77 1
I n d . E n g . Chem. Res. 1989,28, 771-777
Subscripts c = expansion stage CO = carbon monoxide H2 = hydrogen in = inlet m = methanol o = saturated vapor Registry No. Cu, 7440-50-8; Co, 630-08-0;CH,OH, 67-56-1; TEGDME, 143-24-8; S3-85, 112002-43-4.
Literature Cited Chem Systems Inc. Methanol from synthesis gas. Eur. Pat. Appl. 34011, Aug 19, 1981. Graaf, G. H. The synthesis of methanol in gas-solid and gas-slurry reactors. Ph.D. Dissertation, The State University of Groningen, The Netherlands, 1988. Kine, C. J. Separation Processes; McGraw-Hill: New York, 1981; Chapter 8. . Kuczvnski. M.: 't Hart. W.: Westertero. K. R. Binarv vaDour-liauid eqklibria of methanol 'with sulfoiane, tetraethilene glycoi di-
methyl ether and 18-crown-6. Chem. Eng. Process. 1986, 20, 53-58. Kuczynski, M.; Oyevaar, M. H.; Pieters, R. T.; Westerterp, K. R. The synthesis of methanol in a countercurrent gas-solid-solid trickle flow reactor. An experimental study. Chem. Eng. Sci. 1987a, 42(8), 1887-1898. Kuczynski, M.; Browne, W. I.; Fontein, H. J.; Westerterp, K. R. Reaction kinetics for the synthesis of methanol from CO and Hz on a copper catalyst. Chem. Eng. Process. 1987b, 21, 179-191. Westerterp, K. R.; Kuczynski, M. Retrofit Methanol Plants with this Converter System. Hydrocarbon Process. 1986, (Nov), 80-83. Westerterp, K. R.; Kuczynski, M. Gas-solid trickle flow hydrodynamics in a packed column. Chem. Eng. Sci. 1987a, 42,
1539-1551. Westerterp, K. R.; Kuczynski, M. A model for a countercurrent gas-solid-solid trickle flow reactor for equilibrium reactions. The methanol synthesis. Chem. Eng. Sci. 1987b,42, 1887-1898. Westerterp, K. R.; Bodewes, Th. N.; Vrijland, M. S. A.; Kucyznski, M. New converter systems for the methanol synthesis. Technical and economical aspects. Hydrocarbon Process 1988(nov), 69-73.
Received f o r review July 15, 1988 Accepted December 20, 1988
Capacity Expansion Study of a Batch Production Line R o b e r t A. Young* Eli Lilly and C o m p a n y , Lilly Corporate Center, Indianapolis, Indiana 46285
G i n t a r a s V. Reklaitis School o f Chemical Engineering, Purdue university, W e s t Lafayette, Indiana 47907
BATCHES, a batch and semicontinuous process simulator, was used t o develop an economical plan for expanding the capacity of a single-product batch chemical plant. The simulation was necessary in order to incorporate specific storage tank policies, restrictions on shared resources, and variable processing times in evaluating process capacities. Simplifying assumptions were introduced which allowed the process to be decoupled into trains whose performance could be predicted by using analytical cycle time expressions. This set of analytical equations was used t o identify process bottlenecks and t o select alternative process and equipment modifications. The most promising set of modifications was evaluated by using the detailed simulation model. T h e simulation results indicated t h a t a 31% increase in capacity could be achieved through modest modifications of the existing facility. The alternative was t o upgrade a second production facility a t 10 times the cost of the changes proposed for the existing facility. Batch and semicontinuous operation continues as a major method of food, pharmaceutical, and chemical processing. It is of particular importance in the manufacture of low-volume specialty products that do not warrant dedicated facilities. Simulation as a predictor of process requirements or process capacities has special value in batch applications because of the many uncertainties and complex operating policies associated with batch processing. However, because of these complexities, general methods of simulating these processes have evolved much more slowly when compared to steady-state processing. Simulation in many cases may be the only way to design, remove processing delays, or evaluate scheduling strategies in which stochastic variations in processing times and operating techniques occur. Analytical scheduling and network synthesis techniques are restricted to simplified representations of the system. However, the positive aspects of analytical techniques are that they provide quick estimates of capacity and can direct process changes. Simulation of all possible combinations of a large number of alternatives can prove to be cost prohibitive. In addition to this, simulation only evaluates alternatives but does not
suggest them. Simulation, on the other hand, can incorporate the complexities of batch processing. Examples of these complexities are processing times varying from one run to another, variations in raw materials, delays occurring when one unit is ready to discharge and the following unit is not available, nonidentical parallel units, or special intermediate storage tank policies. Simulation also permits experimentation without interruption of the physical system and disruptions resulting from the selection of unsuitable operating conditions. This paper describes the use of simulation of a singleproduct production line coupled with simplified analytical calculations to develop an effective expansion plan for the facility. First we discuss the process itself and the goal of the expansion study. Next a review of some of the unique features of BATCHES is presented, followed by a discussion of the simulation model and the results obtained. Process Description The goal of this work was to increase the process capacity of an existing production building by about onethird. If these levels could not be reached, then the al-
0888-5885/89/ 2628-0171$01.50/0 0 1989 American Chemical Society
772 Ind. Eng. Chem. Res., Vol. 28, No. 6. 1989
FLOW CHART PRODUCT
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Figure 1. Product flow chart.
