Economic Plantwide Control of a C4 Isomerization Process - American

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Economic Plantwide Control of a C4 Isomerization Process Rahul Jagtap and Nitin Kaistha* Department of Chemical Engineering, Indian Institute of Technology Kanpur, Kanpur 208016, India ABSTRACT: Plantwide control system design for economically optimal operation over a large throughput range of a C4 isomerization process is considered. The steady-state process degrees of freedom (dofs; eight in total) are optimized for a given throughput (mode I) and maximum throughput (mode II). At maximum throughput, all of the steady-state dofs are exhausted in driving as many constraints (inequality/equality) active. For this process, it is possible to synthesize a simple decentralized plantwide control system (CS1) for tight control of all of the active constraints at maximum throughput with negligible back-off due to transients with satisfactory inventory regulation and process stabilization. A unique feature of CS1 is the location of the throughput manipulator (TPM) inside the plant (in contrast to that at the process feed) and its relocation due to input saturation in a split range arrangement. A comparison with the conventional structure (CS2) with TPM at the process feed and conventional overrides for handling constraints demonstrates the economic and dynamic superiority of CS1.

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INTRODUCTION In the context of plantwide control of increasingly integrated modern chemical processes, today’s fiercely competitive economic scenario coupled with geopolitical uncertainties translates to large changes in the production objectives (throughput and product grade/quality) to which chemical plants must respond quickly. For example, the desired throughput may vary from significantly below its design value to the maximum achievable. In addition to quickly responding to these changes, for better competitiveness, the installed plantwide control system must provide (near) optimal operation over the entire throughput range. Devising a simple control system for the purpose can be particularly challenging as the active constraint set changes over the large operating window. For example, on increasing throughput from low to high values, process capacity constraints successively become active. One must then account for the loss in a control degree of freedom (dof) due to a constraint becoming active in the design of the plantwide control system. Ideally, the implemented control system should be such that the plant remains operable despite the loss in control dofs. A careful review of the plantwide control literature reveals that the issue of designing a plantwide control system for (near) optimal operation over a large operating window with different active constraint sets has received very little attention. Thus, all reported applications of the nine-step heuristic procedure of Luyben at al.1 study plantwide control for process operation around a base-case design where no hard constraints are active.2−5 Skogestad’s more recent concept of self-optimizing control6,7 lays emphasis on “what to control”, i.e., controlled variable (CV) selection. Much of the analysis is based purely on steady-state simulations and the issue of “how to control”, i.e., the manipulated variable (MV) selection, where dynamic considerations (including input saturation, i.e., a constraint becoming active) play a very significant role, get relegated to the background. Important questions such as throughput manipulator (TPM) selection and how best to pair an MV that optimally saturates are left largely unaddressed. More recently, the question of TPM selection for economically optimal operation has received some attention in the open © 2012 American Chemical Society

literature. It has been quantitatively shown that the TPM should be chosen at or close to the economically dominant hard active constraint to minimize the back-off necessitated by worst-case transients in the constraint.8,9 Jagtap et al.10 use this heuristic to develop an economically optimal plantwide control system for a recycle process with side reaction along with a simple switching scheme for handling changes in the active constraint set over a large throughput range. Notwithstanding these very recent studies, there exists a need for developing guidelines toward plantwide control system design for economically optimal process operation over a large throughput range where the active constraint set changes. Given the specific characteristics of each process that must be addressed by the plantwide control system, the best way forward is to perform focused case studies on a variety of processes and then generalize the common principles into a systematic procedure. This is the approach we have taken in our research. This work is a case study on plantwide control system design for economically optimal operation over a large throughput range for a C4 isomerization process. In refineries, isobutane (iC4) is a more valuable feedstock than n-butane (n-C4) due to its use as an octane-enhancing gasoline blending agent as well as a precursor for isobutyl alcohol production. The isomerization process is therefore used to convert n-C4 to the more valuable iC4. The base-case process design for irreversible reaction kinetics, presented by Luyben et al.,1 is used here in the case study. In the following, the isomerization process is briefly described followed by steady-state optimization results over a large throughput range (low to maximum). From the active constraints at maximum throughput, a plantwide control structure is synthesized for process operation at maximum throughput. This structure is adapted to “take up” control of selfoptimizing CVs at lower throughputs where constraints become Received: Revised: Accepted: Published: 11731

January 13, 2012 August 3, 2012 August 8, 2012 August 8, 2012 dx.doi.org/10.1021/ie3001293 | Ind. Eng. Chem. Res. 2012, 51, 11731−11743

Industrial & Engineering Chemistry Research

Article

drum levels and two sump levels on the columns. Also, two valves will get used to maintain the columns at their design pressures There are then eight steady-state operating dofs for the process: one for the fresh feed, two each for the two columns, one for the reactor feed heater, one for the reactor effluent cooler, and one for the reactor pressure. For robust flowsheet convergence, the chosen eight specification variables are as follows: the fresh C4 feed (FC4), the DIB distillate n-C4 and bottoms i-C4 mole fractions (xn‑C4D1 and xi‑C4B1), the purge column distillate i-C5 and bottoms n-C4 mole fractions (xi‑C5D2 and xn‑C4B2), the reactor inlet temperature (Trxr) and pressure (Prxr), and the cooler outlet temperature (Tcool). Of the eight steady-state dofs, Trxr and Prxr are assumed fixed at their design values and not considered for optimization. This is done as the kinetic parameters were adapted by Luyben et al.1 to match the operating conditions of an existing industrial reactor and are therefore artificial. Also, in industrial processes, gas-phase reactors are usually operated at the design pressure and not lower so the reaction kinetics are as fast as possible. Also there is usually a very limited recommended catalyst temperature range for which the technology licensor guarantees catalyst life. Holding reactor temperature and pressure constant is therefore a reasonable assumption. The remaining six dofs can and should be adjusted for optimizing an economic criterion such as the steady hourly profit or steam consumption per kilogram of product, etc. We consider two process operation modes: mode I where the throughput is fixed (e.g. by market demand−supply considerations) and mode II where the market conditions are such that it is optimal to operate the process at maximum throughput. For mode I, the optimized economic criterion is the yearly profit, 7 , defined as

inactive. A quantitative comparison is performed with a conventional plantwide control structure with the fresh C4 feed as the TPM to show that the synthesized control structure achieves better dynamic control and economic operation. The learnings from the case study toward evolving general guidelines for plantwide control structure synthesis are then discussed. The conclusions summarize the salient findings from the work.

