Control System Design for Energy Efficient On-Target Product Purity

Article pubs.acs.org/IECR

Control System Design for Energy Efficient On-Target Product Purity Operation of a High-Purity Petlyuk Column Pallavi Kumari, Rahul Jagtap, and Nitin Kaistha* Department of Chemical Engineering, Indian Institute of Technology Kanpur, Kanpur 208016, India S Supporting Information *

ABSTRACT: Energy efficient, on-target product purity operation of a high-purity three product benzene−toluene−xylene ternary Petlyuk column is studied. The basic regulatory control system consists of four temperature inferential control loops with a fixed prefractionator vapor-to-fresh feed ratio. An economic control system on top of the regulatory layer adjusts these five set points. It consists of three product purity controllers that adjust three temperature set points along with a reboiler duty reduction controller that adjusts the remaining two free set points in the regulatory layer. The latter makes these adjustments to prevent the downward curvature in the prefractionator and main column middle section temperature profiles from being too large. Closed loop results for large feed composition changes show significant energy savings (up to 15%) are realized via temperature profile curvature control compared to constant set point column operation. The case study highlights the need for innovative control strategies for realizing the sustainability benefit of the integrated complex Petlyuk column during actual operation.

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INTRODUCTION In the process industry, distillation remains the most preferred and widely used unit operation for separating liquid mixtures into constituent pure (pseudo) components.1 The basic idea is to utilize the difference in the volatility of the mixture components to purify it by repeated flashing. This is accomplished via countercurrent vapor−liquid contact on the trays of a simple distillation column with the reboiler providing the vapor stream into the bottom and the condenser providing refluxed liquid to the top of the column. The process is then naturally energy intensive with the reboiler heat driving the separation so that distillation alone can contribute up to 53% of plant energy costs.2 Thus, innovations toward energy efficient distillation configurations for a given separation task have traditionally been of interest to the process industry. The volatility in energy prices in recent years has renewed interest in the synthesis, design, operation, and control of complex column configurations that can be significantly more energy efficient than a conventional light-out-first (direct sequence) or heavy-out-first (indirect sequence) train of simple distillation columns. In pioneering work, Petlyuk et al.3 suggested a complex configuration consisting of a prefractionator followed by a main column with a side draw for separating a ternary ideal mixture into its constituent pure components (Figure 1a). Compared to a conventional two-column direct or indirect sequence, the prefractionator in the Petlyuk configuration mitigates remixing of the middle boiler, which distributes itself between the prefractionator top and bottom products. This reduces the inherent process irreversibility, leading to potentially significant energy savings. Literature reports (see e.g. Triantafyllou and Smith4) indicate impressive energy savings up to 40% for a Petlyuk configuration over a conventional two-column sequence. A further innovation to the Petlyuk configuration is incorporation of the prefractionator within the body of the main column by inserting an appropriately positioned vertical wall, as in Figure 1b. This is appropriately referred to as the divided wall © XXXX American Chemical Society

column (DWC). It is conceptually similar to the Petlyuk configuration with the additional benefit of reduced capital cost. Literature reports suggest that BASF has several (60−70) operating DWCs for improved energy efficiency.5 Since Petlyuk’s original groundbreaking article, researchers have used its basic idea to develop other energy efficient complex column configurations.6−9 The seminal work by Agarwal and coworkers10−12 provides a generalized systematic methodology on synthesis of energy efficient complex column configurations for multicomponent mixtures. The literature on complex distillation configurations suggests a mature understanding of issues in their synthesis and design. Even so, the practical realization of significant energy savings from such a configuration during actual process operation requires a control strategy that ensures near minimum boil-up operation regardless of disturbances, particularly in the feed composition. However, the available literature on minimum energy and optimal operation and control of complex columns is quite limited. Most reported studies consider the operation of a ternary Petlyuk column with a relatively impure side-product (see e.g. Kaibel et al.13). In possibly the earliest work on operation and control of a high-purity ternary Petlyuk column, Wolff and Skogestad14 performed a steady-state bifurcation analysis to suggest that only three product compositions should be controlled and the remaining two degrees of freedom adjusted to minimize energy consumption. To keep the column operation near-optimal, Halvorsen and Skogestad15 suggested holding appropriate feedback variables based on steady-state analysis. In both these articles, no closed loop dynamic results were presented so that the recommendations remain dynamically untested. Received: May 26, 2014 Revised: September 11, 2014 Accepted: September 17, 2014

