The Interface between Design and Control. 2. Process Operability

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Ind. Eng. Chem. Res. 1988, 27, 606-611

The Interface between Design and Control. 2. Process Operability Wayne R. Fisher, Michael F. Doherty, and James M. Douglas* Department of Chemical Engineering, University of Massachusetts, Amherst, Massachusetts 01003

At the preliminary stage of a process design, the optimum steady-state designs of various process alternatives often are not operable. That is, the optimum steady-state design fixes the equipment sizes based on the mean value of the disturbances, but as disturbances enter the plant the fixed equipment sizes may prevent the process constraints from being satisfied or may prevent the operating variables from being adjusted to significantly lower the operating costs. Operability problems can be overcome either by an appropriate amount of flexibility or by developing alternative operating policies, and we want to determine the alternative that has the smallest cost penalty. By evaluating operability alternatives a t the preliminary stage of a process design, we can include some of the economic penalties associated with control as an additional criterion for screening flow-sheet alternatives.

As discussed in part 1 of this paper, we are attempting to develop a systematic, hierarchical approach to the synthesis of control systems for complete plants. The initial level of our hierarchy is focused on steady-state considerations and the incentive for modifying the conceptual designs of various process alternatives in order to improve the potential control of the process. These systematic procedures can be used as the basis for interactive computer programs that would make it possible to rapidly screen flow-sheet alternatives. In part 1 of this series, we presented a systematic procedure for a controllability analysis that can be used to identify the significant disturbances and to ensure that there are an adequate number of manipulative variables to be able to satisfy the active process constraints and to optimize the significant operating variables. Part of the controllability anlysis is focused on flow-sheet modifications to accomplish these goals. In this part of the study we focus on process operability. The goal of the operability analysis is to ensure that there is an adequate amount of equipment overdesign so that we can satisfy the process constraints and minimize a combination of the operating costs and overdesign costs over the entire range of anticipated process disturbances. Thus, we again focus on modifications of the optimum design of an alternative to accommodate disturbances that enter the plant. Most processes are not operable at the preliminary design stage. That is, the optimum steady-state design fixes the equipment sizes based on the mean values of the disturbances. Then, as disturbances enter the plant, the fixed equipment sizes often prevent the process constraints from being satisfied. Similarly, the fixed equipment sizes often prevent some of the operating variables from being adjusted to lower the operating costs as disturbances enter the process (whereas with some additional overdesign it might be possible to obtain significantly reduced operating costs). Our goal, then, is to restore operability with the smallest economic penalty. When process constraints are violated, we restore operability either by equipment overdesign or by looking for an alternative operating policy (i.e., a new manipulative variable) that can be used to satisfy that constraint. Limitations on the optimization of operating variables can also be removed by overdesign, and we must evaluate the economic trade-offs involved. Previous Work The conventional approach to overdesign only considered the use of overdesign to make it possible to increase 0888-5885/88/2627-0606$01.50/0

the capacity of the plant and to allow for uncertainties in design correlations or other design data; i.e., disturbances were not normally considered as part of the overdesign calculations. Since few plants were designed to operate at the optimum design conditions, most of the equipment constraints we are discussing were not encountered. However, now that optimization procedures are being included in design simulators, the problem of adding overdesign to the optimum design will grow in importance. The effects of disturbances are sometimes considered as part of a safety or failure analysis, but a systematic approach to considering the effects of disturbances at the conceptual stage of a process design, where the screening of process alternatives is the primary focus of the design activity, does not seem to be available. An alternative approach considers a statistical distribution of the uncertain design parameters (which could be reformulated as disturbances) and evaluates the equipment sizes that maximize the expected value of the profit (Kittrell and Watson, 1966). A review of this approach has been presented by Grossman et al. (1982). Also, Morari et al. (1979,1980)have developed specialized tools for evaluating the resiliency of heat exchanger networks, and Swaney and Grossmann (1985a,b), Grossmann and Morari (1983) have developed a procedure for evaluating the operational flexibility of a process. Halemane and Grossmann (1983) developed an exact solution procedure for the overdesign problem, which involves solving the optimum steady-state control problem as a function of the disturbances for every value of each of the equipment sizes. The method locates that combination of operating costs and annualized capital costs that maximizes the expected profit. The problem is cast as a mixed integer, nonlinear programming problem which becomes very large and requires a considerable amount of computation for complete flow sheets. Nevertheless, this approach has great potential for application in the final design stages of large projects. At the preliminary design and synthesis stage, where we are screening a large number of alternative flow sheets, we want to keep the size of the problem as small as possible and to keep the calculations as simple as possible. In part 1 of this series, we described a procedure for eliminating disturbance variables that did not have a significant impact on the process economics; i.e., we simplified the problem based on short-cut calculations. Our goal here is similar. That is, we want to undertake a preliminary screening calculation in order to see if either a statistical analysis or the procedure of Halemane and Grossmann (1983) can be justified. Moreover, we want to develop a systematic 0 1988 American