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PROCESS DESCRIPTION Figure 1 shows a schematic of the C4 isomerization process studied in this work. A fresh C4 stream containing n-C4 and i-C4

Figure 1. Isomerization process schematic with salient design and base operating conditions.

7 = [product sale − raw material cost − energy cost]/year

with some C3 and i-C5 impurities is fed to a de-isobutanizer (DIB) column that recovers i-C4 with some n-C4 (heavy key) impurity as the distillate. All of the C3 in the fresh C4 feed leaves in the distillate. The DIB bottoms consisting of n-C4, i-C5, and some i-C4 (light key) impurity is fed to a purge column that recovers i-C5 with some n-C4 (light key) as the bottoms. The purge column distillate consisting of C4’s and some i-C5 (heavy key) is fed to an adiabatic packed bed reactor (PBR) after preheating in a feed effluent heat exchanger (FEHE) followed by heating to the reaction temperature in a heater. The n-C4 isomerizes in the PBR to i-C4. The hot reactor effluent preheats the cold reactor feed in the FEHE and is then condensed in a flooded cooler. The subcooled liquid is rich in i-C4 and is fed to the DIB column above the relatively i-C4 lean fresh C4 feed. The base-case process design and steady-state operating conditions (adapted from Luyben et al.1) are shown in Figure 1. The irreversible reaction kinetic model in their work is used along with the SRK equation of state to model the thermodynamic properties. Aspen Hysys is used for steady-state and dynamic process simulation. Hysys uses the sequential approach for steady-state solution of flowsheets with Wegstein updation at the recycle tear. The inside−outside algorithm is used on the distillation columns with the light key and heavy key impurity mole fractions in respectively the bottoms and distillate as the two column specifications.

The fresh C4 feed (FC4) is fixed at its base-case design value (263.1 kmol/h), and the remaining five dofs are to be optimized. For mode II, the objective is to maximize FC4 using all six dofs (including FC4) as decision variables. The optimization is performed subject to process constraints on the maximum and minimum material/energy flows, maximum column boilup, maximum product impurity, and the maximum allowed reactor temperature. To simplify the optimization, engineering common sense is applied to reduce the number of decision variables. To minimize the loss of precious n-C4 down the purge column bottoms, xn‑C4B2 is chosen to be small at 1% (base-case design value). In addition, the maximum product impurity constraint (xn‑C4D1MAX) should be active for no product giveaway. Finally, the cooler outlet temperature, Tcool, has almost no impact on the economic objective function and is therefore fixed at a reasonable value of 53 °C to ensure the reactor effluent vapor is fully condensed using cooling water. These simple engineering arguments leave two decision variables, xi‑C4B1 and xi‑C5D2, for mode I (FC4 given) optimization. In mode II (maximum FC4), FC4 is an additional third decision variable. The optimization is performed using the f mincon subroutine in Matlab with AspenHysys 2006 as the background steady-state flowsheet solver. The optimization problem formulation and its results are summarized in Table 1. In mode I, the specified FC4,

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OPTIMAL STEADY-STATE PROCESS OPERATION The process has 14 independent control valves. Of these, four valves must be used to control surge levels, namely, two reflux 11732

dx.doi.org/10.1021/ie3001293 | Ind. Eng. Chem. Res. 2012, 51, 11731−11743


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assume that once QhtrMAX becomes optimally active, incrementally higher throughput is achieved by driving V1MAX and V2MAX constraints active. The large throughput range from 263.1 kmol/h to the maximum throughput of 334.5 kmol/h witnesses QhtrMAX, V1MAX, and V2MAX becoming active. These constraints are in addition to the other always active constraint xn‑C4D1MAX and specifications for Trxr, Prxr, Tcool, and xn‑C4B2, the last one being economically important. If we assume that Qhtr is adjusted for a desired reactor inlet temperature of Trxr, then once the QhtrMAX constraint becomes active at a high throughput, a further increase in throughput is made possible by reducing the i-C5 leaking up the purge column distillate and the i-C4 leaking down the DIB column distillate. The reduced i-C4/C5 circulating around the plant causes the flow through the reactor to reduce, allowing more FC4 to be processed while keeping the QhtrMAX constraint active.

Table 1. Isomerization Process Optimization Summary mode I: maximum yearly profita mode II: maximum throughput (FC4)

J process constraints

Trxr = 200 °C

xn‑C4D1 ≤ 0.02

0 ≤ feed/product flows ≤ 2 (base-case) 0 ≤ V1 ≤ 1.3 (base-case) 0 ≤ Qhtr ≤ 1.3 (base-case)

0 ≤ recycle loop flows ≤ 3 (base-case) 0 ≤ V2 ≤ 1.5 (base-case) 0 ≤ other energy flows ≤ 2 (base-case) Tcool = 53 °C

xn‑C4B2 = 0.01 case

Prxr = 45 bar mode I

mode II

FC4, kmol/h

263.1b

334.5c

Trxr, °C Prxr Tcool, °C xn‑C4D1

200 (fixed) 45 bar (fixed) 53 (fixed) 0.02 (max)

200 (fixed) 45 bar (fixed) 53 (fixed) 0.02 (max)

xi‑C4B1

0.0565

0.0125

xi‑C5D2

0.020

0.00022

xn‑C4

B2

optimum J active constraints

0.01 (fixed)

0.01 (fixed)

$17.84 × 106 year−1 xn‑C4D1MAX

334.5 kmol/h xn‑C4D1MAX, QhtrMAX, V1MAX, V2MAX

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PLANTWIDE CONTROL STRUCTURES Pairing Philosophy for Economic Plantwide Control. A plantwide control system is implemented on a process to ensure safe, stable, and economic operation over the expected operating window. Safe and stable operation requires implementing control loops for stabilizing (potential) instabilities such as a reactor thermal runaway as well as non-self-regulatory process variables such as surge tank levels, recycle loop component inventories, and so forth. Loops must also be implemented to avoid drifts in process variables such as column pressures (vapor inventory) or condenser outlet temperatures etc. Lastly control loops are required to ensure that economically important objectives such as product quality and any optimally active constraint variables are controlled tightly. The plantwide control structure design problem may then be viewed as configuring appropriate loop pairings using the available control valves (dofs) to ensure proper control of regulatory (stability) and economic objectives. The conventional approach to loop pairing, attributable to Page S. Buckley,11 is to put in place the regulatory or material balance control structure first and then put in loops for controlling the economic objectives. The approach thus gives higher priority to regulatory objectives so that the control of economic objectives is not the tightest possible. In their seminal design procedure, Luyben et al.3 recommended giving precedence to economic objectives over material balance control to ensure that the flexibility in pairings gets exploited for achieving the tightest possible control of the economic

Heater duty, $9.83 GJ−1; steam, $4.83 GJ−1; cooling water, $0.16 GJ−1; FC4 $32.5 kmol−1; Fi‑C4 $42.0 kmol−1; Fi‑C5 $22.0 kmol−1. bFC4 is specified. cFC4 is optimized for maximum throughput. a

xn‑C4B2, Tcool, Trxr, and Prxr values along with xn‑C4D1MAX active constraint leave two unconstrained steady-state dofs corresponding to xi‑C4B1 = 0.0565 and xi‑C5D2 = 0.02. To maximize throughput (mode II), these two unconstrained dofs along with the additional dof corresponding to FC4 are exhausted to drive the maximum preheater duty (QhtrMAX), maximum purge column boilup (V2MAX), and maximum DIB boilup (V1MAX) constraints active. At maximum throughput, all steady-state dofs thus get exhausted. As the throughput is increased from mode I (FC4 = 263.1 kmol/h), the optimization of the two unconstrained dofs using f mincon shows that QhtrMAX is the first constraint that becomes active at an FC4 of about 320 kmol/h. A further increase in throughput to 334 kmol/h FC4 drives V1MAX active followed by V2MAX becoming active at the maximum throughput of 334.5 kmol/h. The increase in throughput over what is achieved when QhtrMAX becomes active is quite small at ∼4.5%. We therefore

Figure 2. Illustration of (a) large, (b) small, and (c) negligible back-off from hard constraint limits for a single constraint and two constraints. 11733



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Table 2. CVs Corresponding to Control Degrees of Freedom and Their Economic/Regulatory Significance S no.

a

CV

description

1

Trxr

reactor inlet temperature

2

Prxr

reactor pressure

3 4 5 6

Qhtr V1 V2 xn‑C4D1

reactor preheater duty DIBa column boilup PCb boilup product n−C4 mole fraction

7 8

TSpur Tcool

9 10 11 12 13 14

LVLbot1 LVLbot2 LVLRD1 LVLRD2 PDIB Ppur

PC stripping temperature flooded condenser outlet temperature DIB sump level PC sump level DIB reflux drum level PC reflux drum level DIB pressure PC pressure

economic/regulatory significance stabilizes exothermic reaction energy recycle through FEHE; affects reactor conversion; held at specified design value reflects gas inventory inside the reactor; affects reactor conversion (irreversible kinetics only); held at specified design value QhtrMAX active constraint for max throughput V1MAX active for max throughput V2MAX active for max throughput xn‑C4D1MAX always active for no product give-away sets n-C4 (raw material) leakage in PC bottoms ensures condensation of reactor effluent condensables; held at specified design value reflects DIB bottom liquid inventory; no steady-state effect reflects PC bottom liquid inventory; no steady-state effect reflects DIB top liquid inventory; no steady-state effect reflects PC top liquid inventory; no steady -state effect reflects DIB vapor inventory; held at specified design value reflects PC vapor inventory; held at specified design value

De-isobutanizer column. bPurge column.

objectives, acceptable regulatory control usually being possible using the remaining valves. These pairing approaches are applicable for a fixed set of control objectives. When a plant is operated over a very wide throughput range, the economic objectives change due to constraints becoming optimally active or inactive. How does one systematically design a plantwide control structure giving precedence to economic control objectives that change with the active constraints (operating region)? To address this issue, we note that optimal operation requires tight control of all hard active constraints at that operating point. As illustrated in Figure 2, the tighter the active constraint control, the closer the average process operation to the constraint limit (optimum point), the lower the economic loss due to back-off from the constraint limit. Tight active constraint control necessitates pairing the active constraints with close-by manipulated variables (MVs) for fast open loop dynamics and consequent tight closed loop control. Each such active constraint controller would take away a control dof. Only the remaining control valves are then available for controlling the remaining regulatory/economic objectives. Clearly, the most “difficult” control scenario is process operation at maximum throughput (mode II) where the maximum constraints are active so that the fewest number of valves would remain for inventory regulation/ process stabilization. If a robust plantwide control system can be devised for process operation at maximum throughput, it can most certainly be adapted to “take up” additional control tasks by manipulating constraints that become inactive at lower throughputs. On the basis of these simple arguments, our loop pairing approach is to first pair loops for tight control of all economically important variables (including active constraints) at maximum throughput and then put in the remaining loops. This gives the basic economic plantwide control structure for process operation at maximum throughput. The structure is then adapted for throughput reduction (manipulation) and additional economic variable control at lower throughputs by manipulating the unconstrained active constraints. Plantwide Control Structure for Maximum Throughput Operation. We now synthesize a plantwide control structure for near optimal operation over the large throughput

range using the basic rationale above for the isomerization process considered here. The maximum throughput CVs along with their regulatory and economic significance are tabulated in Table 2. To get the best possible pairings for tight control of the economically important objectives at maximum throughput, their loop pairings are first chosen followed by the remaining objectives. At maximum throughput, QhtrMAX, V1MAX, and V2MAX are process inputs (potential MVs) constrained to be active. These are hard active constraints and back-off in these must be minimized for process operation at the maximum possible throughput. In addition, xn‑C4D1MAX constraint, which is a process output (CV), is active along with output specifications for Trxr, Prxr, xn‑C4B2, and Tcool. Of these, tight control of xn‑C4D1MAX and xn‑C4B2 is desirable for respectively on-aim product quality and small loss of precious n-C4 in the purge column bottoms. The analytical measurement xn‑C4B2 is not related to the product quality and therefore unlikely to be available in practice. Because the purge column temperature profile is quite sharp, the average temperature of sensitive stripping tray temperatures, TSpur (14th−16th tray from top), is therefore controlled as an inferential measure of xn‑C4B2. Due to their economic significance, we first pair loops for tight control of Qhtr, V2, V1, and xn‑C4D1 at their maximum limits as well as tight control of TSpur. The Qhtr valve is left fully open for process operation at QhtrMAX. For operating the columns close to their maximum boilup limits (i.e., close to flooding limit) with negligible back-off, the respective reboiler steam valves are used to control the boilups. Thus, V1 is paired with Qreb1 and V2 is paired with Qreb2. Tight control of the product impurity xn‑C4D1 is achieved by manipulating the DIB column reflux (L1). Because V2MAX is active, TSpur cannot be controlled conventionally using boilup, V2, and the feed to the purge column (B1) is used as the MV instead. With the economic loops in place, loops for the remaining objectives are paired. First we pair loops for CVs (objectives) that affect the process steady state and therefore the steady process economics, followed by loops for controlling surge levels that do not affect the process steady state. For effective stabilization of the reactor, its pressure and temperature must be controlled 11734



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Figure 3. Profit for alternative ways of managing the two mode I unconstrained dofs.

tightly. Since QhtrMAX is active, the reactor inlet temperature is maintained at its set point using the reactor feed flow stream (D2). Note that the degree-of-tightness of control in this arrangement would be comparable to Qhtr as the MV since the open loop dynamic response time constants are likely to be comparable. The reactor pressure is controlled at its design value by manipulating the cooler outlet valve. To ensure proper condensation of the reactor effluent, the cooler duty (Qcool) is manipulated to maintain Tcool. The two column pressures (Pcol1 and Pcol2) are controlled at their specified values conventionally using the respective condenser duties (Qcnd1 and Qcnd2). Lastly, we pair loops for the four surge levels on the two columns. Since the purge column distillate is already paired with the Trxr controller, its reflux drum level (LVLRD2) is controlled using the reflux rate (L2). The purge column sump level (LVLBot2) is controlled using the column bottoms (B2). Note that even as B2 is a very small stream, effective level control will be achieved as long as TSpur is controlled, an economic loop already paired. The DIB reflux drum level (LVLRD1) is controlled using the distillate (D1). Since B1 is already paired for purge column temperature control, the DIB column sump level (LVLBot1) is controlled using the fresh C4 feed (FC4). It is highlighted that, in the control structure for maximum throughput operation, the light key i-C4 impurity leaking down the DIB bottoms and the heavy key i-C5 impurity leaking up the purge column distillate are not controlled and float at appropriate values determined by the values of V1MAX and V2MAX as well as the other set points. Control System Modifications for Optimal Operation at Lower Throughputs. We now seek an appropriate strategy for reducing throughput while ensuring (near) optimal operation at lower throughputs. From the optimal mode I and mode II results in the previous section, V2MAX is the last constraint to go active. On reducing throughput, V1MAX is the next constraint to go inactive followed by QhtrMAX. The sensitivity of throughput with respect to the constraint variables decreases in the order

Qhtr, V1, and V2. As explained previously, once QhtrMAX goes active, only an incremental increase in throughput is achieved by reducing the i-C4 leaking down the DIB column (this causes V1MAX to go active) and the i-C5 leaking up the purge column (this causes V2MAX to go active). The simplest way to reduce throughput (option 1) would be to maintain the boilups at V1MAX and V2MAX and reduce QhtrMAX. Even as throughput would reduce, the operation would be suboptimal due to over-refluxing in the two columns (unnecessarily high boilups). For near optimal operation at low throughputs, this over-refluxing must be mitigated. One simple possibility (option 2) is to hold V2 and V1 in ratio with the respective column feeds, with the mode I optimum ratio as their set point. Another possibility (option 3) is to hold the difference between two appropriate DIB column stripping tray temperatures (ΔTDIB = T37 − T32) constant by adjusting V1 and holding V2 in ratio with B1. The set point for these two controllers would be the mode I optimum value. Note that ΔTDIB is controlled instead of a tray temperature as the DIB temperature profile is quite flat. Due care is exercised to ensure that the chosen tray temperature locations are so that the steady-state input output relationship between ΔTDIB and V1 does not show a gain sign reversal (nonmonotonicity) for a ±5% change in V1 (xn‑C4D1 is held constant). The last option (option 4) is to maintain xi‑C4B1 and xi‑C5D2 at their mode I optimum values by adjusting respectively V1 and V2. This however requires two additional composition analyzers, an unlikely scenario in an industrial setting. Figure 3 compares the optimum steady-state profit at various throughputs with the profit achieved using the four different options: (1) process operation at V1MAX and V2MAX at all throughputs; (2) V1/(FC4 + D2) and V2/B1 held constant at mode I optimum until V1MAX and V2MAX become active; (3) ΔTDIB and V2/B1 held constant at mode I optimum until V1MAX and V2MAX 11735



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Figure 4. Economic plantwide control structure CS1 with split range throughput manipulator for maximum throughput operation.

become active, and (4) xi‑C4B1 and xi‑C5D2 held constant at mode I optimum until V1MAX and V2MAX become active. Note that, for the price data used, the operating profit decreases for a throughput increase beyond FC4 ∼ 332 kmol/h. This point then represents an economic bottleneck, and one would operate below this throughput. The economic scenario may however change with significantly higher margins for the product, in which case it may become optimal to operate the process at maximum throughput. Of the various options considered, option 4 is economically the best with almost no economic loss from optimum until a throughout of FC4 ∼ 320 kmol/h, where V1MAX becomes active. The simpler option 3 with no additional composition analyzers is comparable to option 4. The still simpler option 2 using ratio controllers gives slightly higher profit loss (∼1%) at low throughputs. The simplest option 1 is economically the worst with a significantly higher economic loss of up to 8% over the throughput range. These results suggest that option 3 represents

a good compromise between simplicity and minimizing the steady-state economic loss. It is therefore considered for implementation. The overall throughput manipulation scheme in option 3 is then as follows. At low throughputs, Qhtr is used as the throughput manipulator (TPM). Once QhtrMAX goes active to increase throughput, throughput manipulation is shifted to ΔTDIBSP, which must be increased for a higher throughput. Once V1MAX goes active, the TPM is shifted to V2/B1 SP, which must again be increased to enhance throughput. Once the V2MAX limit is reached, the process operates at the maximum achievable throughput. A reverse logic applies for reducing throughput below maximum. The TPM for the entire throughput range is then a split range controller, its output shifting from Qhtr to ΔTDIBSP to V2/B1 SP to increase throughput from low to maximum and vice versa. Figure 4 depicts the economic plantwide control structure, labeled CS1 for convenient reference, including the split-range throughput manipulation 11736



