tion is an unsteady-state heat transfer problem. The time required to quench
an odd shaped bar is to be determined. In order to simplify the geometricel
concepts, it is probably good to choose a rectangle with irregular insulation
or study the converse problem of heating of a rifbt angle bar at one end and
determine the time dependence of the temperature at the other end of the angle
iron as indicated in Figure 1 where Tf if a function of time.
This problem has been programmed by students quite successfully before.
A detailed discussion of the method may be found in q paper by Rudd (4). In
this problem a grid is established over the piece in question and the method
of relaxation is employed to determine the temperature distribution over t
grid at any given point in time.
CHEMICAL ENGINEERING EDUCATION
CROSS-SECTION OF RIGHT-ANGLE BAR
T = 80F.
h = 2 BTU/hr.ft.2 *F.
Insulated Temp. at Edge
T T Bn*_ T = 90F. at 0=0
T ao.t I ? T = 1000*. at 0-046
ANOTHER RATE PROCESSES PROBLEM
The design of tubular reactors is a very common task undertaken on a
computer. In the case usually considered the equations representing the tem-
perature and volume dependence of the system become somewhat complex for ana-
lytical solution. It is therefore necessary to use a set of difference equa-
tions and iterate down the length of the tube. This problem is well suited to
computer solution but one word of caution. The choice of increment size is a
difficult one. Care must be taken not to introduce round-off problems when re-
sults from preceding segments are used as a basis for computing the next seg-
A typical problem might be: the decomposition of S02CI2 to S02 and C12.
The heats of formation and heat capacities for the compounds are
s802C2 (g) AHf = -82,040 cal/gm. sole
Cp = 13.0O42i.oxlO-3T-l4.4xlO-62"
g02 (g) AHf = -70,920 cal/gm. sole
Cp = 8.12+6.825xl9-3T-2.lo3xlo-6T2
C12 (g) ANf = 0
Cp = 7.5755+2.4244xlO-3T-o.965xlo-6T2
and the rate of decomposition may be expressed as follows:
r = A eE/RT
here A = 6.427x1015 1/see
E = -50610 *K cal/gm. mole
Compute the length of .a 1 1/2" I.D. tube required to insure 98,b decomposi-
tion of 418 pounds per hour of S02012 fed at 2000. and 1.2 atm, heat Is
transferred to the tube at the rate of 5000 BIT per square foot per hour.
DESIGN PROBLEM IN REACTION KINETICS
The use of computers in design courses has been quite successful. After
a program of problems in earlier courses, the students often ask to have the
computing facility made available to them. The choice of material taught or
problems assigned to students is very wide so we include an example for illus-
trative purposes of what can be done.
A typical problem would be to determine the optimum reaction time for
a given product if three competing products are formed, that is, mono-, di-
and tri- ethanol amine. If one knows the rate constants as a function of temp-
erature, one can write expressions for the concentration of all the species in
the system. This results in this case in a system of five simultaneous linear
differential equations. These may be readily solved using the standard Runga-
Kutta method which is programmed for most large computing facilities and dis-
cussed in detail in any of a number of texts in numerical analysis (6).
The original reaction data for the ethanol amine reactions were deter-
mined by Ferrero and coworkers (7) and are summarized below with additional
data required to solve the problem. The possible reactions are:
March 1963 CHEMICAL ENGINEERING EDUCATION 9
0 I + 3E5 --1-w 22gCE2CHa
oCH2 k Cg% 2 )
N(CH22 )3 higher products
The velocity constants for the Arrhenius equation
ki = Aie are:
A gm. mole/liter min. E
1. 3.58xlO8 14,500
2. 9.9x109 15,600
3. 2.58x109 15,000
4. 3.93x106 12,650
It is now possible to determine concentrations of each product in the efflu-
ent of an isothermal reactor as a function of the space velocity and the ini-
tial concentrations. If sufficient data is available on the heats of reaction
and specific heats of the constituents the non-isothermal case may be studied.
This problem and similar problems have been very useful in demonstrating
the course of reactions. This and similar problems, it should be mentioned,
are also very suitable for analog computer analysis.
1. Brown, G.O., et.al., Unit Operations, John Wiley, New York, 1950.
2. Katz, D.L. and Organick, E.I. (ed.), Electronic Computers in
Engineering Education, First Annual Report to The Ford Foundation,
Ann Arbor, 1960.
3. Stanton, B.G., Numerical Methods for Science and Engineering,
Prentice-Hall, New York, 1961.
Rudd, D.F., "Temperature Distribution in a Conducting Solid," in
First Annual Report on Computers, Ford Foundation Project, Ann
5. Burnett, G.M., Mechanism of Polymer Reactions, Intersacence, New
6. Ralston, A. and H.S. Wiff (ed.), Mathematical Methods for Digital
7. Ferrero, P., F. Berbs and L.F.Flamme, Bul. Soc. Chim. Belg. L6,
8. "Use of Computers in Engineering Education," Second Annual Report,
Ford Foundation Project, Univ. of Michigan, Dec. 15, 1961.
0 CHEMICAL ENGINEERING EDUCATION March 196i'
The following list of problems were prepared by various staff members and
vilst ng professors at the University of Michigan under the sponsorship of the
Ford Foundation project on "The Use of Computers in Engineering Education" (8).
The titles are included to suggest some more areas where computers have been
and can be used. 'Complete descriptions and programs are available from the pro-
ject at the University of Michigan.
Optimization of Reactor Operation
Approach to Steady-State of an Othmer Still
Temperatures and Heat Flux in a Radiant Thermal Circuit
Heat Balance for an Iron Blast Furnace
Three Component, Two Phase, Counter-Current, Liquid Extraction
Temperature Distribution in a Three Dimensional Body
Solution of a Boundary Value Porblem Using an Initial Value Technique:
Temperature Profile in a Circular Transverse Fin
Velocity Profiles for Flow in Smooth Pipes
Determine Reflux Ratio by McCabe-Thiele Method
Temperature Profile in a Longitudinal Fin Using the Analog Computer
Diffualon and Slow Chemical Reaction
Number of Theoretical Plates in a Multi-Component Distillation Column
Multiple Regression Analysis
Solvent Allocation in Multi-Stage Crosscurrent Extraction
Dynamic Heat Exchange
Storage of Natural Gas in Aquifers
Predicting the Scrap Requirement for the Oxygen-Steel Converting Process
(1) Year in which normally used.
