Ind. Eng. Chem. Res. 1994,33, 1197-1207
1197
Throughput Manipulation in Plantwide Control Structures Randel M.Price: Philip R. Lyman, and Christos Georgakis' Chemical Process Modeling and Control Research Center and Department of Chemical Engineering, Lehigh University, Iacocca Hall, 111 Research Drive, Bethlehem, Pennsylvania 18015
A fundamental characteristic of a well-designed process plant regulatory control system is effective management of the rate of product manufacture and regulation of the inventories within the plant. Designers have tended to concentrate on the design of product quality controls, neglecting the impact of the production rate and inventory controls on final control system performance. Price and Georgakis have proposed guidelines for the development of production rate and inventory controls. These rules help a designer to ensure that these parts of the control structure are effectively designed before proceeding to the design of product quality controls. The structures which result satisfy the control objectives and maintain the plantwide characteristics of the problem. The applicability of these guidelines is illustrated using the complex test problem provided by the Tennessee Eastman Company. When the guidelines are applied to the Eastman problem, several candidate control structures can be developed. The major difference between the alternatives is the method used to adjust the production rate or throughput of the process. Simulation testing of the candidates makes clear that this decision is an important contributor to the success of the resulting control structure. 1. Introduction
An essential characteristic of a process plant regulatory control system is effectivemanagement of the plant's basic operating tasks. Fundamental among these are control of the rate of product manufacture and regulation of the inventorieswithin the plant and its component processing units. A tiered framework for the design of plantwide regulatory controls (Price and Georgakis, 1992)offers a flexible means of structuring the decisions required of the control system designer. The framework divides the control problem into four subproblems, each of which requires a tier of controls and corresponds to a fundamental task of the plantwide regulatory control structures. The designer develops each tier of controlsacross the entire plant before proceeding to the next. As tiers are developed, additional control tasks are satisfied and conflicts with those which precede are reconciled. The flexibility of this design framework makes it particularly well suited for application during early stages of process design, and hence promotes the integration of control design and process design. The most basic tasks of a control structure are production rate and inventory control. These tasks are prerequisite to any form of plant operation. In addition, many tools used in the design of composition or temperature controllers presuppose the existence of an effective inventorycontrol structure. In order to use such tools, designers tend to develop throughput and inventory structures on an ad hoc basis without detailed analysis; hence, despite their great importance, these controls have typically not been the subject of investigation. A set of guidelines for the development of production rate and inventory controls have been presented (Table 1). These provide general guidance for the development of production rate and inventory control structures. The control structures discussed in this paper will be developed applying these guidelines to two different process systems: a CSTRIcolumn and the industrial test problem
* To whom correspondenceshould be addressed. Phone: (215) 758-5432. FAX: (215) 758-5297. E-mail:
[email protected]. + Present address: Department of Chemical Engineering, University of Mississippi, University, MS 38677.
Table 1. Guidelines for Production Rate and Inventory Control Design (Price, 1993) Production Rate Control 1. identify the primary process path 2. list candidates for w e an throughput manipulators (TPMs) 3. prefer process internal flows as TPMs Inventory Control 1. identify inventories which may require control 2. identify manipulators suitable for adjusting each inventory 3. determine how many inventories associated with each processing unit may be controlled 4. considering each inventory along the primary process path, construct a self-conaistent chain of controls 5. construct inventory controls for side chains; work outward and direct disturbances away from the primary process path 6. construct additional inventory control chains along recycle paths 7. assign control loops to govern any process external flows which remain uncontrolled 8. ensure that each component has a suitable entrance and exit point
proposed by the Tennessee Eastman Co. The resulting structures will be examined to illustrate the important consequences of the throughput control decisions. As a prologue to the examples,it will first be necessary to review the general problem of throughput control. The general concept of a tiered framework for control design was presented in a paper by Price and Georgakis (1993). A concurrent effort to understand and control the Tennessee Eastman challengeproblem was conducted and has been presented by Lyman and Georgakis (1993). This paper is intended to serve two purposes: it will illustrate the importance of proper selectionof a production rate manipulator for a process plant and in so doing provide general guidance for designers, and it will show how the tiered framework and guidelines can be used to develop an effective control structure for the Eastman plant and provide a useful context for understanding its behavior. It should also be noted that a much abbreviated account of this work was presented as an invited paper at the 1993 European Control Conference (Price et al., 1993). 2. The Problem of Throughput Control
The problem of controlling the production rate, or throughput, of a process plant has seen scant coverage in
0888-5885/94/2633-1197$04.50/00 1994 American Chemical Society
1198 Ind. Eng. Chem. Res., Vol. 33, No. 5, 1994
Figure 1. Control in the direction of flow.