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scheme. Note that low and high limits are applied on ΔTDIBSP and V2/B1 SP for throughput manipulation. The low limit for both corresponds to the mode I optimum values. The high limits for ΔTDIBSP and V2/B1 SP are chosen slightly above the values for which V1MAX and V2MAX go active, respectively. In Table 3a, the sequence in which the different pairings are implemented to obtain CS1 is listed. Table 3. Loop Pairing Sequence Followed for CS1 and CS2 (a) CS1

(b) CS2

description

CV

hard active constraint control loops

QhtrMAX

Qhtr

V1MAX V2MAX

Qreb1 Qreb1

other economic control loops

other loops with steady-state impact

material balance loops

MV

xn‑C4D1

D1/L1

TSpur

B1

Trxr Tcool Prxr

D2 Qcooler VLV

PDIB Ppur

Qcnd1 Qcnd2

LVLRD1 LVLRD2

L1 L2

LVLBot1

FC4

LVLBot2

B2

description

CV

MV

TPM

FC4

FC4 valve

material balance loops

LVLRD1 LVLRD2 LVLBot1

L1 L2 B1

LVLBot2 Tcool

B2 Qcooler

column vapor inventory loops

PDIB Ppur

Qcnd1 Qcnd2

reactor stabilization loops

Trxr Prxr

Qhtr VLV

column separation regulatory loops

xn‑C4D1

D1/L1

ΔTDIB

V1

TSpur D2/L2

V2 D2

Conventional Control Structure. Conventionally, the feed to a process is used as the throughput manipulator and the plantwide control system is configured with the inventory control loops oriented in the direction of process flow. Such a TPM choice is often dictated in integrated chemical complexes with the plant feed being set by an upstream process. Figure 5 shows such a conventional plantwide control structure, labeled CS2, for the isomerization process. To contrast with CS1, the sequence in which the pairings are obtained for CS2 are noted in Table 3b. In CS2, the column level and pressure controllers are first implemented along with the reactor pressure and temperature loops (material and energy balance control). On the two columns, the top and bottom levels are controlled using respectively the reflux and bottoms. The two column pressures are controlled using the respective condenser duties. The reactor inlet temperature is controlled using the furnace duty. The reactor pressure is controlled using the reactor effluent condenser outlet valve while the condensed reactor effluent temperature is controlled using its condenser duty. With the basic material/energy balance loops in place, pairings for component inventory control are implemented next. The product n-C4 impurity leaking up the DIB column is controlled by adjusting D1/L1. The boilup, V1, is adjusted to maintain ΔTDIB. The purge column distillate is maintained in ratio with its reflux while the bottoms is used to control TSpur. With the TSpur loop, the small purge column bottoms stream would provide acceptable sump level control. With these pairings, the control structure would provide stable unconstrained operation, i.e., mode I operation. The operation would be near optimal for appropriate choice of the steady-state dof set points. Upon

Figure 5. Conventional plantwide control structure, CS2: (a) Basic pairings for mode I (unconstrained) operation; (b) overrides for handling constraints.

hitting constraints such as QhtrMAX on increasing throughput, appropriate overrides are needed to ensure control of crucial CVs is not lost. These overrides are also shown in Figure 5 and are briefly explained below. On increasing the FC4SP to increase throughput, the QhtrMAX constraint would be hit implying loss in control of Trxr. Losing Trxr control is not acceptable and an alternative manipulation handle for maintaining Trxr is needed. The closest manipulation handle that would provide tight Trxr control is D2. An override Trxr controller is therefore implemented with its set point slightly below the nominal set point. When Qhtr is unconstrained, Trxr would be above the override set point causing its output to increase. This output would then be high and the low select block would pass the D2/L2 ratio controller output to D2SP (i.e., D2SP under ratio control). When QhtrMAX is hit, Trxr would start decreasing and go below the override set point, whose output would decrease until the low select ultimately passes this signal to D2SP (i.e., D2SP under Trxr control). 11737



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Table 4. Controller Parameters regulatory controllers CS1

CS2

CV

MV

KC

τi (min)

τd (min)

MV

KC

τi (min)

τd (min)

SP

sensor span

Trxr Tcool TSpur xn‑C4D1

D2 Qcool B1 L1

2 0.2 0.1 0.2

1.5 20 20 120

0.2 2 1.5

Qhtr Qcool V2 L1

2 0.3 0.2 0.15

1 20 15 150

0.1 2 1.5

200 °C 53 °C 63.8 °C 0.02

160−240 °C 40−60 °C 40−80 °C 0−0.04

ΔTDIB

V1

0.2

150

1.39

0−0.03

V1 0.3 CS2 override controllers

150

CV

MV

KC

τi (min)

SP

sensor span

Qhtr Trxr TSpur LVLBot1

V1 D1 B1 FC4

0.05 0.4 0.5 2

150 10 40

1230 kW 199.5 °C 58 °C 70%

0−1294 kW 160−240 °C 40−80 °C 0−50%

ultimately pass the former signal as the set point to the fresh C4 feed flow controller, causing the fresh feed to be cut by the appropriate amount once V2MAX goes active. As recommended by Shinskey,12 external reset on all PI controllers whose output passes through a low/high select block is used to ensure that when inactive, the output is not too far from the selected signal due to reset windup. This ensures quick “taking over” of control so that the duration for which a CV remains unregulated is as small as possible. The external reset is implemented internally in AspenHysys.

It is possible to bring about a near optimal increase in throughput with QhtrMAX active by driving V1MAX and V2MAX active, in that order. To do so, a PI Qhtr override controller with its set point very close to the QhtrMAX limit is implemented. The high select on the Qhtr override output and the ΔTDIB controller output select the greater of the two signals. The selected signal is sent as the set point to the V1 controller through a low select that ensures V1SP does not ever exceed V1MAX. At low throughputs (FC4 low, Qhtr < QhtrMAX) the direct acting Qhtr override controller output would decrease and the high select would pass the ΔTDIB controller output. On sufficiently increasing FC4, Qhtr would increase above the override controller set point, and the controller output would start to increase. The high select would ultimately pass V1SP manipulation to the Qhtr override, which would cause V1SP to increase. If FC4 is high enough (or increased fast enough), V1SP would reach V1MAX. The TSpur controller would increase V2SP to ensure that the n-C4 does not leak out the purge column bottoms. V2MAX going active would signal that fresh n-C4 beyond the processing capacity of the plant is being fed. To automatically reduce FC4 to the maximum processing capacity limit, an override scheme for altering the material balance structure from V2MAX all the way back to the process fresh feed is implemented. When V2MAX goes active, TSpur control is lost implying excessive leakage of precious n-C4 down the purge column bottoms and consequent economic loss. To prevent the same, an alternative manipulation handle for TSpur is needed. The feed to the purge column would provide reasonably tight tray temperature control. A PI TSpur override controller with its set point slightly below the nominal set point is implemented. When V2MAX is inactive, the tray temperature would be higher than the override controller set point so that its output would increase. The low select on the LVLBot1 controller output and the TSpur override controller output would pass the former signal to B1SP (purge column feed under the LVLBot1 control). When V2MAX goes active, TSpur control would be lost and it would decrease below the override controller set point. The override output would then decrease and the low select would ultimately pass B1SP manipulation to the override controller (purge column feed under TSpur control). LVLBot1 control is now lost, and it would increase. A reverse acting LVLBot1 override controller with a set point slightly higher than the nominal set point is implemented. As LVLBot1 increases, its output would decrease (reverse action). The low select on this signal and operator specified FC4SP would

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DYNAMIC SIMULATIONS AND CLOSED LOOP RESULTS Tuning of Controllers. The performance of the two control structures, CS1 and CS2, is evaluated using rigorous dynamic simulations in AspenHysys 2006. To ensure that any differences in the performances are largely attributable to the structure, a consistent tuning procedure is followed for tuning the loops in both of the structures. All flow controllers are tuned with a gain of 0.5 and a reset time of 0.5 min. All pressure controllers are tuned for tight pressure control, which is any way necessary for stabilizing the pressure driven dynamic simulation. All level controllers are P only with a gain of 2. The only exception is the DIB sump level controller in CS1 where a lower gain of 1 is used since the lag between the sump and the fresh C4 feed is significant due to the intervening 20 stripping trays. In all temperature loops, the temperature measurement is lagged by 1 min to account for sensor dynamics. Also, the controller output signal is lagged by 2 min to account for heat-transfer equipment dynamics. The only exception is the cooler temperature controller where a higher 8 min lag is applied to account for the slow dynamics of a flooded condenser. All temperature controllers are PI(D) and tuned using the autotuner with minor refinement for a not-too-oscillatory closed loop servo response, if necessary. In the PI product composition control loop, a 5 min dead time and a 5 min measurement sampling time are applied. The autotuner does not give reasonable tuning, and the open loop step response is used to set the reset time at 2/3rd the response completion time and the controller gain adjusted for a not-too-oscillatory servo response. In both structures, the product composition loop is tuned first with the ΔTDIB loop on manual followed by tuning of the ΔTDIB loop with the composition loop on automatic. This ensures that all of the detuning due to multivariable interaction gets taken in the ΔTDIB 11738



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Figure 6. Mode I transient response to ±5% feed n-C4 composition change: solid black lines, +5% CS1; solid gray lines, −5% CS1; dashed black lines, +5% CS2; dashed gray lines, −5% CS2.

Figure 7. Mode I transient response to ±20kmol/h FC4 change solid black lines, CS1 +20; solid gray lines, CS1 −20; dashed black lines, CS2 +20; dashed gray lines, CS2 −20.

loop and not the product purity loop. This gives tight product purity control, an economically important control objective. In the CS2 override scheme, the override set point for Trxr and TSpur cannot be chosen too close to the corresponding nominal controller set point as that would lead to unnecessary controller output switching during routine transients causing further transients. Accordingly the override controller set point is chosen as close as possible to the corresponding nominal

controller set point for the disturbance that causes the worst-case transients. It is also highlighted that the Qhtr override controller that manipulates V1 is a long loop with slow dynamics. Since its set point must be close to QhtrMAX, a P only controller would require a large gain to ensure V1 gets driven to V1MAX for achieving maximum throughput. The large gain leads to on−off control for routine disturbances at a high but below maximum throughput with the override taking over and giving up V1 11739



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Figure 8. Mode II transient response to ±5% feed n−C4 composition change: solid black lines, +5% CS1; solid gray lines, −5% CS1; dashed black lines, +5% CS2; dashed gray lines, −5% CS2.

Figure 9. Throughput transition for CS1 and CS2: solid black lines, CS1; solid gray lines, CS2.

and a ±20 kmol/h FC4 (throughput change) are considered the

manipulation. A loose PI Qhtr override controller is therefore implemented to ensure its set point is close to QhtrMAX and on− off control is avoided. Table 4 lists the salient controller tuning parameters for CS1 and CS2 using the above procedure. Dynamic Plantwide Responses. The plantwide transient response of the two control structures, CS1 and CS2, is obtained for principal disturbances for mode I and mode II operation. In mode I, a ±5 mol % step change in the fresh C4 feed i-C4 mole fraction with a complementary change in the n-C4 mole fraction

principal disturbances. In mode II, only the feed composition step change is considered the principal disturbances as the throughput gets fixed by the active constraints. The dynamic response is also obtained for a throughput transition from mode I to mode II and back. Figure 6 plots the dynamic response of salient process variables to a feed composition step disturbance in mode I for 11740



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Figure 10. Transient response for +5% feed n-C4 composition change at FC4 = 293.1kmol/h: solid black lines, CS1; dashed gray lines, CS2 aggressive Qhtr override; solid black lines, CS2 loose Qhtr override.

hand, the set point values are held at their nominal values. As seen from the dynamic responses, the plantwide transient response is smooth in both of the structures. Also, tight control of product impurity and the n-C4 leakage down the purge column bottoms is achieved. In CS2, however, the production of i-C4 at the initial and final steady state is slightly lower than in CS1 due to the slightly lower Trxr set point which causes a slight reduction in single-pass reactor conversion as well as higher n-C4 leakage in the purge column bottoms due to the lower TSpur set point. The synthesized control structures are also tested for a large throughput transition from the design throughput (FC4 = 263.1 kmol/h) to the maximum achievable throughput and back. The transient response is shown in Figure 9. In CS1, to increase throughput, the split range scheme switches the TPM from QhtrSP to ΔTDIBSP and then to V2/B1 SP. The switching order gets reversed for decreasing the throughput. The transient response shows that tight product impurity control is achieved across the entire throughput range. The loss of precious n-C4 down B2 is also regulated at a small value. Most importantly, the plantwide transients are smooth and not too severe. In CS2, FC4SP is ramped up causing Qhtr to increase, and as it crosses the Qhtr override controller set point (chosen set point is 95% of QhtrMAX), the override output increases above the ΔTDIB controller output passing V1SP manipulation to the Qhtr override, which slowly keeps on increasing V1SP to V1MAX. As and when QhtrMAX is reached, Trxr decreases and the override Trxr controller takes over D2 manipulation. Meanwhile, V2SP increases rapidly and hits V2MAX as more n-C4 is being fed in than being consumed in the reactor. This causes TSpur to decrease and the override scheme for altering the material balance structure gets activated to cut the FC4 feed. Since the Qhtr override is a long loop, the increase in V1 is slow and even after 75 h, the V1MAX constraint is not approached and the product rate, D1, is about 299 kmol/h

CS1 and CS2. Both structures are observed to effectively reject the disturbance with tight control of the n-C4 impurity in the product. In CS1, FC4 gets adjusted and the flow to the reactor settles to the appropriate value for maintaining Trxr for the set Qhtr, the TPM. In CS2 on the other hand, the FC4 (TPM) remains fixed and the i-C4 production changes in proportion to the n-C4 in the fresh feed. In both structures, the leakage of n-C4 down the purge column bottoms is well-regulated via the action of the TSpur controller. Figure 7 plots the mode I dynamic response for a ±20 kmol/h change in FC4. In CS1, the Qhtr set point must be increased (decreased) by 169 kW (∼21% of base-case Qhtr) to bring about a 20 kmol/h (∼7.6% of base-case FC4) increase in FC4. Similarly, Qhtr must be decreased by 138 kW (∼17.2%) for achieving the decrease in FC4. For the throughput change disturbance, the product impurity is well-controlled in the transient period in both CS1 and CS2. The transient deviations in CS1 are slightly lower than in CS2 due to more severe transients in the recycle loop in the latter. In CS1 on the other hand, the recycle loop transients are less severe (smooth response). In addition to tight product impurity control, both of the structures achieve tight regulation of the n-C4 leakage in the purge column bottoms via the action of the TSpur controller. The transient variability in xn‑C4B2 is significantly higher in CS1 as a large change in Qhtr (TPM) causes a large change in D2 which severely disturbs the purge column material balance. Figure 8 plots the mode II dynamic response to a ±5% feed composition step change. All override controllers in CS2 are active so that, structurally, CS1 and CS2 are very similar. The only significant difference is that the set point of the Trxr and TSpur override controllers in CS2 is slightly lower than the corresponding nominal set point values. In CS1, on the other 11741



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(∼20 kmol/h < maximum steady D1). Even as D1 would eventually reach its maximum steady value, it takes a very long time (>200 h). After 75 h, FC4SP is ramped down to its base value (263.1 kmol/h) and a smooth transition occurs. From the CS2 response in Figure 9, notice that in the small period where V2MAX goes active and TSpur override starts manipulating B1, large transient loss of precious n-C4 down the purge column bottoms occurs. Also, the steady n−C4 loss is higher due to the lower than nominal set point of the TSpur override. Another pertinent comparison is the transients caused due to overrides taking over/giving up control during routine disturbances. We consider a worst-case step disturbance in the fresh feed composition, where the n-C4 composition increases by 5% with initial steady operation at FC4 = 293.1 kmol/h, where none of the constraints are active. The transient response of CS1 and CS2 to this disturbance is shown in Figure 10. CS1 effectively rejects the disturbance with tight product purity control and regulation of n-C4 in the purge column bottoms with the plant settling down at the new steady state in about 30 h. In CS2, on nC4 composition increasing by 5%, a large transient increase occurs in Qhtr due to the snowball effect,13 which triggers the Qhtr override. V1 is then slowly driven toward V1MAX while the additional n-C4 causes V2 to increase. The slow increase in V2 causes the i-C5 circulating in the plant and hence D2 to decrease. For the lower D2 (reactor feed), Trxr control eventually passes back to Qhtr and the plant settles at the new steady state in about 75 h, which is more than twice the time for CS1. If the Qhtr override controller is made aggressive by increasing the proportional gain by a factor of 2, oscillations due to the Trxr override successively going active and inactive are observed (see Figure 10). The dynamic performance thus degrades significantly at high throughputs where the overrides get activated. It is then not surprising at all that operators tend to switch the overrides off and make the necessary adjustments manually. Quantitative Economic Performance Comparison. A quantitative economic comparison of the two control structures is performed for maximum throughput (mode II) operation. We consider a +5% feed n-C4 composition step change as the worstcase disturbance. Table 5 compares the maximum achieved

without any consideration of the constraints that go active at higher throughputs, thus is economically and dynamically inferior to CS1 regardless of the approach used to handle constraints (back-off or overrides). Overall, these results demonstrate that the full active constraint set plays a key role in economic plantwide control system design.

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DISCUSSION This case study demonstrates that it is possible to devise a very simple plantwide control structure with higher prioritization to the pairings for economic CVs to realize economically optimal process operation over a wide throughput range with multiple hard constraints going active. This higher prioritization is possible due to the sufficient number of surge capacities with corresponding control valves being provided in the design of the process. These additional control dofs imply that even if all steady-state dofs are exhausted to drive as many constraints active, control valves would still remain for regulating the surge inventories. The case study also suggests that the basis for a general approach for economic plantwide control system design across a wide throughput range must consist of devising a workable control system at all active constraints, which usually corresponds to the maximum throughput. The economic penalty for deviations away from the optimum solution is usually the highest at the maximum throughput (most constrained) solution, and this is where the most economic benefit of achieving tight active constraint control is realized. To that end, any hard constrained direct manipulation handles (Qhtr, V1, and V2 in the studied example) should not be used for conventional control tasks and left alone for minimum back-off. Alternative pairings should be implemented for control tasks that these constrained handles would otherwise have been used for. This ensures that the regulation of these tasks is never lost over the entire throughput range, regardless of whether the constraint is active or not. Of course, at lower throughputs where these constraints should be inactive, the inactive constraints should be used for maintaining CVs that help further improve plant economics. In this example, this was achieved by V1 maintaining ΔTDIB and V2 being maintained in ratio with B1 to avoid overrefluxing. The case study shows that conventional plantwide control systems with a fixed TPM location at the process feed typically are more complicated, requiring additional overrides to handle constraints, which are often inside the recycle loop. In contrast, for a control structure synthesized to work at all active constraints, the basic regulatory control structure remains the same across the entire throughput range. In the current example, three additional override controllers (Trxr, TSpur, and LVLBot1), all inside the recycle loop, are needed in CS2. The conventional overrides alter the basic regulatory control configuration on a constraint going active, which can be confusing to operators. Even as this way of handling constraints helps in mitigating economic loss compared to backed-off process operation with no overrides, its economic performance remains inferior to the economic plantwide control structure designed to work at all active constraints without requiring any overrides. The advantage of the traditional approach of having the TPM at the feed and using conventional regulatory pairings with material balance control in the direction of flow is that it gives dynamically less severe plantwide transients with tighter product quality control.14 It thus achieves the tightest quality control at low throughputs where no hard constraints are active.