The Integrated Use of the Digital Computer
in Chemical Engineering Education
Paul T. Shannon
"How do you teach a robot to perform process design and optimization calcu-
lations involving recycle streams for any arbitrary process sequence for an arbi-
trary set of equipment?" Our robot has many desirable qualities as well as limi-
tations. He possesses the ability to do simple arithmetic extremely fast and can
remember everything that he is told. He will answer simple questions which have
been unambiguously encoded to him in a form that they are either "yes" or "no" and
he will do exactly as he is told to do. This last quality is both an asset and a
drawback, as any who have done computer programming will testify.
Our robot is not yet built to "see" but he may have this ability in the not
too distant future. At present, however, he will deal only in numbers. Thus, if
we wish to have our robot use any of the visual aids which we as engineers have
found so useful in the study of complex engineering problems, we must find a suit-
able method for numerically encoding our graphical techniques for communication to
and use by our robot. We will find that the answer to this problem, of numerical-
ly encoding graphical aids and their subsequent uses is the key to our problem of
robot education in the field of systems analysis.
Digital computer programming has evolved as a criterion of excellence of un-
derstanding. If you are able to tell an idiot how to perform a given calculation,
taking into account all the possibilities and ramifications of the problem, then
you, as the programmer, truly understand the calculation yourself. I think no one
will argue that one of the most effective ways to teach a student a given calcu-
lational procedure is to ask him to program the problem on a digital computer and
assist him in doing so.
Digital computer programming is a tremendous amount of work. Even simple
problems require a good deal of time and effort and those who have not actually
programmed several problems and experienced the frustrations and relations of de-
bugging have the pat answer, "We'll just solve that set of equations on a compu-
ter." A digital computer program works or it doesn't work. One receives almost
no partial credit.
It has been argued that the student should write each of the digital compu-
ter programs he is to use. Timewise this is just not possible. The engineer in
practice or the student in school must of necessity use programs written by others.
This,also, is a considerable amount of work but not nearly that involved in
writing the program itself.
If the digital computer is to be used extensively by the undergraduate stu-
dent, he must be shown that it is a tool of significant help to him in his course
work. To illustrate this point the successful use of the digital computer in
the Chemical Engineering Laboratory courses at Purdue will be described. Next we
shall consider our question of robot education. A description will be given of
the computer executive system currently under development at Purdue aimed at
answering the posed question. This executive system allows the arbitrary se-
quencing of digital computer programs and thus enables the user to write the com-
puter program for a given problem in essentially the time required in formulating
the problem to be solved. We will find that we arrive at some very powerful gener-
alizations and some fundamental concepts which have bearing on the teaching of
chemical engineering. It will be shown that the executive system develops a basic
conceptual and calculational frame work which is easily taught to undergraduate
Use in the Chemical Engineering Laboratory
Digital computer programming is presently taught and very effectively used
in the Chemical Engineering laboratory course at Purdue. For most students this
is their first introduction to programming since there is not a required course
in programming and numerical methods for all engineering students in their fresh-
man or sophomore year. In Chemical Engineering, an elective one credit hour
course-in computer programming is offered in the fall semester. This course offers
the students additional computer experience and has been taken by about 70 students,
both undergraduate and graduate, each fall.
12 CHEMICAL ENGINEERING EDUCATION March 1963
The first 2-2 1/2 weeks of the chemical Engineering Laboratory course is
spent on an introduction to digital computer programming. Each student is re-
quired to write and run one or two simple programs. Then the "canned" computer
programs (developed by the students and the staff during the last three years)
which will be used in conjunction with the laboratory experiments are explained
in detail. The laboratory time spent on computer programming is "made up" in
that the time formerly allowed during the course for experimental calculations
and report writing is correspondingly decreased. In fact, the students now do
an additional experiment and perform more runs in a given experiment than before.
Sample results from the computer for three of the programs are shown in Appendix A
Perhaps of greatest significance have been the very good "side effects" ac-
companying the integrated use of computers in the laboratory. First, the majority
of what the students referred to as the "mickeymouse" and "dog labor" has been
eliminated with a corresponding significant increase in student interest and en-
thusiasm for the course. Second, each computer program has been written incor-
porating an error analysis. This forces the student to consider the accuracy of
his experimental measurements and their effect on his calculated results. Many a
student has been amazed when his "simple" heat balances on an exchanger turn out
to have an error 50-100%. Third, only the input data need be checked in order to
check the complete calculations thus eliminating "fudged" results. Finally, since
about 90% of the required calculations are done by the "high speed idiot" primary
attention can be focused on the more important questions of "what do you want to
measure and how accurately can you measure it?" and "what is the significance and
use of your results?"
There are, of course, problems associated with the use of "canned" programs
in the laboratory. One is always concerned that the students understand how the
calculations are performed and does not merely follow a "work book" procedure
dictated by write-up of the computer program. The laboratory equipment and the
large classes, requiring three or four laboratory sections each semester, had
made the course quite formalized even before the computer programs were used. It
was these facts that justified the effort of writing the computer programs in the
first place. Realizing this, the staff has been introducing variety into the
laboratory not by constantly changing the equipment and asking each group to per-
form a different experiment, but by asking the students a variety of questions
regarding the interpretation and use of their experimental results.
In summary, the integrated use of the digital computer in the Chemical
Engineering Laboratory has been very successful. The previously boring, repe-
titious calculational portion of the course has been eliminated, and the students
first encounter with a digital computer is its use as a logical means to an end
rather than an end in itself.
The subsequent use of the digital computer by the students in other chemical
engineering courses at Purdue has been very limited. Let us turn out attention
to the generalized executive computer program for doing process design calcula-
tions which is currently being developed at Purdue. Following a detailed presen-
tation of executive program, it will be shown how the program serves as a natural
guide for the truly integrated use of the digital computer in the undergraduate
The PACER Executive System
PACER Process Assembly GOse Evaluator Routine
is a digital computer executive program. PACER is being written to in-
clude eventually three major phases: (1) material and energy .balances transient
and/or steady state; (2) economic analysis; and (3) internal parameter variation.
The PACER program is primarily one which furnishes communication between the equip-
ment subroutines, does a tremendous amount of internal bookkeeping and has the
ability to do trial and error recycle calculations automatically. It is similar
in its function and purpose to engineering calculational programs currently being
developed and used by companies such as C. F. Braun, Humble Oil and Refining,
M. W. ellogg, phillips Petroleum, Shell Oil and Union Carbide. Many of the basic
ideas employed in PACER came from a paper presented by M. T. Tayyabkham of Union
Carbide corporation entitled "Simulating Unsteady State Operation of a plant on a
Digital Computer" which was presented at the AIChE meeting in Cleveland, Ohio, on
May 9, 1961.
The PACER program was developed by studying the structure of the problem of
performing process calculations so that we could teach our robot to do the calcu-
lations for us in the future. The system design specifications which evolved are
shown in Table 1. The major features of PACER are in the use of Stream and Equip-
ment matrices for handling all the information associated with a problem, modular
programming, and the use of the Process Matrix by which the processing sequence
Itself is supplied as input dta4 Table 2 gives the definition of these and othe7
slessly related tes. a
EMarch 1963 CHEMICAL ENGINEERING EDUCATION
System Design Specifications
Process Assembly Case Evaluator Routine
1. Process Sequence, Set of Equipment, Boundary Conditions to
be supplied as Input Data
2. Process Sequence, Equipment Used and /or Operating Conditions
to be easily changed by user
3. PACER is to determine calculations required, do them, and
print requested results
4. PACER is to be able to do both steady-state and transient
5. PACER must be open ended, i.e., able to be expanded and
modified as required
6. PACER must be useable during development
7. PACER must be able to incorporate all past work easily
PACER must be easy to use and understand
9. PACER ultimately must have very large information retrieval
The Process Matrix is the numerically encoded process flow diagram. It is
the heart of the PACER system. By its use, the processing sequence becomes part
of the input data. For any given process such as shown in Figure 1, the Process
Matrix is readily formed as follows. First each piece of equipment is numbered.
Then each stream on the diagram is numbered. The numbering of the equipment is
arbitrary except for one or two restrictions when complex second and third order
branched parallel equipment loops are involved. The numbering of streams is also
arbitrary. However, particular equipment programs may require a certain ordering
of stream numbers in the Process Matrix such as noted in Figure 1. These are very
minor restrictions and do not limit the PACER program. The equipment numbers are
given in the first column of the matrix. Then for each equipment number, the
associated input streams numbers (as positive numbers) followed by the output
streams numbers (as negative numbers) are listed across the row. The Process
Matrix for the flow diagram is also shown in Figure 1. A second more complex
example is shown in Figure 2.
PROCESS SIMULATION SAMPLE PROBLEM #1
PROCESS FLOW DIAGRAM
FIRST ORDER RECYCLE DUMMY
No. Name (Subroutine) Associated Streams
1 MIXER (UNAME3) 1 9 -2
2 TOWER (UNAME2) 2 -3 -4
3 REACTORS (UNAME2) 4 -5 -6
4 TOWER (UNAME2) 5 -7 -8
5 TOWER (UNAME2) 7 -9 -10
NOTE: In subroutine UNAME2:
First output stream number is OVERHEADS.
Second output stream number is BOTTOMS.
1 CHEMICAL ENGINEERING EDUCATION March 1963
Table 2. Definition of Terms
STREAM = ANY CHANNEL OF INFORMATION
The information is contained in the following matrices.
STREAM PARAMETERS LIST
List of values of those variables specifying what you are
STREAM CONTROL VARIABLES LIST
4 list of values of those variables associated with "con-
trolling" the information in the parameters list.
STREAM PARAMETERS MATRIX SN
The composite list of all stream parameter lists. Stream
number = matrix row number.
STREAM CONTROL VARIABLES MATRIX SNC
The composite list of all stream control variables lists.
Stream number = matrix row number.
STREAM FLAG LIST
A list of numbers, one for each stream, which srnals its
status. Stream number = list row number.
NOTE; Format of SN and SNC should be the same for all streams
to allow interchange between equipment
Stream formats us:elly determined by equipment subroutines.
The decision of which variables are "parameters" and which
are "control" is arbitrary.
',UIPIFE::T tNY 1:ATI- .CCAL IODEL OR SET CF PL-S
RN INFO9.. TLi'-; IODIFIER
A UNIT CALCnL-TICN
An EQUIPM'NT takes known Input information contained in
input streams and uses natt.emotici rules to produce output
information in output stre-tns
FCIPIE'31T PARAMETERS LIST
List of values of variables associated with specifying
basic "size" and mode of operation of the 'QUTPMF1NT
,fl-Te'.T CONTROL VARIABLES LIST
List of values of variables ccntrolln e"qui pment operation.
"Cn P!:N,'I ?ARAMITEF!.S '!RiuX X
Composite list of all equlpre-t p-rm-neters lists.
Fquipment number 1 matrix r-o number.
'! :- IT CO. VAR! ".i -3 -_=I -,--
Composite list of all equipment control vrr;=z'es lists.
nquIpment number = metrix row, r'r-cr.
st ot' numeras, one for fn r -v-it, w '- i slii :lE Its
status. equipmentt number = A1}t, 'v- utpr.
:!ote:Fo'0rt oi'- equipment Pnvnters .nJ onri:l V ribloe Lists
need .ct be the same for 11 Fe : nt.
Equipment sa.wys wr tten -,' :sub :c- t 1.
Tne decision of .hic 1 vnri bl r-r vt"r- rn which
are control vnri bless i *rb'tr ry.
pROCE'ss :i"TRIX-E NUTFRICALLY "-UIC 1'2Y '- o. 7' AT10'
An array of the Fqjipmsent rnnm-r i -on th-'r isoci-ted in-
put (positive) and output (reat've) store" r'nurers.
The Process Matrix defines the .yster processs seq -ence)
for PACER and is used to determine how the c-lcul-tions w 11 be
The calculational procedure is Independoent o:'
1. the sequence of equipment in Process :I.tr x
2. the numbering of the streams 'nd equ1p'nert
March 1963 CHEMICAL ENGINEERING EDUCATION 15
PROCESS SIMULATION SAMPLE PROBLEM #2
PROCRSR PLOW DIAGRAM
3 5 7 9
1 1 2 3 5
4 6 8 10
SECOND ORDER RECYLCE DUMMY
PRODUCT PRODU PRODUCT
3 REATOS( 2) 15 13 LPG
MIXER SPLITTER DEBUT
1 14 -1
PROCESS MATRIXa to PACER
Equi the process matrix row number, the equipmentent
SName (Subroutine) Aspndng subrsoited Stre associated
1 MIXER(UNAME3) 1 9 -2
23. TOhe Equipment Pa(UNAMrameter2) 2 -3nd Equpment Control Varables
3 REACTORS(UNAHE2) 15 -5 -6
4 TOWER(AME2) -7and Stream Control Variables Matrices
5. TOWER(UNAME2) 7 -9 -10
6 TOWER(UNAME2) 8 -ll -12
7 SPLITTER(UNAME2) 11 -13 -14
8 MIXER(UNAME3) 4 13 -15
ote: t Output Stream Param etumber nd St Overheads
2nLists used Output Stream Number convergence Bottoms
Table 3. Input Data to PACER
1. Control Cards describing the size of the problem, number
cases to be evaluated and print out desired
2. The Process Matrix. One card for each equipment giving
the process matrix row number, the equipment number,
name of corresponding subroutine and the associated
3. The Equipment Parameter and Equipment Control Variables
4. The Stream Parameter and Stream Control Variables Matrices
5. The Stream Parameter and Stream Control Variables Test
Lists used for testing for convergence in the trial and
error recycle computations
6. Preferred Stream Numbers, if any, used in determining the
calculational procedure for recycle computations.