Figure 2. Control in the direction opposite to flow. the literature. Typically, a control designer selects a single stream flow to serve as a throughput manipulator and develops a system of inventory and flow ratio controllers to transmit changes through the plant. Existing research accounts focus on the basic layout of the inventory controls relative to the stream chosen as the throughput manipulator. The fundamental principles were laid out by Buckley (1964). He describes two basic alternatives: “control in the direction of flow”and “control in the direction opposite to flow”. When control in the direction of flow is applied (Figure 11, a feed to the process system is used as the throughput manipulator. The inventories in each downstream processing unit are controlled by adjusting the flow of materials leaving the unit so that changes in production rate are passed through the plant from beginning to end by the inventory controllers. Control in the direction opposite to flow (Figure 2) uses a product stream as the throughput manipulator. Inventories in each processing unit are controlled by manipulating incoming streams. All of the authors who discuss this issue agree that control in the direction of flow is the most common choice (Stephanopoulos (1984), p 255, is another example), yet many argue that control in the direction opposite to flow offers operational advantages. Transfer function analysis has been used to compare the stability characteristics of the two schemes (Douglas (1972), p 230). The analysis shows that control in the direction opposite to flow leads to fewer stability problems. This scheme is also said to result in reduced internal turndown requirements (Buckley et al. (1985), p 6): for a given change in production rate the required change in manipulated flows is smaller when the inventories are controlled in the direction opposite to flow than when controlled in the direction of flow. In practice, it seems that the key factor in the arrangement of the controls is the selection of the throughput manipulator itself. This problem does not seem to have been addressed within a general context and many designers seem to consider only feed and product streams as candidates. These may comprise only a fraction of the possible choices, and so may prematurely eliminate valid and effective options. Throughput manipulators take two basic forms. Process stream flows can be throttled directly to serve as “explicit” manipulators. Feed and product streams are examplesof explicit manipulators. The other category of throughput manipulators are “implicit”. These are not “real flows”, but rather they are other process variables such as process heat input which influence the quantity of product manufactured or the separation of product from byproduct. Implicit manipulators are often controlled by adjusting utilities such as fuel or coolant streams. When one considers all of these possibilities for manipulating the throughput of a process, it is readily
Figure 3. Process internal throughput manipulator with radiating inventory controls.
apparent that potential throughput manipulators need not be limited to feed or product streams. Such “process external” throughput manipulators typically provide only a fraction of the candidates available for a given plant. Many other candidates are “process internal”-located between processing units in the interior of the plant. From an intuitive standpoint, process internal flows would seem to offer certain advantages with respect to the patterns of propagation of a production rate change through a process. If the throughput adjustment is made at a location internal to the plant, the change in production rate will propagate outward through only part of the plant before the feed flow is affected, and will simultaneously work through the other portion of the plant to change the product flows. In contrast, when an external flow is used to control throughput,the change must propagate through the entire plant from beginning to end (or uice uersa). This observation suggests that internal flows have a substantial chance of more rapidly affecting a throughput change. Other operating advantages seem likely as well. Some plants have a single processing unit which is markedly more difficult to control than the others. Selecting a flow very close to that unit as the throughput manipulator will help minimize or control the variation affecting the unit and so should make it easier to control. The essential element in the performance of a throughput/inventory control structure appears to be the “selfconsistency” of the controls (Price, 1993). An inventory control structure is said to be ”self-consistent”if it is able to propagate a production rate change throughout the process so that such a change produces changes in the flow rates of all major feed and product streams. Self-consistency is a consequence of the arrangement of the inventory controls. The combination of a feed stream as throughput manipulator with control in the direction of flow is self-consistent,as is the combination of a product stream as throughput manipulator with control in the direction opposite to flow. If a process internal throughput manipulator is used, it is not possible to arrange the inventory controls into either of the basic configurations. Instead, self-consistency requires that the chain of level controls be constructured to radiate outward from the throughput manipulator. This implies that level controllers between the feed and the throughput manipulator are in the direction opposite to flow, while those between the throughput manipulator and the main products are in the direction of flow. Additionally, level controllers on streams branching off of the primary path should also be arranged in such an outward direction. An example of an inventory control structure with an outward arrangement is shown in Figure 3.
When an inventory control structure is not selfconsistent, it cannot operate effectively by itself without additional control loops to supplement the action. When such loops are added, they are said to have “remediedthe inconsistency” of the inventory structure such that the structure has a “remedied inconsistency”. It should be stressed that an inconsistent inventory control structure cannot always be remedied by the addition of control loops.
Ind. Eng. Chem. Res., Vol. 33, No. 5,1994 1199 Table 2. Summary of Potential Control Schemes: CSTR/ Column System.
R FO. xO
1 . ”I
F.xr
I I
controlling inventory x b only Xb and X d X b and Xf
B 10 6 4 4
throughput control variable D F Fo a 8 10 10 6 12 4
4
8
4
4
4
total 36 34 20 16
Base level manipulator, base composition manipulator E (B,F, V);accumulator level manipulator,top composition manipulator E (D,R,V);reactor levelmanipulator,reactorcompositionmanipulator E ID, F,Fo). Figure 4. The CSTR/column.