ternative was to upgrade an additional manufacturing building to make the required amount of product. The cost of upgrading an additional facility had been estimated, and the equipment and process changes required in the existing facility had to be weighed against this cost. Figure 1 shows a production flow chart of the process to be modeled, the number of process vessels of each type, and the process capacity for each intermediate. The percent capacities represent the ratio of the actual production rate of each train to the desired production rate. As indicated by the capacities, all three products are below the desired capacity with product Intc rate limiting at 75%. Tanks in a stage have identical functions and are run in parallel but out-of-phase. A description of the process follows. Raw material D is charged into the first available Inta reactor. Raw material P is then charged and is reacted with raw material D until reaction completion is attained. The operator samples the reaction mixture and measures the conversion to determine reaction completion. The two-phase mixture is then transferred immediately to the Inta separator provided that it is empty. Otherwise, the mixture is cooled in the reactor until the separator becomes available. In the separator, the mixture is cooled and then settled for a fixed time, during which a phase separation occurs. The lower layer, an undesired byproduct, is purged. The upper product layer is transferred to the Inta storage tank if sufficient volume to accept the entire batch exists and no transfers out of the storage tank are occurring. Once sufficient material has accumulated in the Inta storage tank, production of Intb begins. The production of Intb and Intc proceeds in a similar manner and will not be discussed in detail (see Young (1988)). The Intb storage tank is operated in the same fashion as the Inta storage tank. The storage tanks allow a change in batch size and provide a buffer capacity between processing trains. Figure 2 shows a detailed equipment flow sheet of the processing tanks and transfer lines used to make the products. The line numbers are important in that they indicate the number of connections between tanks or number of sources of a raw material avaialable. When a transfer is made, a line is assigned an upstream unit and a downstream unit. For example, line 17 is the only line
LVTA IMA SEPARATORS STORAGE
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Figure 2. Flow sheet.
connected to the Intb storage tank. This effectively limits the tank at any given time to the receiving or the transferring of material but not both. This also limits the storage tank to the feeding of one reactor at a time even though it shows connections to all four reactors. In the' case of raw material charges, raw material D is connected to the Inta reactors by one line, which limits the charging of raw material D to only one reactor at a time. In contrast to this, four lines (2-5) are shown for the raw material P charge, which allows all four reactors to charge raw material P simultaneously. Note that the Inta reactors and separators are grouped into two parallel processing trains, both of which share Inta storage.