16 CHEMICAL ENGINEERING EDUCATION 11 0"
The PACER calculational procedure is independent of the numberng of
ea v n, and streams. It is also independent of the order of the equipment
in ;he Process Matrix. The basic program logic of the PACER system is shoa
in Figures 3 and 4. Space and time prohibit a detailed description of PACER
which has been written in FORTRAN for an IBM 7090 computer and consists of
well over 1000 FORTRAN statements. The description and discussion presented
here are independent of the programming language and machine.
As shown in Figures 3 and 4, the Process Matrix is used to determine auto-
matically the sequence of Equipment calculations thus providing the logical re-
lationships for computations. The basic calculational rule used is that if the
input streams are known or have been computed, then the Equipment subroutine can
calculate the corresponding output streams. The streams are treated as entities
in that if a stream is known, all variables in the corresponding Stream Parameter
and Stream Control Variables lists are taken as known, and, when a stream is cal-
culated, the change in any and all variables are computed by the particular unit
calculation alone. During each primary loop the Stream Flags and Equipment Flags
are used to indicate the calculational status of each stream and equipment. PACER
uses these flags to make decisions in determining the calculational procedure.
Following the logic shown in Figures 3 and 4, one would discover that Figure 1 is
a first order recycle problem where stream 9 must be assumed known in order to do
PROGRAM LOGIC FOR PRIMARY LOOP
RESET ALL STREAM FLAGS
SCAN STREAM MATRIX. CALCULATE SPECIAL STREAMS
SET FEED, PRODUCT, SPECIAL STREAM FLAGS
SCAN PROCESS MATRIX ROW BY -
ROW STARTING AT FIRST ROW
HAS EQUIP BEEN CALCULATE ?
ARE ALL INPUT STR AMS KNO7?
CALL EQUIPMENT SUBROUTINE
CALCULATE OUTPUT STREAMS
AND FLAG AS KNOWN
LAST ROW OF PROCESS MATRIX?
--O TO NEXT ROW ARE ALL STREAMS FLAGGED KNOWNt
PRIMARY LOOP COMPLETED WERE ANY STREAMS
RECYCLE CALCULATIONS REQUIRED.
FIND SHORTEST CLOSED LOOP. SET
UP AND PERFORM REQUIRED TRIAL
AND ERROR CALCULATIONS
BIoh 1963 CHEMICAL ENGINEERING EDUCATION 17
,"-oIjUat-ji0ons. Tor Sample Problem #2 in Figure 2, Streas Tand5 miiinatbe
5"nfed known so that it is a second order recycle problem.'
D The values given in the Equipment and Stream Matrices represent a snapshot
picture of the entire process at any given time. In each primary loop, the
values of the variables are recomputed. For time independent problems, the pri-
mary loop is calculated only once. In transient behavior problems, each primary
loop corresponds to a small interval of time. The user supplies the initial boun-
dary conditions and corresponding steady state answers are obtained by repeated
primary loop calculations. Tayyabkham discusses the unsteady state case in detail.
In his paper he cites the simulation of an organic chemical plant consisting of
50 flow streams and 30 pieces of equipment on a IBM 7090 computer. About 100 sub-
routines were used. Each primary loop, equivalent to 0.1 hours, could be calcu-
lated about 20 to 25 times a minute so that 2 hours of computer time corresponds
to about 300 hours of real time.
As seen in Figures 3 and 4, the Process Matrix is scanned several times in
completing a primary loop. PACER recognizes the need for trial and error re-
cycle calculations when no additional equipment can be calculated by repeated
scanning of the Process Matrix and all streams have not been calculated. The
executive program then makes an ordered list of unknown input streams. The list
is ordered in the sense that the user can supply PACER with a list of preferred
stream numbers and these stream numbers are placed at the top of the unknown
stream list. PACER then takes the first stream number in the unknown stream list,
flags the stream as temporarily known and scans the Process Matrix to see if an
equipment calculational loop can be found such that the assumed known stream would
be calculated as an output stream. If this is not possible, then the next stream
in the unknown stream list is assumed known and the search repeated. First all
single streams are assumed known one at a time in trying to find a calculational
path. Then all possible combinations of two streams are tried and finally all
possible combinations of three streams. Tne order of the recycle equals the
number of streams which have to be assumed in order to establish a closed calcu-
Once a calculational loop consisting of an ordered list of equipment numbers
is found such that all assumed known streams are calculated output streams, PACER
eliminates all equipment from the list which is not required to complete the cal-
culational loop. This is done since non-required equipment merely increases cal-
culational time. The present values of the variables are taken as the starting
values for the trial and error recycle calculations. Once the shortest order list
of equipment has been determined, the necessary booking is done and the equipment
repeatedly calculated in order until convergence is obtained. Following some ad-
ditional bookkeeping, PACER returns to the primary loop scan to complete the cal-
culations for the primary loop.
It is emphasized that the term Equipment and Streams must be used in the
broadest sense of their definition in order to see the scope and magnitude of the
PACER system. An Equipment subroutine may or may not correspond to a piece of real
hardware such as a heat exchanger or distillation tower. It can be any set of
mathematical rules. For example, it might be a program for changing the format of
Stream Parameters and Control Variables Lists so as to be able to incorporate a
previously written subroutine into the PACER library without having to rewrite the
subroutine. In the same manner, the definition of Stream is used in the broadest
The requirement of a uniform format for all Stream Parameter and Stream Con-
trol Variables lists allows the complete interchange of Streams and Equipments.
This gives the PACER user the ability to quickly study various process sequences
and so be able to handle a whole new class of problems on the computer. The PACER
executive program is independent of the Stream and Equipment Matrices format in
that it will handle any consistent set.
Appendix B gives a brief description of two simple Equipment subroutines and
the format of their associated Stream and Equipment matrices. The relationship
between the equipment subroutines and the formats of the Stream and Equipment
matrices is typical. These two Equtpment and subroutines are sufficient to simu-
late the processes shown in Figures 1 and 2. These two simple programs and PACER,
could be used effectively to illustrate many, if not most, of the aspects of pro-
cess design and optimization for students in their first course in chemical engi-
M1r. Henry Mosler, one of my graduate students at Purdue who is developing PACER,
pointed out that Sample Problem 2 is only a first order recycle problem. This
was discoveredu when PACER solved the problem. Streams 5 and 15 are common to
the two calculations. loops. Assuming 5 or 15 as known, all equipment can be
calculated. The author, and perhaps the reader had been conditioned not to
guess Intermediate streams in this type of problem.