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Ind. Eng. Chem. Res., Vol. 27, No. 4, 1988 607 COOLING WATER TEMPERATURE

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procedure for these screening calculations. A procedure of this type is presented below. Approximate Optimum Overdesign We assume that we start with an estimate of the optimum steady-state design conditions that is based on the mean values of the disturbances for a particular flow sheet. In addition, we assume that we have identified the significant disturbances and have ensured that there are enough significant manipulative variables to satisfy all of the process constraints and to optimize the significant operating variables. Now we consider the effect of the significant disturbances on the operating costs associated with a particular piece of equipment designed to be optimum a t the mean disturbance values. We can classify the results into three categories: 1. The costs vary linearly. 2. The costs become unbounded for some anticipated disturbances or the process constraints cannot be met. 3. The costs vary nonlinearly. Statistical methods provide no useful information for problems in the first category. For problems in the second category, we normally want to change the design of some equipment before we undertake a statistical analysis. Similarly, for problems in the third category, we can often develop "reasonable", approximate solutions without the need to undertake a detailed statistical study at the conceptual stage of a process design. We discuss each of these problems in greater detail below. Linear Problems. In many cases, the effect of disturbances on the total operating costs of the plant may appear to be linear even though the plant equations are nonlinear; Le., the nonlinearities are not excited over the complete range of the disturbances. For these situations, the expected value of the operating cost is identical with the operating cost at the time-averaged value of the disturbances, which is the value that we used for the optimum steady-state design calculations. This result is independent of the distribution function of the disturbances, and therefore, a statistical study is not justified. For this linear response case, no equipment overdesign is the optimum policy. This is the reason our operability, analysis is based upon the optimum design for the mean

values of the disturbances. We prefer the optimum overdesign policy to be dependent only on the process disturbances and not on the result of an arbitrary base-case design. As an example, the operating costs associated with the partial condenser (flash drum cooler) of the HDA process (see part 1)are shown in Figure 1. The optimum design approach temperature primarily trades off the capital cost of the exchanger and the cooling water costs vs the losses of aromatics in the purge stream. Once the exchanger area is fixed at this base-case (optimum) value, the optimum approach temperature for steady-state control trades off only the cooling water costs vs the aromatics losses. The resulting optimum operating costs are shown as a function of the production rate and cooling water temperature in Figure 1. Since the expected value for the linearly varying operating costs equals the base-case value, no overdesign can be justified. One-sided Inoperable Problems. Often, equipment can easily handle disturbances which tend to decrease their load (heat duty, flow rates, etc.) but become inoperable for even small disturbances, requiring an increased load. If saturation of this equipment prevents the process constraints from being satisfied or results in rapidly rising operating costs for (reasonable) expected disturbances, a worst-case overdesign policy is often appropriate. Now, some knowledge of the distribution function of the disturbances would be needed so that a reasonable estimate can be made of the penalty associated with no overdesign vs overdesign based on the Yworst-casenconditions (that fix the maximum equipment loads). However, the penalties paid for not satisfying the process constraints are often very large, so that overdesign based on worst-case conditions is normally justified. The benzene product column of the HDA process provides a useful example of this type of problem. Without overdesign of the column vapor capacity, any additional toluene fed to the process that produces benzene in the reactor cannot be recovered as product. Thus, any additional benzene produced will exit in the product column bottoms stream. In the recycle column, this benzene will displace the toluene from the overhead stream, forcing the incremental toluene to the fuel byproduct stream. As shown in Figure 2, poor recovery of benzene in the product column overhead raises the column operating costs sharply.