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dx.doi.org/10.1021/ie5021409 | Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

Industrial & Engineering Chemistry Research

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Figure 1. Ternary Petlyuk column configuration: (a) conventional configuration and (b) dividing wall configuration.

on-target product purity operation is crucial in today’s fiercely competitive markets. In particular, minimum product quality guarantees to the customer dictate the value-added product premium that can be charged to the customer. This premium determines the overall profitability of the process. We also note that the focus of this paper is on control strategy design for optimal operation of an existing column and not on optimum column design. In the following, the BTX Petlyuk column design with basecase operating conditions is first described followed by a systematic synthesis of the regulatory control system for closing the total material, component, and energy balances. We then develop the economic control system consisting of the product quality control loops and temperature profile straightening loops that adjust free regulatory layer set points for reboiler duty reduction. Closed loop dynamic results are then presented to quantify the reboiler duty reduction benefit compared to constant set point process operation. After a brief discussion of the results, the article ends with the conclusions that can be drawn.

In possibly the first article on high-purity Petlyuk DWC control with closed loop dynamic results, Ling and Luyben16 developed a control structure for a benzene−toluene−xylene (BTX) column, where the principal impurity in the three product streams is controlled along with the xylene spillover from the prefractionator top. The work is further extended to temperature inferential control of the BTX DWC,17 where controlling the difference between appropriately chosen tray locations in the prefractionator top, main column rectification section, middle section, and stripping section is shown to provide near minimum energy column operation. However, a closer examination of the closed loop results in both papers shows that the side-draw product (toluene) purity shows noticeable deviations from its 99% purity target. In a very recent paper, Dwivedi et al.18 comprehensively evaluate four decentralized control structures with appropriate composition controllers for (near) optimal operation of a ternary Petlyuk column and show that overrides are needed to mitigate excessive light component leakage down the prefractionator bottom for very large feed composition changes. In their work, too, the side-draw product purity deviates from its target value as the feed composition changes. All of the high product purity ternary Petlyuk column control studies in the literature thus allow the side-draw product purity to float away from its target value while pursuing minimum energy operation. Therefore, the moot question is how to control a highpurity Petlyuk column for near optimal (minimum energy) operation with on-target purity of all three product streams. To the best of our knowledge, this has not been studied in the extant literature. The purpose of this article is to demonstrate the challenges in the systematic development of a control strategy capable of effectively handling large disturbances while maintaining the purities of all three product streams at their specified targets with reduced reboiler duty operation for a high-purity BTX Petlyuk column design. We highlight that

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PETLYUK COLUMN DESIGN The industrially significant ternary separation of benzene, toluene, and p-xylene (BTX) in a Petlyuk column is studied here. Hysys with the SRK property package is used for steadystate and dynamic modeling. We want to design a ternary Petlyuk column, which contains 6 tray sections (TS1−TS6) as in Figure 1, to process 100 kmol/h of equimolar BTX feed into 99 mol % pure constituents. The BTX normal boiling points are, in order, 79.8, 109.8, and 137.8 °C, respectively. A condenser pressure of 100 kPa is then considered appropriate, giving a condenser temperature of ∼80 °C (nearly pure benzene distillate) for a water-cooled condenser. At atmospheric pressure, the BTX relative volatility in order, is about 5.16:2.21:1, implying that the separation is not a difficult B



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Figure 2. Petlyuk column design and optimized operating conditions.

To fix the number of trays in each of the tray sections, we note that a divided wall arrangement requires the number of prefractionator trays to equal the number of middle section (TS4 and TS5) trays in the main column. Because the prefractionator split is much easier (benzene−xylene split with large relative volatility of ∼5) compared to the middle section splits for TS4 and TS5 (relative volatility 2.2−2.7), it follows that TS4 and TS5 together set the prefractionator height. We then need to obtain only the number of trays in the main column tray sections (TS3−TS6). These are set to twice the Fenske minimum trays necessary for achieving a principal impurity leakage of 1 mol % for the particular tray section, which corresponds to a separation factor of ∼500. This gives 11, 12, 12, and 11 trays for TS3, TS4, TS5, and TS6, respectively. The prefractionator then has 24 trays. The feed to the prefractionator is chosen to be on 14th tray, as altering its location up or down tends to increase the reboiler duty (QR). The next step is to adjust any unconstrained steady-state degree of freedom (dof) to minimize the reboiler duty. For a condenser pressure of 100 kPa, a pressure drop of 0.44 kPa per tray gives a bottom pressure of 120 kPa (Figure 2). For the given feed and column pressure profile, the column steady-state operating dof is 5. The specification variables, toluene impurity in distillate (xD,T), toluene purity of sidestream (xS,T), toluene impurity in bottom (xB,T), xylene impurity in sidestream (xS,X), and vapor side draw to prefractionator (VP) are used to exhaust the five degrees of freedom and robustly converge the column. Of these five specifications, three get used up for fixing the three product purities at 99 mol % each. This is most easily accomplished by setting xD,T = 1 mol %, xS,T = 99 mol %, and xB,T = 1 mol %. The remaining 2 specifications (xS,X and VP) are then manually adjusted to obtain the minimum boil-up operating

one. The design degrees of freedom for the Petlyuk column for a given pressure is 11. These correspond to the number of trays in the six tray sections (TS1−TS6) and the five steady-state operation degrees of freedom. The economic optimum design problem is a complex mixed integer nonlinear programming problem and has been well-studied in the literature.19,20 While solving the problem has its own relevance, operating columns are almost always reasonable but not strictly optimal designs. This is because economic prices change over a period so that an initial optimum design does not remain optimum any longer. In addition, in many cases, existing distillation equipment is salvaged and retrofitted for a different separation application. Suboptimal but reasonable designs are thus the norm and not the exception in practice. Accordingly, we use a sequential design procedure to obtain a reasonable but not strictly optimum design and then develop a novel control strategy for reduced reboiler duty operation for large disturbances. The sequential design procedure applies well-known heuristics to fix the number of trays in the six column sections, as in Figure 1. This is followed by optimization of the unconstrained steady-state operating degrees of freedom to minimize the reboiler duty. In the prefractionator, TS1 prevents p-xylene from leaking up the top in its vapor product (VM). Similarly, TS2 prevents benzene from leaking down the bottom in its liquid product (LM). In the main column, TS4 prevents the benzene in the prefractionator top product from moving down and contaminating the side-draw toluene product (S). Similarly, TS5 prevents the xylene from the prefractionator bottom product from moving up and contaminating the side-draw. TS3 prevents toluene leakage up the top in the benzene distillate product (D), and TS6 prevents toluene leakage down the bottom xylene product (B). C



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Figure 3. QR variation with VP for different values of xS,X.

condition. This “brute-force” minimization of QR is shown in Figure 3, which plots its variation with VP for different values of xS,X. A minimum reboiler duty of 1619 kW is thus obtained for xS,X = 0.0092 and VP = 111 kmol/h. The column temperature and composition profiles at this base-case are shown in Figure 4. The design constitutes a reasonable near-optimum design but not a strictly optimum design. Note that any xylene (heavy component) that spills over from the prefractionator top necessarily moves down the main column and hence contaminates the side-draw. Similarly, any benzene (light component) that spills over from the prefractionator bottom necessarily moves up the main column and hence contaminates the toluene side product. Of these two spillovers, as insightfully pointed out by Ling and Luyben,16 heavy xylene would prefer the liquid phase while light benzene would prefer the vapor phase. Because the toluene product stream is a liquid side draw, the impurity distribution in the toluene side draw is then naturally predominantly xylene (0.92%) with some benzene (0.08%).