The BATCHES Simulator To date, most B/SC chemical process simulations have been developed using general purpose simulation languages such as GASP IV, SLAM, or GPSS. Youle (1960),Pritsker (1974), Overturf et al. (1978), Minor et al. (1980), Felder (1983), Felder et al. (1983,1985), and Barnette and Sommerfeld (1987) provide examples of this. These applications have resulted in specialized, single-purpose models. However, since the early 19809, significant effort has been undertaken to produce a general-purpose flow-sheeting system. At least four efforts at developing general-purpose flow-sheeting packages have been reported: Fruit et al. (1974), O'Brien (1982), Czulek (1988), and Joglekar and Reklaitis (1984) and Joglekar et al. (1987). The motivation for these packages has been to obtain a tool for modeling B/SC processes which might function as the batch counterpart to continuous flow-sheeting packages. One of the key distinctions of these simulators from simulation languages is that model development is data driven rather than code driven. If the model or process changes, only the data changes; the simulator itself does not. BATCHES is a general-purpose simulation package which is designed to accommodate the special requirements of B/SC processes: (1) discontinuities in the state of the system (state and time events); (2) dynamic selection of processing paths dependent on the product and state of the system; (3) constraints on the shared resources such as operators and utilities; (4) frequent changes in dimensionality of the system which occur as a result of changes in equipment status, changes in the number of species, or product changes. BATCHES accommodates these requirements by using combined discrete and continuous simulation methodology to model the start-up, execution, and shut-down of batch operations. Although modular in structure, it is equation oriented in its handling of the continuous dynamic seg-
Ind. Eng. Chem. Res., Vol. 28, No. 6, 1989 773 I n t a Reactor
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ments and uses state-of-the-art integration and equationsolving methods to process the associated system of simultaneous differential/algebraic equations. Both timeevent-triggered (predictable) and state-event-triggered (computable from state variable conditions) discontinuities are accommodated, and generalized facilities are provided for the decision-making logic associated with such discontinuities. Process parameters of a stochastic nature are handled via well-known Monte Carlo methods. In BATCHES, process and product entities are represented in terms of two networks: the process equipment network and the product task network. In general, the former consists of a directed graph of equipment items joined by transfer lines. The graph connections correspond to all feasible equipment connections, while the transfer lines are viewed as resources that are allocated to effect specific material transfers. The product task network represents the ordered collection of individual processing steps associated with the production of individual products. Each task is composed of a sequence of subtasks which constitute individual chemical/physical operations, such as filling, heating, holding, and cooling. The details of the operation which occur in each subtask are described via a model and associated model parameters. BATCHES provides a library of 23 processing models, such as Batch Cooling, Filling, Delay, and Batch Reaction, which can be selected to represent subtasks. Thus, the level of detail of a task is controlled by the user both through the selection of the number of subtasks into which the task is decomposed and the sophistication of the models chosen to represent individual subtasks. Each task is carried out in its entirety in a process vessel, and in general any given task may be performed in several possible process vessels. The flow of batches of material through the process is controlled through user-specified product-processing sequences and queue-priority disciplines. The former define the quantity and order in which the required batches are made, while the latter is the mechanism for assigning batches to downstream units during the course of recipe execution. For further informaiton on BATCHES, the reader is referred to BATCHES User's Manual (1988) or to previous publications (Jogkelar and Reklaitis, 1984; Joglekar et al., 1987). Model Development of a BATCHES simulation requires definition of the equipment network, creation of the task network, and specification of the simulation parameter tile. In the present instance, the input information for the equipment network consists of the connections shown in Figure 2, the size and heat-transfer area of each process vessel, and the processing rates associated with the transfer lines.
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In this study, it is convenient to represent the task network in terms of three components, one for each of the three identifiable intermediates (Inta, Intb, Intc). Figure 3 shows the task network for Inta, with each task subdivided into its component subtasks. (The task networks for Intb and Intc are similar in character but differ in the details.) The second line in each subtask block indicates the BATCHES model used for the subtask. Since species level dynamics were not critical in this process study, simplified subtask models sufficed for most purposes. For instance, in the case of task 1, the Filling model with constant conditions and flow rate was used for the Charge subtasks, the Delay model with normally distributed random processing time was used for the React/Cool subtask, and the Emptying model with constant conditions and flow rate proved adequate for the Transfer subtask. A more detailed reactor model employing kinetics and species balances was used for some of the reaction steps primarily to evaluate the effects of the specific operating changes. But as the species level effects do not affect the overall plant simulation, these models were used on a stand-alone basis. In the cases of tasks 2 and 3, the General Tank model was used for situations where simultaneous filling and emptying or variable rate transfers had to be accommodated. In all cases in which parameters were known to exhibit variability, the parameters were assumed to be normal with means and variances calculated from historical data logged on the process computer. Validation In this section, the methods used to measure and evaluate the results of a simulation are presented. Variability in the simulation results and model validation are then discussed. Capacity measurements were used in evaluating simulation results and were taken after steady state was achieved. Each simulation run provides a summary of the total number of batches made and the equipment utilization and queue statistics. The utilization and queue statistics were generally used for diagnostic purposes rather than for comparison of alternatives. A t least three sources of variability in capacity were important to the model results: variability created by process interactions, variability created by sampling from the normal distributions used to model subtask times, and transients occurring prior to achieving steady state. The first two sources of variation are reflected in the simulation capacity results. The third source was eliminated by delaying the data collection start time until after steady state was achieved. Figure 4 shows the average daily production
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Ind. Eng. Chem. Res., Vol. 28, No. 6, 1989
expressed as percent of the goal production rate for a period of 15 days, measured in the Inta train. As indicated by the figure, steady state begins at or before 3 days of processing. This was selected as the time to achieve steady state in all subsequent simulation runs. Four-day averages and their associated confidence limits are also shown in Figure 4. Four-day averages of the overall capacity, because of their lower variability, were used to evaluate capacities for each run. Extended simulation times and the use of different random number seeds for the subtask time distributions indicated that the 95% confidence limit for a significant difference between capacity results is about 1.2%. The initial conditions for all of the runs used to establish this statistic were the same. Validation of the model was carried out by comparing simulation results against production results. Both process delay times (average waiting time per batch) and process capacities (average daily production rate) were compared. The differences between the delay times predicted by the model were generally less than 10%. The predicted overall process capacities were within 0.5%,that is, 74.4% of the goal for the model versus 74.1% from production measurements.