18 CHEMICAL ENGINEERING EDUCATION Mareh 1963
One of the powerful features of the PACER system lies in the fact that *af
t' : eculpment calculations are written as subroutines. Each equipment subrou-
t. sa a 'unit calculation", a simple extension of the fundamental chemical en-.
gineering concept of the "unit operation." This gives rise to the concept of
modularity in programming which is extremely useful. The subroutines are "com- 4
plete" in the sense that they are written to calculate the output streams using
only the data contained in the input streams and the Equipment Parameters and Con-
trol Variables lests. Hence a library of equipment unit calculations may be de-
veloped consistent with a basic stream and equipment matrices format. Several
unit calculations of increasing complexity can be written for a given type of
equipment such as a distillation tower calculation. Then the user of PACER may
choose the level of mathematical description required by his particular problem.
Another great advantage lies in the fact that only one subroutine is required for
a given equipment no matter how many times that equipment is used in a process.
Input information for the PACER executive program consists of the data listed
in Table 3. The routine for reading the input data is such that individual rows
in the Process, Equipment, and Stream Matrices are read in separately. Thus, the
user can easily change any portion of these matrices with a minimum of effort. If
additional equipment subroutines not in the PACER library are to be used, these
are read into the computer prior to the data called for in Tqble 3. The process
Matrix specifies the problem to be solved and is used to determine the method of
solution. The Stream and Equipment Matrices supply the initial boundary conditions
for the case to be evaluated and after solution, contain the computed results.
With PACER almost all the "bookkeeping" is done within the computer. The
program user does not have to be directly concerned with all the intermediate
stream results. Previously, assuming the equipment subroutines were available in
"closed form," the user would have to prepare the data sheets for the first pro-
gram, punch the cards, run the problem, examine the results, prepare the data
cards for the second program (which probably require a different format), run the
problem, etc. This took all of his time and effort. He would only have time to
make one or two complete process calculations; his calculations would not have
PRIMARY LOGIC FOR RECYCLE CALCULATIONS
FORM ORDER LIST OF UNKNOWN INPUT STREAMS
CHOOSE INPUT STREAMS ASSUMED "KNOWN"
TRY ALL COMBINATIONS OF 1,2 or 3 STREAMS
RECYCLE ORDER = NUMBER OF STREAMS ASSUMED
SCAN PROCESS MATRIX. CAN ASSUMED INPUT
STREAMS BE CALCULATED AS OUTPUT STREAMS?
MODIFY CHOICE OF DETERMINE SHORTEST, ORDERED LIST
"KNOWN" INPUT STREAMS OF EQUIPMENT HAVING ASSUMED INPUT
STREAMS AS OUTPUT STREAMS
DO BOODEKEPING REQUIRE D FOR ITERATIVE RECYCLE CALCULATION
SELECT EQUIPMENT FROM ORDERED LIST
CALL EQUIPMENT SUBROUTINE AND CALCULATE OUTPUT STREAMS
TEST OUTPUT STREAMS FOR CONVERGENCE
NO HAS ALL EQUIPMENT BEEN CALCULATED? YES
I S HAVE ALL STREAMS CONVERGED?-NO -
TRANSFER RESULTS TO STREAM MATRIX
RETURN TO PRIMARY LOOP
March 1963 CHEMICAL ENGINEERING EDUCATION 19
converged, and he would then "adjust" his answers and report his results. This
need no longer be the case.
When the user of PACER specifies the Process Matrix he has written a complete
digital computer program in the time it took him to write the Process Matrix. In
most cases, the resulting computer program is of such magnitude as to have been
prohibitive if it had had to be written from the beginning. The great advantage
of modularity and the "open ended" approach in programming as used in PACER is il-
lustrated in the fact that for PACER, Sample Problems #1 and #2 are the "same"
problem. It is the same problem for any specification of the unit calculation
equipment subroutines to be used. Thus PACER' and a library of equipment sub-
routines gives the user a tremendous computational ability.
While it has not been possible to present a detailed description of the PACElR
system it is hoped that a clear picture has been given of the basic approach and
fundamental concepts involved. It is hoped to have the first phase of PACER opera-
tional on the IBM 7044 at Purdue next Spring. A more detailed description of the
PACER system will be made available at that time.
Now let us consider how the PACER system might be effectively used in the un-
dergraduate chemical engineering curriculum. At the same time we shall see how
this would lead to the integrated use of digital computers in the students under-
graduate courses and be of tremendous use in his senior year courses in Process
Design and Process Dynamics and Control.
The basic ideas and operation of PACER are simple and could easily be taught
to students in their first course in chemical engineering. What more effective
way to teach a student process recycle calculations then have him learn to teach
a stupid robot? The use of the Stream and Equipment Matrices certainly represents
an orderly way to handle the information associated with a problem. Using simple
unit calculations such as given in Appendix B, the students could very quickly be
introduced to the concepts and problems of process design. The decision aspects
of engineering and the description function of science are dramatically illustra-
ted in this approach. The Equipment Unit calculations are the scientific descrip-
tion. It can be pointed out that the majority of his future courses are aimed at
giving him the ability to understand and develop specific unit calculations.
The engineering decision aspects come in his ability to decide what should be
studied in the first place and his ability to interpret the results of the calcu-
lations in arriving at a decision. A series of decisions results in a design, the
essential function of an engineer which distinguishes him from the scientist and
the technician and operator. In fact, the fundamental ideas of PACER, particular-
ly the use of the Process Matrix and the concept of the unit calculation, could
well serve as a basis conceptual framework for all of his subsequent engineering
In his courses in heat transfer, fluid flow, equilibrium stage calculations,
kinetics, etc. the use of the digital computer would arise naturally. Following
a thorough grounding in the fundamental concepts, specific unit calculations are
generally developed in detail. It would then only be required that the student
be asked to write a digital computer program for the specific calculational techni-
que just studied. This would serve as an acid test of his understanding of the
material. Or, he might simply be shown the computer program and be required to
use it in solving several problems. This would be done in each of his courses.
Thus he would be building up a library of Equipment unit calculations, each of
which he had studied in depth at the time the fundamental concepts, basic assump-
tions, and limitations were his primary concern. The PACER framework would serve
to show where and how each course fits into the total picture and emphasize to the
student the interrelationships between his courses and that what he is being taught
today in fluid mechanics will be used tomorrow in design.
