ABSTRACT. Many similar problems will come to mind, often associated with design

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1 Manufacturing~Engineering DESIGN AND MODIFICATION OF STEAM SYSTEMS WITH THE AID OF COMPUTERS D. B. Batstone Bureau of Sugar Experiment Stations Bundaberg, Queensland, Australia ABSTRACT The use of a general program in computer-aided design is illustrated by an investigation into a proposal for increased vapour bleeding. A distinction is drawn between programs written specifically for 1 plant and general programs used for design. The latter requires a less detailed knowledge of theprocess as design basically needs to be less accurate than process analysis. Detailed models can be incorporated in a general.program as they become available and when it becomes desirable. The structure of a general program, the data required for an investigation, and the way a data package is prepared are all described in terms of the example. General programs make a feature of little or no reprograming for alternative processes, bringing many positive benefits, especially if the engineer is not an expert programer. INTRODUCTION Process analysis, improvement, and design by computer are gradually becoming routine in the petroleum and chemical industries. The techniques have been adopted slowly in the sugar industry. There are reasons. One is the small size of sugar factories. But, most importantly, we do not know enough about the processes in sugar making. We cannot even measure all the components of what is coming in, let alone predict what happens to the rather variable raw material. These circumstances favour a different approach to computer applications where process analysis by simulation is typically the first step. The rewards can be very great if an adequate model of the process exists. Brooks (1962) in his pioneering work at Crockett refinery described the benefits of simulation. Others, such as Lui (1966, 1967), Wright and White (1968), Murry and Russell (1969), and Higgins (1970), have contributed towards a better description of a sugar factory. Much remains to be done before individual factories use a simulation program for routine supervisory functions. Now consider a different approach, which solves a different type of problem, a type which seems to arise fairly regularly. The following exercise is a small but typical example. Fig. 1 shows the existing heater and evaporator arrangement at 1. Queensland mill. Management wanted to increase vapour bleeding for overall steam economy and at the same time hoped to increase juice capacity. The obvious modification is shown in Fig. 2. But there was some doubt that vapour temperatures would be high enough to obtain the desired juice temperature. Many similar problems will come to mind, often associated with design 1370

2 D. B. BATSTONE 1371 JUICE Fig. 1. Existing arrangement of the evaporators and heaters. Fig. 2. Modified arrangement for vapour bleeding. and modification for increased steam economy, throughput, or extraction. The steam system is a particularly fruitful area. How are the techniques different from the simulation approach, described earlier, and why is a good model of the process not as important? Briefly, in answer to the last question, often in design a high order of accuracy is not necessary or not possible. After all, we are dealing with the future, and the future conditions can only be predicted imperfectly. However, the best use of available information can be made by using machine computation. Certainly there is a need to upgrade our knowledge, to improve the accuracy of predictions, but in the meantime plants must be modified and a design must be produced. Let the design be as good as it can be. Unlike the analysis of a single process, design requires a program which can be used to simulate many different arrangements. In the normal design activity the designer will select one alternative from many. The screening may be on the basis of experience, as was the exclusion of all other possible arrangements in the example. A 'general design program provides the facility for screening alternatives on a less arbitrary basis. The performance of various alternatives is determined, and the one with the most satisfactory or best performance is chosen. The terminology- so far, has been deliberately loose. A clear distinction had to be made between the analysis of a single factory and design and modification. The latter, it was said, required a program which could be used for many arrangements of units-a general design program. The distinction becomes quite blurred whenla- general program is used to simulate a single factory for process analysis. tt can be used for this purpose, but it may not be as efficient in computing as a program written especially for that factory.