Simulation Results The approach to finding a low-cost feasible solution consisted of two stages. In the first stage, simplifying assumptions were introduced which would allow the process cycle time to be calculated by using straightforward analytical expressions. The simplifying assumptions generally corresponded to constraint relaxations, the result of which is that the analytical calculations lead to upper bound estimates of the actual process capacity. The simplified process representation was then used initially to establish whether the desired capacity expansion could be achieved and second to identify the most promising modifications from the set of possible process changes. In the second stage, the simulation model was used to verify and evaluate proposed modifications in light of actual process constraints and nonidealities. The final design changes were selected based on the economic aspects of each option. Simplified Capacity Estimate. The production goal was a one-third increase in capacity. The first step was to make sure that goal levels could be reached with changes that could be made to the process and the equipment in the manufacturing building. Five mechanisms were used to increase the capacity: (1) Eliminate processing step interactions that could lead to delays. (2) Increase batch size. (3) Increase the number of parallel units. (4) Reduce processing times. (5) Increase transfer rates. Yeh and Reklaitis (1987) define a set of relations that can be used to calculate the capacity of a processing stage. Given batch equipment type j and semicontinuous equipment type k,the following equations can be written to estimate batch cycle times: B,, = min ( V j / S j ) for all j between storage tanks where B , is the maximum batch size, V, is the size of equipment type j , and S, is the size factor for equipment j , Xk = B / R k
(2)
where X k is the transfer time using equipment k , B is the batch size, and Rk is the transfer rate for equipment k , (3) where Ti is the cycle time at stage j , X,,? is the filling time,
P, is the processing time, X,, j ) is the emptying time, and mj is the number of parallel units operating out-of-phase, Ti = BiTj/Bj (4)
for changing batch sizes across storage tanks where Ti is the cycle time corrected for batch size, Bi is the batch size for stage i, T, is the cycle time for batch size j , and Bj is the batch size for stage j . As discussed above, the first step was to eliminate potential interactions between processing steps. This included interactions around storage tanks and shared raw material sources between processing steps. Assuming adequate storage capacity a t the storage tanks and no restrictions on the transfer of material into and out of the tanks eliminated storage tank interactions. Raw material W and raw material L are shared from common sources between the Intb and Intc processes. A second raw material W source and raw material L source were added to eliminate potential delays that could occur due to the sharing of these resources. This decoupling of processing trains allowed the capacities of the three trains to be computed separately by using the above relations. With the processing trains decoupled, process changes that would provide an upper bound on the capacity of the facility were proposed. If this upper bound capacity is less than the required capacity, then no further work on the existing facility is warranted, and effort should be directed to the new facility. Since the goal was to provide a quick estimate of the upper bound, changes that could be made with a high degree of certainty were selected first. For example, the amount that a process time can be reduced must be extrapolated based on experience. The implementation requires experimentation and production trials. As a result, a change in the product recipe carries with it a higher degree of uncertainty and then addition of a parallel unit. For this reason, equipment changes were generally the first choice where physical space constraints were not present. The results of applying eq 1-4 to the process stages are shown in Table I. Note that, to protect proprietary information, the time units reported are relative units which are defined in terms of the batch size of Inta, B,, which is fixed by the size of the Inta reactors, and the target production rate of Inta, B,/T, where T is the cycle time of the Inta reactor stage. The time scale has been chosen so that B,/(B,/T) = 100 and thus all time quantities are scaled by this time factor. In particular, the column of task times is reported in these scaled units. Given these task times and the number of parallel equipment, the column of initial cycle time is next computed. Note that the Intb and Intc cycle times listed are not the direct train cycle times but instead have been translated via eq 4 to equivalent Inta reactor stage cycle times so as to provide a common basis for comparison. Note further that, as a result of the choice of the relative time scale, an Inta reactor stage cycle time of 100 will result in the production of Inta at the goal production rate. Thus, in order to meet the goal production rate, all of the stages must achieve a new cycle time of less than 100. As evident from the initial cycle time column, all of the stages will require modifications in either task time or number of units. A set of feasible process changes (to be discussed individually subsequently) which can lead toward achievement of the target cycle time are summarized in the next column. Finally, when the revised task times and equipment numbers resulting from the proposed changes are used with eq 1-4, the new cycle times shown in the last column of Table I are obtained. Note again that the Intb and Intc