In the student's senior year design course he would have at his disposal a
large library of unit calculations, each of which he had previously studied in
depth. Emphasis could then be shifted back to consideration of the behavior of
the total system. He would thus be in a position to attack a wide variety of de-
sign problems of increasing complexity. The PACER system would provide the abili-
ty to write the complex digital computer programs required for specific problems
in the time required to write the Process Matrix and assemble the appropriate in-
put data. In addition, he would be able to do a great many problems which our
present seniors cannot even attempt. In this approach, the use of a digital com-
puter would become as natural to the student as the use of his slide rule, text-
books and the library in the solution of the engineering problems he faces today
and will face tomorrow.
(Authors note: Copies of the PACER program accompanied by extensive
documentation for use by university staffs for educational purposes
will be available in the near future. Requests should be addressed
to the author at his present address.)
CHEMICAL ENGINEERING EDUCATION
CH. E. 339
UNIT OPERATIONS LABORATORY
SHELL AND TUBE HEAT EXCHANGER
A. EXPERIMENTAL CONDITIONS
2. STEAM RATE
3. WATER RATE
1. KEROSENE RATE
2. STEAM RATE
3. WATER RATE
B. HEAT BALANCES
1. HEAT SUPPLIED BY SHELL FLUID
2. HEAT ABSORBED BY KEROSENE
3. HEAT LOST BY RADIATION
4. HEAT LOST BY CONVECTION
NET HEAT LOST BY SYSTEM
6. SAME, AS FRACTION OF ABSORPTION
1. HEAT SUPPLIED BY SHELL FLUID
2. HEAT ABSORBED BY KEROSENE
6. FRACTIONAL HEAT LOSS
C. HEAT TRANSFER COEFFICIENTS
1. SHELL SIDE 5422746421
2. TUBE SIDE 5285549319
3. FOULING 5420000000
4. OVERALL 5291234129 5268398291
1. SHELL SIDE 5223215443
2. TUBE SIDE 5116514913
4. OVERALL 5210243823 5112318093
Note: Numbers representation
pp nnnnnnnn = 0.nnnnnnnn X 10-50
-5271200000 -7.12 e
4532350000 0.3235 X 10o-5
THE ART OF FILTRATION
SLURRY TEMPERATURE F.
PRESSURE DROP PSIG
BEST X COORDINATE
BEST Y COORDINATE
Y INTERCEPT BB
SPECIFIC CAKE RESISTANCE ALPHA
FILTER MEDIUM RESISTANCE RM
SLURRY CONCENTRATION CS
ALUMINUM HYDROXIDE, PERCENT
SILICON DIOXIDE, PERCENT
OPTIMUM FILTRATE VOLUME
OPTIMUM FRAME THICKNESS
Note. Numbers representation pp-50
+pp nmnnnnnm =t O.nnmnnnnn X 10
-5271200000 = -7.12
4532350000o = 0.3235 X 10-5
CHEMICAL ENGINEERING EDUCATION
CH. E. 440
UNIT OPERATIONS LABORATORY
IDENTIFICATION NO. 0000000002
PERIMENTAL CONDITIONS, ACTUAL
MASS FLOW RATE GY
INLET, DRY BULB
INLET, WET BULB
EXIT, DRY BULB
EXIT, WET BULB
MASS FLOW RATE GX
EXPERIMENTAL AND THEORETICAL RESULTS
INTERFACE AREA PER UNIT VOLUME A
HEAT TRANSFER COEFFICIENT HYA 5287410747
HEAT TRANSFER COEFFICIENT BY 5118436434
MASS TRANSFER COEFFICIENT KYA 5335388967
MASS TRANSFER COEFFICIENT KY 5174641436
ERROR EXPERIMENTAL ERROR
5286395293 5322719407 5312451326
5118213901 5147919148 512622280k
5335190623 5391981407 5350409656
5173740236 5219400465 5210616399
Note; Numbers representation
#4pp nnnnnnnn =" 0.nnnnnnnn X 10'50
-5271200000 = 7.12
4532350000 = 0.3235 X 10-5
APPENDIX B. EXAMPLE SET OF EQUIPMENT SUBROUTINES
AND EQUIPMENT AND STREAM MATRICES FOR USE WITH PACER
EQUIPMENT SUBROUTINE UNAME2
DISTILLATION AND REACTOR SIMULATION
This program can be used to simulate distillation towers and re-
actors. It is written to handle five components. One FEED stream
is split into an OVERHEAD and a BOTTOMS stream.
In Process Matrix, first output stream is OVERHEADS, second output
stream is BOTTOMS.
|STR(1:13) | EC(EE,) T-S O(2,13)
Method of Calculation
1. Calculate amounts of each component in OVERHEADS and BOTTOMS.
2. Sum component amounts to find total amount of OVERHEADS and
3. Calculate percentage compositions of OVERHEADS and BOTTOMS.
4. Calculate Fictitious Head Load.
MATRIX formats are shown on the following pages.
UNAME2 is compatible with UNAME3.
EQUIPMENT SUBROUTINE UNAME3 COMPONENT MIXER
UNAME3 is a MIXER subroutine which adds the amounts of each compo-
nent in each input stream, splits the total input amounts of each
component equally between the output streams and then calculates
the percentage compositions of the output streams.
22 CHEMICAL ENGINEERING EDUCATION March 1963
STREAM: P RAMETERS LIST SN and STRMI and STRMO (NS,13)
Same format required for all streams.
1 Stream Number always required
2 Stream Flag always required
3 Total Quantity of the stream W
percent of Component 1 0. 1.0
SPercent of Component 2 0. 1.0
6 percent of Component 3 0. 1.0
7 Percent of Component 4 0. 1.0
8 percent of component 5 0. 1.0
Y a 1.0
9 Amount of Component 1
10 Amount of Component 2
11 Amount of Component 3
12 Amount of Component 4
13 Amount of Component 5
STREAM CONTROL LIST SNC and STRMCI and STRMCO (NS,3)
1 Stream Number always required
2 Stream Flag
3 Light Key Component Number 1 or 2 or 3 or 4
Note: Stream Type Stream Flag
product + 2
Special Feed + 3
EQUIPMENT PARAMETER LIST EN(NE,8)
1 Equipment Number always required
2 Equipment Flag
3 Fictitious Head Load Q
4 Fraction of Component 1 in FEED appearing in OVERHEAD
5 Fraction of Component 2 in FEED appearing in OVERHEAD
6 Fraction of Component 3 in FEED appearing in OVERHEAD
7 Fraction of Component 4 in FEED appearing in OVERHEAD
8 Fraction of Component 5 in FEED appearing in OVERHEAD
NOTE: (1. Fraction of Component in OVERHEAD) = Fraction of Com-
ponent in BOTTOMS.