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distributions of the disturbances, and, instead, we can combine the results of two linear analyses. For example, if we compare 0%, 5%, lo%, 15%, and 20% overdesigns of the compressor in the refrigeration loop on an acetic anhydride plant (Fisher, 1985),we obtain the set of (almost piecewise linear) curves shown in Figure 3. Now for any selected distribution function for the disturbance (production rate), it is a simple matter to use the piecewise linear weighting of the distribution function to calculate the expected total annual cost, i.e., the incremental annualized capital plus expected operating cost.

Flow-Sheet Decomposition and Operability Analysis 004In order to develop a systematic procedure for classifying equipment into the categories discussed above, we follow the same hierarchical procedure as we used in part 1 of this series. At each level, we will ensure that the process constraints can be satisfied by either overdesigning satu002rated, “bottlenecking”equipment or implementing suitable operating policies to avoid equipment saturation. OvI 80% 100% 120% erdesign policies for the nonbottlenecking equipment can PRODUCTION RATE be specified by estimating the effect of disturbances on the Figure 3. Effect of production rate disturbanceson the refrigeration operating costs. vapor recovery system operating costs. Level 2 Decisions: Input-Output Structure of the Flow Sheet. The level 1 decision refers to the batch vs Equivalently, we can state that the desired production continuous process decision. Again, we are limiting our levels cannot be attained. With only a modest vapor caanalysis to continous processes. pacity overdesign, however, high recoveries of benzene are There is no equipment introduced at level 2 (except for possible at all production rates and the operating costs possibly a feed compressor), and hence there are no ovbecome essentially linear. erdesign policies to consider. It is important to evaluate Nonlinear Problems. If the operating costs associated the operating policy for the feed streams, however, because with a piece of equipment are a nonlinear function of the this will affect the loads on the process equipment. Usudisturbances, the time-averaged operating costs are comally, the feed streams either enter the process as a dismonly greater than the optimum design value. Since the turbance or are varied to satisfy production rate conbase-case (optimum) equipment size traded off capital vs straints. Only rarely may they be adjusted to prevent operating costs at the mean disturbance values, the equipment saturation. base-case equipment size cannot be optimum. Thus, some Level 3 Decisions: Recycle Structure. The major equipment overdesign is usually warranted to offset the equipment introduced at level 3 is the reactor (with its underestimated operating costs. associated heating/cooling equipment) and possibly a gas Even though the operating costa associated with a piece recycle compressor. The process contraints, operability of equipment vary quite nonlinearly with disturbances, alternatives, and overdesign problems commonly encounthese costs may be relatively insensitive to equipment tered at this level are described below. overdesign. Thus, the capital investment for even a small Reactors. The primary objective of the reactor is to amount of overdesign may not be justified by the associconvert enough of the limiting reactant to satisfy the ated decrease in operating costs. For this piece of equipproduction rate requirements. Also, minimum or maximent, no overdesign may closely approximate the optimum mum temperature constraints, or molar ratio constraints, policy. may be imposed. An important economic consideration On the other hand, the operating costs for a nonlinear is the effect of disturbances on the product distribution. problem may be very sensitive to equipment overdesign. Overdesign of both the reactor volume and the heatNow, substantial capital investment in equipment oving/cooling equipment may be used to ensure process erdesign may be warranted. For this problem type, it is operability. The reactor disturbances include both the feed useful to define a Yworst-casenoverdesign factor which and recycle flow rates, compositions, and temperatures. provides a reasonable upper bound on the optimum value. For the optimum design reactor volume, the production Rather than determine the rigorous optimum overdesign rate can often be maintained by modest adjustments in based on a statistical analysis for this class of problems, the reactor operating temperature. Unless the necessary we will first compare the “base-case” and Yworst-case” heat duty can be attained for all disturbances, however, overdesign policies. If one alternative is obviously better, wild variations in reactor conversion may result. Thus, a the overdesign problem can be characterized as “linear” “worst-case” overdesign policy of the reactor heating/ or “one-sided inoperable”. Only if the change in annualized cooling equipment normally is appropriate. costs for both alternatives is significant would a more Overdesign of the reactor volume may be warranted if detailed statistical analysis be considered. the operating policy above violates temperature constraints Piecewise Linear-Nonlinear Processes or results in very nonlinear operating costs (e.g., selectivity Whenever it can be established that the nonlinear relosses). For example, the reactor volume of the HDA sponse to disturbances is composed of two linear segments, process (see part 1)was overdesigned to avoid the outlet such as shown in Figure 3, then the problem of determining temperature constraint. Temperature constraints also the expected value of the profit (or cost) for various ovusually require worst-case overdesign, while a more detailed analysis is required to offset nonlinear operating erdesign policies becomes simplified. That is, it is not necessary to run complete plant simulations with statistical costs. The pioneering work of Kittrell and Watson (1966),

