I’
THEODORE J. WILLIAMS
Analog Compu Petroleum Indu Past and Present
the analog computer can Obtain for the industry in the cheapest and quickest possible manner the data it needs for such problems as
)Most probable reaction anisms and kinetic parametersof processes by computerevaluation
point of dynamic behavior and automatic control. )Optimum schedulingand operatingconditions for both batch and continuous reactorsto assure maximum yields. However, the analog computer has definite limitations as a general Purpose computer for chemical and chemical engineering Problems, and its procurement by a particular company should be justified only on the basis of a contemplated workload in the fields of automatic process control and chemical process transients.
t
electrical circuits (78) and the use of flowing water streams to represent the flow of air a t supersonic velocities over airplane wings (37). Here there is a physical counterpart for each element of the system under study. These devices are usually small and are designed specifically for solving one problem or small
McCann (22). They have found use in heat transfer computations where the studies of Paschkis (28) and of Kayan (79)areespeciallynotable. Fluid flow, particularly flow through porous media, has been another important field for these devices. Reservoir behavior analyzers are prime examples
General-Purpose Analog Computers. The first important “indirect” analog computer, the one which brought the first true flexibility and large scale computing ability to the field was the mechanical differential anal vented by Bush and coworker late 1920% time math cally ordinary differential equations, were solved as such by computers. While the use of a machine of this type has been demonstrated for the solution of chemical industry problems by such studies as those of Pigford, Tepe, and (37) on batch distillations and’ Crank, and Twigg (42) on the reactions, it has been
vior analyzers is still very important. Several petroleum production companies such as Magnolia, Sun, Pan American, and Continental, to name a few, make extensive use of them for this purpose. These computers were first used in the early 1940’s for the above types of problems, and thus their use antedates that of digital computers which were first used in the late 1940’s for chemical problems (76). This is the only important type of direct analog computer used for mathematical computation purposes, and it is the one referred to in discussing direct analogs above. There has recently been a great deal of activity on the part of the computer manufacturers to adapt computers of
IF you are thinking of using analog computers for process simulationsHere are the advantages relative to digital computers.. , Analog Computer Simulates behavior of any system by action of easily manipulated and measured variables Simulation is continuous, permits inclusion of concepts such a s distance, velocity, acceleration Results presented a s family of graphs of variation of dependent variable (same data obtained with recorder connected to process) Speed of problem solving is direct function of actual speed of physical system, is independent of size or complexity of system Programmed so that parameter magnitudes are entered a s settings on variable potentiometers ; parameter values can be changed at will
BUT there are disadvantages, too..
...
Digital Computer Performs arithmetic operations with numbers Operates discontinuously; can only approximate higher order effects Results presented as tables of numbers; must be plotted Speed is direct function of problem complexity and size, relatively independent of operating speed of process Flexibility not present without special programming precautions
.. .
Analog Computer Size of computer (number of computing components) determines size of problem which can b e solved; simplifying assumptions often made to reduce complexity Specifically designed for solution of ordinary differential equations; other problemse.g., solution of simultaneous algebraic equations-made by trial and error. Less complex partial differential equations solved if converted to ordinary differential equations and one variable assumed constant; family of solutions for different values of variable results (15)
Digital Computer Problem size reflected in computing time; no limit to size of problem if time is available Useful in nearly all types of problems. Complex partial differential equations more amenable to solution by digital equipment
NOW-if
you think the advantages outweigh the disadvantages, here are some of the things that analog computers can do for you as compared to digital computers,, ,
.. .