A structure with a retained inconsistency may be able to respond to some disturbances, but fail to respond effectively to changes in throughput. One particular class of inventory control problem is of particular interest to the student of plantwide control. Recycle systems will be encountered in almost any plant design which is complex enough to require a plantwide approach to control design. Recently, controlling these systems has been the subject of some attention and Luyben (1992)has offered three generally applicable principles for inventory control of recycle systems: 1. Throughput changes must change reactor conditions. 2. Fix a flow rate somewhere within the material recycle loop. 3. The flow rate of a reactant makeup stream can be fixed only if that component is completely consumed in a single pass through the reactor. These rules provide a useful check on control structures developed using the tiered framework.
3. A CSTRKolumn Example Many of the complications inherent in the design of plantwide control systems can be grasped best by consideration of appropriate examples. Much can be learned from simple yet representative process systems. One such is a CSTR/column with recycle (Figure 4) involving an isothermal A B reaction with recycle of unreacted feed. An extensive series of simulations has been used to study the consequences of decisions made during throughput and inventory control design (Price, 1993). There are four good candidates for use as throughput manipulators (TPMs). Two are process external (the feed Foand product B),and twoare process internal (the column feed F and the recycle D). The throughput control structure is completely determined by selecting the variable to be used for throughput control. Three processing unit inventories need to be controlled-liquid in the reactor, the column base, and the accumulator. Each inventory can be controlled in several ways. These can be stated using set notation, x E (a, b, c), which is read ux is an element of the set containing a, b, and c”. The rules used for level control in the CSTR/ column system are
-
RLM E {D, F, Fo) ALM E P, R , Vl BLM E (B,F, VI where the abbreviations RLM, ALM, and BLM stand for reactor level manipulator, accumulator level manipulator,
and column base level manipulator, respectively. These rules are a way to codify design decisions. Another designer might choose a more liberal set of rules; for instance, reflux might be used for base level control. Given these rules, enumeration yields 18 distinct three variable combinations for controlling the system levels. When combined with the throughput control options (TPM E (B,D,F,Fo)), the number of possible throughput/ inventory structures is 36. The next design step is to allocate composition controllers. Certainly, the final product composition Xb must be controlled. One of the two intermediate stream compositions, Xd or xr,might also be controlled in hope of improving overall performance. Some inventory structures do not permit any acceptable composition control structures where others offer two alternative single end structures. Of the 36 possible inventory control structures, only 34 produce valid composition control structures. Selection of a throughput control variable or the decision to control a specificintermediate compositionhas a marked impact on the flexibility afforded the control system designer. For example, Table 2 illustrates that although there are 34 possible single end structures, selecting the bottoms flow for use as the throughput manipulator reduces the number of options to 6. Similar arguments make clear that the choice of level controls has a significant impact on the remaining composition control problem (Skogestad et al. (1990)make an equivalent observation). It is thus apparent that once a throughput manipulator is chosen the control design problem is greatly simplified, but the extent by which the selection limits possible solutions makes a good choice of throughput manipulator imperative. The complete simulation study investigated 70different structures for the control of the CSTR/column. Each structure was examined in a variety of implementations. These depend on the tunings used for the level controllers and the type of composition controller (proportional only or PI) used to control intermediate composition. A total of 318 implementations were examined. Each implementation was simulated twice: once to determine the response to a step change in feed cornpositionand again to determine the effect of a step change in throughput. In this discussion, both input changes are referred to as “disturbances” because of their effect on the process, but the reader should keep in mind that one of these inputs is an operator-imposed change in production rate. In each simulation, the integral absolute error (IAE) of the final product composition relative to setpoint is tabulated. These IAE values are used to rank and compare the various control implementations. The basic observations of the simulation study have been summarized elsewhere (Price and Georgakis, 1992). Two of these describe the characteristics of the throughput and inventory control structures:
1200 Ind. Eng. Chem. Res., Vol. 33, No. 5, 1994
Table 3. Prevalence of Throughput Manipulators in Feed Composition IAE Ranking TPM
no. of implementations 10 20 30 40 50
no. of B 0 2 3 4 4
%B
no. of D 4 4 5 6 10
%D
0 10 10 10 8
all (295)
61
21
74
25
40 20 17 15 20
Observation 1: The control structure implementations which produce the smallest IAE in response to disturbances are those whose inventory control structure is selfconsistent and directed along the primary process path. Observation 2: If all else is equal, throughput manipulators internal to the process tend to produce smaller IAE than external throughput manipulators. Control in the direction of flow tends to produce smaller IAE than control in the direction opposite to flow. The first of these observations, requiring a self-consistent inventory structure, appears to be the single most important factor in the performance of the controlled process. The principle of self-consistency has already been defined, but it may also be necessary to define the "primary process path". When a process flow sheet is examined,the primary process path is that single flow path which begins with the major feed streams and ends with the major products, tracing the most significant process streams in between. For the