Ind. Eng. Chem. Res., Vol. 27, No. 4, 1988 609 curiously entitled “Don’t Overdesign Process Equipment”, warns of applying arbitrary overdesign factors to these critical units. Gas Recycle Compressors. If the gas recycle stream contains a reactant in limited supply, increased production rates may not be attainable without overdesign of the gas recycle compressor. If the ratio of reactants at the reactor inlet can be maintained by increasing one of the fresh feed flow rates, however, the process remains operable. When an additional feed flow is used to overcome a compressor constraint, the operating (raw material) costs will vary nonlinearly over the range of assumed production rates. Level 4 Decisions: Separation System. General Structure. The only equipment introduced at level 4 is the partial condenser and flash drum for gas-phase or two-phase reactor effluent systems. While there are no constraints on the flash drum, its operating conditions fix the loads on both the liquid and vapor separation system. As demonstrated earlier (Figure l),the operating costs associated with the flash drum usually vary smoothly and quite linearly as a function of the disturbance values, so that there is little incentive for overdesign. Levels 4a Decisions: Vapor Recovery System. The operability alternatives at level 4a depend upon the location and the type of vapor recovery system used. Douglas (1985) suggests that the vapor recovery system be placed on the purge stream if valuable components must be recovered, on the gas recycle stream if components that degrade the reactor performance or product distribution must be removed, or on the flash vapor stream if both of these conditions are present. He also notes that the four major types of systems are (1)condensation, (2) absorption, (3) adsorption, and (4)membrane separation processes. The operability of the two most common types, absorption and low-temperature condensation (refrigeration), are discussed below. Absorber Vapor Recovery Systems. There are two important overdesign problems associated with gas absorbers: overdesign of the number of trays and overdesign of the column diameter. The number of trays has only a small effect on the range of disturbances for which the column is operable but may strongly affect the process operating costs (via losses of valuable materials, etc.). The column diameter, however, determines the range of operability of the absorber (flooding) but does not affect operating costs. Thus, these problems are easily separated. The vapor rate through the column cannot be significantly increased without overdesign of the column diameter. If deleterious materials must be removed from the vapor stream, the column is inoperable for increased loads. If part of the vapor feed may be diverted, the column remains operable, but at the expense of high material losses. In either case, we expect that the worst-case overdesign of the column diameter is appropriate. For operable columns (with no diverted feeds), the fractional recovery of the solute is a function of the operating temperature, the solvent flow rate, and the number of trays. While the recovery can be maintained by varying the solvent flow rate, the cost of recovering the solvent can be expected to vary nonlinearly with the process disturbances. Thus, some overdesign of the number of trays in the column may be warranted to reduce the solvent requirements at the (reasonable)extreme disturbance values. Refrigeration Vapor Recovery Systems. Again, there are two major overdesign problems to consider: the condenser area and the refrigerant compressor capacity. There is generally no limit on the vapor flow rate through a partial condenser, so the system is “operable” for all