which it eventually settles. These set points may further be adjusted to drive the process to an economically favorable steady state. The much slower economic or supervisory layer on top of the regulatory layer performs this adjustment. Regulatory Control Structure. In the Petlyuk column, the regulatory control objectives include controlling the reflux drum and main column sump levels (first and second objectives) to balance the respective total liquid inventories. It is assumed that as in a dividing wall column, the liquid from the prefractionator drains under gravity to the main column so that there is no control valve on LM. Also, the column pressure must be controlled to balance the process total vapor inventory (thrid objective). Further, on the prefractionator, the xylene and benzene leakage up the top and down the bottom, respectively, must be regulated (fourth and fifth objectives). Similarly, on the main column, the toluene impurity in the distillate and the bottoms must be regulated (sixth and seventh objectives). Finally, the side-product toluene purity must be regulated (eighth objective). These last five regulatory objectives (fourth to eighth) correspond to closing the independent component inventory balances on the prefractionator and the main column. Instead of measuring composition, which is typically expensive, slow, and unreliable, we prefer to use temperature-based measurements to infer the particular component inventory. Of the eight regulatory objectives, total liquid and vapor inventory regulation is more important, as large drifts in the total inventory levels would necessarily lead to safety issues such as an overflowing or dried-up surge drum or a ruptured disc due to high-pressure differential, etc. Also, total inventory regulation indirectly regulates the component inventories. We therefore pair loops for total inventory regulation first, followed by loops for component inventory regulation. To close the liquid and vapor inventory balances (first three objectives), conventional “local” pairings are used. Thus, the

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CONTROL STRUCTURE DESIGN The Petlyuk column has eight control degrees of freedom (independent control valves), discounting the feed valve, which is set by an upstream process or, equivalently, sets the processing rate/throughput (see Figure 5). These eight control valves must be used to effectively close the independent overall component, material, and energy balances so that all accumulation (total material, component, or energy) terms are quickly driven to zero. This constitutes the basic regulatory control system in which typically fast, cheap, and reliable process variables such as flows, levels, pressures, and temperatures are controlled using dynamically fast pairings for effective closure of the material and energy balances. The regulatory loop set points determine the process inventory levels and the corresponding steady state at D



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Figure 4. Petlyuk column base-case profiles: (a) temperature profile and (b) composition profile.

top xylene spillover indirectly regulates the bottom benzene spillover. This may be inferred from the steady-state simulation data in Supporting Information, which show that even for large changes in the feed composition (feed rate remains fixed at basecase value), the prefractionator bottom benzene composition change is small with xD,T, xS,T, xB,T, VP, and xS,X chosen as the five convenient column specifications and fixed at their respective base-case values. Thus, at a fixed feed rate, maintaining xS,X constant at constant VP provides tight self-regulation of the benzene spillover down the bottom. Accordingly, we hold VP in ratio with the fresh feed rate (F), the ratio being necessary for handling large throughput changes. Maintaining a sensitive enriching section tray temperature and VP/F thus closes the two independent component balances on the prefractionator. On the main column, the three independent component balances to be regulated correspond to toluene leakage in the

reflux drum level is regulated by manipulating the distillate (D), the main column sump level by manipulating the bottoms (B), and the condenser pressure by manipulating the condenser duty (QC). With the total liquid and vapor balance controllers in place, we focus attention on component inventory regulation. On the prefractionator, we have two independent component balances. Of these, regulating the xylene spillover up the top is critical as this sets the principal impurity level in the liquid side-draw product (xS,X). Accordingly, a sensitive prefractionator enriching tray temperature is controlled for tight regulation of the same. On the other hand, loose regulation of the benzene spillover down the bottom may be acceptable as benzene prefers the vapor phase and is therefore the minor impurity in the side-draw. Given that the prefractionator is highly overdesigned in terms of the number of trays for the easy benzene−xylene split, regulating the E



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Figure 5. Petlyuk column regulatory control structure.

It is useful to understand why the tray temperature location dramatically affects column stabilization at increased throughputs. Consider a large feed rate increase of 20%, for which TM33 control fails while TM16 control works well. We take the workable control system with TM16 being controlled and the column settled at its increased throughput steady state. We then perform a series of dynamic simulations changing the set point TM16SP around its base-case value. Figure 7 plots the variation in the final steady-state value of TM33 with respect to TM16SP for different throughputs. The TM33 value at the base case throughput, which would be the TM33SP were we to control TM33 using the side draw, is also shown in Figure 7. At 20% higher throughput, clearly TM33SP is an infeasible set point. If TM33 is controlled, the control system ends up seeking an infeasible set point and fails. Trying to control TS1 (tray section above prefractionator feed) temperature and TS5 (tray section below side draw) temperature, as dictated by temperature sensitivity analysis, is prone to temperature set point infeasibility. This is because the prefractionator and main column middle section temperatures are highly correlated. Thus, controlling prefractionator top and middle section bottom temperature forces the temperature profiles across both the prefractionator and the middle section toward little or no movement (relatively stationary). Because the pressure profile across the column changes with internal flows (throughput) for a pressure-driven dynamic simulation, the temperature profile in the prefractionator and middle section must be allowed to float appropriately. Controlling TS1 and TS5

distillate and the bottoms and maintaining the side-draw toluene purity. To accomplish the same, sensitive tray temperatures in the enriching, middle, and stripping sections are controlled by adjusting the reflux rate (R), side-draw rate (S), and reboiler duty (QR), respectively. The basic regulatory control structure discussed above is schematically depicted in Figure 5 and is labeled CSR for convenient reference. To obtain the sensitive control tray temperature locations, sensitivity analysis with respect to the four manipulated variables, namely, LP, R, S, and QR, is performed. Figure 6 plots the temperature sensitivities. From the plot, prefractionator tray 7 (TP7), main column rectification section tray 7 (TM7), middle section tray 33 (TM33), and stripping section tray 40 (TM40) are candidate control tray locations. However, subsequent dynamic simulations exhibited extreme difficulty in getting the column to settle at a higher throughput steady state with these four tray temperatures being controlled. To stabilize the column effectively, we choose to control an alternative tray temperature, TM16, above the side draw. Note from the base-case temperature profile (Figure 4) that TM16 is in the region where the temperature profile is still sharp. It is then an appropriate location for sensing the movement of the separation zone due to accumulation or depletion of toluene in the column middle section and adjusting the side-draw rate for closing the toluene component balance. Subsequent dynamic simulations showed that this alternative tray temperature location results in effective stabilization for large throughput changes in both directions. F



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Figure 6. Petlyuk column tray temperature sensitivities.

Figure 7. Variation in the final steady-state value of TM33 with respect to TM16SP.

temperature tries to prevent floating, and temperature set point infeasibility results. On the other hand, if we control TS1 and TS4 (above side draw) tray temperatures, the temperature profile toward the lower portion of the prefractionator and middle section can float as needed, thus avoiding temperature set point infeasibility (or vice versa). It thus appears to us that

making temperature inferential control work on the Petlyuk column requires that prefractionator and middle section temperatures toward the same end, and not opposite ends, be controlled so that temperature set point infeasibility is avoided. An alternative is to control a differential temperature (difference of two tray temperatures) instead, as has been reported by other G



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Figure 8. Quality control system on top of regulatory structure.

Product Quality Control System. On-target product quality control requires that the impurity leakage in the product streams be tightly controlled. This is accomplished by cascade composition controllers that manipulate appropriate regulatory layer temperature set points, as shown in Figure 8. The distillate product composition controller adjusts TM7SP to maintain the toluene impurity at 1 mol %. The distillate contains no xylene so that the distillate purity then is 99 mol % benzene. Similarly, the bottoms product composition controller adjusts TM40SP to maintain its toluene impurity at 1 mol % for a 99 mol % pure xylene product. The side-draw stream contains xylene as the principal impurity (0.92 mol %) with some benzene impurity (0.08 mol %). For on-target 99% pure toluene side-draw, the most convenient option is to maintain both the xylene and benzene impurities in the side-draw at their base-case values. This is accomplished by a side-draw xylene impurity controller which adjusts TP7SP and a toluene purity controller which adjusts TM16SP. Note that adjusting TP7SP changes the prefractionator top xylene spillover, which achieves tight control of the principal xylene impurity in the side draw. When the xylene impurity is controlled tightly, controlling the side-draw toluene purity is equivalent to controlling its benzene impurity because xS,B = 1% − xS,X for xS,T = 99%. For convenience, we have chosen to control xS,T instead of xS,B because then the toluene purity controller set point, xS,TSP, remains constant at 99% regardless of the choice of the xylene impurity set point, xS,XSP. The decentralized quality control structure on top of the regulatory control system is shown in Figure 8 and is labeled

researchers (see ref 17, for example). In our case, because we are able to effectively stabilize the column for large disturbances using single-point temperature measurements, we do not explore differential temperature control and proceed to designing the economic control system. Control Structure for Economic Operation. The regulatory control structure CSR closes the material and energy balances and drives the process to a steady state. Of the eight regulatory layer set points, the liquid level set points have only a transient effect and do not affect the final steady state at which the process settles. We also assume the pressure controller set point is kept fixed at its design value to avoid pressure compensation of temperature set points. The remaining five set points, namely, VP/FSP, TP7SP, TM7SP, TM16SP and TM40SP, then determine the final steady state at which the process settles. It is desirable that this steady state be such that the process profitability is maximized. This requires appropriate adjustment of the regulatory set points by the economic control system. For the Petlyuk column, the first and foremost economic operation requirement is that the purity of the three products be on-target at 99 mol % each. These would consume three regulatory layer set points leaving two free set points that may be further adjusted to reduce or minimize the reboiler duty and hence the energy consumption per kilomole of feed processed. The economic control system thus consists of the product quality control system and the reboiler duty reduction control system. These are developed in the following sections. H



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CSCC for convenient reference. The set points xD,TSP, xB,TSP, xS,TSP, xS,XSP, and VP/FSP correspond to the five steady-state operating degrees of freedom. Of these, the first three set points are fixed for on-target product quality. The last two set points are then adjustable for reducing the reboiler duty (QR) toward enhanced process energy efficiency. We can operate the column using CSCC at fixed base-case optimum values for the two free set points, VP/FSP and xS,XSP. The control system should provide on-target quality control regardless of changes in the feed composition. However, because the two unconstrained set points are kept fixed postdisturbance and not reoptimized, QR is likely to be suboptimal, i.e., more than the minimum achievable reboiler duty (QRMIN) for the altered feed composition. To get a quantitative feel for the suboptimality in QR with fixed set point operation, Table 1 compares QRMIN