CSTR/column, the primary path begins with the feed stream Fo,follows the reactor outlet F,and ends with the product stream B. The second observation suggests process internal throughput manipulators. The simulation results show that the best performance is obtained when F is the throughput manipulator, with FOthe second choice. One way to see this is to look at Table 3. This table shows the prevalence of the possible throughput manipulators within the ranked set of simulation results. Of the 20 implementations with the least IAE, 75% use an internal throughput manipulator (F or D). Contrast this number to the totalsin the bottom line of the table. Less than half of all implementations considered (135 of 295, or 46% ) use internal manipulators. Clearly, these manipulators are preferred in the best structures. It is also worthwhile to note the fraction of the best implementations using each of the external manipulators, FO and B. The feed flow provides the second largest fraction of the 50 best implementations and is always the preferred external manipulator. The use of product flow, and hence inventory control in the direction opposite to flow, is less attractive than any other alternative. This is contrary to the recommendations of many authors (discussed in section 2) favoring product flow TPMs. One possible reason for the disagreement is the focus of our study on disturbance rejection rather than the response time of the rate change, as is often the case with other researchers. 4. The Tennessee Eastman Test Problem
Added insight into the complexities of throughput control can be gained by studying the test problem provided by the Tennessee Eastman Co. (Downsand Vogel, 1993). An extensive treatment of the problem and its solution has been prepared by Lyman (1992,1993). The problem involves two gas-phase reactions with liquid products:
no. of F 4
%F
% internal
% external
11 14 16 20
no. of FO 2 3 8 14 16
%Fo
40 55 47 40 40
20 15 27 35 32
80 75 63 55 60
20 25 37 45 40
61
21
99
34
46
54
A(g)
+ C(g) + D(g)
+
G(h)
Both reactions are exothermic, as are the two possible side reactions:
3D(g)
-
2F(liq)
Reaction rates are Arrhenius functions of temperature and first order with respect to each reactant concentration. Figure 5 shows a process and instrumentation drawing of the process. Gaseous feeds enter the reactor and form liquid products. Heat of reaction causes the mixture within the reactor to vaporize and leave the reactor as gas, pass through a condensor, and pass into a vapodliquid separator. The desired products, byproduct, and unconverted reactants are present in this stream. Components not condensed (mostly light reactants) are compressed and recycled. Condensed material is sent to a product stripper where any remaining reactants are removed. The reactor is equipped with a cooling water jacket to remove excess heat of reaction. There are four feed streams: stream 1is component A, stream 2 component D, stream 3 componentE, and stream 4 a mixture of components A (51% ) and C (48.6 % 1. A small amount of inert material (0.4% component B) enters with the C feed in stream 4. All of the feed streams except for stream 3 come directly from other units and have limited upstream holdup. The recycle stream contains all of the components but is mostly A and C. The desired product is a mixture of G and H; the ratio is itself a product specification (base case value is about 1:l). 1nert.a (component B) and byproducts (component F) are removed in a purge stream. Supplied with the problem is simulation code and suggested setpoint changes and preprogrammed disturbances which can be used to test condidate control structures. The Eastman problem is particularly challenging because it combines highly exothermicreactions with a large recycle stream. The recycle flow makes up 64% by weight of the feed to the reactor at design conditions. Because this stream is so large, even slight variations in reactor operating conditions can be amplified and returned to the reactor. Three mechanisms can be identified which in combination provide a highly interactive relationship between reactor temperature, reactor pressure, and the reaction rate. The first mechanism is a mole reduction upon reaction: the reactants consist of 6 mol of gas and the products only 2 mol. This mole reduction tends to reduce the pressure when reaction rates increase. A second mechanism is seen in the kinetic rate expression for the reactions, Arrhenius temperature dependence, and roughly third-order dependence upon the reactor pressure. The
Ind. Eng. Chem. Res., Vol. 33, No. 5, 1994 1201
I C
/
4
LI
Figure 5. Tennessee Eaetman problem: process and instrumentation drawing.
last mechanism depends on the liquid-vapor equilibrium existing in the reactor between the liquid products and the gaseous reactants. The combination of these effects causes the reactor pressure, the reactor temperature, and the reaction rate to interact strongly and can lead to destabilizationof the system unless proper control actions aretaken. These operating problems mandate an effective throughput and inventory control structure. 4.1. Applying the Throughput Control Guidelines. When the guidelinesfor throughput and inventorycontrol are applied to the Eastman problem, several candidate control structures can be developed. The major difference between the structures is the method used to adjust the throughput. To illustrate, each guideline for production rate control will be considered in turn. Identify the primary process path: The primary process path traces the process from the reactant feeds to the final product. The route would be straightforward except that the C feed enters through the product stripper and merges with the recycle ahead of the reactor. Thus one might define two different primary paths, one beginning with the C feed and the other beginning with the A, D, and E feeds. Since the C feed is all vapor, the dynamic delay resulting from the different entry points is probably insignificant. Additionally, it can be observed that although the C feed is a sizable stream, it is made up of components which are in significant excess in the reactor and recycle loop. This suggests that it is of slightly lesser importance in defining the primary process. Thus, the primary process path will be defied to begin with feed streams 1,2,and 3; flow through the reactor, separation drum, and stripper; and end with the stripper bottoms product stream.
List candidate TPMs: It appears that the production rate can be controlled by adjusting any of several flows along the primary process path the feed streams, the final product stream, or the separator drum bottoms flow. One implicit manipulator is also available-the flow of coolant to the reactor condenser may be manipulated to control the amount of liquid separated from the reactor product stream and consequently the amount of final product produced. The four candidates to be examined are illustrated in Figure 6. All of the process flows identified as potential TPMs appear to be large enough to be effective manipulators. The only stream on the primary process path which seems to be too small is the A feed, which is less than 1% of the total reactor feed and only 10% of the size of the D and E feeds. Examination of the steady-state mass balances shows that essentially all of component D entering the reactor is converted. Components A and C are in significant excess. Component E is also in excess, but to a lesser extent. This suggests that manipulating component D flow (stream 2) is perhaps the most effective handle of the feed streams, since a change in its flow will have a more immediate effect on the reactor than the alternatives. Prefer internal flows: The guidelines for control design recommend using an internal flow as the throughput manipulator. Both the separator drum bottoms and the condenser duty qualify, and so are preferred candidates if no more important factors come into play. All four candidates will be examined in order to assess the validity of the recommendation. 4.2. Applying the Inventory Control Guidelines. Each candidate throughput structure results in a different
1202 Ind. Eng. Chem. Res., Vol. 33, No. 5, 1994
A
I
I
I,D
I
I
Structure2
J
0 L
8
E
........................* structure3
[
c
)
fk
4 W
1
:: ....@
Figure 6. Tennessee Eastman problem: posaible TPMs.
inventory control structure. These are developed using the guidelines for inventory control design. Identify inventories which may need control: The inventories in the system are identified as the reactor liquid (level) and vapor (pressure), the separator drum liquid (level) and vapor (pressure), and the stripper base liquid (level). Vapor in the stripper is not considered to be an inventory as it cannot be contained within the unit process. It should be noted that the entire vapor space of the process is functionally one inventory, and that the pressure within the reactor, stripper, and separator drum differ only by the pressure drop caused by the intervening piping and equipment. In particular, the reactor and separator operate at essentially the same pressure (in the base case, the pressures are 2705 kPa in the reactor, 2634 kPa in the separator, and 3102 kPa in the stripper). For this reason, the two vapor inventories will be considered as a single inventory during inventory control design. Identify inventory control manipulators: Possible manipulators can be listed in rule form: Reactor level manipulator, reactor pressure manipulator E (stream 1,stream 2, stream 3,stream4, condenser duty, jacket duty). Another designer might choose to exclude stream 4 from consideration if it is judged to be too "far" from the reactor to be effective; however, because vapor flow changestend to be extremelyfast and the vapor space of the system forms a single inventory, it will be accepted for use in this discussion. This stream is also the largest of the feeds, and so should prove to be a good manipulator for the reactor inventories.
Separator level manipulator E (condenser duty, separator bottoms) and separator pressure manipulator E (condenser duty, purge, compressor flow}. Stripper level manipulator E {vaporboilup, separator bottoms, product flow). Determine which inventories can be controlled A degree of freedom analysis suggests that both separator inventories can be controlled. For the stripper, there is enough freedom to control the only inventory present. The reactor is more complicated and the degree of freedom calculation less straightforward. It appears that only one inventory can be controlled in the reactor. Since the vapor space can possibly be controlled elsewhere, the level will be chosen as the controlled inventory. Note, however, that the freedom analysis of the reactor is sensitive to the control design decision sequence-as manipulators are assigned to control tasks, the reactor degrees of freedom may be changed (if the recycle rate is fixed, for example). Construct a self-consistent chain of inventory controls along the primary process path: The chain should proceed outward from the throughput manipulator. The reactor, separator, and stripper levels will be controlled, while the pressure in the vapor space will be allowed to float. Structure 1: TPM = D Feed Stream. The inventory structure should be arranged in the direction of flow. The condenser duty will be chosen to control reactor level. The separator drum level is next on the path. An exiting flow is required, so the drum bottoms will be placed on
Ind. Eng. Chem. Res., Vol. 33, No. 5,1994 1203
..........................