3 1372 MANUFACTURING--ENGINEERING METHOD General Design Program One general program has been used since 1967 for the design andmodification of sugar factory steam systems (Batstone and Prince, 1967, 1969). The intention is to describe the use of the program by the example quoted earlier: The comments could apply equally as well to the use of other programs which have been reviewed by Evans, et al. (1968), some of which are available.. The following parts make,up a typical design program: 1) executive program, 2) unit subprogram, 3) convergence, 4) ordering, 5) optimization, and 6) physical property. Executive program: The executive program has a control function and consists of the following: a) initialization, b) read-in, c) test for ordering, d) test for optimization, e) calling unit subprograms-in order, f) test for convergence, g) test for non-convergence, h) error diagnostics, and i) print-out. The other parts of the program ani subroutines, and without too much detail each has a specific task. Unit subroutine. Each unit is described by a different set of equationsthe mathematical model. The subprogram is written to solve these equations for specified or known inputs. A unit is treated as a box with input streams and output streams. 1 the input streams are known, solving the equations of the model will provide known values for the output streams. Variables in each stream are theflowrates of each component (sugar, water, impur.ities and vapour in the example) and temperature. Convergence. The unit subprograms give outpufs from inputs. Sometimes the inputs are not all known. The condition can arise from recycle or if the output is specified. The convergence subroutine refines an initial guess or estimate of the unkown stream by comparing it with a calculated value. Thus, the calculation starts at a unit-usually with a feed stream-and works from unit to unit in a certain order. The unknown streams are guessed where necessary, and at the end of the calculation the guesses and the calculated values of the same stream are compared. 1 the guesses are close enough, the calculation has converged. 1 not, the convergence subprogram calculates a better guess at the unknown streams. Ordering. It is easy to visualize that the less guesses which have to be made the easier it would be to converge the calculation. Up to a point this is correct. But it is not always easy to find the order of units which minimizes the number of guesses. Techniques have been described by Batstone and Prince (1970) and Christensen and Rudd (1969) which solve the problem numerically. Optimization. Optimization was spoken about indirectly when the words process improvement, best design, and objective were used. The optimization subroutine provides a way of obtaining the objective of best design or best operating policy. The objective must be written out in a special way: maximize or minimize a function f of one or more variables x, i.e. maximize or minimize f (Xi)' The function depends on the system to be optimized but in all cases the function is maximized or minimized by the choice of values of control variables. The 0J;timiza~ion subroutine does this by searching for better values of the con-

4 D. B. BATSTONE 1373 trol variables. There are constraints on the choice of variables. One is the viability of the system. To put the whole business in a better perspective, consider again the example in Fig. 2. Assume the management's objective was now to maximize the juice capacity by vapour bleeding to the pan stage. This is a simple case I control variable (vapour rate) to the pan stage, I term in the objective function (juice capacity). Vapour bleeding affects juice capacity (Crawford, 1953; Batstone and Prince, 1969), and there must be some value of the bleed rate which will maximize capacity (it could be zero). The constraints are the model of the process,. and the rate of vapour bleeding must be zero or greater. In a somewhat different but quite useful application, the optimization subroutine can be used to measure the performance of a plant. The problem arose in the quoted example. The only information supplied by the mill is listed in Table 1. But we need to know the overall coefficient of heat transfer to predict Table 1. Parameter Data supplied by the mill. Value Juice capacity Juice brix Syrup brix Steam pressure Vapour pressures No.1 No. 2 No. 3 No. 4 No ,000 Ibjh 16 bx 72 bx 15 Ibjin. 2 (max.) 6 8 Ibjin Ib/In.s 0 2 Ibjin in.hg, in.hg. the performance of each evaporator vessel. If the objective function is made the expression: 6 f (XI) = ~ V Xi - Xi *) 2, i = I where x, = measured juice capacity, x 2, x g, X4>X 5' Xa, = measured vapour temperatures and Xi* the corresponding calculated variable, we can by choice of U i _ l (the overall coefficients of heat transfer for the 5 vessels, now the control variables) minimize the error between measured and predicted performance. The optimization subroutine based on the simplex technique described by NeIder and Mead (1965) was used to control the search for the coefficients U i _ l Physical properties. There are several ways of handling the prediction of physical property data. In the example quoted-boiling point elevation-specific heat of sugar solution and thermodynamic data for steam are all required. The relationships here have been written into each unit subprogram and take the form: (for boiling point elevation) BPE 4.2 X B B

5 1374 MANUFACTURING-ENGINEERING where BPE = boiling point elevation and B = product brix. Other programs have more refined physical property packages of special subroutines. The Investigation The stage is set. The information has been supplied by the mill (Fig. 1; 2 and Table I), and a program is.available. In outline, this investigation was in 2 stages: I) to measure coefficients of heat transfer for each vessel using' the method outlined under optimization and 2) to evaluate the performance of the modified arrangement. ' The first task is to translate the information from the mill into a form suitable for input with the program. The specific items of datil are listed: I) problem identification, 2) flowsheet, 3) order of calculation (if knownj, 4) specified variables, 5) estimated variables, and 6) unit parameter. Problem identification. The mill name, calculation number, number of units, streams, recycle streams (if known), and variables are included on a single data card. Flotosheet, The program is a general one. Any arrangement of units can be simulated with little or no reprograming. To achieve this the flowsheet must be presented as part of the data. The flowsheet in Fig. 3 is the same as Fig -. 2 (,'" Fig. 3. Flowsheet suitable for computation. modified for the program. Note that all units and streams have been numbered and extra units for junctions and splits of streams have been added. The structure of theflowsheet is now represented for computer input as a matrix M (i, j) i = I, NS and j = I, 3, where M (i, I) = unit at the head of stream i, M (i, 2) = unit at the tail of stream i, M (i, 3) = the number of unknown variables in stream i, and NS = number of streams. Further information on the flowsheet is contained in a list of call cards in the body of the program. The call card for unit I, the first evaporator vessel, has the form I CALL EFFET (4,5,6,7,8, 12000, P (1, I), P (1,2),0.0, 0.0, 0.0), where I is the statement number, 4, 5, 6, 7, and 8 are stream numbers, is the area for heat transfer, P (I, I) is the unit parameter coefficient of heat transfer, and P (1, 2) is the unit parameter fractional heat recovery. The two units 8 and 9, which have been added to the flowsheet, are hypothetical units which cater for the output variables, final vapour temperature, and final syrup brix which are specified in the problem. Order ot calculation. The order of calculation is quite clear in this exam-