Fictitious Read Load Equation:
QS A* OVERHEAD B Pkey key 1 x l10) *C
EQUIPMENT CONTROL LIST ENC(NE,5)
1 Equipment Number always required
2 Equipment Flag
3 lst Constant of Heat Equation (A in above equation)
4 2nd Constant of Heat Equation (B in above equation)
5 3rd Constant of Heat Equation (C in above equation)
The Use of Analog Computers in Teaching Process Control
James E. Stice and Bernet S. Swanson
Illinois Institute of Technology, Chicago
The use of indirect electronic analog computers is steadily increasing in
both industry and engineering education. Such computers are used primarily for
the solution of linear and non-linear ordinary and partial differential equations,
and for the simulation of systems. An analog computer facility for educational
purposes which is reasonably accurate and large enough to handle linear problems
of moderate complexity can be obtained for $2,000. Increasingly accurate equip-
ment with greater capacity and specialized auxiliary components requires a corres-1
pondingly larger investment.
The minimum equipment requirements include an analog computer with the nec-
essary computing resistors and capacitors and some sort of readout device. Some
of the manufacturers of small analog computers and computer components are Ap-
plied Dynamics, Inc., 2275 Platt Road, Ann Arbor, Michigan; Donner Scientific
Division, Systron-Donner Corp., 888 Galindo St., Concord, California; Electron-
ic Associates, Inc., Long Branch, N. J.; The Heath Company, Benton Harbor, Michi-
gan; George A. Philbrick Researches, Inc., 127 Clarendon St., Boston 16, Massa-
The necessary computing resistors and capacitors (if not built into the com-
puter) may be made up by the user or they may be purchased ready to use. The re-
sistors may be made up by attaching precision resistors having the desired resis-
tance (one percent tolerance or better) to General Radio double plugs. Computing
capacitors may be similarly made up, but it is difficult to obtain capacitors
which have exactly the capacitance desired, so that trimming is almost always
necessary. Further, condensors of radio quality do not have high enough leekage
resistances for accurate computation purposes. Computing resistors and capaci-
tors may be purchased from several sources, such as Donner Scientific Division of
Systron-Donner Corp. and Southern Electronics Corp., 239 West Orange Grove Ave.,
Burbank, California. The precision capacitors are expensive.
The readout device may be an oscilloscope or some sort of recorder. A re-
corder is recommended for educational use, so that the student may obtain a per-
manent record of the solution. Recorders tested here which are quite acceptable
for analog computer readout include the Brush Mark II, the Offndr Type 542 and
Type RP DynoCraphs, the sanborn Model 1525460, the Varian G-11A, and the EAI
Model 1100E variplotter (an X-Y recorder). The July 1962 issue of Instruments
and Control Systems contains a survey of 1,000 recorders.
A group of laboratory experiments follows which were developed at Illinois
Tech for the process control laboratory course given in the Chemical Engineering
curriculum. These experiments introduce the student to the use of the computer
gradually. There are eight experiments, and a two- or three-man team of students
should be able to work all of them in nine three-hour laboratory periods without
too much supervision. The experiments are written for the 15-amplifier Heath
Group C Computer ($945), although any computer with nine amplifiers would suffice,
with the exception of the Heath Model EC-1 Computer, which can be used for only
seven of the experiments.
The recorder used here was the Offner Type 542 Dynograph ($1,145). This is
a two-channel, galvanometer-type recorder which is also used for a great variety
of other applications around the department. If money is tight, excellent re-
suits should be obrained with a single-pen, potentiometer-type recorder such as
the Varian G-11A recorder (base price with Type B-1 Input Chassis is $540). The
range of applications of such recorders is not as broad as that of the galvano.
meter-type recorders, since the potentiometric recorders cannot be used for sig-
nals having frequencies above one cycle per second. However, the equations can
be time-scaled so that good results can be obtained with these recorders.
The computing capacitor requirements for these experiments are: one
0.01 ufd, one 0.1 ufd, and four 1.0 ufd capacitors. Resistors required are:
two 0.1 megohm, one 0.2 megohm, one 0.4 megohm, four 0.5 megohm, eight 1.0 megohm,
two 2.0 megohm, one 5.0 megohm, and one 10.0 megohm resistors (one percent toler-
ance or better).
In addition to the equipment already specified, the second part of Experi-
ment Two requires a diode function generator (DFG) for the generation of the valve
characteristic curve. There are a number of diode function enerators on te mar-
ket, but by far the least expensive is the Model ES-600 (kit) manufactured by the
Heath Company ($72.95). This DFG provides only ten straight line segments, and it
is understandably less accurate than a DFG costing $450, but it is adeqg"tq r.o
instructional purposes and the price is attractive.
20 CHEMICAL ENGINEERING EDUCATION Mareh 1963
These experiments have worked out very well; the students have learned how td
solve relatively simple process control problems on the computer. There have, in7
addition, been some bonus results which were not anticipated when the program was
begun. Students tend to get rather disconcertingly enthusiastic about the compu-
ter after they begin to understand how to operate it, and they leave the labora-
tory only after repeated threats of bodily harm. They concoct their own problems
and return to the laboratory on their own time. Further, they experience a re-
newed interest and a more mature understanding for differential equations, and the|
electrical engineering department reports that our students are'badgering their
staff to give them more electronics. This awakening of intellectual curiosity in
nearly all the students who have worked with the computer has been a delightful,
if somewhat wearing, experience for the staff members who teach this laboratory.
Building an analog computer laboratory poses the problem of how many students
can be handled at one time. A team should consist of no more than three students,
and two is better. A class of twelve students may thus imply four to six compu-
ters, and this becomes an expensive operation. The Donner Model 3500 and Model
3400 computers have removable problem boards, as do many of the larger computers
(Applied Dynamics, Electronic Associates, Berkeley Division of Beckman Instru-
ments). Also, Prof. James 0. Osburn of the Chemical Engineering Department, State
University of Iowa, Iowa City, has devised a plugboard for use with the Heath
Group C computer. This plugboard has connections to four of the computer ampli-
fiers, three of the initial condition power supplies, and a 100-volt and a -100-
volt supply. Each plugboard also contains four integral coefficient potentio-
meters. A plugboard costs about $15.50 to make. A team of students can patch up
a problem on their own plugboard and when wiring is completed the board is at-
tached to the computer and the solution can be run off in a short time. In this
way one computer can serve a class of perhaps ten to twelve students. Osburn's
plugboard is described in the Journal of Chemical Education, 38, 492 (1961), and
further details may be obtained direct from Dr. Osburn.