Figure 7. Tennessee Eastman problem: inventory control chain TPM = condenser.
level control. The only inventory in the stripper is the level; it will be paired with product flow. Structure 2: TPM = Condenser Duty. Inventories downstream from the condenser must be controlled using outlet manipulators; upstream inventories must be controlled with inlet manipulators. The reactor level will be controlled using the C feed because it is the largest feed stream and affects both primary reactions. The other feed streams which are large enough to use affect only one of the two primary reactions. The separator level will be controlled using the bottoms flow, and the stripper level will be controlled using the product flow. The resulting system is shown in Figure 7 and serves as an example of a primary path inventory control chain. Structure 3: TPM = Separator Bottoms. The downstream inventory, the stripper level, should be controlled using the product. The separator is an upstream inventory, so its level will be controlled using an inlet manipulator, condenser duty. The reactor also requires an upstream manipulator, so its level will be controlled using the C feed. Structure 4: TPM = Product Flow. The chain must be constructed in the direction opposite to flow, working backward from the product. Stripper inventory must be controlled and an inlet flow must be used, so separator drum bottoms will be assigned to control stripper level. The level in the separator drum must be controlled using an inlet flow. The only option acceptable in light of the proximity rules is the condenser duty. The reactor level must be controlled using an entering stream. The C feed will be assigned.
Construct side-chain inventory controls: There are no inventories in side chains in this process. Construct recycle path inventory controls: There are no inventories in the recycle path. Assign controllers to remaining process external streams: The remaininguncontrolledfeeds and the purge must be controlled so that they can enter or leave the process as needed. The purge functions to remove inerts and byproducts. Thus, its flow should be controlled and adjusted for changes in composition. The remainingfeeds need to be added on flow ratio or composition control. Since the D:E ratio determines the product ratio, it should be monitored and possibly controlled. The A and C streams will be controlled to maintain reactor inlet compositions. Checkentrance and exit points for the components: It is essential that each component entering or created within the process be able to leave, while components consumed can enter. Entrance and exit points for this problem are shown in Table 4. It is apparent that adequate purge flow is essential. If too little material is purged, components B and F (inert and byproduct) will soon build up within the recycle loop. Similarly, if something happens to upset the reactor so that less feed is consumed, components A, C, and E also might build up. As an immediate step to address the need for good purge control, the purge flow controller setpoint will be provided by a composition analyzer so that the controller can be reset if inerta begin to accumulate. The inventory control structures should be reviewed to reflect Luyben’s suggestions for recycle system control
1204 Ind. Eng. Chem. Res., Vol. 33, No. 5, 1994
..........................
I
I
I
I
+ 5
I
1
[email protected] e 20
4
I
Ifi LI
Produa
............................................................... Figure 8. Example of complete control structure.
(Luyben, 1993; Tyreus and Luyben, 1993). Luyben suggests that recirculation rate needs to be directly controlled. When possible, this will be done by using the spillback around the compressor to control the gas recycle. It is not possible to control recycle flow in structure 1 (TPM = D feed) without overspecifying the system. A controller is added to the other three structures to control the recycle flow and hold it at a fixed value. A second suggestion is that a flow ratio controller may be inadequate to insure stoichiometric amounts of D and E in the reactor. For this reason, flow ratio control will not be used; instead, direct control of reactor inlet composition is chosen. Higher tier control loops are also required to obtain adequate operation of the Eastman process. The logic behind the development of these loops will not be discussed here (the interested reader is referred to Price (199311, but the loops will be briefly described. The tasks which must be addressed are reactor temperature control, product ratio control, and the purity of the final product. All may be addressed with straightforward controllers. Reactor temperature can be controlled using the jacket coolant flow. Structure 1includes feedbackof production rate and product ratio to set the D and E flows,respectively. In the other structures, D and E are added on composition control. The A and C feeds will be manipulated to maintain a specified reactor inlet composition. The purity of the product will be controlled by manipulating the stripper reboiler based on analyzer output. These loops are the same for all four candidate first tier control structures with the exception of the product ratio feedback
Table 4. Tennessee Eastman Problem: Points comDonent enters A A feed, C feed B C feed C C feed D D feed E feed E F produced G produced H produced
Entrance and Exit leaves consumed, purge purge consumed, purge consumed, purge consumed, purge purge, product product, purge product, purge
loop in structure 1. An example of a structure including higher tier controls is provided in Figure 8. 4.3. Testing and Evaluation. All four structures are able to sustain the base case operation of the process. Since the interactions within the process tend to make it unstable even when disturbances are not present, this is a significant achievement; however, it should be noted that structure 3 operates with notably higher variation in the system pressure (Figure 9) than the other structures. The variation is a result of interaction between the control of the recycle flow and the separator level, since both controllers are manipulating the recycle gas stream. Since the oscillation results from structural effects, improved tuning cannot be expected to substantially improve performance. Supplied with the Eastman problem are a set of 20 disturbance inputs and 4 setpoint changes for use in evaluating the performance of proposed solutions. All four proposed control structures were subjected to the full range
Ind. Eng. Chem. Res., Vol. 33, No. 5, 1994 1205 Table 6. Summary of Disturbance Tests: Tennessee Eastman Problem disturbance no. disturbance description 1 stream 4, A/C feed ratio, B composition constant stream 4, B composition, AIC ratio constant 2 stream 2, D feed temperature 3 4 reactor cooling water inlet temperature condensor cooling water inlet temperature 5 stream 1, A feed loss 6 7 stream 4, C header pressure loss-reduced availability stream 4, A,B,C feed composition 8 stream 2, D feed temperature 9 10 stream 4, C feed temperature 11 reactor cooling water inlet temperature condensor cooling water inlet temperature 12 reaction kinetics 13 reactor cooling water valve 14" condenser cooling water valve 15" Unknown 16" Unknown 17' unknown 18O unknown 190 Unknown 2cp production rate change SP1 product mix change SP2 reactor pressure change SP3 purge gas composition of B SP4
type step step step step step step step random variation random variation random variation random variation random variation slow drift sticking sticking Unknown Unknown unknown unknown Unknown step step step step
running time (h) structure 1 structure 2 structure 3 structure 4 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 7.5 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 19 28 50 50 50 49.9 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 7.5 8 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50
0 These disturbancesare to be used in conjunction with another disturbance or setpoint change. In this study, they were used with setpoint 1 (a 15% reduction in the production rate).