Ind. Eng. Chem. Res., Vol. 28, No. 6, 1989 775 Table I. Current Cycle Times and Initial Modifications stage task time no. of equip initial cycle timea Inta reaction 490 4 123 separation 205 2 103 ~~
~
new cycle time' 85 77
208
Unlimited Storage: Simultaneous Fill and Draw 1 111 increase to maximum batch size reduce reaction time by 6 1 103 increase to maximum batch size
98 84
835 186
Unlimited Storage: Simultaneous Fill and Draw 4 115 add one reactor 1 103 reduce process time by 6
92 96
Intb reaction
215
wash Intc reaction wash RWMD RWMP RWML RWMW RWMA a
changes reduce reaction time by 150 reduce process time by 52
Raw Material Sources 64 15 51 13 135
no changes no changes add one source add one source add one source
64 15 26 6.5 68
Reported as equivalent Inta reactor stage cycle times.
cycle times are reported as equivalent Inta reactor stage times. We next discuss the rationale for the process changes listed in Table I, beginning with the Inta reactor stage. It is evident from the initial stage cycle time of 123 that the cycle time is unacceptable. It can be reduced either by adding another reactor or by revising the recipe so as to reduce the task time. While adding a fifth reactor would reduce the stage cycle time to less than 100, insufficient building space existed and historical data indicated that a significant reduction in reaction time might be possible. The data indicated that the reaction time could be cut by 150, yielding a task time of 340. The result was a stage cycle time of 85. A similar case existed for the separators. In the case of Intb, only part of the available tank volumes was being used. This batch size had been set by plant personnel at 57 70of the available tank volume based on empirical production data that suggested this gave optimum overall capacity given the interactions that existed around the Inta storage tank. However, since in this step processing times other than transfer and charge times could be assumed to remain constant with a change in batch size, maximizing the batch size will maximize the amount of product that could be processed in a given time increment. Therefore, our simplified analysis indicates that increasing the batch size to the maximum allowed by tank capacity would be desirable. In addition, the proposed change also included decreasing the process time by 6 units for reasons similar to those discussed for the Inta tasks. Finally in the case of Intc, physical space in the facility allowed the addition of a fifth Intc reactor. Spreading the task over five reactors instead of four would reduce the stage cycle time from 115 to 92. Improvements in the wash tank cycle time could only be achieved via a reduction in processing time since additional space in the facility did not exist for a second tank. Thus, a reduction of 6 time units was proposed. A cycle time can also be calculated for the raw material sources by treating them as semicontinuous equipment. This is done by summing the usage times for the stages that share a common raw material. Adding a raw material source might mean simply installing a second metering source, while in other cases a new supply system might be required. Finally, since only raw material A has a cycle time greater than 100, a second raw material source was added to meet the capacity requirements. The second raw material sources for raw materials L and W were added to eliminate potential interactions across the processing
Table 11. Simulated Independent Train Capacities (Percent of Goal) upper bound train unmodified capacities capacities Inta 82 113 Intb 82 105 74 109 Intc Table 111. General Effects Quantified through Simulation caDacitv case 1: storage tank policies condition: storage tank policy: do not allow simultaneous fill and draw changes : allow simultaneous fill and draw a t both storage +5.0% tanks allow simultaneous fill and draw a t Inta storage +5.0% tank only case 2: variable process times condition: use average process times in model changes: use variable process times based on distribution of -3.1% production data case 3: equipment-dependent process times condition: Inta tasks have the same process time distributions changes: use actual process time distributions for each train -1.5%
trains as discussed earlier in this section. To confirm the adequacy of the above proposed changes, simulation runs were made of the process under conditions in which the process trains were decoupled. The results, shown in Table 11, are reported in terms of percent target production rate achieved, based on a 4-day average production during the steady-state portion of each simulation run. The column labeled unmodified capacities corresponds to the percent desired production rate that the original process could achieve if the trains are decoupled. These rates correspond quite closely to the historical capacity averages under the actual operating conditions shown in Figure 1. The column labeled upper bound capacities gives the percent target capacity if the process changes discussed earlier are implemented. Note that these are upper bounds since the process has been decomposed into independent trains. These figures provide assurance that the proposed changes are likely to achieve the desired production goal. Case Evaluations. As discussed earlier, the results presented in Table I1 represent an upper bound in that train interactions have been removed and thus are esti-