Equipment and plant design
Instrumentation and data reduction
Process control Simulations search)
(re-
Chemical plant applications Research in processes
basic
Research in unit operations Plant operations and management technique studies
1 632
INDUSTRIAL AND ENGINEERING CHEMISTRY
Analog Show great promise for working out relative sizes of plant equipment by solving dynamic equations of plant performance Small, special purpose analogs important in converting and plotting single variable and directly correlated multiple variable data in form of graphs Best tool in existende for studying resulting phenomenon ; limitation on system complexity imposed by computer size Definite promise a s final control elements for units of highly automated chemical plants Well suited to simulation of chemical reaction kinetics involved in chemical process development Well suited for study of transient state such a s heat transfer, distillation
Digital Superior for details of mechanical design-e.g., stresses, sizing of members, costswhich are trial and error arithmetical problems
Flexibility and accuracy of digital computers better for control of whole plants Better for determination of kinetic parameters by statistical data reduction where necessary Better suited for steady-state studies which are usually arithmetical or statistical Better here because statistics and arithmetical operations predominate
COMPUTER^
IN THE CHEMICAL
WORLD
A typical analog computer specifically designed for chemical procssss control investigations
Telephone Laboratories and to their work on the M9 fire control computer (77). The first general-purpose electronic analog computer based on the operational amplifier was that of Ragazinni, Randall, and Russell (33). The work of G. A. Philbrick, another pioneer in the field, appeared soon afterward (29). These machines were early put into commercial form by Reeves Instrument Co. (72) and by George A. Philbrick Researches, Inc. (30). They found almost immediate acceptance in defense industries because of their ability to solve complex problems of aircraft and missile design and of control systems performance beginning to plague these industries at that time. Analog computer installations-used by the aircraft companies continued to grow exponentially with time as supersonic aircraft and missiles became common. Now all of the large companies have installations, each containing from several hundred to 1000 or more operational amplifiers, the basic unit of these machines. All of these are of the electronic differential analyzef- type. In addition, some of these companies have moderately sized installations of the net- work analyzer type of computer.
’
Table I. Typical Proportion of Analog Computer Components for a Chemical Process Control Computer Based on 100 operational amplifiers Number Component Operational amplifiers 100 (total) 40 Summers Integrators 60 Servomultipliers (high 20 accuracy, each with two tapped pots) 10 Diode function generators Computing conshes 2 Operational relays l2 (at least) Pot padding sets 20 Extra problem boards sets (at least)
Applications of Electronic Differential Analyzers to Chemical Problems I
Past Uses. Published applications of electronic differential analyzers to chemical problems have been quite varied but are still small in number in relatiQn to published digital applications. The earliest were the studies of heat transfer calculations by Howe (75) and the automatic control studies of fluid flow systems by Chien, Hrones, and Reswick (8). These were followed soon afterward by the absorption column study of Acrivos and Amundson (7). Since that time, interesting applications have been published in the fields of chemical reactor dynamics (2-4), nuclear reactor dynamics (77, 74, 23), distillation column transients and control (35, 36, 38, 39), heat transfer and control (27, 25, 32,40), and fluid flow transients
(47). Analog Computers and Process Control. The current popularity of automatic chemical process control has created a great interest in computers, particularly analog computers, which is readily explained. Before automatic process control can be applied to individual plant units, let alone complete plants, the dynamics or transient behavior of these plant units must be known, as well as their responses to types of control. Furthermore, possible type of control for these units must be selected. This information can be developed in either of two ways. The first is throagh experiments on actual plant type equipment, PO: sibly of smaller size. The second IS through “simulation” of the responses of the actual equipment by mathematical means. Interests of economy, . speed, _ . and breadth of data possible all point to the use of mathematical simulation for the great mass of this work whenever possible, with an allowance for verification tests of selected items of the data on actual
equipment. The latter prove the validity of the mathematical model being use. However, calculations of this sort for chemical engineering operations of practical interest are fantastically complex, hence the interest in computers as a means of solving the resulting equations. Computer Simulation. When carried out on a computer, mathematical simulation becomes the art of “programming” or wiring the various components of the computer (usually an analog computer) together in such a manner that the differential equations which could be written for the computer system thus formed are as closely as possible the same as those of the physical system to be studied. Here a system generally refers both to the chemical apparatus or process under investigation and the associated control devices to be applied. Therefore, the group of differential equations comprising a mathematical model will include equations defining the action of the control devices as well as equations defining the apparatus or process under study. Thus, in contrast to much present-day chemical industry practice, both the process and the control devices must be considered as inseparable parts of a larger, over-all system. In the case of the analog computer, the dependent variable observed is the voltage at the output of any one of the several computing elements involved. Because the differential equations of the two devices are the same in form, any variation of these voltages represents directly the corresponding variations in the dependent variable of the system under study a t the corresponding locations in that system. For example, if a chemical reactor system was simulated with the analog computer, voltage in the computer could represent composition in the physical system. Then the variation of voltages in the computer would be exactly analogous in magnitude frequency of oscillation, and the amount of damping present to the corresponding variation VOL. 50, NO. 11
NOVEMBER 1958
1633
Table 11.