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process disturbances. If the equipment sizes are fixed at the optimum design values, however, the operating costs become very nonlinear for (desired) heat duties above the base-case values. The operating costs for a system of this type have been calculated for a process to produce acetic anhydride (Fisher, 1985). The results, plotted in Figures 3 and 4, can be interpreted as follows. For increases in production rate or flash drum temperatures, the refrigeration system heat duty is limited by the compressor capacity; overdesign of the condenser area cannot affect the operating costs. In this case, only overdesign of the compressor will reduce the severe nonlinearity in operating costs. If a worst-case compressor overdesign policy is used (Le., 20% overdesign for 20% changes in the production rate), the operating costs become quite linear for all disturbances. Since the optimum condenser area trades off the exchanger capital cost vs these operating costs, the base-case area should remain nearly optimum. Level 4b Decisions: Liquid Recovery System. Fisher et al. (1985) discuss in detail the effect of overdesign on distillation column operability. For simple columns, there are two overdesign problems: the column vapor capacity and the number of trays. The maximum required vapor rate through the column couples the overdesign of the reboiler, condenser, and column diameter. A reasonable operability criterion for distillation columns is that the design distillate and bottoms compositions be attainable for all feed flow rate and composition disturbances. As pointed out by Fisher et al. (1985), the range of operability is easily expanded by using vapor capacity overdesign but is relatively insensitive to overdesign of the number of trays. The recommended overdesign policy for simple columns is then to use worst case overdesign of the vapor capacity (to ensure operability) and to consider overdesign of the number of trays only if the resulting operating costs are very nonlinear with respect to disturbances. Level 5: Heat Exchanger Network. In order to characterize the overdesign problem for heat exchange equipment in a tightly energy-integrated process, we must distinguish between “hard” and “soft” target temperatures and heat duties. For example, a distillation column re-

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boiler duty represents a ”hard” constraint; the column is not operable unless its heat duty is satisfied. Worst-case overdesign of the reboiler area would then be required to generate the maximum required vapor rate. On the other hand, a reactant feed stream leaving a feed-effluent heat exchanger and entering a preheater or nonadiabatic reactor may have a “soft”target temperature. If the disturbances in this target temperature can be tolerated by the reactor heat-transfer equipment, the process is operable without overdesign of a feed-effluent heat exchanger. In this case, however, overdesign of the energy integration system may decrease the overdesign required in the reactor heat-transfer equipment (as well as decreasing the expected operating costs). The temperature of the product stream entering a storage tank is another “soft” constraint commonly encountered in a chemical process. The economic penalty of missing this target temperature is difficult to assess, however, and the overdesign required to maintain the target value for the full range of disturbances may be excessive.

Example: HDA Process An operability analysis of the process to produce benzene by the hydrodealkylation of toluene (Figure 5) is summarized below. The decomposition of the HDA process using the hierarchical decision procedure of Douglas (1985) was presented in part 1. The economic performance of this process with respect to anticipated disturbances is presented as a case study by Fisher and Douglas (1985). For this example, the operability decisions encountered at each level will be reviewed, and simple overdesign policies will be proposed. Level 2 Decisions: Input-Output Structure. The toluene fresh feed stream is adjusted to satisfy a seasonal production rate variation of *20%, and in part 1 of this paper we found that the feed composition disturbances of this stream were not significant. The hydrogen feed stream is available in sizable excess, but its composition is expected to vary in the range 0.93 < YFH < 0.99, and these disturbances are important. Level 3 Decisions: Recycle Structure. The equipment overdesign problems at level 3 are for the gas recycle compressor,the reador volume, and the furnace heat duty. The gas recycle compressor is operable for all disturbances because the hydrogen fresh feed rate can be varied to satisfy the hydrogen-to-toluene ratio constraint at the reactor inlet. The resulting hydrogen purge losses, however, vary nonlinearly. A reasonable “worst-case” overdesign policy for the recycle compressor is that the design purge composition be attainable for the highest production rate and the lowest hydrogen feed composition. This policy requires about a

20% overdesign of the compressor capacity, increasing its annualized capital cost by $20 OOO/year. For rectangularly distributed disturbances, the expected operating costs are reduced by about $30000/year. Thus, the worst-case overdesign policy appears more favorable than no overdesign. Since the total annualized cost for the process ( ~ $ X5 10*/year) is increased by less than 0.5%, there seems to be little incentive to calculate the exact optimum overdesign policy. The overdesign policy for the reactor is subject to an outlet temperature constraint. For the optimum base-case design, this constraint is active. In order to increase prodution rate, however, the inlet temperature (and, hence, the outlet temperature) must increase. Worst-case overdesign of the reactor volume (again, ~ 2 0 % must ) be implemented to keep Tmout< 978 K. Because the furnace was designed with a modest heat flux in the radiant section, the required heat duty can be attained by varying the furnace fuel flow rate (without danger of overheating the furnace tubes). Level 4 Decisions: Separation System. General Structure. As noted earlier, the partial condenser (flash drum cooler) overdesign problem can be classified as linear, and no overdesign is approximately optimum. Level 4b Decisions: Liquid Recovery System. In order to increase the production rate of benzene as the toluene feed flow rate increases, overdesign of the product column vapor capacity is needed. Because the incremental toluene feed would otherwise be lost to the diphenyl waste stream, a worst-case overdesign policy is proposed. The toluene recycle column, however, will remain operable for increased production rates if the conversion per pass is also increased. The selectivity losses (diphenyl production) will then vary nonlinearly with the toluene feed rate. Thus, a reasonable “worst-case” overdesign policy for this column is that the design conversion be attainable at the highest production level. The stabilizer column will also remain operable if the flash drum temperature is increased to reduce the dissolved methane in the flash liquid. However, this policy would greatly increase the benzene losses in the purge stream. Worst-case overdesign of the vapor rate appears to be nearly optimum for both of these columns, increasing the total annualized costs for the process by about 1% . The composition of the feed to the liquid recovery system varies only slightly, however, providing little incentive for overdesign of the number of trays in any of the columns. Level 5 Decisions: Heat Exchanger Network. Overdesign of the feed-effluent heat exchanger in Figure 1 is not required for process operability; the reactor inlet temperature can be adjusted with the furnace fuel flow rate. The exchanger efficiency varies slightly with the process disturbances, so the furnace duty and fuel costs also vary nonlinearly. For our example, no overdesign of the exchanger area is nonetheless nearly optimum. If a more tightly heat-integrated flow sheet were considered, however, many additional operability problems would certainly be encountered.

Operability and Optimum Steady-State Control The proposed overdesign policies for the HDA process result in a 3% increase in total annualized costs (as compared to the optimum base-case design value). Thus, the expected variations in the disturbance variables should have only a small effect on the plant’s profitability. Of course, without any overdesign, the process would be utterly inoperable when disturbances are present. The main goal of this operability analysis has been to ensure that the steady-state control optimization problem

Ind. Eng. Chem. Res. 1988,27, 611-615 would always have a “sensible” solution. That is, the process constraints can be satisfied without a severe economic penalty. The goal of our control system is then to drive the process toward ita optimum operating conditions for all disturbances. In part 3 of this series, we consider the optimum steady-state control of the plant.

Conclusions and Significance The flow-sheet decomposition procedure of Douglas (1985) was used to specify some of the alternative operating and equipment overdesign policies that satisfy the process constraints at each level for the complete range of the anticipated disturbances. In addition, nearly optimum overdesign factors were selected for each piece of equipment to minimize the effect of disturbances on the total process costa. Often, overdesign policies corresponding to either “worsbcase” or “base-case”operating conditions are appropriate. More detailed operability analyses are only recommended when (1)neither the “worst-case” nor the “base-case” alternative is obviously favorable and (2) both policies significantly reduce the profitability of the process. With this approach, the appropriate equipment overdesign factors can be quantitatively related to the magnitude of the anticipated disturbances entering the process. Acknowledgment The authors are grateful to the National Science

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Foundation for providing financial support under Grant CPE-8105500.

Literature Cited Douglas, J. M. AZChE J . 1985, 31, 353. Fisher, W. R. Ph.D. Thesis, University of Massachusetts at Amherst, 1985. Fisher, W. R.; Douglas, J. M. Comp. Chem. Eng. 1985, 9, 449. Fisher, W. R.; Doherty, M. F.; Douglas, J. M. Znd. Eng. Chem. Process Des. Deu. 1985, 24, 593. Grossmann, I. E.; Morari, M. “Operability, Resiliency, and Flexibility-Process Design Objectives for a Changing World”. 2nd Int. Cong. of Found. of Computer-Aided Process Design, Snowmass, CO, June 19-24, 1983. Grossmann, I. E.; Halemane, K. P.; Swaney, R. E. Comput. Chem. Eng. 1982, 7, 151. Halemane, K. P.; Grossmann, I. E. AZChE J . 1983,29, 425. Kittrell, J. R.; Watson, C. C. Chem. Eng. Prog. 1966, 62(4), 79. Morari, M.; Lenhoff, A. M.; Marselle, D. F.; Rudd, D. F. “Deseign of Resilient Energy Integrated Processing Sysems”. 72nd Annual AIChE Meeting, San Francisco, 1979, paper 28c. Morari, M.; Marselle, D. F.; Rudd, D. F. “Synthesis of Resilient Energy Management Systems”. 73rd Annual AIChE Meeting, Chicago, 1980, paper 3f. Swaney, R. E.; Grossmann, I. E. AZChE J . 1985a, 31, 621. Swaney, R. E.; Grossmann, I. E. AZChE J. 198513, 31, 631.

Received for reuiew July 15, 1986 Revised manuscript received July 23, 1987 Accepted August 17, 1987

The Interface between Design and Control. 3. Selecting a Set of Controlled Variables Wayne R. Fisher, Michael F. Doherty, and James M. Douglas* Department of Chemical Engineering, University of Massachusetts, Amherst, Massachusetts 01003

By solving the optimum steady-state control problem in terms of the significant disturbances and manipulative variables, we often find that the optimum values of some of the operating and/or manipulative variables lie at constraints. If we select these constrained variables as controlled variables, the resulting feedback system will have near optimal performance without the need for measuring all the disturbances or for calculating the entire optimum steady-state control policy on-line. In many cases it is possible to propose heuristics to identify the constrained controlled variables. In parts 1 and 2 of this series, we have presented systematic procedures for identifying the significant disturbances, for ensuring that there are an adequate number of manipulative variables to be able to satisfy the active process constraints and to optimize the significant operating variables, and to ensure that there is an adequate amount of overdesign to obtain optimum steady-state control while satisfying the process constraints. Moreover, we considered modifications of the flow sheet (we intend to apply the procedures at the conceptual stage of a process design, so that flow-sheet modifications are still possible) in order to accomplish these goals. Our goal now is to select a set of controlled variables. We require that the control system to be developed satisfies the active process constraints and, in addition, gives close to the optimum steady-state performance after dynamic transients have decayed. Thus, it seems reasonable to select controlled variables that correspond to the solution of the optimum steady-state control problem. If we can accomplish this goal, it will not be essential to solve the optimum steady-state control problem for these variables on-line. 0888-5885/88/2627-0611$01.50/0

The primary control objective is the profitable operation of the process. Other control objectives include product quality specifications, production goals, safety and environmental regulations, and other process constraints. Many of these control objectives for the process are well defined even at the conceptual design stage. In recent years, synthesis strategies have been introduced for determining the interconnections between manipulated and controlled variables. These methods generally assume that the process flow sheet is fixed and the controlled and manipulated variables are specified. The Relative Gain Array approach developed by Bristol (1966) has been applied extensively to distillation columns and other simple processes. Govind and Powers (1982) present a nonnumerical algorithm which generates alternative control structures for complete plants based on a causeand-effect representation of the process. In a similar spirit, Morari and Stephanopoulos (1980a) developed structural controllability as a basis for generating alternative feasible control structures. The selection of the best set of controlled variables from the hundreds of process state variables is not a trivial task. 8 1988 American Chemical Society