776 Ind. Eng. Chem. Res., Vol. 28, No. 6, 1989 Table IV. Inta Subtask Time Variations train 1 distribution av std dev Inta subtasks 29 4.0 charge RWMD charge RWMD 38 4.0 10.0 244 react/cool 2i 3.0 transfer 10 0.0 cool/separate 26 0.0 separate RWMD transfer prod 10 0.0
train 2 distribution av std dev 28 1.4 40 8.0 245 10.0 28 4.0 10 0.0 34 0.0 10 0.0
mates of what can actually be achieved. Table I11 shows the results obtained when interactions and processing variabilities are introduced into the simulation. The full impact of these changes cannot be determined in an analytical calculation or an analysis using Gantt charts. As discussed earlier, the 95% confidence limits for a significant difference in capacity results is about 1.2 70. The initial storage tank policy was to allow only feed or withdrawal but not both. This meant that tanks upstream of the storage tank might be delayed while waiting for a tank downstream of the storage tank to withdraw material and vice versa. While an analytical model can show that these tanks are large enough to prevent delays in processing, the analytical model does not allow incorporation of actual storage tank operating policies. As indicated in case 1 of Table 111, this storage tank policy only created significant delays when it was in effect for the Inta storage tank. Capacity was not affected by this storage tank policy for the Intb storage tank. While the storage tanks are identical in size, the batch sizes for the tasks feeding and withdrawing material from the two storage tanks differ. For the Intb storage tank, the batch size in is about 2 times as large as the batch size out. For the Inta storage tank, the batch size in is about one-fourth the batch size out. While both storage tanks could be modified to operate in a simultaneous fill and draw mode, modifying only the Inta storage tank will be sufficient to achieve the desired increase in capacity. Case 2 in Table I11 indicates the impact that stochastic variations in processing times can have on capacity. In the base case, only average process times for the Inta process were used. Table IV shows the variations actually present in each Inta train based on historical data. When the distributions reflecting the actual variability of the production times, neglecting equipment differences, were used, the simulation predicted a 3.1 % reduction in overall capacity. In case 3, the train-dependent processing times were incorporated into the model. Initially both trains were assumed to follow identical process time distributions as presented in case 2. Using the actual processing time distributions for each train reduced the capacity by about 1.5%. The importance of these results to plant personnel is that, if the variations in the Inta steps could be eliminated, then nearly a 5% gain in capacity could be realized. Table V shows a case study of a batch size change complicated by resources shared across processing steps. The shared resources are the storage tanks and the raw material sources L and W. The Inta storage tank is operated with a policy allowing simultaneous fill and draw while the Intb storage tank is not. Only one tank can draw raw material L at a time with the current configuration. If two tanks require raw material L, one will be delayed until the other completes its charge of L. The same constraint applies to raw material W. Case 1 in Table V was used as a reference point. Capacities are presented as a percentage of the goal capacity. The calculated cycles times indicate that the rate-limiting
Table V. Case Study of Shared Resources and Batch Size Interactions (Caoacities as Percent of Goal) % capacities relative to goal case Inta Intb Intc overall 1. base case calculated 103 108 105 103 simulated 99 2. reduce Intb batch size calculated 103 102 105 102 simulated 92 3. eliminate interactions simulated 99 102 100 4. one RWML and RWMW source (no storage tank constraints) simulated 100 92 100 5. two RWML and RWMW sources (reapply storage tank constraints) simulated 100
