Plantwide Control for Throughput Maximization: A Case Study

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Ind. Eng. Chem. Res. 2010, 49, 210–221

Plantwide Control for Throughput Maximization: A Case Study Rahul Kanodia and Nitin Kaistha* Department of Chemical Engineering, Indian Institute of Technology Kanpur, Kanpur 208016, India

The impact of the basic plantwide regulatory control structure on maximizing the throughput using an explicit optimizing controller is quantitatively evaluated for a simple process module. The module consists of the reaction A + B f C occurring in a continuously stirred tank reactor followed by a distillation column separating the product from the recycled unreacted reactants. The column vapor boilup hitting a maximum acts as the bottleneck constraint limiting the throughput due to column flooding. Through an evaluation of reasonable plantwide control structures, the location of the throughput manipulator, the composition analyzer for overall component inventory balancing and the “local” column reflux management policy are shown to significantly affect the maximum throughput. Quantitative results show that locating the throughput manipulator close to and where possible at the bottleneck constraint reduces the throughput derating necessary due to disturbances. Designing the plantwide regulatory control system to minimize the process variability propagated into the bottleneck constraint emerges as the key heuristic from the case study. Introduction The plantwide control system is crucial to the safe, stable, and economic operation of complex chemical processes. Typically, it consists of a basic regulatory control system with possibly an economic optimization layer on top. The former ensures safe and stable (and sometimes, economic) operation. The latter optimizes key set points of the basic regulatory control system for maximizing the plant operating profit or an equivalent economic criterion. The design of the basic plantwide regulatory control system has received much attention in the literature. The omni-presence of material/energy recycle even in the simplest of chemical processes leads to unique regulatory control issues such as the snow-ball effect1 and component inventory control issues2 that must be addressed. In particular, the choice of loop-pairings, also referred to as the control structure, is of fundamental importance in plantwide control.3 Owing to the combinatorial complexity of the control structure design problem, research on the same has mostly taken the form of process specific casestudies highlighting the key plantwide issues.4-10 The heuristic plantwide control structure design procedure of Luyben et al.11 captures the essence of the various case-studies and reflects the mature understanding that has evolved over the years through sustained research. In contrast to basic plantwide regulatory control, the economic optimization of process operation has received relatively less attention in the extant open literature. Skogestad12 recognized the importance of the regulatory control structure as a key determinant of the achievable operating profit and proposed the concept of a self-optimizing structure as the one that entails “acceptable” economic loss for process operation at constant set points. A self-optimizing structure thus obviates the need for an explicit economic optimization layer. The quest for a self-optimizing control structure is however an open-ended research problem. Also, what constitutes “acceptable” economic loss is subjective and a quantitative evaluation of the economic benefit from an explicit optimization layer on top of the basic regulatory control system is always desirable. For continuous chemical processes manufacturing bulk chemicals, maximizing the operating profit typically boils down * To whom correspondence should be addressed. E-mail: nkaistha@ iitk.ac.in. Tel.: +91-512-2597513. Fax: +91-512-2590104.

to maximizing the process throughput. This requires operating the process as close as, or if possible, at the bottleneck constraint(s) that limits production. Recent studies indicate that the degree of closeness of process operation to the bottleneck constraint and hence the maximum achievable throughput depends on the choice of the plantwide regulatory structure.13-15 Even so, a systematic quantitative study that evaluates its role in throughput maximization and the incremental benefit of an explicit optimizing controller on top of the regulatory layer has seldom been performed in the open literature. Such a systematic quantitative study for an example process is the basic motivation behind this work. In this article, the impact of the basic plantwide regulatory control structure on maximizing the throughput with and without an explicit optimizing controller is quantitatively evaluated for a simple process module. In the following, details of the process module and the regulatory control structures evaluated are presented. The structures are then compared for the maximum achievable throughput with and without the optimizing controller. The effect of the optimizing controller algorithm, PI versus DMC, on the maximum throughput is also evaluated. An attempt to rationalize and where possible generalize the case-study results is made in the Discussion section. A summary of the main findings concludes the article. Process Module The module consists of a continuously stirred tank reactor (CSTR) with the reaction A + B f C, C being the heaviest component, followed by a distillation column separating the product from the recycled unreacted reactants. The module, though simple, is representative of many complex chemical processes that consist of a reaction section and a product separation section with recycle of unreacted reactants. The reaction kinetics and hypothetical component details are provided in Table 1. The hydrocarbon estimation procedure in Hysys is used to estimate the critical temperature, pressure, acentricity, etc. for thermodynamic property calculations. The Peng-Robinson equation-of-state is chosen as the thermodynamic fluid package. A base-case steady state design is developed in Hysys for producing 99.92 kmol/h of 99.9 mol % pure product C stream.