30I
n/
Production Rae
I
26
22 -
S
II
50 tlme fin)
m e (hn)
Figure 9. Steady-state response, TPM = separator bottoms flow (structure 3).
of inputs. Of the 24 input sets, structure 2 was able to satisfy all 24, structure 1 failed only once, structure 3 failed twice, and structure 4 failed for 3 of the 24 disturbances. A summary of the all of the runs is presented in Table 5. The best performing structure is one which uses an internal throughput manipulator, in this case the condenser duty. The second choice alternative employs a feed stream as the throughput manipulator, and the least attractive alternative uses a product stream. The parallel with the simple CSTR/column system presented earlier lends important support to the design guideline preference for internal throughput manipulators. Much can be learned by examining the disturbances which caused difficulties and the relationship between the throughput manipulator used and structure performance. We will focus on the four input sets that caused problems. These offer lessons which may be extrapolated to other process systems. The reader interested in full details of other input sets should consult Lyman (1992). The first disturbance of interest is a loss of stream 1, the A feed (Tennessee Eastman (TE) disturbance 6).
Structure 1 failed 7.5 h into this disturbance; the other structures rejected it successfully. When the A feed is lost, stream 4 becomes the only source of A. It contains slightly more C than A and the components react on an equimolar basis, so excess A remains. Reaction rates decline sharply, causing a buildup of raw materials and eventually overpressurization and shutdown of the reactor. Steps to counteract this disturbance include a production rate reduction of 15% to reduce the flow rate of raw materials and a shift in the purge flow controller to reduce the amount of C in the process. These steps are implemented in all four structures as soon as the concentration of C exceeds A in the purge-an indication that the A feed has been lost. The reduction in reaction rates tends to reduce the molecular weight of the recycle stream, which increases the flow of recycle (this flow rate is uncontrolled in structure 1). Structures 2-4 compensate for this reduction in recycle molecular weight and allow the pressure to remain under the shutdown limit. Random variation in the condenser cooling water temperature (TE disturbance 12) shows how the choice of a throughput manipulator affects system disturbance rejection. Figure 10 shows the impact of the disturbance on production rate; Figure 11 shows the impact on reactor pressure. The relative locations of the throughput manipulator and the disturbance govern the impact of the disturbance. In structure 1, where the throughput is controlled upstream of the disturbance, and structure 2, where they are in the same location, the disturbance variation is transmitted along the primary process path and is seen as fluctuations in the production rate. In contrast, structures 3 and 4 fix the flow in the primary process path at a point downstream from the disturbance so that the variation is forced into the recycle stream and is seen in the reactor pressure. The disturbance induced variation thus remains in the process and eventually forces shutdown of both structures 3 (at about 28 h) and 4 (at about 19 h). One of the most severe disturbances is a slow drift in reaction kinetics (TE disturbance 13) as might result from poisoning of the catalyst or something similar. The
1206 Ind. Eng. Chem. Res., Vol. 33, No. 5, 1994 Product Flowrate. Disturbance 12 30
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structures 2 and 3, provide the most rapid response to the throughput change; the process external manipulators, structures 1 and 4, perform less well. Of the four candidates, structure 2, which uses the condenser duty as the throughput manipulator, appears to be the best alternative. Its operating costs are comparable to the other structures, and it was able to reject all the test disturbances and accomplish the setpoint changes. .Structure 1(TPM = D feed) is the second best alternative. This preference order is in line with the design guidelines and with the results of the CSTR/column study. 5. Summary and Conclusions
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degradation of the catalyst performance causes the concentration of raw materials to rise in the reactor. Since these materials have a high vapor pressure, the reactor pressure rises also. Eventually the high pressure overcomes the catalyst degradation and forces a higher reaction rate, consuming the raw materials and reducing the pressure. This cycle continues, driving the unstable oscillation in reactor pressure. Structure 4 is shut down by this disturbance after about 48h (Figure 12). Setpoint changes are also used to evaluate the performance of the structures. The effect of a 15% decrease in production rate is shown in Figure 13. Structure 1is seen to provide the slowest response to the production rate change; this is expected, since using the D feed as the throughput manipulator requires the change to propagate through the entire process before becoming apparent. The two structures with process internal throughput manipulators,
