Plantwide Control for Maximum Throughput Operation of an Ester

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Plantwide Control for Maximum Throughput Operation of an Ester Purification Process Ojasvi *, and Nitin Kaistha Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.6b02997 • Publication Date (Web): 08 Nov 2016 Downloaded from http://pubs.acs.org on November 10, 2016

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Industrial & Engineering Chemistry Research

Final Revision Submitted to IECR

Plantwide Control for Maximum Throughput Operation of an Ester Purification Process

Ojasvi and Nitin Kaistha Department of Chemical Engineering Indian Institute of Technology Kanpur Kanpur 208016

Submitted on 7th Nov 2016

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Plantwide Control for Maximum Throughput Operation of an Ester Purification Process Ojasvi and Nitin Kaistha* Department of Chemical Engineering, Indian Institute of Technology Kanpur, Kanpur 208016.

Abstract Plantwide control for maximum throughput operation of an ester purification process consisting of a liquid-liquid extractor (LLX), a distillation column and material recycle is evaluated. The extractor uses water solvent and is necessary to cross a distillation boundary making pure ester product recovery feasible. Extraction capacity is the bottleneck constraint. A steady state analysis reveals the occurrence of steady state multiplicity induced infeasibility for too high fresh feed rates and for too low water feed rates. To avoid infeasibility due to the multiplicity behaviour, we recommend using the extractor feed rate as the throughput manipulator (TPM) with the fresh feed rate adjusted as a make-up stream (CS1). The other control loop pairings are conventional. Rigorous closed loop dynamic results show that CS1 is significantly more robust than the conventional control structure (CS2) with fresh feed rate as the TPM. In particular, CS1 achieves more than 25% higher maximum throughput compared to CS2 for large feed composition changes in specific directions. This is attributed to the self-regulatory nature of the recycle inventory control in CS1. In contrast, CS2 is susceptible to failure due to overfeeding induced steady state infeasibility. The article highlights the central role of control structure / strategy design for robust plant operation.

*

To whom all correspondence should be addressed. Email: [email protected]; Phone: +91-512-2597513; Fax: +91-512-2590104.

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Introduction Plantwide control system design has been extensively researched over the past three decades. A vast majority of the literature focuses on the design of a robust regulatory control system for closing all the independent material / energy balances of a complete material / energy integrated (recycle)1-5 plant. In almost all reports, reaction-separation-recycle processes are studied (see e.g.6-10 as well as the celebrated Tennessee Eastman challenge plantwide control problem11). The key issue in the design of a robust regulatory plantwide control system for these reactor-separator-recycle processes is the proper management of the non-linearity associated with recycle loops. The established plantwide control structure design heuristic is to configure the basic inventory control system such that the fresh feeds are fed as make up streams to hold appropriate component recycle inventories going around the plant12. It is the basis of Luyben’s rule13 of holding a flow inside the recycle loop constant to mitigate snowballing14 in the recycle loop. Given that material / energy recycle is a key concept that has found widespread use in all industrial process systems, including non-reactive systems, the almost exclusive focus of the extant plantwide control literature on reactor-separator-recycle processes is quite surprising. In this work, we evaluate plantwide control system design for an ester purification process consisting of a liquidliquid-extractor (LLX) followed by a product ester recovery distillation column with distillate recycle. The system is inherently non-linear with liquid-liquid phase separation as well as separation constraints due to distillation boundaries. When coupled with the non-linearity due to material recycle, the plantwide control system design problem becomes particularly challenging for robust high throughput process operation. The original motivation for studying an ester purification process came from a recent perspective article by Downs and Skogestad15. In the article, one of the described industrial plantwide control success stories is the dramatic increase in the maximum achievable throughput for an existing ester recovery process at Tennessee Eastman, Kingsport, via proper choice of the



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throughput manipulator (TPM) location. The description however, is sketchy, purely qualitative and largely silent on the process details. Here we specifically focus on designing a plantwide control system for maximizing throughput (feed processing rate) of the ester purification process. In today’s patent monopoly driven sellers' markets, maximizing throughput is often equivalent to maximizing profit. Continuous manufacturing processes are thus increasingly required to operate at their maximum achievable production capacity. Typically, the maximum achievable throughput is limited by bottleneck capacity constraints such as a column approaching its flooding limit or inherent steady state infeasibility. The maximum process throughput achieved in operation is then determined by the ability of the process control system to drive the process as close as possible to the hard bottleneck/feasibility constraint limit without violating it for the worst-case disturbance scenario. The severity of transients in the constraint determines the back-off necessary from the constraint limit to guarantee avoiding constraint violation, which fixes the achieved maximum production. The constraint transient severity, in turn is strongly influenced by the implemented plantwide regulatory control system. A key decision in configuring the basic plantwide regulatory control system is the choice of the throughput manipulator (TPM), which is the setpoint adjusted for setting production. As noted by Price and Georgakis16, the TPM location dictates an outwardly radiating orientation of the inventory controllers. The upstream inventory controllers are then oriented in the reverse direction of process flow while the downstream inventory controllers are oriented in the direction of process flow (see Figure 1). From the point of view of propagation of transients, the outwardly radiating inventory control system implies flow transients are propagated away from the TPM location. Thus, to mitigate transients in the constraint and hence reduce the back-off from the constraint limit, it has been suggested that the TPM be located at the bottleneck constraint17. Conventional industrial practice however is to use a fresh feed rate as the TPM with the downstream inventory control system oriented in the direction of process flow18.


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In recent articles, it has been quantitatively shown that by locating the TPM at the bottleneck constraint and designing a consistent inventory control system around it, the maximum achievable production can be significantly enhanced compared to a conventional control system with the TPM at the fresh feed19-22. As noted earlier, all these studies are however on reactorseparator-recycle systems. Thus, to the best of our knowledge, this is the first contribution on plantwide control system design for maximum throughput operation of a recycle process that does not fall in the category of reactor-separator-recycle processes. The specific example studied here is LLX based recovery of near pure ethyl acetate (EtOAc) from a ternary EtOAc-ethanol-water mixture. In the following, we describe a base-case design of the LLX-distillation-recycle process for recovering nearly pure EtOAc product from an EtOAc-ethanol (EtOH)-water mixture. Extraction capacity due to a maximum constraint on the extractor fresh water feed rate is the constraint limiting production. A steady state bifurcation analysis is then performed to illustrate the occurrence of steady state multiplicity with the recycle rate exhibiting high sensitivity to throughput changes in the high throughput operating region (snowball effect14). Two basic control structures, in which fresh feed is fed either as a make-up stream (CS1) or as an independently set stream (CS2) are then synthesized. Their closed loop performance for principal disturbances around the base-case design is then presented. This is followed by an evaluation and discussion of their performance for the maximum achievable throughput in the presence of large fresh feed composition disturbances. The article ends with a summary of the main findings from the work.

Ester Purification Process Process Description Figure 2 shows a schematic of the Eastman LLX-distillation-recycle ester purification process. The ternary EtOAc-EtOH-H2O fresh feed and hot recycle stream are mixed, cooled and fed to the extractor. The extractor uses pure water solvent to preferentially soak the alcohol in a countercurrent mixer-settler arrangement. The alcohol-rich extract is discharged for further downstream 4 ACS Paragon Plus Environment


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processing. The ester-rich raffinate is distilled to recover pure ester as the bottoms product. The distillate is recycled to the extractor. Such a process typically exists as part of an ester manufacturing facility with an upstream reaction section as well as a downstream alcohol-wash processing section.

Thermodynamic Modelling Details Aspen Plus is used for solving the steady state material and energy balances of the ester purification process. Rigorous dynamic simulation is performed in Aspen Dynamics. The EtOAc-EtOHwater system phase equilibrium is highly non-linear with large positive deviations from ideal solution behaviour resulting in liquid-liquid phase split. Accordingly, the NRTL activity coefficient model is used for the liquid phase. The ESIG equation of state is used for the low pressure vapor phase. The residue curve map (RCM) along with the liquid-liquid envelope is shown in Figure 3. Note the EtOHwater and EtOAc-EtOH homogenous minimum boiling azeotropes as well as the heterogenous EtOAc-water azeotrope. There also exists the ternary heterogenous minimum boiling EtOAc-EtOHwater azeotrope. These azeotropes partition the composition space into three distillation regions (Figure 3). The process fresh feed composition is in Region II and simple distillation cannot give pure ester product due to the Region II – Region III boundary. The LLX with water solvent pulls the overall extractor composition into the liquid-liquid phase envelope to give an ester rich raffinate composition in Region III. Simple distillation of this raffinate stream gives a nearly pure ester bottoms product (stable node) and a distillate composition close to the Region II - Region III distillation boundary. This distillate is recycled. The process flowsheet of Figure 2 is then feasible with all three components having a way out of the process. The ester leaves in the column bottoms while the alcohol and water leave in the LLX extract stream (alcohol wash).

Base-Case Process Design The base-case process design and operating conditions for the ester purification process are shown in Figure 2. The fresh feed rate is 100 kmol/h. Using a fresh water to fresh feed ratio of 1.7, 5 ACS Paragon Plus Environment

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the extractor fresh water rate is 170 kmol/h. The extractor uses a traditional counter-current mixersettler arrangement. A typical value of six mixer-settler stages is used here23. Figure 4 shows the six stage material balance lines as well as the important plant balance lines at the base-case design. The stage organic-aqueous layer compositions do not fall exactly on the liquid-liquid envelope as the extactor is adiabatic and solution non-ideality results in slight variability in the stage temperatures. The Figure 2 data suggests that the ester product recovery is ~70%, since some ester is lost in the alcohol-wash stream. It is pertinent to note that the ester recovery plant studied here typically exists as part of a complete ester manufacturing facility consisting of a reaction section as well as a downstream alcohol-wash processing section. For the specific ethyl acetate process example studied here, the alcohol wash stream may be distilled to recover nearly pure water down the base and an alcohol rich distillate containing some water and ester. This alcohol rich distillate gets recycled back to the reaction section. Thus, the ester in the alcohol wash is not wasted but gets recycled back to the reactor. The overall plant ester recovery is then ~100% even as the “single pass” ester purification process recovery is only ~70%. The whole point of studying the ester purification process, which is only a subsection of the entire ester manufacturing plant, is that this subsection limits the maximum ester production possible for the facility, as noted in Downs and Skogestad15. Further, we note that the focus of the work is control system design for maximizing throughput so that strict "optimality" of the base-case design is not considered here. Even so, the extractor fresh water feed rate is the most important design variable. As this rate is increased (i.e. more fresh water is added), the recycle rate and associated costs go down with the overall extractor material balance line being "pulled" downwards towards the EtOAc-H2O base. However, the downstream alcohol wash (extract) processing cost as well as the fresh water cost goes up. For a fresh water to fresh feed ratio below 1.12, we could not get the flowsheet to converge, which is due to infeasibility of the overall plant material balances, as described later. We therefore use a ratio of 1.7, which is about 50% more than the minimum feasible ratio. The fresh water rate then is 170 kmol/h. For maximum throughput operation, the maximum permissible water solvent rate to the 6 ACS Paragon Plus Environment


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extractor acts as the capacity bottleneck that limits production. The extractor cannot take in any more water solvent due to hydraulic constraints. Without any loss of generality, we assume that the fresh water rate in Figure 2 is this maximum water rate limit.

Steady State Bifurcation Analysis The steady state characteristics of the flowsheet are now analysed using the Aspen Plus steady state solver. Excluding the extractor feed cooler, which is used to set the feed temperature at 35 °C, the steady state operation degree of freedom (dof) for the process is four; one each for the fresh feed and fresh water streams, and two for the distillation column. Of these, the ester product purity is fixed at 99.0 mol%. The simplest steady state solution strategy then is to specify the fresh feed and fresh water rates, and use the design spec vary feature to hold the column bottoms ester purity at 99.0 mol% at a given reflux ratio. We are particularly interested in the variation in process material and energy flows with (a) water flow rate (constant fresh feed rate: 100 kmol/h); and (b) fresh feed rate (constant water rate: 170 kmol/h). In exploratory steady state simulations, we found that with the above conventional specification variables, the recycle tear does not converge for the fresh feed rate specified too high or the fresh water rate specified too low. The non-convergence of the recycle tear suggested the possibility of steady state infeasibility. To better explore the steady state solution space, we searched for a more robust specification set corresponding to the steady state dofs. In this context, we note that one of the major plantwide control heuristics for material recycle systems is to not fix the fresh feed rate and instead adjust it to hold an appropriate material recycle rate (Luyben’s rule). In terms of specification variables, this corresponds to specifying a material flow rate (independent variable) inside the recycle loop with the fresh feed rate getting calculated (dependent variable). Several studies in reactor-separator-recycle systems show that this strategy is inherently more robust, both from the steady state convergence as well as the dynamic plantwide control perspectives24-25. We therefore explored extractor feed rate (recycle + fresh feed) as an alternative 7 ACS Paragon Plus Environment

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specification replacing fresh feed rate. The other three specifications remain the same. A significant improvement in the flowsheet steady state convergence behaviour was observed. In Aspen Plus, this alternative specification is implemented using a calculator block with the fresh feed rate being calculated as the difference between the specified extractor feed rate and the (current) recycle rate. The specification set of extractor feed rate, fresh water rate, column bottoms ester purity and column reflux ratio allows us to explore the variation in the process flows with extractor feed rate at a given fresh water rate. We are also interested in obtaining the variation of the process flows with the fresh water rate at a fixed fresh feed rate. To simulate this, we vary the water rate so that the fresh feed rate, calculated for a specified extractor feed rate, is driven to the desired value. The above innovations allowed us to comprehensively explore the process steady state solution space. The variation in the extractor feed rate, recycle rate and the column reboiler duty with the fresh water rate (constant fresh feed rate) is shown in Figure 5a. The corresponding variation with the fresh feed rate (constant water rate) is shown in Figure 5b. Severe process nonlinearity with steady state multiplicity is evident in all the plots. In particular, notice that for sufficiently high and low fresh feed and fresh water rates respectively, a steady state solution does not exist, implying closure of the overall plant material balances is infeasible. The multiplicity behaviour has major consequences on the design of the regulatory control system (discussed later). The turning points in the Figure 5 bifurcation diagrams have infinite slope with respect to the fresh water and fresh feed rates. Let us consider the lower branch (solid lines) solutions, which are of practical interest due to the lower reboiler duty and recycle rate for a given fresh feed / fresh water rate. On this branch, the recycle rate and the reboiler duty exhibit a very sharp rise as the water is rate is reduced below 130 kmol/h (Figure 5a). As the water rate is reduced below 111.9 kmol/h, a steady state solution does not exist. Similarly, high sensitivity in the recycle rate and reboiler duty is evident in the high throughput region with the % recycle rate increase per % fresh feed rate increase being >> 1 (Figure 5b). This is the classic snowball effect14 in recycle systems.



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Consider the variation in the extractor overall material balance with fresh water rate at a given throughput. As the water rate is reduced sufficiently, the overall extractor feed composition (fresh feed + water + recycle) moves up in the composition triangle. Due to the shape of the LLE envelope, the length of the tie lines is then shorter so that the degree of separation in the extractor decreases and both the extract and raffinate compositions move up along the LLE envelope. The lower separation degree implies that the raffinate has lower ester mol fraction with more alcoholwater. Even as this raffinate can be distilled to obtain pure ester down the bottoms, the distillate composition is constrained at the Region II – Region III boundary. The relative ester enrichment of the column distillate with respect to the raffinate (column feed) composition then reduces. This causes the recycle rate to increase sharply as the water rate is reduced sufficiently. Of course, for high enough water rate, the raffinate composition remains almost constant, close to the organic phase composition on the EtOAc-H2O edge (see Figure 4). This implies an almost invariant material balance on the distillation column. The recycle rate and reboiler duty variation with fresh water rate is then a flat curve. A complementary argument applies to the sharp rise in recycle rate and reboiler duty with throughput in the high throughput operating region. At high throughputs, the extractor becomes water starved as the water rate is constant. The extractor overall composition then moves up into the composition triangle with consequent high recycle rate sensitivity.

Plantwide Control System Design Control Stucture Synthesis We are interested in designing a control system that robustly delivers the maximum achievable throughput, which is constrained by the feasibility of closing overall plant material balances at the maximum fresh water rate (extraction capacity constraint). To understand the implication of the observed steady state multiplicity on control system design, we plot the steady state relationship between extractor feed rate and fresh feed rate in two ways, namely, fresh feed rate as the independent x-axis variable (Figure 6a) and alternatively, the extractor feed rate as the 9 ACS Paragon Plus Environment

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independent x-axis variable (Figure 6b). If we have a conventional control system with fresh feed rate as the throughput manipulator (TPM), then Figure 6a clearly shows that the TPM setpoint (independent variable) can be set too high and the control system would fail as it seeks an infeasible steady state. Clearly, a conventional regulatory control structure is not recommended for this system in light of the steady state multiplicity behaviour that makes it susceptible to infeasibility. A convenient robust alternative is to use the extractor feed rate as the TPM, with the fresh feed rate being manipulated to hold it at the desired value. The fresh feed rate is then drawn in as a make-up stream, consistent with Luyben’s recommendation13 for reactor-separator-recycle processes. From Figure 6b, notice that a feasible steady state solution exists for a very wide range of extractor feed rate setpoint (independent variable) values. Steady state feasibility is then guaranteed, which is a significant advantage compared to a conventional control system. With the extractor feed rate as the TPM, the remainder of the regulatory control system is straightforward. The extractor feed cooler duty is manipulated to hold the extractor temperature. On the extractor decanters, the aqueous draw rate is manipulated to hold the aqueous layer level while the organic draw-rate is manipulated to hold the organic hold up (total liquid height - aqueous layer height). The fresh water to the extractor is flow controlled and maintained at its maximum rate of 170 kmol/h. Conventional single-ended temperature control is applied to the distillation column. The reflux drum and bottom sump levels are thus regulated using the distillate and bottoms rates respectively. The column pressure is controlled using the condenser duty. The reflux rate is maintained in ratio with the feed rate. A sensitive stripping tray temperature is controlled by manipulating the reboiler duty. The temperature setpoint is updated by an ester product water impurity controller that guarantees on-target product quality control. The synthesized control structure is shown in Figure 7a and referred to as CS1. Purely for comparison purposes, we also consider a conventional control system with the fresh feed rate as the TPM. It is shown in Figure 7b and referred to as CS2. Except for the TPM loop configuration, all other loops are the same as in CS1. Note that CS1 and CS2 are fundamentally 10 ACS Paragon Plus Environment


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different in that CS1 pulls in the fresh feed as a make-up stream while in CS2, the fresh feed is specified and it is expected that the plant will process the fed fresh feed.

Control System Tuning The decentralized control structures, CS1-CS2, are simulated in Aspen dynamics. It has a built in LLX module that may be used to significantly speed up the dynamic simulation compared to simulating six decanters in series. The extractor internal flows are then free (dependent) variables that get calculated by the internal aqueous/organic inventory controllers (these are P controllers with a specifiable gain). The reflux drum and bottom sump are sized for a residence time of 10 mins at 50% level at the base-case steady state. Since the process is susceptible to snowballing at high throughputs, the distillation column diameter is chosen at 50% of flooding velocity for high rangeability. This is a practical choice which can be implemented using bubble cap trays that are known to have a high turndown ratio of 3-5. All temperature measurements are lagged by 1 min to account for sensor dynamics. A 2 min lag is also applied to all directly manipulated energy streams (condenser duty, reboiler duty and extractor feed cooler duty) to account for heat transfer dynamics. Lastly, the ester product composition measurement is lagged by 2 min. A dead time of 5 mins and a sampling time of 5 minutes is also applied to the composition measurement. The various decentralized controllers are tuned as follows. All flow controllers are PI and use a controller gain of 0.5 and a reset time of 0.5 mins for a fast servo response. The flow span is thrice the base-case steady state flow. All extractor organic/aqueous inventory controllers are P only and use a high gain of 10. A high gain is used for tighter aqueous-organic inventory regulation on the extractor, the bottleneck. The reflux drum, bottoms sump and holding tank level controllers are also P only and use a lower gain of 2 for effective smoothening of flow transients. In all cases, the level sensor span is twice the base-case level. The distillation column pressure controller is PI and tuned aggressively for tight pressure control. The column stripping section temperature controller is tuned to the Tyreus-Luyben settings with the ultimate gain and period obtained from the relay feedback 11 ACS Paragon Plus Environment

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test. With the temperature controller tuned, the bottom product composition controller is tuned by hit and trial for a slightly underdamped servo response. The controller tuning obtained as above, and used to generate the transient results discussed subsequently, are tabulated in Table 1.

Closed Loop Dynamic Results The closed loop dynamic performance of CS1-CS2 is evaluated using rigorous dynamic simulations. Specifically, we test the control systems for a ±10% throughput change as well as ±4 mol% feed composition changes around the base-case. We then evaluate the control structures for maximum throughput operation in the face of large feed composition changes.

Dynamic Operation at Base-Case Design One of the most important load disturbances that the control system must handle is a throughput change around the base-case design value. We evaluated CS1-CS2 for effecting a ±10% change in the fresh feed rate (throughput) via a step change in the TPM setpoint. Note that in CS2, since the TPM is the fresh feed rate itself, a ±10% throughput change directly corresponds to ±10% TPM setpoint change. In CS1, on the other hand, since the TPM is an internal flow stream inside the recycle loop, the change in the TPM setpoint necessary to effect a 10% throughput change is not known apriori. We obtained the necessary CS1 TPM setpoint change from the final steady state value at which the internal TPM stream rate settles for ±10% CS2 TPM change. The dynamic base-case throughput change responses for CS1-CS2 are shown in Figure 8. Both control systems effectively handle the load disturbance. Overall, the plantwide dynamic response is slow due to the large dynamic lag associated with the extractor. The plant flow transients settle in ~80 hrs while it takes ~140 hrs for the product quality (composition) transient to complete. The transients in both CS1 and CS2 are very smooth. The response also shows marginally tighter product quality control using CS2 compared to CS1. The maximum product purity deviation in both structures is comparably small and the product quality control is deemed acceptably tight. 12 ACS Paragon Plus Environment


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Another important load disturbance that the plantwide control system must effectively reject is a change in the fresh feed composition due to variability in the upstream reaction section. There are three independent directions in which the mol fraction of a ternary stream can change. We considered a ±4 mol% step change in the mol fraction of a particular component (EtOAc, EtOH or H2O) along with a complementary proportional change the other two component mol fractions. Both CS1 and CS2 effectively rejected all the six tested feed composition change disturbances. In Figure 9, we show the dynamic response of salient process variables to a step ±4 mol% feed ester composition change is shown. Other feed composition change responses are not shown for reasons of brevity. As seen from the dynamic responses, both CS1 and CS2 effectively reject the disturbance with a smooth plantwide response and acceptably tight product quality control. In CS2, the fresh feed rate remains constant while in CS1, where the TPM is inside the recycle loop, the fresh feed rate smoothly shifts to a new lower/higher value due to the action of extractor feed rate controller. As a consequence of the change in the fresh feed rate, the change in the ester product rate is lower than in CS2, where the feed rate is held constant. We also tested CS1-CS2 for larger feed composition changes, which may occur due to e.g. a severe upset in the upstream reaction section. CS1 was able to robustly reject large feed composition changes of up to 10 mol% (larger changes not tested). CS2, however was found to succumb to infeasibility due to water starvation for specific disturbance directions. The worst-case feed composition change direction, for which infeasibility occurs for the smallest magnitude composition change was found to be a decrease in the fresh feed water mol fraction. Figure 10 plots the dynamic response of CS1 and CS2 to a 10 mol% decrease in the fresh feed water composition. CS1 effectively rejects the disturbance by reducing the fresh feed rate appropriately and thus avoids infeasibility due to extractor water starvation with smooth plantwide transients. On the other hand, in CS2 the recycle rate and reboiler duty blow up along with a (delayed) sharp fall in the aqueous layer hold-up in the decanter feed stage indicating extractor water starvation. A significant amount of the fresh feed alcohol does not get extracted into the alcohol wash and keeps accumulating in the 13 ACS Paragon Plus Environment

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recycle loop. Even as the simulation can be made to run till the extractor feed stage decanter aqueous layer disappears, in practice the column is likely to flood much earlier due to the large increase in its boil-up. It is also possible that the two liquid phases in the extractor disappear due to e.g. a drastic reduction in the stage efficiency along with severe hydraulic problems. For large enough feed composition change in the worst-case direction, operating the process with CS2 can thus result in a very severe process upset. Operator intervention over of prolonged period is then needed to drive the alcohol that has accumulated in the recycle loop out of the process and transition back to normal operation. In contrast, CS1 is robust to very large feed composition changes with the process guaranteed to settle at a steady state.

Maximum Throughput Operation We now evaluate CS1-CS2 for maximum throughput operation. The simplest option of a constant TPM setpoint policy is explored. We choose an appropriate TPM setpoint value and let the process run at that setpoint regardless of disturbances. Note that in CS2, the TPM setpoint value beyond which the process operation goes infeasible is not known apriori. Further, even if the near maximum throughput TPM setpoint value is somehow obtained, it is likely to change due to disturbances. In particular, a change in the fresh feed composition alters the individual unit operation and overall plant material balances. The maximum achievable throughput therefore varies with the fresh feed composition. This composition is usually unmeasured and in severe upstream reaction section disturbance scenarios, exhibits significant variability. When the change is such that it pushes CS2 operation beyond the feasibility limit, a severe process upset would occur. To ensure the infeasibility limit is never hit for the expected worst-case composition change, the CS2 TPM setpoint needs to be lowered (backed-off) sufficiently. In contrast, CS1 is robust in that feasibility is guaranteed with the extractor feed rate controller appropriately changing the fresh feed rate. For a quantitative comparison of the maximum throughput achieved using CS1 and CS2 in the face of feed composition changes, we first obtained the nominal maximum throughput solution 14 ACS Paragon Plus Environment


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at the base-case feed composition. At this solution, the fresh feed rate is 147.3 kmol/h. The feed composition is then varied along the three independent feed composition change directions as a step change of increasing magnitude up to ±10 mol%. In CS1, the extractor feed rate (TPM) is simply maintained at the value corresponding to the nominal maximum and the simulation is allowed to settle at the new steady state corresponding to the altered feed composition. The fresh feed rate at this final steady state is the maximum throughput achieved using CS1. The obtained variation in the CS1 maximum thoughput with feed composition change is shown in Figure 11. The theoretical maximum achievable feed rate obtained by readjusting (optimizing) at the altered feed composition is also shown in the Figure. The results in Figure 11 show that the theoretical maximum feed rate varies monotonically with feed ester / water mol fraction. It decreases with feed ester mol fraction and increases with feed water mol fraction. On the other hand, the theoretical maximum feed rate increases as the feed alcohol mol fraction is varied around its base-case value. Further, the achieved maximum throughput in CS1 using the constant extractor feed rate (TPM) setpoint operating policy is nearly the same as the theoretical maximum. In fact the loss from the theoretical maximum is quite small for feed composition changes within ±6 mol% around the base-case. For example, for an ester mol fraction increase of 6 mol%, the achieved throughput at 134.7 kmol/h is only 0.05% below the maximum achievable throughput of 135.5 kmol/h. The throughput loss due to no reoptimization of the CS1 TPM setpoint is thus very marginal for moderate size feed composition changes. Holding the extractor feed rate at its nominal value may therefore be deemed as self-optimizing26 with respect to moderate changes in the feed composition, the principal disturbance into the process. The loss in throughput using the constant TPM setpoint policy in CS1 becomes noticeable only for larger feed composition changes approaching ±10 mol%. In such cases, it is appropriate to readjust the CS1 TPM setpoint, using e.g. extremum seeking control techniques, to drive the process operation close to the theoretical maximum throughput.


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In CS2, the TPM setpoint must be backed-off for the worst-case disturbance direction such that a severe upset due to process infeasibility is avoided. The magnitude of the back-off is expected to increase with the magnitude of the disturbance. Since the fresh feed composition is an unmeasured disturbance, the backed-off CS2 TPM setpoint will have to be implemented, regardless of whether the disturbance occurs or not. This guarantees avoiding steady state infeasibility should the worst case feed composition change disturbance (direction and magnitude) occur. We know that a fresh feed water mol fraction decrease is the worst case disturbance direction. As the feed water composition decreases, the theoretical maximum achievable throughput decreases (Figure 11). Consider a feed water composition decrease of a particular magnitude. If the CS2 fresh feed rate setpoint (TPM) is above the reduced theoretical maximum at this altered composition, a severe process upset due to overfeeding induced steady state infeasibility is guaranteed. If the fresh feed rate setpoint is set slightly below the theoretical maximum throughput at the decreased feed water composition, closure of the overall plant balances is feasible and the process may settle to a new steady state. Subsequent closed loop dynamic simulations confirmed that this indeed occurs. This implies the back-off necessary in the CS2 TPM for feed composition changes within ±Δx mol% around the base-case equals the decrease in the theoretical maximum throughput for a Δx mol% decrease in the fresh feed water mol fraction. In other words, the backed-off CS2 TPM setpoint equals the theoretical maximum achievable throughput for decreased fresh feed water mol fractions. This variation in the CS2 maximum throughput with disturbance magnitude is also shown in Figure 11. Notice that the backed-off CS2 maximum throughput curve is symmetric about the y-axis as the back-off must be implemented regardless of whether the expected worst case feed composition disturbance occurs or not. For the same reason, the backed-off CS2 maximum throughput curve is the same for a change in the fresh feed water / ester / alcohol mol fraction. The backed-off CS2 maximum throughput results in Figure 11 show significant loss in throughput from the theoretical maximum even for moderate size feed composition changes. For 16 ACS Paragon Plus Environment


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example, for a fresh feed water mol fraction increase of 6 mol%, the CS2 TPM setpoint needs to be backed-off from the base-case maximum of 147.3 kmol/h to 133.6 kmol/h. The theoretical maximum throughput at the altered feed composition is 164.6 kmol/h. If the altered fresh feed water mol fraction stays there for a prolonged duration, then the loss in throughput from the theoretical maximum is very significant at 18%. Even if the fresh feed composition returns to its nominal value, for a worst-case disturbance magnitude of 6 mol%, we must operate the plant at the backed-off CS2 TPM setpoint, which then represents a nominal throughput loss of ~10.0%, which again is large. In CS1 on the other hand, the achieved maximum throughput curve remains quite close to the theoretical maximum throughput for feed composition change magnitudes up to 6 mol%. For the 6 mol% fresh feed water mol fraction increase disturbance, if the altered feed composition stays there for a prolonged duration, the achieved maximum throughput is very close to the theoretical maximum implying negligible loss. Further, if the feed composition returns back to its nominal value, the loss in throughput from the nominal maximum is strictly zero since the extractor feed rate (CS1 TPM) setpoint is maintained constant at the nominal optimum value. Table 2 provides a quantitative comparison of the loss in maximum achievable throughput using CS1 and CS2 at the nominal feed composition and at altered feed compositions for a 6 mol% feed composition disturbance magnitude. The CS1 loss in throughput at nominal feed composition is consistently zero, as expected. The corresponding CS2 throughput loss is 9.8% due to the necessary CS2 fresh feed rate setpoint back-off that must be implemented to guarantee stable process operation. Further, the CS1 throughput loss from the theoretical maximum at the altered feed compositions is consistently below 1%, except for fresh feed alcohol mol fraction change of +6 mol%, where the loss is somewhat higher at 2.2%. The corresponding CS2 data shows that the loss can be very high up to 25% depending on the feed composition change direction. The quantitative results demonstrate the overwhelming superiority of CS1 over the conventional control structure, CS2.


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Discussion Overall, the dynamic results suggest that CS1 preferable over CS2, both from the perspective of robust process regulation as well as maximum throughput operation. The reason for the significantly superior performance of CS1 is the inherent self regulation in the overall plant balances due to the fresh feed being brought in as a make-up stream. Specifically, consider a large increase in the recycle rate due to snowballing. In order to hold the extractor feed rate constant, the extractor feed rate controller must proportionately reduce the fresh feed rate. A reduction in the fresh feed rate ensures that the fresh water rate, which is constrained at its maximum, remains high enough relative to the reduced fresh feed rate to guarantee feasibility of the overall material balances. In other words, the process fresh water to fresh feed ratio then remains above the minimum ratio below which infeasibility occurs. In CS2, on the other hand, since the fresh feed rate is independently specified, there is always the danger of overfeeding induced infeasibility. As a further appreciation of CS1 over CS2, consider the case where the process is operating at the base-case design conditions, away from the infeasibility limit. The management then asks the operators to deliver the maximum possible throughput, due to highly favourable market conditions with the product demand far exceeding the supply. In the case of CS2, the fresh feed (TPM) setpoint limit beyond which the process succumbs to a severe upset due to infeasibility is unknown. Further, the rise in recycle rate with throughput is quite sharp above a feed rate of 130 kmol/h (see Figure 6b). When coupled with flow sensor biases and variability in feed composition as well as extractor temperature, which causes the LLE envelope to shift, the operator would have to necessarily be very conservative in increasing the TPM setpoint, always making sure the process operates at a throughput that is well below the snowballing region. The fresh feed rate (TPM) would then be set significantly below the theoretical maximum achievable limit, implying a large loss in production. Now consider transitioning the process from base-case throughput to maximum throughput using CS1. The same operator would simply increase the extractor feed rate setpoint (TPM) and observe the fresh feed rate at which the process settles. A decrease in the fresh feed rate in 18 ACS Paragon Plus Environment


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response to an increase in the TPM setpoint would indicate that the setpoint has been moved beyond the maximum in the Figure 6a curve. The TPM setpoint can then be decreased appropriately to achieve (near) maximum throughput operation. The fact that CS1 guarantees stable operation for TPM setpoints over a large range above and below that corresponding to the maximum production, gives the operator the confidence to keep tweaking the TPM setpoint till the process settles at (near) maximum production (top of the hill in Figure 6b). Alternatively, an automatic hill-climber27 can be implemented to maintain the process operation at (near) maximum. The main point is that in contrast to the fragility of the conventional control system, CS1 guarantees stable operation over a very large TPM setpoint range. This allows the operator or an optimizer to experiment and drive the process operation to (near) the theoretical maximum in the face of large feed composition disturbances. Significantly higher economic benefit in terms of the achieved maximum throughput can thus be reaped using CS1, compared to the conventional control system. During the review process, it was pointed out that the overall flowsheet topology is very important for a meaningful plantwide control study because each recycle stream can create an additional propagation path for transients in the overall system. We also interacted with James J Downs from Eastman Chemical Company, Kingsport, Tennessee, and gathered that their reported ester purification process15,28 exists as a sub-section of a complete ester manufacturing facility. Thus, as discussed previously, there is an upstream reaction section and a downstream alcohol wash processing section. Typically, the alcohol wash stream is distilled to recover water down the bottoms. A part of the water bottoms is recycled to the extractor as solvent with the remaining being purged to close the overall plant water balance. A distillate stream, containing mostly alcohol with some water and ester, leaves up the top. This alcohol rich distillate is sent back to the reaction section. The expanded flowsheet as discussed above is shown in Figure 12. A pertinent question then is the usefulness of our analysis of the truncated flowsheet (blue envelope in Figure 12) studied here and also discussed by Downs and co-workers 15,28.


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Let us first consider the water recycle loop for the case of maximum throughput operation of the expanded flowsheet in Figure 12. The extractor water solvent rate is then constrained at a maximum limit with the extractor unable to take in any more water (capacity bottleneck due to extractor hydraulic constraints). For maximizing extraction capacity (bottleneck), the water solvent rate should be held at its maximum limit, as indicated in Figure 12. The truncated blue envelope process then gets operated at a fixed (maximum) water rate to the extractor. This is exactly what has been done here. The water purge provides a way out for the water in the fresh feed for feasible closure of the overall water balance. The purge rate is manipulated to regulate sump level of the water recovery column as shown in Figure 12 and thus close the plant overall water balance. The fixed water recycle rate prevents variability from propagating in the water recycle loop and the action of the sump level controller propagates water inventory transients out of loop. If a dynamic simulation of the Figure 12 process is done at fixed water recycle rate, then the only additional bit that one gets are the transients associated with the water recovery column. The extractor and first column transients remain exactly the same as reported for the truncated process. All plantwide control maximum throughput results for the studied truncated process and conclusions drawn based on those results thus remain equally valid for the Figure 12 process. Now consider the recycle of the alcohol rich distillate stream back to the upstream reaction section. For the recommended control system, CS1, on the ester purification process (water solvent rate is fixed at maximum), its feed is a make-up stream and cannot be independently set by e.g. an upstream level controller. The orientation of the upstream inventory controllers must then be in the reverse direction of process flow all the way up till the fresh reactant feed(s) to the reaction section. The TPM at the extractor feed (CS1), as indicated in Figure 12, thus forces the upstream inventory control system to be such that the fresh reactants are brought in as make-up streams. Flow and composition variability in the alcohol rich distillate recycle stream would then manifest as transients in the upstream fresh reactant rates as well as changes in the concentration of the feed to the ester purification process. The former would simply result in some variability in the level of the large 20 ACS Paragon Plus Environment


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reactant feed tanks, and is therefore not an issue. With respect to the latter, the robustness of the recommended control system (CS1) has already been demonstrated. So handling the alcohol recycle to the reaction section is not really a major issue, provided the control system is CS1. It seems to us that it is for the above reasons that Downs and co-workers deliberately limit their attention to the truncated process and exclude the downstream alcohol wash processing section in their reports15,28. This study too, through its exclusive focus on the bottleneck plant section (truncated process), remains relevant and useful, as the control system on the bottleneck determines the maximum production achieved for the entire ester manufacturing facility. A robust control system (CS1) on the bottleneck section ensures smooth operation of the entire facility with consequent economic benefits.

Conclusion We have evaluated plantwide control system design for an ester purification recycle process that exploits liquid-liquid extraction with water solvent for crossing a distillation boundary. The process exhibits multiplicity induced steady state infeasibility for too high throughput as well as for too low fresh water rates. The recycle flow exhibits high sensitivity to a throughput increase (water decrease) in the high throughput operating region (snowball effect). A conventional plantwide regulatory control system with the throughput manipulator at the fresh feed (CS2) is not recommended as it is susceptible to failure due to overfeeding/water starvation induced infeasibility. Instead, we recommend holding the total extractor feed rate (TPM) by manipulating the fresh feed rate so that the fresh feed is a make-up stream (CS1). Rigorous dynamic simulation of CS1 and CS2 show that both structures effectively handle nominal throughput and feed composition changes around the base-case design condition. For maximum throughput operation however, CS1 is way better than CS2 as it avoids overfeeding the process with the control system automatically reducing the fresh feed should the recycle rate snowball. This inherent self regulation in the process feed rate avoids the steady state infeasibility issue using CS1. Quantitative back-off results show that 21 ACS Paragon Plus Environment

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at constant TPM setpoint, CS1 achieves more than 25% higher maximum throughput compared to CS2 for specific feed composition change directions. The work highlights the crucial importance of plantwide regulatory control structure design for robust process operation.

Acknowledgments The financial support from the Department of Science and Technology, Government of India, is gratefully acknowledged.

Literature Cited 1. Morud, J.; Skogestad, S. Effects of Recycle on Dynamics and Control of Chemical Processing Plants. Computers Chem. Engng. 1994, 18(Suppl.), S529-S534. 2. Luyben, W. L. Design and Control of Gas-Phase Reactor/Recycle Processes with Reversible Exothermic Reactions. Ind. Eng. Chem. Res. 2000, 39, 1529-1538. 3. Larsson, T.; Govatsmark, M.S.; Skogestad, S.; Yu, C. C. Control Structure Selection for Reactor, Separator and Recycle Processes. Ind. Eng. Chem. Res. 2003, 42 (6), 1225-1234. 4. Skogestad, S. Control Structure Design for Complete Chemical Plants. Comput. Chem. Eng. 2004, 28(1–2), 219–234. 5. Murthy Konda, N.V.S.N.; Rangaiah, G.P.; Krishnaswamy, P.R. Plantwide Control of Industrial processes. Ind. Eng. Chem. Res. 2005, 44(22), 8300-8313. 6. Araujo, A.; Skogestad, S. Control Structure Design for the Ammonia Synthesis Process. Comput. Chem. Eng. 2008, 32 (12), 2920-2932. 7. Luyben, W. L. Design and Control of a Methanol Reactor/Column Process. Ind. Eng. Chem. Res. 2010, 49, 6150-6163. 8. Luyben, W. L. Design and Control of the Methoxy-Methyl-Heptane Process. Ind. Eng. Chem. Res. 2010, 49, 6164-6175. 9. Luyben, W. L. Design and Control of the Butyl Acetate Process. Ind. Eng. Chem. Res. 2011, 50 (3), 1247–1263. 10. Luyben, W. L. Design and Control of the Acetone Process via Dehydrogenation of 2-Propanol. Ind. Eng. Chem. Res. 2011, 50 (3), 1206–1218 11. Downs, J. J.; Vogel, E. F. A Plant-Wide Industrial Process Control Problem. Comput. Chem. Eng. 1993, 17, 245-255. 12. Luyben WL. Principles and case studies of simultaneous design. Hoboken NJ: John Wiley and Sons; 2011. 13. Luyben, M. L.; Tyreus, B. D.; Luyben, W. L. Plantwide Control Design Procedure. AIChE J. 1997, 43(12), 3161–3174. 14. Luyben, W. L. Snowball Effects in Reactor/Separator Processes with Recycle. Ind. Eng. Chem. Res. 1994, 33(2), 299–305. 22 ACS Paragon Plus Environment


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15. Downs, J. J.; Skogestad, S. An Industrial and Academic Perspective on Plantwide Control. Annual Reviews in Control. 2011, 35, 99–110. 16. Price, R. M.; Lyman, P. R.; Georgakis, C. Throughput manipulation in plantwide control structures. Ind. Eng. Chem. Res. 1994, 33(5), 1197– 1207. 17. Jagtap, R.; Kaistha, N. Throughput Manipulator Location Selection for Economic Plantwide Control. In: Rangaiah, G. P.; Kariwala, V. A, editors. Advances in Plantwide Control. Upper Saddle River, NJ: John Wiley and Sons, 2012. 18. Buckley, P. S. Techniques of Process Control. Upper Saddle River, NJ: Wiley, 1964. 19. Kanodia, R.; Kaistha, N. Plant-Wide Control for Throughput Maximization: A Case Study. Ind. Eng. Chem. Res. 2010, 49, 210-221. 20. 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(14), 8571–8584. 21. Gera, V.; Panahi, M.; Skogestad, S.; Kaistha, N. Economic Plantwide Control of the Cumene Process. Ind. Eng. Chem. Res. 2013, 52, 830−846. 22. Jagtap, R.; Pathak, A. S.; Kaistha, N. Economic Plantwide Control of the Ethyl Benzene Process. AIChE J. 2013, 59 (6), 1996-2014 23. Horvath, Milos.; Hartland, Stanley. Mixer-Settler-Extraction Column: Mass Transfer Efficiency and Entrainment. Ind. Eng. Chem. Proc. Des. Dev. 1985, 24, 1220-1225. 24. Percell, E. S.; Moore, C. F. Analysis of the Operation and Control of a Simple Plant-wide Module. Proceedings of American Control Conference. 1995, 1, 230-234. 25. Luyben M.L.; Floudas C.A. Analyzing the interaction of design and control-2: reactor-separatorrecycle system. Comput Chem Eng. 1994, 18, 971–994. 26. Skogestad, S. Plantwide Control: The Search for Self-Optimizing Control Structure. J. Proc. Cont. 2000, 10(5), 487– 507. 27. Kumar, V.; Kaistha, N. Hill Climbing for Plantwide Control to Economic Optimum. Ind. Eng. Chem. Res. 2014, 53 (42), 16465−16475. 28. Downs, J.J.; Caveness, M.H. influence of process variability propagation in plantwide control. Eds: Rangaiah G.P.; Kariwala, V. Plantwide Control: Recent Developments and Applications. Chichester, West Sussex: John Wiley and Sons, 2012.