10.1021/ie900366r CCC: $40.75  2010 American Chemical Society Published on Web 11/17/2009

Ind. Eng. Chem. Res., Vol. 49, No. 1, 2010 Table 2. Salient Process Design and Operating Parameters

Table 1. Process Model Parameters

reaction model

r ) k · xA · xB k ) A · exp(-E/RT) A ) 6 × 108 kmol/m3/s E ) 69780 kJ/kmol ∆H°rxn ) -5 × 104 kJ/kmol

hypothetical components

A B C

211

Process Design

NBP

MW

80 °C 110 °C 150 °C

78 96 174

Figure 1 provides a schematic of the process along with the base-case column temperature and composition profile. Salient equipment design and base-case operating conditions are provided in Table 2. The reactor is operated in excess A environment (B limiting). This mimics typical industrial scenarios where excess of a reactant in the reactor is necessary to suppress undesirable side-reactions. To avoid column flooding, the vapor boilup must be maintained below a maximum. This limit acts as the bottleneck constraining throughput. Plantwide Control System Regulatory Control Structures. Four reasonable basic regulatory control structures, labeled CS1 to CS4, are evaluated in this work. These are schematically depicted in Figure 2. The four structures differ from each other in the choice of the throughput manipulator (the set point adjusted to effect a production rate change) and the consequent orientation of the CSTR and reflux drum level controllers. In CS1, the feed to column (FCOL) is the throughput manipulator. The fresh B stream (FB) is used to control the CSTR level while the distillate (FRCY) controls the reflux drum level. In CS2, the total flow to the reactor (FTOT) is the throughput manipulator. The CSTR level

Figure 1. (a) Process module schematic and (b) Basecase column profiles.

CSTR

volume temperature pressure duty

15 m3 80 °C 500 kPa 5.024 × 106 kJ/h

column

no. of trays feed tray pressure reboiler duty reflux ratio

18 10th from top 260 kPa 1.225 × 107 kJ/h 1.435

Operating Parameters molar flow (kmol/h) FA FB FTOT bottoms FCOL

100 100 274.2 99.92 175

molar composition (A, B, C) Pure A Pure B 0.58, 0.417, 0.0005 0, 0.0006, 0.9994 0.338, 0.084, 0.571

is controlled by FCOL and the reflux drum level is controlled by FRCY. In CS3, the sum of the recycle and fresh A flow rates (FA+R) is the throughput manipulator. The reflux drum level is controlled by FRCY while the FCOL controls the CSTR level. CS4 uses FRCY as the throughput manipulator. The reflux drum level is then controlled by adjusting FCOL and FB controls the CSTR level. In the column control structure, single-ended temperature control is used with the vapor boilup maintaining a sensitive stripping tray (tray no. 10) temperature. Note from the column temperature profile in Figure 1 that its slope is large around tray 10 making it an appropriate tray location for temperature control.16 Single-ended control is used as feed composition sensitivity analysis17 shows that the reflux does not change significantly in order to maintain the distillate and bottoms impurity levels for a change in the column feed composition. The column bottoms level is controlled by the bottoms flow rate. With regard to the fresh feeds, FA is kept in ratio with FB in all the structures. Since the unreacted A and B are recycled with only traces leaving from the column bottoms, the plant acts as an integrator with respect to component A and component B inventories. These are thus nonself regulating so that a composition controller is required to compensate for a slow build-up or depletion of a reactant due to a transient stoichiometric imbalance by adjusting the FA to FB ratio set point. Here, the mol fraction of component A is controlled using the ratio set point. The best location for the composition analyzer is a pertinent plantwide issue requiring systematic evaluation. We consider three possible locations for the analyzer, namely, the reactor inlet (C1), the reactor (C2), and the recycle stream (C3). Given that the column vapor boilup hitting a maximum is the bottleneck constraint limiting production, the “local” column reflux management policy can have a potentially significant impact on the maximum throughput. This is because a change in the reflux indirectly causes the boilup to change through the action of the temperature controller. Accordingly, an evaluation of the maximum throughput for column operation at a fixed reflux rate (L) or a fixed reflux ratio (L/D), the two most common reflux management policies, is also considered. By default, the composition analyzer location is the reactor inlet (C1) with column operation at constant reflux. Wherever applicable, alternative analyzer locations (C2 or C3) and column operation at a constant reflux ratio are respectively indicated as a subscript and superscript on the basic control structure label.

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Ind. Eng. Chem. Res., Vol. 49, No. 1, 2010

Figure 2. Basic plantwide regulatory control structures.

For example, CS1C2L/D refers to the plantwide control structure CS1 using reactor (C2) composition for stoichiometric feed balancing with column operation at constant reflux ratio (L/D). Optimizing Controller. The economic control objective for the process is to maximize the process throughput. The vapor boilup must never exceed a maximum to avoid column flooding, the bottleneck constraint. Consider the ideal case of process operation with no disturbances. To maximize throughput, an operator would slowly increase the throughput manipulator set point until the constraint variable approaches its limiting value. The implemented throughput manipulator set point must however be appropriately derated so that the constraint is never violated in the presence of disturbances. For process operation at a constant throughput manipulator set point, the derating must be sufficient for handling the worst-case disturbance without violating the constraint. Alternatively, a simple optimizing controller that adjusts the throughput manipulator to maintain the constraint variable at its set point can be implemented as shown in Figure 3.18 A properly tuned optimizing controller would cause tighter control of the constraint variable around its set point so that the throughput derating would be lower compared to process operation at a constant derated throughput manipulator set point. In this work, the throughput benefit of such an optimizing controller is quantified. To understand the benefit, if any, of advanced control algorithms, the simple PI

Figure 3. Schematic of an optimizing controller.

algorithm and the more sophisticated DMC algorithm19,20 are implemented in the optimizing controller. Dynamic Simulation and Controller Tuning. A dynamic simulation of the process module is built in Hysys 3.1. An inert nitrogen stream connection to the CSTR is provided with the outlet stream being manipulated to maintain the CSTR pressure. Without such an arrangement, the CSTR pressure shows large fluctuations and the Hysys dynamic solver crashes. A tight PI controller that manipulates the nitrogen outflow is used for


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a

Table 3. Controller Settings

tuning parameters SP

span

Kc

τi (min)

Common Loops column CSTR

184.3 °C 250 kPa 104.0 °C

TC PC TC

100-250 °C 0-500 kPa 50-160 °C

0.8 10 0.8

9 0.5 8

Structure Specific Loops CS1 CS2 CS3 CS4

CC CSTR CC CSTR CC CSTR CC CSTR

LC LC LC LC

0.5806 80.3% 0.5806 80.3% 0.5806 80.3% 0.5806 80.3%

0.05-1 0-100% 0.05-1 0-100% 0.05-1 0-100% 0.05-1 0-100%

3 1 2 1 3 1 4 1

60 20 70 12 100 10 120 12

All level controllers (except reactor): Kc ) 2. All valves 50% open at base case. All FC’s: Kc ) 0.65, τi ) 0.15 min. a

CSTR pressure control (nitrogen feed under flow control). The column pressure is controlled tightly by manipulating the condenser duty. The column reflux drum and reboiler level controllers are P only with a gain of 2. The CSTR level is controlled using a tight PI controller to minimize variability in the reactor residence time. A 2 min lag is applied to the CSTR and column tray temperature controllers to account for the cooling circuit and reboiler dynamics, respectively. For consistency across different structures, the autotuner in Hysys is used to tune these controllers. In the stoichiometric feed balancing loop, a 10 min sampling time (roughly equivalent to a 5 min dead time) is applied to the composition measurement. To avoid sustained plantwide oscillations, the corresponding composition controller needs to be slightly detuned from the autotuner settings. Table 3 reports the controller tuning parameters for the various controllers in the regulatory control structures CS1-CS4. All these control structures effectively handle a (10% change in the throughput manipulator set point. For illustration, Figure 4 plots the dynamic response of key variables to a (10% throughput manipulator set point change for CS1 and CS2. The overall plant response takes about 8 h to complete. CS3 and CS4 also handle a 10% throughput change in either direction with a relatively longer response time of about 10 h (data not shown). Throughput Maximization Results There are four basic plantwide regulatory control structures (CS1-CS4). The choice of the reflux management policy (L or L/D) and the three possible composition analyzer locations (C1-C3) gives a total of 24 (4 × 2 × 3) structures with subtle structural variations. In view of the large number of structures, a pragmatic approach for a concise yet comprehensive study is to first evaluate the four basic structures for the default fixed analyzer location (reactor inlet, C1) and column operation at constant reflux. The two basic structures that are found to be most effective for throughput maximization are then further evaluated for the effect of composition analyzer location (C1-C3) and the column reflux policy (L or L/D) on maximum throughput as well as the increase in throughput using an optimizing controller with the best analyzer location and reflux policy. For convenience, the base-case vapor boilup (361.3 kmol/h) is taken as the maximum boilup constraint. The base-case production rate of 99.92 kmol/h then represents the maximum throughput (no derating) for all the structures for the ideal case

Figure 4. Transient response for a (10% change in throughput manipulator set point for (a) CS1 and (b) CS2.

of process operation with no disturbances. The possibility of disturbances necessitates control structure dependent throughput derating. A step increase in the B impurity in the fresh A feed (FA) is considered as the primary disturbance. In the following, the derating to avoid violating the maximum column boilup constraint as the magnitude of this step disturbance increases is quantitatively evaluated for the different control structures. Effect of Throughput Manipulator Location. The maximum throughput for a particular magnitude step change in the FA composition in the plantwide control structures, CS1-CS4, is obtained by adjusting the throughput manipulator set point so that the peak in the vapor boilup transient response just touches the maximum constraint. This corresponds to the derated maximum achievable throughput without violating the bottleneck constraint and is illustrated in Figure 5 for a 10 mol % step change in FA composition for CS1-CS4. The magnitude of the transient vapor boilup overshoot is in the order CS4 > CS3 > CS1 > CS2 so that the throughput derating necessary to avoid violation of the bottleneck constraint is also in the same order. Accordingly, the maximum achieved throughput is in order CS2 > CS1 > CS3 > CS4 with the derated product rate being 97.45, 96.49, 94.59, 88.81 kmol/h, respectively. Depending on the control structure, a 2.5 to 11% (approx.) throughput

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Figure 5. Transient vapor boilup and product rate response of CS1-CS4 to a 10 mol % FA composition step change.

Figure 6. Variation in throughput derating with FA composition disturbance for CS1-CS4.

derating from the maximum product rate of 99.92 kmol/h is necessitated owing to the disturbance. CS2 and CS1 are the two best structures with CS4 being the worst requiring significantly higher derating. A more elaborate comparison of the maximum achievable throughput with the disturbance magnitude varying from 0 to 20 mol % is shown in Figure 6. As the magnitude of the disturbance increases, the maximum achievable throughput for all the structures expectedly decreases. The throughput derating magnitude is however dependent on the control structure and is the lowest for CS2, followed, in order, by CS1 and CS3. For a 20 mol % step disturbance, the maximum achievable throughput decreases from 99.92 to 93.47, 92.68, and 87.83 kmol/h for CS2, CS1, and CS3 respectively. CS4 fails to handle such a large disturbance. The results suggest that the throughput

manipulator choice, the main difference between CS1-CS4, is of fundamental importance in throughput maximization. Effect of Composition Analyzer Location. The previous results suggest that CS2 and CS1 are the two best structures in terms of handling large disturbances with the least throughput derating. These structures are now further evaluated for the effect of composition analyzer location on the maximum process throughput. Figure 7 plots the transient vapor boilup and product rate response at maximum throughput to a 15 mol % step change in FA composition with the composition controller located at three possible locations, namely, the reactor inlet (C1), reactor (C2), and the recycle stream (C3). For CS1, the overshoot in the transient vapor boilup is smallest when the reactor inlet composition is controlled. Accordingly, the derated throughput for CS1C1 at 94.88 kmol/h is higher than for CS1C2 and CS1C3 at 93.29 kmol/h and 92.08 kmol/h, respectively. For CS2, the transient overshoot in the vapor boilup is the least for analyzer locations C1 and C2 and is noticeably higher for location C3. Accordingly, the derated throughput for CS2C1 and CS2C2 is comparable at 95.70 kmol/h and 95.27 kmol/h, respectively, with the corresponding value for CS2C3 being lower at 92.96 kmol/h. For the example process, an improper choice of the analyzer location can thus result in up to a 3% (approx.) throughput loss. Another composition control issue is the choice of the measured component mol fraction. We found that controlling A or B mol fraction for locations C1 (reactor inlet) and C2 (recycle) are equivalent. For analyzer location C2 (reactor composition), controlling component B mol fraction results in very marginal improvement in throughput derating with the increase in throughput being less than 0.1% for a 20 mol % step change in FA composition for CS1 and CS2. These results indicate that at least for this case-study, the choice the component whose composition is controlled does not significantly affect the throughput derating.


215

Figure 7. Derated transient vapor-boil up and product rate response for alternative composition analyzer locations (C1-C3): (a) CS1, (b) CS2.

Figure 8. Variation in throughput derating with FA composition disturbance for CS1and CS2 for constant reflux rate and constant reflux ratio.

Effect of “Local” Column Reflux Policy. Figure 8 compares the variation in the maximum product rate with the disturbance magnitude varying from 0 to 20% using CS1 and CS2 for column operation at a fixed reflux rate and a fixed reflux ratio. For both the structures, the maximum achievable throughput for a given disturbance magnitude is higher for column operation at constant reflux compared to constant reflux ratio. For example, at a disturbance magnitude of 20 mol %, the maximum throughput for CS1 is 92.68 kmol/h while for CS1L/D the value is 91.72 kmol/h. The corresponding values for CS2 and CS2L/D are 93.47 and 90.46 kmol/h, respectively. A constant reflux rate policy can thus result in more than 3% higher throughput compared to a constant reflux ratio policy. Another commonly used reflux policy is maintaining the reflux in ratio with the column feed, that is, holding L/F constant. For CS1, since the column feed is under flow control, the

constant L/F policy is equivalent to the constant L policy for the principal disturbance, a step change in FA composition. For CS2, the column feed is under level control and for a constant L/F policy, the reflux would change in response to a change in the column feed. Rigorous simulations show that for a 15 mol % step change in FA composition, the derated throughput for CS2L/F is 94.23 kmol/h. The corresponding values for CS2 and CS2L/D are respectively, 95.72 and 92.82 kmol/h. Thus, even as a constant L/F policy results in an increase in throughput over the constant L/D policy, the throughput is ∼1.5% lower than the constant L policy. For this case study, the constant reflux rate policy thus is the best with minimum throughput derating. The results highlight that the “local” control structure for a unit operation can have significant plantwide implications. Effect of Optimizing Controller. The SISO optimizing controllers for CS1 and CS2 are schematically depicted in Figure 9. The simple PI algorithm and the more sophisticated DMC algorithm are implemented in the controller. For a fair comparison, a 10 s sampling is applied at the input and output of both the controllers. Approximate PI controller tunings are obtained using the autotuner feature in Hysys and slightly adjusted so that the overall plantwide response does not exhibit sustained oscillations. In a similar manner, the move suppression and scaling factor for the DMC controller are adjusted. Details of the PI and DMC optimizing controllers for CS1 and CS2 are provided in Table 4. Figure 10 compares the transient vapor boilup and product rate response to a 15 mol % step change in FA composition for CS1 and CS2 with a PI/DMC optimizing controller. In both the structures, application of the more sophisticated DMC controller reduces the magnitude of the transient vapor boilup overshoot with consequently lower throughput derating. Also, notice that the transient boilup deviations in CS1 are smaller than in CS2. The steady state product rate for CS1 is 98.29 and 99.23 kmol/h for, respectively, a PI and a DMC optimizing controller. The corresponding values for CS2 are 96.84 and

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The significantly higher throughput benefit using an optimizing controller in CS1 compared to CS2 is due to the location of the controller manipulation handle with respect to the bottleneck constraint. In CS1 and CS2, the column feed set point and the total reactor feed set point are the respective manipulation handles for the optimizing controller. Considering the location of the handles with respect to the primary bottleneck constraint (vapor boilup), the reactor hold-up considerably slows down the open loop dynamics of the CS2 optimizing controller. For the CS1 optimizing controller, on the other hand, the dynamics are much faster which translates to tighter boilup control around the set point with a significant reduction in the boilup overshoot due to the disturbance. Discussion

Figure 9. SISO optimizing controller for (a) CS1 and (b) CS2. Table 4. Optimizing Controller Settingsa P1 b c

K CS1 CS2

1.201.21 0.10.1

DMC

τi (min)

γ

M

P

R

slew rate

1210 6054

5 1

200 100

1000 2000

0.5 0.5

(12 kmol/min (12 kmol/min

b

γ ) move suppression factor; R determines the reference trajectory speed of approach to set point; M ) control horizon; P ) prediction horizon. b Hysys autotuner settings reported as subscripts. a

97.43 kmol/h. The application of an optimizing controller in CS1 thus gives a larger throughput benefit compared to CS2. Figure 11 quantitatively compares the maximum throughput as the disturbance magnitude increases from 0 to 20 mol % for CS1 and CS2 with and without the optimizing controller (PI or DMC) in place. In both CS1 and CS2, an optimizing PI controller gives an incremental throughput benefit. The benefit however is much larger in CS1 than in CS2. A DMC optimizing controller gives a further throughput benefit of about 1% for both CS1 and CS2. The same may be used to justify the additional cost associated with installing and maintaining the more sophisticated DMC controller. Note that for process operation using CS1 with a DMC controller, the derated throughput for a 20 mol % disturbance is 99.00 kmol/h. This represents a marginal derating with respect to the nominal throughput of 99.92 kmol/h. Process operation using CS1 with a DMC optimizing controller thus entails the least throughput derating for large disturbance magnitudes for the structures considered.

Summary and Interpretation of Results. It is worth-while to summarize the main results from the work and attempt a rational explanation for the same. The main findings from the case-study are as follows: (i) Of the four basic regulatory plantwide control structures, CS1-CS4, evaluated, CS2 and CS1, in that order, were found to exhibit the least throughput derating for the principal disturbance. (ii) Controlling the reactor inlet composition was found to be the best for throughput maximization. (iii) Operating the column at constant reflux entailed a lower throughput loss compared to operation at constant reflux ratio or reflux to feed ratio. (iv) The optimizing controller mitigated throughput derating with the DMC algorithm giving a further throughput benefit over PI control. The throughput benefit using an optimizing controller was significantly higher for CS1 (compared to CS2). To understand the above trends, consider the regulatory plantwide control structure which consists of various control loops. A control loop adjusts the manipulated variable in order to hold the controlled variable at set point. It thus transforms the variability from the controlled variable to the manipulated variable. The plantwide regulatory control system may then be simplistically viewed as effecting the transformation of process variability from one location to another through the action of the controllers and the process interconnections (including recycle streams).21 Given that there are several possible reasonable regulatory control structures for any process, structures that minimize the overall variability transformed toward the bottleneck constraint would allow process operation closer to the constraint with consequently lower throughput derating. This simplistic “transformation of variability” perspective is useful in explaining the main case-study results summarized above. The principal disturbances that cause the vapor boilup to change in order to maintain the stripping control tray temperature are the column feed rate and composition as well as the reflux rate. Clearly, holding the reflux rate constant eliminates reflux flow variability into the column so that the fixed reflux rate policy requires lesser throughput derating compared to a fixed reflux ratio policy, where the reflux varies in ratio with the distillate. One would imagine that the throughput derating in CS1 should be lesser than in CS2 as the former eliminates flow variability into the column. It turns out that even as CS1 does eliminate feed flow variability into the column, the variability in the column feed component B (heavy key) flow rate is higher in CS1 as illustrated in Figure 12 for a 15 mol % step change in the FA composition. Notice that the peak deviation in the component B flow rate into the column is 10.09 kmol/h for CS1 and 8.04 kmol/h for CS2. Holding the total flow to the reactor constant as in CS2 thus mitigates the downstream heavy key component flow variability better than


217

Figure 10. Transient response for optimizing controller with DMC and PI algorithms for (a) CS1 and (b) CS2.

Figure 11. Variation in derated throughput with disturbance magnitude for process operation with and without an optimizing controller.

CS1. Among the basic regulatory control structures evaluated, CS2 is thus the most effective in terms of minimizing the overall variability transformed toward the bottleneck constraint. With regard to the composition analyzer location, controlling the reactor inlet composition gives the best derating. This is likely because a change in the feed composition is detected earlier at the reactor inlet compared to the reactor outlet or the recycle composition. To better visualize the transformation of variability toward the bottleneck constraint in realistic situations where the principal disturbance is seldom a sharp step-change, we consider process operation with the FA composition varying as a timeseries. Figure 13 compares the closed loop response of the column control tray temperature, the vapor boilup, and the product rate for CS1 with and without a PI optimizing controller.

Figure 12. Derated transient component B flow rate into the column using CS1 and CS2 for 15 mol % FA composition step disturbance.

Notice that the variability in the control tray temperature is much smaller using the optimizing controller. This causes the variability in the boilup to be smaller so that average boilup of 359.2 kmol/h compared to 350.1 kmol/h without the optimizing controller is much closer to the limiting value of 361.3 kmol/h. Accordingly, the derated average throughput for CS1 with the PI optimizing controller is about 2.2% more than for CS1 sans the controller. Alternative Simple Control Structure. In the context of the current case study, notice that in all the evaluated control structures, the bottleneck constraint variable (boilup) is manipulated for holding a stripping tray temperature constant. The manipulation of the constraint variable for tray temperature control necessitates throughput derating to avoid constraint

218


Figure 13. Derated process operation CS1 with and without a DMC optimizing controller for continuously fluctuating feed composition. Table 5. Derated Throughput Comparison between CS5 and CS1 with a SISO DMC Optimizing Controller C production rate (kgmol/h)

Figure 14. Simple alternative control structure, CS5.

violation during disturbances. This derating can be avoided if the constraint variable is held constant and not used for control. The constraint variable set point then acts as the throughput manipulator and the remainder of the control structure can be configured around it. The control structure, CS5, so obtained is illustrated in Figure 14 with the reboiler steam flow controller being the throughput manipulator and the tray temperature being controlled using the feed to the column. Flow controlling the reboiler steam allows for process operation at the bottleneck constraint of maximum allowed boilup through appropriate

step change in FA mol fraction

CS5

CS1, DMC OC

0% 5% 10% 15% 20%

99.92 99.84 99.73 99.64 99.52

99.92 99.70 99.47 99.23 99.00

choice of the steam flow controller set point. Rigorous dynamic simulations for feed composition step change disturbances show that the throughput derating using this control structure is almost negligible. This is quantitatively shown in Table 5 that compares the throughput derating of CS1 with a DMC optimizing controller and CS5. For a 20 mol % step change in FA composition, the derated throughput in the former and latter are 99.52 and 99.00 kmol/h, respectively. The simple CS5 control structure that uses only traditional PI controllers thus outperforms all the other structures studied including ones with an advanced optimizing controller on top of the regulatory control layer. Multivariable DMC Optimizing Controller. In the casestudy, the optimizing DMC controller is SISO as we have considered a single bottleneck constraint, the column boilup. Typically, the optimum operating point corresponding to maximum throughput in recycle processes lies at the intersection of constraints. A multivariable DMC optimizing controller on top of a basic regulatory control system may be configured for driving the process operation close to these constraints. For the present case-study, true throughput maximization would require that in addition to the boilup, the reactor level also be maintained at near maximum since any unutilized reactor volume represents spare production capacity. A 2 × 2 DMC optimizing controller can be designed for the purpose, where the throughput manipu-


Figure 15. Schemes for operating reactor at near maximum level in CS1 and CS2 (a) 2 × 2 DMC optimizing controllers; (b) ratio-based level control. Table 6. Comparison of Multivariable and SISO DMC Optimizing Control Schemes control structure

optimizing control scheme

level product rate derated level controller (kmol/h) set point (%)

derated boilup set point (kmol/h)

CS1

2 × 2 DMC simple SISO DMC simple SISO DMC ratio based

100.03 99.23 100.81

85.0 80.3 88.6

358.55 358.40 358.91

CS2

2 × 2 DMC simple SISO DMC simple SISO DMC ratio based

98.70 98.68 98.72

89.2 89.0 89.4

349.96 349.75 350.17

lator and the reactor level set points are adjusted to maintain the column boilup and reactor level, the two active constraints for maximizing production. This is illustrated in Figure 15 for CS1 and CS2 as the basic regulatory structures. The manipulation of the reactor level set point mitigates the transient deviation in the reactor level for tighter level control with consequently lower derating in the DMC level set point. There are also simpler and yet effective ratio-based level control schemes for tight reactor level control shown in Figure 15 for CS1 and CS2. In CS2, the ratio controller maintains the total inflow to outflow ratio with the level controller adjusting the ratio set point. In CS1, the difference in total outflow and recycle flow is maintained in ratio with FB. Here, since FA is maintained in ratio with the FB, the total flow of fresh reactants matches the difference between the reactor outflow and recycle flow. For a quantitative comparison, Table 6 reports the derated reactor level and column boilup set points and the achieved steady state throughput for a 2 × 2 DMC optimizing controller and a SISO DMC boilup optimizing controller with a simple reactor level controller and a ratio-based reactor level controller. The disturbance is a 15 mol % step change in the FA composition. The maximum constraint in the reactor level is taken as 90% level. In CS1, significant improvement in the derated reactor operating level is achieved from 80.3% using a simple level controller to 85.2% using a 2 × 2 DMC optimizing controller to 88.4% using a ratio-based level controller. The increase in the operating reactor level causes the achieved throughput to increase in that order. In CS2, since the total feed

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to the reactor is under flow control, the level set point derating is very small at

Plantwide Control for Throughput Maximization: A Case Study

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