dynamic mode simulations were noticeably different. This is likely because in the steady-state mode, Hysys assumes a fixed column pressure profile regardless of column internal flows, whereas in dynamics mode, the local tray pressure drops vary with column internal flows. This variation in the column pressure profile can cause the temperature profile to be different between the two modes. Because we are interested in operating the column in dynamics mode, we compare the temperature profiles obtained in dynamics mode and use differences between the optimal profile and the profile for fixed set point operation to extract an appropriate temperature-based process variable for driving QR toward QRMIN. Figure 9 compares the final optimum steady-state temperature profiles of the prefractionator enriching section (TS1) and the main column middle section below side-draw (TS5) for the feed composition disturbances with the corresponding profile for fixed VP/F and xS,X (i.e., no reoptimization of free set points). The base-case optimum temperature profile is also shown for reference. All the optimum temperature profiles are relatively straight, and the QR suboptimality due to fixed VP/F and xS,X operation is most clearly visible in the large downward curvature of the temperature profiles. For the case of a benzene-rich feed, the TS5 temperature profile is curved significantly downward. For a benzene-lean feed on the other hand, the TS1 profile curves significantly downward. A careful evaluation of the temperature profiles also shows that at constant set point operation, a large downward curvature occurs in either TS1 or TS5 for a toluenerich or lean feed and a xylene-lean feed but not a xylene-rich feed. This then suggests that preventing downward curvature in the TS5/TS1 temperature profiles by adjusting the two free set points should help drive QR toward QRMIN for most of the feed composition changes, including the most severe disturbance of a benzene-rich feed. We now need a convenient metric for TS1/TS5 temperature profile downward curvature. The simplest method is to draw a straight line between two appropriate fixed tray locations and obtain the curvature as the deviation of the actual profile around this line. As shown in Figure 10, when the actual tray temperatures are all above/below the straight line, the curvature magnitude would be large. On the other hand, in the case when some of the actual temperatures are above and others below the straight line, cancellations would occur and the curvature magnitude would be small. More specifically, let TM and TN be the chosen lower and higher tray temperature locations, respectively. Then, the straight-line interpolated temperature of the ith tray above TM (i = 1 to N − M − 1) is

Table 1. Comparison of QR Using CSCC and QRMIN for Feed Composition Disturbances disturbance (mol %)

QR

QRMIN

QR − QRMIN

% suboptimality

B 39 B 27 T 39 T 27 X 39 X 27

1859 1740 1736 1758 1651 1798

1600 1690 1704 1576 1615 1664

259 50 32 182 36 134

16.19 2.95 1.88 11.55 2.23 8.05

with QR at fixed base case values of the two free setpoints for ∼6 mol % feed composition change in either direction for each component, with the other two components remaining equimolar. The table data suggests that the degree of QR suboptimality depends strongly on the direction of the feed composition disturbance. It is most severe when the benzene mole fraction in the feed increases from 33% to 39%, for which QR is a significant 16% more than QRMIN. Less severe suboptimality with QR being ∼12% more than QRMIN is observed for a toluene-lean feed. For a xylene-lean feed, QR is about 8% more than QRMIN. For the other composition disturbances, the QR increase over QRMIN is no more than 3%. This suggests that for particular feed composition disturbances, fixed set point operation can result in significant energy inefficiency. There then exists incentive to adjust the two unconstrained set points, xS,XSP and VP/FSP, to reduce QR toward QRMIN. Control System for Reboiler Duty Reduction. The conceptually simplest way of ensuring near minimum reboiler duty operation is to adjust VP/FSP and/or xS,X to control appropriate process variable(s) that remain invariant (or close to invariant) at the QRMIN solution. Luyben refers to such control structures as eigenstructures,21 while Skogestad refers to them as self-optimizing.15 However, what constitutes such a process variable is not straightforward. For the present case, we avoid process variables that require tray composition measurements and limit ourselves to appropriate combinations of tray temperatures. This is a reasonable assumption as today’s columns are quite well-instrumented with multiple tray temperatures across the entire column being available, whereas composition measurements remain cumbersome, expensive, unreliable, and delayed. To obtain the appropriate self-optimizing process variable(s), we compare the column final steady-state temperature profiles for the feed composition disturbances for (a) fixed VP/F and xS,X and (b) VP/F and xS,X adjusted to minimize QR. In our simulations, we found that the temperature profiles obtained in Hysys steady-state mode simulations and pressure-driven

ti = TM + i(TN − TM )/(N − M + 1)

The curvature (summed deviation) of the actual tray temperatures around this line then is N−M−1

∑

C=

(Ti − ti)

i=1

Because we want to make adjustments only when the profile moves significantly downward, i.e., the curvature becomes large negative, the process variable to be controlled, y, is defined as y=

C + α if C < −α 0

otherwise

The above definition ensures y is zero for positive or slightly negative (>−α) curvatures. When we control y with ySP = 0, I



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Figure 9. Variation in steady-state temperature profile with feed composition change for CSCC operation at constant set points (dashed lines) and reoptimized set points (solid lines).