Table 5. Mode II Throughput Loss Comparison for +5 mol % Feed Composition Step Change CS1

CS2

FC 4

334.5 kmol/h

329 kmol/h

product Fn‑C4B1

317.6 kmol/h 0.16 kmol/h

312.3 kmol/h 0.33 kmol/h

profit % loss

21.51 m$/year 0

21.1 m$/year 1.8

steady throughput (FC4) along with the corresponding n-C4 component flow (loss) in the purge column bottoms, the i-C4 product rate, and the operating yearly profit for CS1 and CS2. Expectedly, no back-off and throughput loss is observed for CS1, which has been designed for process operation with all of the hard active constraints at their maximum limits. In contrast, in CS2, due to the need for the Trxr and TSpur override set points to be lower than nominal, a yearly profit loss of $0.45 × 106 (∼2%) occurs compared to CS1. The override controller set point offsets have been chosen to be as small as possible at 1 °C for Trxr and 5 °C for TSpur to ensure that the overrides do not get triggered during routine transients. CS2, which was obtained 11742



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However, once constraints start going active, overrides anyway must come into play to alter the material balance structure for maintaining process stability and this dynamic advantage is lost, particularly at high throughputs with associated significant economic loss. Further, these overrides can cause unnecessary transients for routine disturbances at lower throughputs due to successive taking over and giving up of control (on−off control). Thus, for purposes of operating a plant over a wide throughput range encompassing multiple hard constraints going active, we recommend the approach applied here. In the special case where only a single hard active constraint goes active, the approach would boil down to using the set point to the hard constraint variable control loop as the TPM over the entire through range, which is in line with recent literature reports on plantwide control for maximum throughput operation.8,9 Finally, we highlight that in reactor−recycle systems, when throughput is to be maximized, typically the hard constraints that go active with significant economic loss per unit back-off are inside the recycle loop. This is a direct consequence of the snowball effect,13 which by definition implies a high sensitivity of the recycle flow rate to changes in throughput. Luyben’s rule1 of fixing a flow somewhere inside the recycle loop to mitigate snowballing then also mitigates the transients and hence back-off in any active constraints inside the recycle loop. In the isomerization process example, it is the QhtrMAX constraint that sets the flow through the recycle loop and gives conceptual consistency with Luyben’s rule. The rule, though derived from purely regulatory control considerations, also helps achieve economic process operation.

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REFERENCES

(1) Luyben, W. L.; Tyreus, B. D.; Luyben, M. L. Isomerization Process, Plantwide Process Control; McGraw-Hill: New York, 1999; pp 273−293. (2) Luyben, W. L. Design and Control of an Autorefrigerated Alkylation Process. Ind. Eng. Chem. Res. 2009, 48, 11081−11093. (3) Luyben, M. L.; Tyreus, B. D.; Luyben, W. L. Plantwide Control Design Procedure. AIChE J. 1997, 43 (12), 3161−3174. (4) Luyben, W. L. Plantwide Control of an Isopropyl Alcohol Dehydration Process. AIChE J. 2006, 52 (6), 2290−2296. (5) Luyben, W. L. Design and Control of the Methoxy-MethylHeptane Process. Ind. Eng. Chem. Res. 2010, 49, 6164−6175. (6) Skogestad, S. Control Structure Design for Complete Chemical Plants. Comput. Chem. Eng. 2004, 28 (1−2), 219−234. (7) Skogestad, S. Plantwide Control: The Search for the SelfOptimizing Control Structure. J. Process Control 2000, 10 (5), 487−507. (8) Kanodia, R; Kaistha, N. Plantwide Control for Throughput Maximization: A Case Study. Ind. Eng. Chem. Res. 2010, 49, 210−221. (9) Singh, S.; Lal, S.; Kaistha, N. Case Study on Tubular Reactor HotSpot Temperature Control for Throughput Maximization. Ind. Eng. Chem. Res. 2008, 47, 7257−7263. (10) Jagtap, R.; Kaistha, N.; Skogestad, S. Plantwide Control for Economic Optimum Operation of a Recycle Process with Side Reaction. Ind. Eng. Chem. Res. 2011, 50, 8571−8584. (11) Buckley, P. S. Techniques of Process Control; Wiley; New York, 1964. (12) Shinskey, F. G. Process Control Systems: Application, Design and Tuning; McGraw Hill: New York, 1996. (13) Luyben, W. L. Snowball Effects in Reactor/Separator Processes with Recycle. Ind. Eng. Chem. Res. 1994, 33, 299−305. (14) Luyben, W. L. Inherent Dynamic Problems with on-Demand Control Structures. Ind. Eng. Chem. Res. 1999, 38, 2315−2329.

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CONCLUSIONS In conclusion, this case study on plantwide control of the C4 isomerization process demonstrates that a simple decentralized plantwide control system for achieving near optimal and smooth process operation over a wide throughput range can be synthesized. The active constraints at maximum throughput form the key to devising the control system. These constraints dictate the pairings for tight control of these active constraints and the consequent pairings for inventory regulation as well as the throughput manipulation strategy. Quantitative results show that a conventional control structure with the TPM at the process feed with overrides for handling constraints is economically inferior with a steady profit loss of ∼2% at maximum throughput due to the offset needed in the override controller set points. The conventional scheme is also found to be dynamically inferior. The case study demonstrates the crucial role of the active constraints in economic plantwide control structure synthesis.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel.: +91-512-2598362. Fax: +91512-2590104. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The financial support from the Department of Science and Technology, Government of India, for plantwide control research is gratefully acknowledged. Prof W. L. Luyben’s insights on handling of constraints using overrides are also gratefully acknowledged. 11743


Economic Plantwide Control of a C4 Isomerization Process - American

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