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(a) TPM FC

UNIT 1

LC

UNIT 2

LC

UNIT 3

LC

UNIT 4

LC

(b) TPM LC

UNIT 1

LC

UNIT 2

UNIT 3

LC

LC

UNIT 4

FC

(c) TPM LC

UNIT 1

LC

UNIT 2

FC

UNIT 3

LC

UNIT 4

LC

Figure 1. Outwardly radiating inventory control orientation around TPM



QCnd

1 atm FH2O

170 kmol/h xwater = 1

463.9 KW

Stage1 Org Aq

FCol 2

L

D 16.15 kmol/h xester = 0.593 xalcohol = 0.014 xwater = 0.393

Stage2 Org Aq

12

Extractor

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Stage3 Org Aq

41.57 kmol/h xester = 0.836 xalcohol = 0.006 xwater = 0.158

RR: 2 Dia: 0.72 m 23

Stage4 Org Aq

QReb 539.4 KW

Stage5

FEster 25.42 kmol/h xester = 0.99 xwater = 0.01

Org Aq

Stage6 Org

35oC FTot QCool

Aq

4 KW

FAlcohol-Wash

FFeed 100 kmol/h xester = 0.35 xalcohol = 0.35 xwater = 0.30

243.5 kmol/h xester = 0.04 xalcohol = 0.141 xwater = 0.819 Figure 2. Liquid-liquid extraction based ester purification process


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(b)

(a)

I

II Fresh feed

III

Figure 3. Ethylacetate-EtOH-Water system phase equilibrium (a) Residue curve map (b) Liquid-liquid equilibrium and distillation regions

26



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(b)

(a)

Stage feed composition Alcohol wash

LLX Feed

S6 -Aq S5- Aq

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Fresh feed LLX feed EtOH-H2O recycle

Stage 6 Org Stage 5 Org Stage 4 Org

Column feed

Stage 1 Org

Water

Figure 4. Ester purification process material balances (a) Liquid-liquid extractor stage balances (b) Unit operation and overall balances

27


Product

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(a)

No steady state region

Snowballing Region

(b)

No steady state region

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Snowballing Region

Figure 5. Steady state variation in salient process variables (a) By changing fresh water rate (b) By changing fresh feed rate



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(a)

Infeasible setpoint

(b)

No setpoint Infeasiblity

Figure 6. Steady state relationship between extractor feed rate and fresh feed rate (a). Independent variable: Fresh feed rate (b). Independent variable: Extractor feed rate


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(b) CS2

(a) CS1 PC

max

PC

max FC LC

FC

X

FC

H2O

LC

FC

X

LC

H2O

LC

LC

LC LC

LC

LC

TPM

*

TC

LC

Product TPM

LC

FC

*

TC

Product

LC LC

FC

LC

Feed Feed

TC

Alcohol-wash

LC TC

Alcohol-wash

Figure 7. Basic regulatory control structures with alternative TPM locations * setpoint adjusted for product quality control

30


LC


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(a)

(b)

Figure 8. Transient response of salient PVs to ±10% throughput change around base-case (a). ±10% throughput for CS1 (b). ±10% throughput for CS2


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(a)

(b)

Figure 9. Transient response of salient PVs for ±4 mol% fresh feed ester composition change around base-case (a). ±4 mol% ester change for CS1 (b). ±4 mol% ester change for CS2



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(a)

(b)

Figure 10. Transient response to 10 mol% decrease in feed water composition (a). CS1 (b). CS2


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(a)

147.3 kmol/h

(b)

147.3 kmol/h

(c)

147.3 kmol/h

Figure 11. Variation in maximum throughput with feed composition change (a). Feed ester mol fraction change (b). Feed water mol fraction change (c). Feed alcohol mol fraction change



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L TPM

L

Ester Product

X FC

Feed (Ester-Alc-water)

Alcohol Wash

Alcohol rich stream recycled to rxr

Max FC

Water

LC

Water Purge

(LLE solvent)

Figure 12. Ester purification process with downstream alcohol wash processing


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Table 1: Salient controller parameters for ester purification process CV

KC

TSCol PCol

2.73 5 0.25

xB2H2O@

τimin 34.2 1 80

SP

PV Range&

MV Range&

73.11 oC 1 atm 0.01

40-160oC 2 atm 0.02

5 MW 5 MW 80-160oC

Sensor dead time / lag min 0/1 -/5/5

&: Minimum value is 0, unless specified otherwise @: Cascades column TC. xB2H2O- TSCol

Table 2. Maximum throughput achieved for fresh feed composition change disturbance Fresh feed composition change (mol%) EtOAc Water EtOH

+6% -6% +6% -6% +6% -6%

Theoretical maximum Achieved feed rate* maximum* feed rate 135.49 134.74 177.79 177.29 164.61 164.03 133.65 132.72 155.87 154.8 150.08 146.8

CS1 % loss# 0.55 0.28 0.34 0.69 0.68 2.18

CS2 % Achieved nominal maximum loss& feed rate* 0 132.72 0 132.72 0 132.72 0 132.72 0 132.72 0 132.72

% loss# 2 25 18 0.69 14.8 11.5

% nominal loss& 9.8 9.8 9.8 9.8 9.8 9.8

*: kmol/h #: Over theoretical maximum feed rate at altered feed composition &: Over nominal maximum feed rate (147.31 kmol/h) at nominal feed composition



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Figure for Table of Contents

Water Feed

L L X Feed


Ester Product Alcohol Wash

Plantwide Control for Maximum Throughput Operation of an Ester

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