6 D.B. BATSTONE 1375 pie. The order of units 7, 6, 1, 10, 2, 11, 3, 4, 5, 8, and 9 imply that one variable in each of streams 2 and 5 is unknown. Two recycle variables must be converged in the calculation. No other order will give less unknown variables. Specified uariables. Steam temperature, vapour temperature, juice brix, and syrup brix are all specified. These variables are entered onto specified variable cards, 1 stream to each card. Estimated variables. The user can enter his guesses at the likely values of the recycle variables, in the example steam and juice rate. Again 1 card is used for each recycle stream. Unit parameter. These cards allow the user options in varying such parameters as coefficient of heat transfer or fractional heatrecovery in the example. The data package for the original flowsheet contained 9 data cards and 10 call cards. With the addition of 2 extra call cards and 2 extra data cards, the data package was changed for the modified flowsheet. RESULTS The search for the heat transfer coefficients for the existing arrangement gave the results in Table 2. The problem of validation should be raised here. Table 2. Comparison of measured and predicted temperatures and evaporator capacity. Measured. range (lb/h= 332,000) Predicted (lbjh= Vessel Coefficient 328,568) Ino.) (btujhft2 F) Vapour temp (OF) no. I I 340 no no : no no Our approach would be quite incorrect had the programs and unit subprograms not been tested prior to this application. The programs have been tested in other applications and the results discussed elsewhere (Batstone and Prince, 1969). With satisfactory prediction of the current operation, the modified vapour bleeding was then simulated. No optimization was used this time. All that was required was an estimate of vapour temperatures to the heater and total juice capacity of the station. The results of calculations for different conditions are presented in Table 3. DISCUSSION The low coefficient of heat transfer of the 1st vessel has unfortunate consequences for vapour bleeding. At the highest steam pressure in case 1, the margin of vapour temperature above thedesired juice temperature of 220 F is only

7 1376 MANUFACTURING-ENGINEERING Table 3. Vapour temperature and predicted evaporator capacity for modified vapour bleeding. Steam pressure Temperature of vapour (OF) Elfet capacity (lb/in. 2g) for vessel no. (lb/h) Case I ,000' Case , Heat transfer coelf. (btu/hft2 F) for vessel no Case I Case ',,: 10 F. The margin is increased by 6 F if the coefficient is improved to a reasonable figure of 550 btu/hft2 F. The example is a rather straightforward exercise with a recommendation to improve the operation of the first vessel. Still it contains all the ingredients and benefits of computer-aided design. The question of costs may be of interest. Considering only the running costs of the program on a PDP 10 machine at the University of Queensland, the cost was $1 per simulation, or less when more than 2 runs were contained in the same batch. The costs vary, but a controlled search to measure the operating performance of the evaporator station, assuming 15 search points, would cost about $15. The costs are quite insignificant when compared to the cost of hand solution. REFERENCES Batstone,D. B., and R. G. H. P. Prince Plant design and modification by digital simulation. Proc, QSSCT, 34: Batstone, D. B., and R. G. H. P. Prince Planning evaporator stations by computer simulation. Proc. QSSCT, 36: Brooks, R. M A sugar refinery simulation model. Management Technology, 2 (2) :1l Crawford, W. R~ The capacity of evaporators. Proc. QSSCT, 20: Evans, L. B., D. G. Steward, and C. R. Sprague Computer-aided chemical process design. Chern. Eng. Progr., 64(4) : Higgins, I. S Evaporator heat balance calculations using a digital computer. British Sugar Corp. Ltd., 20th Technical Conf. Lui, E. J Digital computer applications for the factory. Haw. Sugar Tech. Annual Conf., 25: Lui, E. J Digital computer applications in the factory-simulation. Haw. Sugar Tech. Annual Conf., 27:156~162.

8 D. B. BATSTONE 1377 Murry, C. R., and G. E. Russell A simulated crushing experiment. Proc. QSSCT, 36: NeIder, ]. A., and R. Mead A simplex method for function minimization. Computer]., 7: Wright, P. G., and E. T. White A digital simulation of the vacuum pan crystallization process. Proc. ISSCT, 13: