Znd. Eng. Chem. Res. 1988,27, 597-605
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PROCESS ENGINEERING AND DESIGN The Interface between Design and Control. 1. Process Controllability 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 are often uncontrollable; i.e., there are not enough manipulative variables in order t o satisfy the process constraints and t o optimize all of the operating variables. Controllability can be restored by (1) modifying the flow sheet t o add more manipulative variables, (2) overdesigning certain pieces of equipment so t h a t the process constraints never become active for the complete range of the process disturbances, or (3) ignoring the optimization of the least important operating variables. The goal of a controllability analysis is t o determine which of these alternatives has the smallest cost penalty. This paper describes a systematic procedure for assessing process controllability a t the preliminary stages of a process design, so that some of the economic penalties associated with control can be used as a n additional criterion for screening process alternatives. There has been a growing interest in process control in recent years. Changing economic factors have provided a significant incentive for making plants as profitable as possible, and there is a widely recognized need to improve product quality. Process control provides a way of satisfying both of these needs. In addition, the dramatic improvements in digital computers now makes it possible to implement control strategies that were impossible 20 years ago. According to Nishida et al. (19811, the development of a control system requires the specification of (1)a set of control objectives, (2) a set of controlled variables, (3) a set of measured variables, (4) a set of manipulated variables, (5) a structure interconnecting the measured and manipulated variables. Unfortunately, there is no systematic procedure available for translating the results from a process design into these specifications required for synthesizing a control system. Current practice is to focus on the control of individual process units. The basic assumptions behind this approach is that if each unit is properly controlled, the control of the total plant will be satisfactory. However, we would expect that a systematic procedure for defining a control system specification for a process unit would be different than a procedure for defining control system specifications for a complete plant. Since a systematic procedure for defining the control system specifications is lacking, experience and intuition are required to obtain a satisfactory control system design. This approach to process control has worked quite well in the past. Only about 10% of the plants exhibited major control problems (Lee and Weekman, 1976; Ellingson, 1976), and most of the problems were of a steady-state nature rather than a dynamic nature. However, recently there has been a rapidly growing interest in using on-line steady-state optimum control (Haggin, 1984) in order to improve the profitability of the process. In the optimum steady-state control problem, the optimum values of the manipulated variables are calculated (as well as all the other state variables via steady-state process models) as a function of the disturbances that enter 0888-5885/88/2627-0597$01.50/0
the plant. Thus, it is not necessary to define a set of controlled variables with this approach. However, in order to provide a feedback for the plant, the results from the on-line optimum steady-state control analysis are normally used to make set-point changes in a set of prescribed feedback controllers, rather than using the solutions to change the manipulative variables directly. Hence, we would like to specify these controllers in the best possible way.
The Interface between Design and Control In all of the existing literature on control system synthesis, it is assumed that the structure of the flow sheet and the equipment sizes are fixed. A t present, the interface between design and control is almost a discontinuity. That is, a designer designs the process, and using experience and intuition suggests a control system for the plant. This control system is reviewed by control engineers, and normally changes are made; e.g., additional measuring points may be added so that, if problems are encountered after the plant has been built, the source of these problems can be traced more easily. However, in some cases conflicts arise between designers and control engineers. For example, as Rinard (1982) notes, the designer’s approach of only considering steady-state operation with no disturbances often leads to the underdesign of final control elements. That is, the vapor rate in a distillation column must have the capacity to generate enough vapor to be able to cope with the disturbances, and we say that the reboiler is a final control element. Another way of expressing this conflict is that designers (and contractors in particular) almost never evaluate the incremental capacity required to handle the disturbances that enter the process. The interface between design and control should be based on the translation of the results from the design study into the set of specifications described above by Nishida et al. (1981). However, it should be recognized that when the impact of disturbances on the behavior of the plant is considered, an optimum steady-state design might not even be operable; i.e., the plant might be able to tolerate disturbances which decrease the load on the 0 1988 American Chemical Society
598 Ind. Eng. Chem. Res., Vol. 27, No. 4, 1988
plant but might not be able to tolerate any increase in the load. Hence, the initial control study should focus on flow-sheet modifications (both in equipment sizes and in the structure of the flow sheet) that might be needed to be able to cope with disturbances. If we consider potential flow-sheet modifications as the initial focus of any control system synthesis activity, then the first control system considerations should begin at the conceptual stages of a process design, where the emphasis is placed on the screening of flow-sheet alternatives. That is, as soon as a designer has identified that a process appears to be profitable and has identified four to six promising process alternatives, it seems to be reasonable to include some of the costs of control to help screen these alternative flow sheets. Certainly a t this stage of development of a project we can estimate the effect of disturbances on the steady-state behavior of each process alternative, we can assess the possibility of encountering equipment constraints, we can determine whether or not there are an adequate number of manipulative variables, etc. Of course, when a new process is being developed, there is a large incentive to get into the market as quickly as possible. Hence, we need to have new tools available that make it easy to screen process flow sheets based on control considerations. It should be possible to use short-cut methods to simplify the analysis problems, similar to the short-cut methods that are used for the conceptual design. In this paper we describe a systematic procedure for a preliminary control analysis that can be applied at the conceptual stage of a process design and that can be used as an aid in the screening of process alternatives. This preliminary procedure does not lead to a final control system because it does not consider the process dynamics, but it will make it possible to avoid conflicts between design and control at later stages of the development of a process. In order to illustrate what topics are considered by the procedure, we review the specifications listed by Nishida et al., although we have changed the order of the items. Control Objectives at the Conceptual Stage of a Process Design. At the conceptual stage of a process design, where we are screening process alternatives, the control objectives include satisfying the process constraints (including product quality and environmental constraints), as well as minimizing the operating costs over the complete range of expected disturbances. (Actually, we do not consider extreme disturbances that might be encountered very infrequently, but we attempt to select a reasonable range so that we can evaluate the impact that the disturbances have on the flow-sheet alternatives.) similarly, we do not attempt to undertake a detailed safety study until after we have fixed the flow sheet, although we do consider the safety aspects of the materials we are handling, explosive limits, etc. Nor do we consider start-up, shut-down, failures a t the conceptual design stage. Manipulated Variables. When disturbances enter the process, the plant will normdy move to a new steady state. However, we can alter the new steady-state values if we change some of the input variables to the process, i.e., the feed flow rates, the power input to a gas recycle compressor, the flow rate of cooling water to a partial condenser, the fuel flow to a furnace, etc. We call these process inputs the manipulative variables. In some cases the disturbances might make the plant become inoperable; i.e., we cannot satisfy all of the process constraints and minimize the operating costs. In these situations, we can often make the process operable by
modifying the flow sheet (either changes in equipment sizes or the structure of the flow sheet). Hence, the first question we should consider in our control assessment is whether or not there are an adequate number of manipulative variables for each of the process alternatives under consideration and/or the costs associated with ensuring that the alternatives can be made to be operable. Knowing that the process will be operable over the complete (reasonable) range of the disturbances will also mean that we will have well-defined problems when we start to construct dynamic models. Controlled Variables. Normally the controlled variables are the state variables that we desire to maintain at constant values. However, as disturbances enter the process, the optimum steady-state behavior normally will change, and so we might want to change the set points for the controlled variables. Of course, if some of the state variables always remain constant at the optimum steadystate conditions when disturbances enter the process, then these can be chosen as controlled variables. In some cases, equipment constraints might be encountered and the minimum cost might correspond to a constrained value of a manipulative variable. In these cases we can choose the constrained manipulative variable as a controlled variable. We would like to use the results of our preliminary control analysis to select the controlled variables for each process alternative under consideration. Measured Variables. The measured variables are used as the inputs to the controllers to generate error signals; Le., they are compared to the set points, which are the desired values of the controlled variables. Hence, we normally use the controlled variables as the measured variables. In cases where the controlled variables cannot be measured, then we must resort to inferential control. Control Structure Relating the Measured and Manipulative Variables. Once we have selected a set of controlled variables and we are certain that there are an adequate number of manipulative variables, then we can start proposing control structures. The relative gain array (RGA) and singular value decomposition (SVD) can be used to eliminate proposed control structures that will have significant interactions in the control loops. However, a dynamic analysis is required to find the best control structure alternative. Degrees of Freedom and Variable Classifications. During the conceptual design of a process, there are a certain number of degrees of freedom, and we call the design variables the variables that we use to fix these degrees of freedom. After the design has been completed and some of the design variables have been used to fix the equipment sizes, the number of degrees of freedom is reduced. We call the variables that are used to fix the reduced degrees of freedom the operating variables, because they can be adjusted to satisfy the process constraints and to minimize the operating costs of the process. The manipulative variables correspond to “handles” in a process (power input to a compre8sor, valve settings on a steam or a cooling water line, etc.), but since these normally are directly related to process flows and since it is easier to think about the process in terms of flows, we often refer to the flows as manipulative variables. A Hierarchical Approach to Control System Synthesis for Complete Plants. A hierarchical approach for the synthesis for complete plants has been proposed by Fisher et al. (1985); see Table I. This hierarchical approach to control system synthesis represents a top-down, least commitment strategy for control system synthesis. That is, we ensure that there is adequate flexibility in the
Ind. Eng. Chem. Res., Vol. 27, No. 4, 1988 599 Table I. Hierarchical Approach to Control System Synthesis level 1: steady-state considerations la. Controllability. Identify the economically significant disturbances, and ensure that there are an adequate number of manipulative variables in order to be able to satisfy the process constraints and to optimize the operating variables over the complete range of the anticipated disturbances. lb. Operability. Ensure that there is close to the optimum amount of overdesign to be able to satisfy the process constraints and to minimize the “expected” operating costs for the complete range of anticipated disturbances. IC. Select the controlled variables. Select a set of controlled variables so that the steady-state operating costs will be essentially minimized. Id. Steady-state screening of control structures. Assess the amount of interaction in alternative control structures. level 2: normal dynamic operation-small perturbations from steady state 2a. Inventory control. Ensure that the plant material and energy balances can be closed, and assess the need for intermediate storage capacity. 2b. Dynamic control. Assess the stability of the control structure alternatives, and ensure robustness. The analysis includes flow-sheet modifications (e.g., additional overdesign) to ensure process operability in the dynamic state. level 3: abnormal dynamic operation 3a. Start-up and shut-down. Assess the need for special control systems for the start-up and shut-down of the plant. 3b. Diagnostics and failure recovery. Ensure safe operation when equipment failures are encountered. level 4: implementation 4a. Distributed control. Organize the levels of local unit control, plant control, and supervisory control. 4b. Human interface. Ensure that the operators can operate the plant.
flow sheet (or we change the flow sheet) before we consider dynamic modeling. Similarly, we ensure that the process and a control system are stable and have a satisfactory response to small disturbances (or else we modify it) before we consider how the control system will respond to a failure. However, it is essential to note that every step in the procedure must be considered in order to develop a good control system. The interface between design and control that we are considering corresponds to the first part of the first level in the hierarchy. In part 1 of this paper, we describe a systematic procedure for evaluating the controllability of the process, where we identify the economically important disturbances, we develop a list of the economically significant operating variables that can be used to satisfy the process constraints and to minimize the operating costs, and we evaluate whether there is an adequate number of manipulative variables to be able to satisfy the process constraints and to minimize the operating variables, In part 2 we consider the operability of a process, where we evaluate the amount of flexibility (overdesign)that can be justified to be able to satisfy the process constraints and to minimize the operating costs when disturbances enter the process. Finally, in part 3 we consider the use of an optimum steady-state control analysis to select a set of controlled variables for the process, and we present some heuristics that can also be used for this selection. Once we have selected a set of controlled variables and are certain that there are an adequate number of manipulative variables (possibly by modifying the flow sheet) and that there is adequate flexibility in the flow sheet (again, possibly after some modifications), then we are in a position to start proposing alternative control structures. Hence, the emphasis would shift from flow-sheet alternatives to control system alternatives.
Controllability At the preliminary stages of a process design, most plants are uncontrollable. That is, normally there are not enough manipulative variables in the flow sheet to be able to satisfy all of the process constraints and to optimize all of the operating variables as disturbances enter the plant. There are three ways that the controllability of the plant can be restored: 1. Modify the flow sheet to include more manipulative variables (e.g., add bypasses, add purge streams, add auxiliary condensers and reboilers, etc.). 2. Modify the design so that some of the process constraints never become active over the complete (reasonable) range of disturbances that enter the process (e.g., modify the reactor design so that a maximum temperature limit where undesired side reactions occur is never exceeded for any values of the disturbances or any manipulative variable settings within the range of interest). 3. Neglect the least important optimization variables. Of course, experience indicates that designers seldom encounter a difficulty in the design of a controllable process. They use experience and intuition to select one of the three methods presented above to accomplish this task. However, the costs associated with the three corrective actions described above are different, and our goal is to develop a systematic, quick screening procedure that makes it a simple matter to select the cheapest alternative. A Systematic Procedure for Controllability Analysis This initial attempt to develop a systematic procedure for the controllability analysis for a process is limited to continuous, vapor-liquid, low molecular weight, petrochemical processes that produce a signle product. There are numerous processes that satisfy these restrictions. Also, we do not consider membrane separators because a design procedure and cost correlations do not seem to be available in the open literature. We assume that several alternative, preliminary process designs have been generated and that the optimum design conditions for each alternative have been estimated. We always complete a preliminary design screening before we consider controllability, because if no process alternative is profitable we abandon the project without considering control (experience indicates that less than 1% of the ideas for new designs ever become commercialized). In order to develop a systematic procedure for a controllability analysis, we use the design decision hierarchy described by Douglas (1985) as the decomposition procedure. That is, we consider a series of simple controllability problems corresponding to the levels shown in Table 11, rather than attempting to evaluate the controllability of the complete flow sheet. It should be noted that this hierarchical procedure always focuses on the total plant, but additional levels of detail are added as we proceed from the early to the later levels. At each level, we do the following 1. We identify the new input streams, and we classify these as being either disturbances or manipulative variables. 2. We evaluate the sensitivity of the total annual cost (TAC) to the disturbances, and we neglect disturbances that have less than a 2% effect on the TAC. 3. We identify the process constraints that are introduced. 4. We determine the number of new design variables and equipment sizes that are specified, and then we calculate the number of operating variables that can be optimized.
600 Ind. Eng. Chem. Res., Vol. 27, No. 4, 1988 Table 11. Hierarchy of Decisions for Process Design level I: batch vs continuous 1. The development of a batch process (and its control system) is considered to be an extension of the synthesis procedure for its corresponding continuous process. Thus, the preliminary control structure synthesis strategies for both cases are identical. level 2: input-output structure of the flow sheet 1. Is a gas recycle and purge system required? 2. How many product streams are required? 3. Should the feed streams be purified or should the impurities be processed? 4. Should reversible byproducts be recovered or recycled to extinction? 5. What selectivity losses are associated with complex reactions? level 3: recycle structure of the flow sheet 1. Is more than one reactor required? 2. How many recycle streams are there? 3. Do we want to use an excess of one reactant at the reactor inlet? 4. Is a gas recycle compressor required? 5. Should the reactor be operated adiabatically, with direct heating or cooling, or with a diluent acting as a heat carrier? 6. If the reactor is equilibrium limited, do we want to shift the equilibrium? level 4: general structure of the separation system 1. Is a phase split of the reactor effluent possible? 2. Is part of the reactor effluent in the vapor phase? Can part of the vapor be condensed at ambient temperature? level 4a: vapor recovery system 1. Where should the vapor recovery system be located? 2. What type of vapor recovery system should be used? level 4b liquid recovery system 1. How many of the separations can be accomplished by distillation? 2. What arrangement of distillation columns should be used? 3. How should the light components be removed? 4. Should the light components be vented to the atmosphere, sent to fuel, or recycled to the vapor recovery system? 5. How should we accomplish the other separations?
5. We check to see if the number of manipulative variables is equal to the number of constraints plus operating variables, as well as if the constraints and operating variables provide a well-posed problem, i.e., a nonsingular Jacobian. 5a. If the answer is yes, we say that the process is controllable a t that level. 5b. If the answer is no, we have several options, and we want to find the cheapest. 1. We modify the flow sheet to include more manipulative variables, (e.g. add bypasses, add purge streams, add auxilliary condensers and reboilers, etc.). 2. We modify the design (equipment sizes) so that some of the constraints never become active (e.g., modify the reactor design so that a maximum temperature limit where undesired side reactions occur is never exceeded for any (reasonable) value of the disturbances or manipulative variable settings within the range of interest). 3. We neglect the least important optimizations variables. 4. We continue on to the next level with the hope that extra manipulative variables will be introduced at that level. Since we often modify the flow sheet in order to change the degrees of freedom associated with the control problem, we must ensure that the control problem continues to be well posed, i.e., that the Jacobian does not become singular. However, the hierarchical decomposition procedure greatly simplifies the task of correctly accounting for the degrees of freedom because we only need to consider a few equa-
Table 111. Monthly Production of Benzene in the U.S. in 1977” (in Millions of Pounds) June Julv Aurr SeDt Oct Nov Dec 896.8 917.8 949.5 914.6 828.1 920.1 976.0 nFrom Raman and Shimoda, 1978
tions at a time. Some more detailed types of the problem that are encountered a t each level are discussed below. Level 1: Batch vs Continuous. We limit our attention to continuous processes. Level 2: Input-Output Structure of the Flow Sheet. The inputs are the feed streams. The flow rates of these streams are the manipulative variables, and the compositions and temperatures are the disturbances. We do not consider temperature disturbances until level 5, except for the inlet temperature of a gas feed stream that enters a gas compressor. Then, we evaluate the effect of the feed composition disturbances over the range of interest on the stream costs in order to determine the significant disturbances (those that effect the stream costs by more than 2%), and we drop insignificant disturbances from further consideration. Constraints. We treat the desired production rate as a process constraint, since usually it varies with time (see Table I11 for an example of the monthly production of benzene in the U.S. during 1977 (Raman and Shimoda, 1978)),and we consider the case where we want our plant to be able to follow this fluctuating demand. We can satisfy this constraint by using the fresh feed rate of the limiting reactant as a manipulative variable. Equipment Design and Operating Variables. The only equipment design we consider a t this level is when we use a feed compressor to raise the pressure of a make-up gas stream from its supply pressure to a higher reactor pressure. The reactor pressure might correspond to a constraint given in the problem statement or it might correspond to a design variable, i.e., for gas-phase reactions where the number of moles decreases (a higher pressure increases the reaction rate and shifts the equilibrium conversions to higher values, but a larger feed compressor is required and more expensive equipment is needed to handle the high pressure). If a process has a gas recycle and purge stream (see Douglas (1985) for the criterion), the purge composition of the reactant is an optimization variable. Similarly, if air or water is the reactant that is not recovered and recycled, then the excess feed rate is an optimization variable. For complex reactions, the product distribution may depend on conversion, molar ratio of reactants a t the reador inlet, reactor temperature, and reactor pressure. Any of these variables that effect the product distribution correspond to an optimization variable. Normally, processes with complex reactions are uncontrollable a t the level 2 stage of analysis, because there are no “handles” to manipulate conversions, molar ratio at the reactor inlet, etc. However, for these variables we always carry on to the next level without considering flow-sheet modifications because new manipulative variables that effect these operating variables are introduced a t level 3. Level 3 Recycle Structure. At this level we calculate the recycle material balances, and we calculate the sizes and costs of a gas recycle compressor and the reactor during the design study. Disturbances and Manipulative Variables. The only new disturbance that needs to be considered at this level is the initial temperature of a gas recycle stream,
Ind. Eng. Chem. Res., Vol. 27, No. 4, 1988 601 which only effects the gas recycle compressor operation. However, the flow rate of a gas recycle stream becomes a new manipulative variable. The recycle flow of the limiting reactant is fixed if we fix the conversion, and the recycle flows of the nonlimiting reactants are fixed if we fix the molar ratios a t the reactor inlet. Constraints. There may be several types of constraints introduced, primarily on the reactor conditions. For example, the molar ratios of reactants (particularly hydrogen to aromatics) might be fixed at a minimum level to minimize undesirable side reactions (coking) or to force a reaction close to complete conversion. The reactor outlet temperature might be constrained and/or a quench may be needed immediately after the reactor also to avoid undesirable side reactions. Similarly, the maximum conversion may be limited to avoid side reactions, and the reador inlet temperature that must be exceeded to obtain a reasonable reaction rate may be specified. Materials of construction used in the design also may constrain the reactor temperature and pressure. Equipment Design and Operating Variables. For single reactions, reactor conversion and molar ratio of reactants become new optimization variables, and for single, reversible, exothermic reactions, reactor temperature also becomes a new optimization variable. As mentioned before, we calculate the size of a gas compressor and the reactor size a t this level. If the process is uncontrollable a t this level because we cannot satisfy all of the reactor constraints and optimization variables, we usually modify the reactor design (bypass streams, the use of a series of beds with interchangers, adding a heating/cooling jacket or coils, etc.). A lack of controllability a t this level because of reactor limitations usually cannot be remedied by adding more detail a t later stages. Level 4: Separation System. Processes with Flash Drums. For vapor-liquid processes where we use a phase splitter, the temperature of the flash drum becomes a new optimization variable, the inlet cooling water temperature to either the cooling coils in the flash drum or the partial condenser preceding the flash drum is a new disturbance, and there is a constraint on the cooling water return temperature. Thus, fluctuations in the cooling water inlet temperature cause the flash drum temperature to vary, and this variation causes the load on the vapor recovery system or the purge losses to change. It is always desirable to operate the flash drum at as low a temperature as possible; thus, we usually do not want to maintain the temperature of the flash drum constant. Normally, we don’t calculate the size or cost of flash drums a t the preliminary stage of a design where we are screening alternatives because their costs are small compared to the costs of other equipment. A controllability analysis often indicates that the cooling water return temperature constraint should be satisfied and that the temperature optimization should be neglected. Processes with Gas Absorbers. If a gas absorber is used as the vapor recovery system, the inlet solvent temperature normally becomes a new disturbance (the solvent is usually cooled by cooling water, and the inlet cooling water temperature fluctuates). The solvent flow rate and fractional recovery become new optimization variables. Of course, we calculate the size of the gas absorber. Processes with Condensers. If a condensation process is used to recover liquids from a vapor stream, then there may be trade-offs between a compressor used to obtain a high pressure and a refrigeration loop used to obtain a low temperature. The load on the system fluctuates, and
cooling water temperatures also act as disturbances. Processes with Distillation Columns. The load on the liquid separation system (usually a train of distillation columns) will often fluctuate because feed composition disturbances will propagate through the reactor and often the conditions in a phase splitter will fluctuate. The optimization variables and manipulative variables have been extensively discussed in the literature, so there is little value in repeating them here. Level 5: Energy Integration. The new energy integration procedure (Linnhoff et al., 1982; Boland and Hindmarsh, 1984; Linnhoff and Vredeveld, 1984) has also been extensively discussed in the literature and, therefore, will not be considered here, except for the problem of heat-integrated distillation columns. Controllability problems often arise when a process stream is used as the energy source for a reboiler (and similar cases) because the thermal coupling removes a degree of freedom from the system; Le., a manipulative variable is removed from the flow sheet. However, by installing bypass lines or auxilliary heaters, it is a simple matter to restore the controllability. Developing an Interactive Computer Program To Assess Controllability. The systematic procedure described above can provide the basis for an interactive computer program for assessing process controllability. With a program of this type available, it should be possible to screen the controllability of alternative flow sheets very rapidly. Thus, controllability analysis can be used as one of the criteria for selecting the best process alternative. Example: The Hydrodealkylation of Toluene To Produce Benzene. In order to illustrate the utility of the hierarchical decomposition scheme for a steady-state controllability analysis, we consider a process for producing benzene by the hydrodealkylation of toluene (HDA process). The reactions of interest are
+ Hz
-
+ CH4 2(benzene) e diphenyl + Hz
toluene
benzene
(1) (2)
We assume that a feed stream containing 99.8% toluene and 0.2% heavy, inert impurity is available at a nominal rate of 125 kmol/h. Also, a hydrogen stream containing 95% Hz and 5% CHI is available at 311 K (100 O F ) and 3790 kN/m2 (550 psia). It is desired to produce benzene a t a purity exceeding 99.97 % . The exothermic reaction takes place in the gas phase at a pressure of 3450 kN/m2 (500 psia). The reactor temperature must exceed 895 K (1150 OF) in order to obtain a sufficiently large reaction rate, but the reactor outlet must be kept below 978 K (1300 O F ) to prevent hydrocracking reactions. In order to minimize coking in downstream equipment, the hydrogen to aromatics ratio at the reactor inlet must exceed 5/ 1and the reactor effluent must be quenched rapidly to 895 K (1150 O F ) . Douglas (1985) has discussed the synthesis of a flowsheet structure for this process using the hierarchy of decisions procedure; see Figure 6. The general design decisions made a t each level in the hierarchy are listed in Table 11, and the specific decisions made in the development of the HDA process flow sheet are summarized in Table IV. For this example, the effect of these flow-sheet structure and design decisions on steady-state controllability will be studied a t each decomposition level. Level 1 Decision: Batch vs Continuous Process. The HDA process is assumed to be continuous. Moreover, the synthesis procedure presented by Douglas (1985) and this controllability analysis is restricted to continuous processes. Level 2 Decisions: Input-Output Structure of the
602 Ind. Eng. Chem. Res., Vol. 27, No. 4, 1988
345r
Table IV. Design Decisions for the HDA Process level 2 decisions 1. Do not purify the hydrogen feed stream. 2. Use a gas recycle and purge stream. 3. Recover diphenyl from the toluene recycle stream, so that there are three product streams (purge, benzene product, diphenyl byproduct). level 3 decisions 1. Use a single reactor. 2. Use a gas (H2 and CH4) and a liquid (toluene) recycle stream. 3. Use a 5 / 1 hydrogen-to-toluene ratio at the reactor inlet to prevent coking (although this could be treated as an optimization variable). 4. A gas recycle compressor is needed. 5. Use an adiabatic, plug-flow reactor. 6. Don’t consider equilibrium effects (reversible byproduct removed, not recycled). level 4a decisions 1. Don’t use a vapor recovery system. level 4b decisions 1. Make all separations by distillation. 2. Use direct column sequence of simple columns. 3. Remove light ends in a stabilizer column. 4. Send light ends to fuel. level 5 decisions 1. Use a feed-effluent heat exchanger. 2. Quench the reactor outlet stream to 895 K using the flash drum liquid stream.
11PURGE
’I 3 30
A EASE CASE DESiGN
I l
094
096
HYDROGEN FEED COMPOSITION lyrMl
7-
3 34
H21
BENZENE
PROCESS
TOLUENE HYDROGEN
~
IO0
0 98
1
0994
0996
,
l
0 998
l
too0
TOLUENE FEED COMPOSlTiON ( y r r 1
Figure 2. Effects of hydrogen feed composition and toluene feed composition on the economic potential of the HDA process.
DIPHENYL
Figure 1. Input-output structure for the HDA process.
Flow Sheet. The input-output structure for the HDA process is shown in Figure 1. A purge stream is used to remove the methane byproduct/feed impurity (rather than separate it from the recycled hydrogen stream). Also, the heavy toluene feed impurity is processed and removed from the system with the diphenyl byproduct. A t the stated reactor conditions, the selectivity (benzene a t the reactor outlet divided by the toluene converted in the reactor) can be related to the conversion per pass of toluene by S = 1 - 0.0036/(1 - x ) ~ . ~ ~ ~ (3) Diphenyl and methane are assumed to be the only major byproducts. Degrees of Freedom Analysis. The toluene feed flow rate (a manipulative variable) is adjusted to satisfy the benzene demand (a constraint). The hydrogen feed flow rate must exceed the stoichiometric requirements for the two reactions, eq 1 and 2. The minimum hydrogen feed flow rate and the diphenyl byproduct flow rate are dependent upon the reactor selectivity. As the hydrogen feed exceeds the minimum required, the purge composition of hydrogen increases. Thus, the process input-output flows can be written in terms of the three design degrees of freedom-the hydrogen purge losses, the benzene production rate, and the product distribution. There are no equipment design specifications a t level 2; the control and design degrees of freedom are identical. Process Material Balances. The two feed streams shown in Figure 1are the connections to the environment. The compositions of these streams are disturbances and the flow rates are manipulative variables. Short-cut,
overall, material balances can be obtained by using the procedure described by Douglas (1985), and these are production of benzene = PB (4) toluene feed: production of diphenyl: PD= P B ( 1 - s)/2s
(6)
total flow of heavy material: Pheavy = pD + (l - YFT)FBT
(7)
(diphenyl plus heavy impurities in toluene feed stream)
Level 2: Economic Model The economic potential at level 2 is simply the product value plus the fuel value of the purge and the heavy stream minus the raw material costs EPZ = CBPB - CHFG - CTFFT + C F l P G + CFZPHeavy (10) Significant Disturbances at Level 2, For variations of the hydrogen feed composition in the range from 0.93 to 1.0, this disturbance has a significant effect on the economic potential, see Figure 2a. However, for variations of the impurity in the toluene feed stream in the range from 0.0 to 0.007, this disturbance has a negligible effect on the economic potential; see Figure 2b. Thus, the only significant disturbance at level 2 is the hydrogen feed composition. Constraints a n d Operating Variables at Level 2. We consider that the production rate is a constraint that must be satisfied. If we specify the production rate, the
Ind. Eng. Chem. Res., Vol. 27, No. 4, 1988 603
.
Fl
s 4 S RECYCLE
PURGE
COMPRESSOR SEPAR4TION
HYDROGEN RE4CTOR
FURNICE TOLUENE
SYSTEM
4
BENZENE DIPHENYL
TOLUENE RECYCLE
Figure 3. Recycle structure for the HDA process.
conversion, and the purge composition of hydrogen, we can calculate all of the material balances. The conversion and the purge composition of hydrogen are design optimization variables (i.e., at high conversions there are large selectivity losses and large reactor costs, whereas a t low conversions there are large toluene recycle costs; a t high purge compositions of hydrogen there are large hydrogen feed costs, whereas a t low purge compositions there are large gas recycle costs). Of course, other variables could equally as well be specified as design variables; i.e., we only need to be certain that we have a sufficient amount of information to be able to calculate the overall material balances. We do not design any equipment a t level 2 (except for feed compressors), and therefore the number of operating variables is equal to the number of design variables. Thus, we have one constraint, i.e., production rate and two operating variables, which we choose as the conversion and the purge composition. However, we have only two manipulative variables, i.e., the feed rates of toluene and hydrogen. The feed rate of toluene has a significant effect on the production rate, and the feed rate of hydrogen has a significant effect on the purge composition, but there is no manipulative variable that effects conversion. Thus, we say that the process is uncontrollable at level 2. We proceed to level 3, rather than attempting to modify the flow sheet, because we expect that a new manipulative variable that will have an effect on conversion will become available.
Level 3: Recycle Structure The recycle structure of the HDA flow sheet is shown in Figure 3. We retain the reactor heating system (furnace) as part of the reactor system for the controllability analysis because a reactor heating/cooling system provides a new manipulative variable. Disturbances at Level 3. The new disturbances that are introduced a t level 3 are heating value of the fuel fed to the furnace, which we can compensate for by simply adjusting the fuel flow rate, and the inlet temperature to the gas compressor, which we can compensate for by adjusting the power input to the compressor. Since we can compensate these disturbances locally, we do not include them in the set of significant disturbances. Constraints and Operating Variables at Level 3. The gas recycle flow is a new manipulative variable, whereas the liquid recycle flow is fixed when we fix the conversion. Also, the fuel flow to the furnace is a new manipulative variable (we can adjust the fuel flow both to compensate for changes in the fuel quality and also to change the temperature of the stream leaving the furnace). The recycle material balances can be approximated by the expressions toluene recycle flow: F T R = Fm(1 - X ) / X PB(1 - x)/SXY, (11) recycle gas:
RG =
5pB/xs
- FGYFH YPH
where we have included the constraint of a 511 hydrogenlaromatics ratio a t the reactor inlet. We also have a
constraint that the reactor exit temperature must be kept below 978 K (1300 O F ) in order to prevent hydrocracking reactions. Thus, there are two new constraints added at level 3. All of the other pocess flows can easily be calculated. Now that we have developed expressions for all of the process flows, we can also calculate the process energy balances. Moreover, for design we can calculate the sizes of the furnace, the adiabatic reactor, and the gas recycle compressor (based on the mean values of the disturbances). Once the equipment sizes have been fixed, we can still vary the recycle gas flow by varying the power input to the compressor, and we can vary the furnace exit temperature by changing the fuel rate to the furnace, assuming that we do not encounter equipment constraints (we discuss the interaction between equipment constraints and disturbances in the next paper in this series). Thus, we introduce two new manipulative variables. The toluene recycle flow is fixed when we fix the production rate and conversion, see eq 11, and the specification of the reactor size removes a degree of freedom from the analysis; Le., there is a constraint (the reactor design equation) that relates the reactor temperature, conversion, and the flow through the reactor. Thus, we can select the reactor conversion and the purge composition of hydrogen as operating variables, i.e., the conversion trades off high selectivity losses at high conversions vs high liquid recycle operating costs a t low conversions, whereas the purge composition trades off large hydrogen feed costs at high purge compositions of hydrogen vs large gas recycle operating costs a t low purge compositions. Of course, we could just as well select other variables as our operating variables (excess hydrogen fed to the process, purge split fraction, etc.), providing they are related to conversion and purge composition. We have added two new constraints (H,/aromatics = 5 at the reactor inlet and the reactor exit temperature < 978 K), and we still have two operating variables that must be optimized (conversion and purge composition). The manipulative variables we have available are the makeup gas rate, F G , the power input to the gas recycle compressor or the recycle gas rate, the fuel supply to the furnace, or the reactor inlet temperature. We know that purge composition is sensitive to the makeup gas rate, see eq 8, that the H2/aromatics ratio is sensitive to the recycle gas flow rate, see eq 12, and that the reactor conversion is sensitive to the reactor inlet temperature. However, there is no additional manipulative variable available that we can use to ensure that the reactor effluent temperature from the adiabatic reactor does not exceed 978 K. Hence, we say that the process is uncontrollable at level 3. There are several ways that we could attempt to restore the process controllability: a. We could reduce the conversion for certain disturbances to keep Tr,out < 978 K always. b. We could design the reactor to operate with an exit temperature C 978 K a t the worst case conditions (which requires an overdesign of the reactor), so that the disturbances never cause this constraint to be violated. c. We could introduce a new manipulative variable by changing the reactor design, i.e., we could install a cooling jacket around the reactor, we could use a series of adiabatic reactors with either heat exchangers between the beds or a bypass of some of the feed around the initial reactor sections, etc. Each of these alternatives imposes some economic penalty, and we need to evaluate all of the alternatives to find the least expensive option. For the purpose of this
604
Ind. Eng. Chem. Res., Vol. 27, No. 4, 1988 R
G A S RECYCLE
r
CWPRESSOR
HYDROGEN
-
TOLUENE
-
YIDI1OOEN FURNACE
~
REICTOR
FURNICE
REACT&?