step is Inta at 103%. However, the simulated overall capacity because of variabilities discussed earlier is only about 99%. This constitutes a satisfactory capacity relative to the goal given that the 95% confidence limit for a significant difference is 1.2%. Upon further plant evaluations, it was concluded that the proposed Intb batch size increase of 75% was not possible. Production implementation indicated that the batch size could only be increased by 16% because of other processing constraints. To model the impact of this constraint, the Intb batch size had to be reduced to 68% of that used in case 1. As shown in case 2, in spite of calculated rates above the goal capacity, the overall capacity of the process dropped to 92%. The purpose of cases 3-5 was to determine why the overall capacity was limited at 92%, when the rate-limiting step had a calculated capacity of 102%. Case 3 shows the elimination of all processing step interactions, such that the independent train capacities could be simulated. This is equivalent to adding a second source of raw material L and W and relaxing the storage tank constraints. Relaxation of the storage tank constraints converted the storage tanks to infinite sinks and sources for the intermediates. As indicated by the increase in the Intb train capacity from 92% to 102%, either the storage tanks or the raw material feed systems were causing processing delays which reduced the overall capacity. In case 4,the constraint of only one raw material source, namely, L and W, for the entire process was reapplied. The result was a drop in the Intb train capacity to 92% with the rest of the train capacities unaffected. Case 5 was used to confirm this finding by reapplying the storage tank constraints while providing two raw material L and two raw material W sources. This result indicated the raw material sources were causing processing delays, while the storage tanks were not. Furthermore, to eliminate these delays and reach goal capacities, an additional source of L and W would be required. Thus, in spite of the fact that the batch size could only be increased by 16%, the desired capacity could still be achieved in the existing facility. The above results provide only representative examples of the information that the simulation model provided. Numerous additional simulation studies were run to evaluate alternative equipment configurations, processing changes, and changes in processing policies. For a complete record of these case studies, the reader is referred to Young (1988). Production Implementation Only partial implementation of the recommended changes to the production facility has been implemented
Ind. Eng. Chem. Res., Vol. 28, No. 6, 1989 777 Table VI. Process Modifications 1. reduce Inta task 2 process times by 22.7% 2. simultaneous fill and draw from Inta storage tank 3. reduced Intc task 1 time a. reduce raw material A charge time by 9.5% b. reduce process time by 15.6% c. increase batch size by 7% 4. two raw material A meters 5. increase Intb batch size by 16% 6. reduce tk47 process time by 40% 7. reduce tk15 process time by 25% Table VII. Production Results (Capacities as Percent of Goal) process model actual initial 74.4 74.1 modified 82.4 82.1
a t this time. The changes that have been implemented in production are listed in Table VI. The actual production results and the model predictions are compared in Table VII. As indicated by the results, the differences between the capacities predicted by the model and those measured in production are small. The final capacity predicted by the model was 82.4% of the goal, while actual production results were 82.170for a 1-month period. This difference is well within the 1.2% error estimated for the model. These results indicate the effectiveness of simulation as a predictive tool for proposed process changes. The other recommendations required to reach the goal capacity will be implemented pending equipment delivery and selection of the most appropriate shutdown schedule.
Summary The simulation predicts that nearly 100% of the goal capacity can be reached with only moderate changes to the existing facility. The cost of modifying the existing facility is about lll0 the cost of upgrading a second production facility, even when the increased operating costs associated with a second production building are not included. Through simulation, a low-cost feasible solution has been selected without interrupting the process. Several expensive alternatives which had been proposed were avoided by making the changes that gave the most cost-effective improvement in process capacity. While only part of the recommended changes have been implemented a t this point, the simulation accurately predicted the increase in capacity that would occur with these changes. The result of these initial changes was a 10% increase in the production capacity. When the rest of the recommended changes are implemented, the simulation predicts that the capacity of the starting network will be increased by 31% . These simulation results indicate the effectiveness of BATCHES in the modeling of a batch process. The simulator proved useful in achieving production goals. Simulation results targeted the parts of the process requiring changes and predicted the impact of process changes. The
technique of using analytical methods to select process changes followed by simulation studies proved an effective method for making processing improvements.
Acknowledgment Many employees at Eli Lilly and Company collected the data used in the model and guided the implementation of the simulation results. The authors gratefully acknowledge their support, which made this study possible. The employees of Batch Technologies Incorporated assisted in the application of the BATCHES simulator. In particular, the authors gratefully acknowledge the invaluable assistance provided by Girish Joglekar, Steve Clark, and Dave Carmichael.
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