Large-Scale Analog Computer
Year Acquired
Location Midland, Mich. Wilmington, Del.
tro mu pliers
1954
20
(1950) (1955) 1958
30
50 120
20
20
1957
116
21
24
1957
48
10
6
1949 1956 1957
20 24 24
Whiting, Ind.
19551 1957/
168
Cleveland, Ohio
1955 1957
90 10
4
1956 1957
30 30
4 3
St. Louis, Mo. Denver, Colo. Emeryville, Calif.
Union Carbide Che’inicals S. Charleston, W. Va.
of the composition of various components in the chemical system. I n addition, voltages can be imposed onto the input of the model system on the computer to represent any desired external influence on the actual physical system. Furthermore, because the computer is protected by its design features from damage due to excessive voltagesLe., by fuses and circuit breakers-we are free to determine, if desired, just how severe a disturbance the control system can correct, the effects of controller instability, or even, if desired, the limits of the corresponding physical system before actual physical damage or destruction would occur. Thus, the utility of a technique such as this is selfevident in such fields as aviation, with the testing of new and unusual types of aircraft. These same techniques can be applied to the design and control prob lems of the chemical industries. The results will not be as glamorous as those in aviation but can be just as far-reaching in their effects. Frequency responses are also found by
1634
Amplifiers
Servomultipliers
6
2 2
INDUSTRIAL AND ENGINEERING CHEMISTRY
1 1 12 4
20 8 6
simulation by applying sinusoidal inputs to the computer. Thus a complete study of the control of a particular chemical system can be made, provided only that the assumptions upon which the simulation is based are accurate. This accuracy can only be proved by direct experiment, however, and thus some small amount of experimental data is vitally needed for all computer simulations, at least until greater proficiency in analyses is attained and the assumptions used in deriving basic equations can be trusted completely. One partial solution to the problem of simplifying assumptions often involved in computer solutions us. experimental collection of data is that of “real time simulation.” This refers to the adjustment of the operating speed of the computer so that it is the same as that of the process or device being simulated. When this is the case, components of the real or physical system can be actually connected into the computer mechanism. The only additional requirement is that the proper transducers
2
4 2
5
2 2
Electronic Associates
must be available to convert the operating variable of the process element into a voltage which can be used by the computer elements which represent the rest of the process loop. An example of such a case is the problem of determining the applicability of a particular pneumatic contrcller to a chemical reactor. The reactor can then be simulated on the computer and the controller connected into the computer system by voltage to pressure and pressure to voltage transducers. Now the controller can be adjusted directly and the setting which gives the best control of particular reactor situations as simulated by the computer, can be determined. The analog computer texts cited (77, 20) discuss more fully how this technique is actually accomplished in practice. A relatively unexpected gain from the process simulations necessary for automatic control studies is the tremendous aid that this technique provides for chemical process development. Just as process simulations show the effect of external disturbances on control functions,
COMPUTERS IN THE CHEMICAL WORLD they also show the effect of environmental factors on process yields, product quality, and other vital points concerning the process. Thus the computer can help specify those operating conditions which will give a maximum return from the process.
including Berkeley Division, Beckman Instruments Co., Goodyear Aircraft Co., Mid Century Instrumatics Co., and Reeves Instrument Co., all make computers of equivalent size and capability.