TOLUENE
II I---
.PLPGE
cw TOLUENE
'IECICLE
1
----ti7 ii0"ID
BENZENE
SEPLRATION
TOLdENE RECYCLE
S"STEM
DIPHENYL
Figure 4. General structure of the separation system for the HDA process.
case study, we will assume that the overdesign of the reactor, option b, is the cheapest.
Figure 5. Liquid separation system structure for the HDA process. 0 1 s RECYCLE
Level 4: Separation System. General Structure Since the reactor effluent is a vapor, we cool this stream with cooling water and attempt a phase split. Since a fairly sharp split is possible, we select the general structure of a separation system shown in Figure 4 (Douglas, 1985). We include the partial condenser in the controllability analysis at level 4 because it fixes the temperature of the flash drum and, therefore, the splits between the vapor and liquid streams. The partial condenser includes both a new disturbance, i.e., the cooling water inlet temperature, a new manipulative variable, i.e., the cooling water flow rate; and a new process constraint, Le., the cooling water return temperature must be kept below 322 K (120 O F ) to prevent scaling in the closed cooling water system. The new design degrees of freedom are the flash drum temperature and the cooling water return temperature. However, the specification of the area of the partial condenser removes one degree of freedom for the controllability analysis. As an operating variable, we can select the flash drum temperature, because there are large purge losses of aromatics a t high flash drum temperatures which are balanced against high cooling water costs for the partial consenser at low flash drum temperatures. The cooling water inlet temperature is a significant disturbance because it has a large effect on the purge losses of aromatics. Thus, we have added a new constraint, i.e., the cooling water return temperature, and a new operating variable, i.e., the flash drum temperature, but we have added only one new manipulative variable, i.e., the cooling water flow rate. Thus, we find that the process is not controllable at level 4. If the optimum flash drum temperature corresponds to the cooling water outlet temperature exceeding 322 K, the cooling water flow rate must be increased in order to satisfy the process constraint. This situation is not completely undesirable because the recovery of aromatics in the flash liquid also increases. Thus, we can restore controllability by neglecting the optimization of the operating variable, and we use the new manipulative variable to satisfy the process constraint. Level 4a: Vapor Recovery System. For the flow sheet that we are considering, there is no vapor recovery system; see Figure 5. Level 4 b Liquid Separation System. The distillation train used for the HDA process is also shown in Figure 5 . The cooling water inlet temperatures to the condensers and the steam inlet temperatures to the reboilers represent new disturbances, and the cooling water flows, steam flows, and reflux ratios are new manipulative variables. The cooling water return temperatures are constraints, and the product composition is a new constraint. The specification of the reflux ratios and the fractional recoveries (except product composition) for each column
COMPIESSOR
r
---~___
-WENCH
I
I I
I
TOLJENE FEED
DP*EN"L
-
-+-2-
Figure 6. Heat exchanger network structure for the HDA process.
represent the design degrees of freedom, but the specification of the number of trays in each column removes a degree of freedom. Thus, the fractional recoveries for all but the product stream become the operating variables. The trade-offs for the fractional recoveries balance large heating and cooling costs at high recoveries vs large penalties (product or raw material losses, or increased recycle costs) at low recoveries. Thus, we have two operating variables, i.e., either the fractional recoveries or the end compositions of the key components, for each column, but we also have two manipulative variables, i.e., the steam flow rate or the vapor rate and the reflux ratio, so that the process is controllable a t level 4b.
Level 5: Energy Integration The only energy integration considered for this case study, see Figure 6, is the feed-effluent heat exchanger (FEHE) between the reactor effluent and the furnace inlet stream (we considered the furnace and the partial condensor earlier). There is a new constraint, which is the quench temperature after the reactor outlet. There are no new disturbances, but the quench flow rate is a new manipulative variable. The new design degree of freedom is the approach temperature between the quenched reactor outlet temperature and the temperature of the feed stream. However, specifying the area of the FEHE removes one degree of freedom. Hence, we have one constraint, the reactor quench temperature, and one manipulative variable, the quench flow rate, so that the process is controllable at level 5 . It should be noted that in extensively energy-integrated processes manipulative variables introduced at earlier levels are often eliminated. In particular, if the column condensers and/or reboilers are energy integrated with process streams, we normally lose manipulative variables. However, controllability can be restored by installing bypasses around some of the exchangers or by installing auxilliary condensers or reboilers.