The development of these experiments and the manual which accompanied them
was supported by a National Science Foundation grant.
INTRODUCTION TO THE HEATH GROUP C ELECTRONIC ANALOG COMPUTER
This experiment is intended to familiarize the student with the basic tech-
niques of analog computation on the Heath Group C electronic analog computer.
After the various mathematical operations which the computer can perform have been
studied, they can be utilized to solve a classical rpoblem in physics, such as the
body falling freely in a vacuum from a position of rest.
PART I1 Use of the Computer to Generate Functions
An analog computer can be used to generate a variety of functions for use as
PART II: Use of the Diode Function Generator
COMPUTER SOLUTION OF LINEAR SECOND-ORDER DIFFERENTIAL EQUATIONS
Ordinary linear differential equations occur commonly in science and engi-
neering. The examples used here will be limited to differential equations with
constant coefficients, so that function multipliers will not be required. A class-
ioal problem in mechanics is the mass-spring-damper system, in which a mass is
supported by a spring and a dashpot.
FREQUENCY RESPONSE DIAGRAM FOR A MECHANICAL SYSTEM
In the previous experiment, the analogy between the mass-spring-damper sys-
tem and the time-scaled R L C circuit was developed, and the transient response
of these systems was studied for the case with no forcing function applied. In
this experiment, the mechanical system will be forced to oscillate by impressing
a ainusoidal forcing function on the mass. The system will be subjected to
forcing functions of different frequencies, and a frequency response diagram will
be constructed for the system.
March 1963 CHEMICAL ENGINEERING EDUCATION 25
COMPUTER SIMULATION OF SYSTEM COMPONENTS
One of the most important applications of analog computers is the simulation
of physical systems. The computer is programmed to solve the differential equa-
tion or set of equations which represent the system. When this has been done, it
turns out that certain portions of the computer circuit represent identifiable
parts of the physical system under study, so that it becomes natural to think of
these circuit components as though they were the corresponding components of the
physical system. This will be illustrated in the several parts of this experi-
PART I: Single-Tank Liquid Flow Process
This is illustrated by a liquid flow process in which liquid flows into a
tank at a rate of F (t) cubic feet per minute, and flows out at a rate of Fl(t)
cubic feet per minute. The capacity of the tank is C1 cubic feet of liquid per
foot of depth, which is numerically equal to the cross-sectional area of the tank
in square feet. To keep the problem simple, assume that the cross-sectional area
of the tank is uniform from top to bottom, as would be the case with a vertical
cylinder or a rectangular tank. The head of liquid in the tink is hI feet. The
Fo(t) Capacity = Ci ft3
per ft of depth
Figure 5-1: Single-Tank Liquid Flow Process
liquid flowing out of the tank suffers head losses due to contract on and expan-
sion, and friction in the piping and fittings. All of tiese factors are lumped
into one equivalent resistance term which is designated 1 (foot) (minutes) per
cubic foot of flowing liquid. This equivalent resistance is equal to the slope
of the head versus flo curve in the region of interest. This curve is not nor-
mally linear, but it .y be ap-roximately linear in the region of interest. gajin
in the interests of keeping the problem simple, the curve which relates head to
flow F1 will be assumed to be a straight line.
PART II: Second Single-Tank LiquId Process
1 second tank will be sinulfted, the new tank being similar to the first.
The process time constant will be different, since the second d tln will alree a
irgeer cross-sectlonu l rrea capacityy) and a somewhat different equivalent res p -
tbnce. fos before, ciprcity and resistance will be assumed constant. The flow in-
to Ink 2 -will be Fl(t) cubic feet per minute, and the flow out will be F2(t) cu-
bic feet per minute.
PART III: Two-Tank Liquid Flow PFrcess
Tank 1 is the tank of Part T n1 d Tant: 2 's the tank of p-rt It it is de-
sired to know what the traslent response of t 's system will be *f n step input
eis applied suddenly inc resa sn flow a (t). "en t ie t i-slent response curve has
been obtained, it will bae use s to ca puacte t e tme c cnstants of' the process.
Io(t)he I dCapacity CI
Figure 5-3: Two-Tank Liquid Flow Process
26 CHEMICAL ENGINEERING EDUCATION March 1963
OPEN-LOOP RESPONSE OF PROCESS
The two-tank process of Experiment Five is to be instrumented to maintain a
flow rate of twenty gallons per minute for flow F2(t). The control valve and the
flow sensing device will be simulated in this experiment and the open-loop res-
ponse of the system will be studied. In Experiment Seven the pneumatic controller
will be studied. The controller will be added to the rest of the equipment in
Experiment Eight, and the e]osed-loop behavior of the entire system will be ob-
served for various controller settings.
Flow F2(t) out of Tann 2 will be maintained constant by controlling flow
Fo(t) into Tank 1. Flow 21,(t) is an intermittent stream which also flows into
Tank 1 Pt Rrb:trsry intervals and for varying lengths of time. To simplify the
analysis, it will be assumed that the nature of the process is such that Tank 1
will never run dry or overflow.
CC"'TOTR SIMULTITON OF A PEIUMATIC CONTROLLER
In order to control the system in the previous experiment, some sort of con-
troller is necessary. This controller receives the air pressure signal from the
flow sensing device, subtracts this signal from the set point signal to produce
an error signal, and acts upon the error signal to reposition the control valve.
Pneumatic controllers can be obtained with up to three modes of control,
these being proportional, derivative (also called rate or preact), and integral
(also called reset rate) modes. The particular process under study can be con-
trolled very nicely by a controller having proportional and integral action, and
this is the type of controller which will be simulated.
BEHAVIOR OF THE CLOSED-LOOP PROCESS
The complete process of Experiment 6 will be simulated and the effect of
various controller settings will be observed. The pertinent facts about the pro-
cess are summarized below.
(1) It is desired to maintain a constant flow of twenty gallons of liquid
per minute out of the bottom of the second of two non-interacting, series-con-
nected tanks. This flow is designated Fp(t). To accomplish this a pneumatic con-
trol valve regulates the flow of liquid Into the top of the first tank, the regu-
lated stream being Fo(t).
(2) In addition to Fo(t) there is an intermittent stream, FL (t), which also
flows into the top of the first tank. This flow is unregulated, and occurs in
varying amount and on no regular schedule. The amount of this flow is small com-
pared to Fo(t).
valve Pneumatic 0
F (- ) Controller
T --- F 2Ct)
Figure 6-1: Automatic Control of Flow in Liquid Process