Advantages for Process Simulation.
which summarizes available data on the types and relative sizes of analog computers now owned by chemical apd petroleum companies, gives a general picture and is not complete as data are often not made available for publication by the companies involved or only approximate numbers are given. In addition, several companies have small stallations of the GAP/R fasttime- le computer of G. A, Philbrick Researches, Inc., or one of the very small com the “do it yourself” kit by the Heath Co., Benton Harbor, Mich.
Having defined process simulation and pointed out its value to the chemical industry, it is well to show why the analog computer was chosen as the machine to be used for this purpose. Applications in Other Fields. While analog computers are admirably suited for process control and process development simulations, they have less application in many other fields. The field of statistical data reduction is almost completely a digital computer province. Other applications, such as most types of final design computations, are also better adapted to digital computation.
Scientific Computations Symposiums,” International Business Machines Co., Endicott, N. Y., 1949, 1950. (17) Johnson, c, L., Computer Techniques,” p. 1, McGraw-Hill, New York, 1956. (18) Johnson, W. C., “Mathematical and Physicd Principles of Engineering Analysis,” McGraw-Hill, New York, 1944. (19) Kayan, c, F., T ~ ~sot. Mech. ~ ~ Engrs. 47, 713-18 (1945). (20) Kern, G. A., Kern, T. Ma, “ E k Computers,” 2nd ed., McGraw-Hill, New York, 1956. (21) Kourim, G., Regelungstechnik 5, 165-7 302-7 (1957). (22) McCann, G. D., Mathematical Tables and Other Azds to Computations 3, pp. 50111 (1949).
Present Installations in Chemical Industry* The map On page
Acknowledgment Analog Computer Installations
Procuring an Analog Computer. There are many factors to be considered in procuring an analog computer. One of the most important of these is size. Study of typical chemical problems of practical size which have been solved showed that a t least 40 operational amplifiers seem to be an absolute minimum requirement for a computer of satisfactory applicability. Every addibeyond this number which can be procured will, of course, very greatly increase the flexibility of the machine. Many large chemical and petroleum companies are now actively considering the purchase of computers with 100 or more operational amplifiers or have already bought them. I n addition to this large number of amplifiers, a very generous proportion of nonlinear components such as multipliers, function generators, and relays are necessary to represent adequately the complex relations involved in practical chemical kinetic and heat transfer functions. This proportion of nonlinear elements will probably amount to two or three times that usually considered optimum for a computer to be used solely for such purposes as missile control system design. A possible distribution of these components is shown in Table I. Servomultipliers are recommended rather than electronic multipliers because most chemical systems are quite slow in response; therefore, a very fast multiplier is not necessary for real-time simulation. In addition, the present higher accuracy potential of the servo is welcome in chemical process simulations. The particular computer shown is manufactured by Electronic Associates, Inc., although several other companies,
The author wishes to thank J. D. Kennedy of Electronic Associates, Inc., for his help in collecting the data of Table 11.
Literature Cited (1) Acrivos, A., Amundson, N. R., IND. ENQ.CHEM.45, 467-71 (1953). ( 2 ~ B ~ ~ ~ S ~ ’ J ~ ~ n ~ ~ (3) Beutler, J. A., Roberts, J. B., Chem. ogr. 52, 69F-74F (February (4
O k h , Amundson, N. R., Journal 1, 513-21 (1955);
(6) Bush, V., Caldwell, S. H., J . Franklin h t . 240,255-326 (1945). V., Gage, F. D., Stewart, H. R., K. L., Hrones, J. A., Reswick, (9) Electronics Associates, Inc., Long Branch, N* J*, “Operations Control Computer” (January 1956)’ (10)