Ind. Eng. Chem. Res., Vol. 27, No. 4, 1988 605 Table V. Operating Variables, Process Constraints, a n d Manipulative Variables variable variable operating manipulated operating manipulated PB Y Pn
&ITa
RRC
vsc
X
VPC VRC
Tcw,retumn
FQ
xD,SC xD,PCn
[none] [none]
Treated as process constraints.
Summary of the Controllability of the HDA Process Our controllabilityanalysis indicated that there are three disturbances that have a significant impact on the process economics, i.e., the production rate, the feed composition of hydrogen, and the cooling water inlet temperature to the partial condenser. An optimum steady-state design of the process is uncontrollable, although we could restore controllability by (a) overdesign of the reactor so that the constraint on the reactor exit temperature never becomes active and (b) neglecting the optimization of the temperature of the flash drum. Other alternatives for restoring controllability were also discussed. The manipulative variables, operating variables, and process constraints are listed in Table V, and there are two important operating (optimization) variables, i.e., conversion and purge composition of hydrogen. Limitations of the Controllability Analysis The controllability analysis is based on the assumption that the sizes of various pieces of equipment do not constrain the operation of the process. In order to evaluate this assumption we must examine the flexibility of the process. This topic is treated in the next paper in this series. It is also important to recognize that our controllability analysis a t this point is based only on steadystate considerations. When the process dynamics are considered, new controllability limitations might arise. However, this simple steady-state analysis does help us to understand the effect that disturbances have on the process operation. Conclusions and Significance A previously published flow-sheet synthesis decomposition tool (Douglas,1985) can also be used to evaluate the steady-state controllability of a complete chemical process. At each decomposition level, new manipulated variables and operating variables representing the economic and noneconomic (process constraints) control objectives are easily identified. If the available manipulated variables are compared with the constraints and operating variables introduced a t each level, the preliminary controllability criterion can often be satisfied. Otherwise, uncontrollable flow sheets can be improved in three ways: (1)modify the flow sheet so as to create new manipulated variables (introduce new equipment, recycle flows, bypasses, etc.), (2) design away from process constraints (explosive limits, etc.) so that noneconomic-controlled variables are not important for the full range of anticipated disturbances, or (3) ignore the least important economic controlled variables. When this analysis is conducted at the preliminary design stage, these alternatives may be screened rapidly by using short-cut economic models. In this way, the most important causes of uncontrollability can be avoided at the minimum penalty. Thus, this approach provides a tool for both the design engineer (who must develop controllable
processes) and the control engineer (who must operate processes profitably).
Acknowledgment The authors are grateful to the National Science Foundation for providing financial support under Grant CPE-8105500.
Nomenclature C B = cost of benzene, $/mol C H = cost of hydrogen, $/mol CT = cost of toluene, $/mol C F =~ fuel value of the purge, $/mol C F 2 = fuel value of the heavy components, $/mol F,, = cooling water flow rate to partial condenser FFT = toluene feed flow rate FG = hydrogen feed flow rate FTR = toluene recycle flow rate FQ = reactor quench flow rate Ffuel= furnace fuel flow rate H 2 / T = hydrogen to toluene ratio at reactor inlet HDA = hydrodealkylation of toluene t o benzene process P B = production rate of benzene P D = production rate of diphenyl byproduct P H= t~ otal flow ~ rate of heavy materials (diphenyl plus heavy impurities in toluene feed stream) R = reflux ratio Rc = gas recycle flow rate S = selectivity Tcw,return = cooling water return temperature Tflash= flash drum operating temperature Tr,out = reactor outlet temperature TQ= reactor outlet quench temperature V = column vapor flow rate x = reactor conversion XB = bottoms composition XD = distillate composition Y F H = hydrogen feed composition ym = mole fraction of pure toluene in the toluene fresh-feed stream YPH = hydrogen purge composition Subscripts cw = cooling water PC = product column RC = recycle column SC = stabilizer column Literature Cited Boland, D.; Hindmarsh, E. Chem. Eng. Prog. 1984, 80(7), 47. Douglas, J. M. AZChE 1985, 31, 353. Ellingson, W. R. AZChE Symp. Ser. 1976, 72, 159. Fisher, W. R.; Doherty, M. F.; Douglas, J. M. Chem. Eng. Res. Des. 1985, 63, 353. Haggin, J. Chem. Eng. News 1984, April 2 , 7 ; 1984, May 2 1 , 7 ; 1984, June 4, 7. Lee, W.; Weekman, V. W. AIChE J. 1976,22, 27. Linnhoff, B.; Vredeveld, D. Chem. Eng. Prog. 1984, 80(7), 33. Linnhoff, B.; Townsend, D. W.; Boland, D.; Hewitt, G. F.; Thomas, B. E. A.; Guy, A. R.; Marsland, R. H. A User Guide on Process Integration for the Efficient Use of Energy; Inst. Chem. Eng.: Rugby, UK, 1982. Nishida, N.; Stephanopoulos, G.;Westerberg, A. W. AZChE J. 1981, 27, 321. Raman, A. K. S.; Shimoda, S. M. Chemical Commodities Indicator, 1978 Forecasts; First Boston Corp.: New York, 1978. Rinard, I. "Control Systems for Complete Plants-The Industrial View", In Process Control 2; Proc. Eng. Found. Conf., Sea Island, GA, 1982; 541ff. Received f o r review July 15, 1986 Revised manuscript received July 23, 1987 Accepted August 17, 1987