Decisions made during the design of throughput and inventory control structures have a significant impact on the overall performance of plantwide control systems. Guidelines for throughput and inventory control design have been developed which assist a control designer in producing structures which provide effectiveperformance. The guidelines are generic in nature, applicable to avariety of processes, and adaptable for use with many different control design tools. The guidelines can be readily adapted to the revamp of an existing process plant. In these situations, the control designer begins work with a good idea of the critical disturbances and most effective manipulators. With such knowledge, a less rigorous application of the guidelines is suggested, but the underlying principles of regulating, diverting, and attenuating disturbances within the process remain unchanged. The key factor in the performance of an inventory control structure is its self-consistency. Self-consistent structures are those where any change in the throughput manipulator is automatically translated into changes in the feed and product flows. Performance advantages can be obtained by using process internal streams as throughput manipulators. Their use is recommended, but is of lesser importance in overall performance than other requirements, especially self-consistency and control of disturbance propagation. These facets of throughput manipulator selection have been illustrated using a CSTR/column system and the Tennessee Eastman test problem. Both examples provide insight into the problems of throughput manipulator selection and control of recycle systems. The examples agreed in that both performed best when an internal throughput manipulator was used.
Ind. Eng. Chem. Res., Vol. 33, No. 5, 1994 1207 Best results in the CSTR/column study were achieved when the throughput was controlled using the reactor outlet/column feed stream. Performance is improved when disturbances are not allowed to propagate through the recycle loop. The best throughput/inventory control structure for the Eastman problem is one in which production rate is controlled by manipulating the duty of the reactor condenser and hence adjusting the rate of separation of product from the recycle. Both cases are characterized by the use of a process internal throughput manipulator and self-consistent inventory control structures. The second choice in both cases uses a feed stream as the throughput manipulator.
Literature Cited Buckley, P. Techniques ofProcess Control; John Wiley: New York, NY, 1964; Chapter 13, pp 98-111. Buckley, P.; Luyben, W.; Shunta, J. Design of Distillation Column Control Syetems; Instrument Society of America: Research Triangle Park, NC, 1985. Dough, J.M.RocessDynamicsandContro1,Vol.2 ControlSystem Synthesis; Prentice-Hall, Inc.: Englewood Cliffs, NJ, 1972. Downs,J.; Vogel, E. A plant-wide industrial process control problem. Comput. Chem. Eng. 1993,17 (3), 245-255. Luyben, W. L. Dynamics and control of recycle systems. 3. Alternative process designs in a ternary system. Znd. Eng. Chem. Res. 1993, 32 (6), 1142-1153.
Lyman, P. R. Plant-wide control structures for the Tennessee Eastman process. Master's Thesis, Lehigh University, 1992. Lyman, P. R.; Georgakis, C. Plant-wide control of the Tennessee Eastman problem. Submitted for Dublication to ComDut. Chern. Eng. 1993, Price, R. Design of Plant-Wide Regulatory Control System. Ph.D. Dissertation, Lehiah University, 1993. Price, R.; Georgakis, C. A plant-wide regulatory control design procedure wing a tiered framework. Presented at the AIChE Annual Meeting-Miami, 1992. Price, R. M.; Georgakis, C. Plantwide regulatory control design procedure using a tiered framework. Znd. Eng. Chern. Res. 1993, 32 (ll),2693-2705. Price, R. M.; Lyman, P. R.; Georgakis, C. Selection of throughput manipulators for plant-wide control structures. In ECC '93 Proceedings of the Second European Control Conference;GroninBen, The Netherlands, June 28-July 1, 1993; pp 1060-1066. Skogestad, S.; Lundstr6m, P.; Jacobsen, E. Selecting the best distillation control confiiation. AZChE J. 1990, 36 (5), 753764. Stephanopoulos, G. Chemical Process Control: An Introduction to Theory and Practice; Prentice-Hall, Inc.: Englewood Cliffs, NJ, 1984. Tyrew, B. D.; Luyben, W. L. Dynamicsand control of recycle systems. 4. Ternary system with one or two recycle streams. Znd. Eng. Chem. Res. 1993,32 (6), 1154-1162. Received for review July 14, 1993 Revised manuscript received February 10,1994 Accepted March 2, 1994. e Abstract published in Advance ACSAbstracts, April 1,1994.