In this example, yTS1 is defined as taking the tray immediately above the feed tray as the lower tray (TM) and the prefractionator top tray as the higher tray (TN). For the TS5 downward curvature, yTS5, TM is taken as tray 36 (middle section bottom tray) and TN is taken as tray 29 (five trays below side-draw). This choice of tray locations allows for easier temperature profile curvature-based distinction in the fresh feed composition. This is evident from Figure 11, which plots the curvatures, CTS1 and

control action gets taken only when y becomes large negative, i.e., the temperature profile curves significantly downward. The parameter α may be used as a controller tuning parameter for enhanced reboiler duty reduction while avoiding limit cycles because of the on−off switch inherent in the definition of y. We are interested in regulating the temperature profile downward curvature of the prefractionator enriching section (TS1), yTS1, and middle section below side-draw (TS5), yTS5. J



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yTS5. The straightforward decentralized pairing is to maintain yTS1 by manipulating VP/FSP and regulate yTS5 by adjusting xS,XSP. Because the xS,XSP controller is likely to be slow because of large lags associated with composition measurements, a dynamic improvement is to let the yTS5 controller bypass the xS,X controller and directly manipulate the prefractionator tray temperature controller set point, TP7SP. This completes the overall control system with the regulatory control loops, the quality control loops, and the reboiler duty reduction loops. The full control system for economic operation, CSEC, is shown in Figure 12.

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DYNAMIC SIMULATIONS AND CLOSED LOOP RESULTS To test the proposed control system, a rigorous dynamic simulation is built in Hysys, and closed loop results are obtained for principal disturbances, namely large changes in the fresh feed composition and a ±20% step change in the fresh feed rate (throughput). Feed composition changes are tested for each component (B, T, or X) changing as a step from 33 mol % (basecase) to 39 mol % or 27 mol % with the other two components remaining equimolar. Equipment Sizing and Plumbing. The equipment is sized using heuristics to fix hold-ups and hence the equipment dynamic time constants. The prefractionator and main-column inner diameter (ID) are chosen for a 0.6 m/s maximum vapor superficial velocity assuming 20% coverage by the tray downcomers. The condenser and reboiler are sized for ∼10 min liquid residence time at 50% level at the base-case conditions in Figure 2. For a pressure-driven simulation, the tray resistance to vapor flow is calculated at the base-case steady-state vapor flow−pressure profile. Appropriate plumbing (pumps and valves) is provided on the distillate, side-draw, and bottoms lines. Note that Hysys allows direct setting of the reflux rate and the vapor and liquid rate to the prefractionator so that no plumbing is configured on these lines. Controller Tuning. After appropriate sizing and plumbing modifications for a pressure-driven simulation, the regulatory and economic layer controllers are installed and tuned. A 2 min lag is applied in all temperature loops to account for sensor and heat-transfer dynamics. The composition measurements have a 5 min delay and are sampled every 5 min. The PI pressure controller uses a large gain and small time constant for tight column pressure control. The two level controllers are P with a gain of only 2. The feed flow controller is PI and tuned for a fast but nonoscillatory servo response. The four temperature controllers are PI and tuned sequentially using the Hysys autotuner with further refinement of the tuning for a slightly underdamped servo response. First, the prefractionator temperature loop (TP7−LP) is tuned (all other temperature loops on manual) followed by the main column loops in bottom-up sequence, i.e., TM40−QR, TM16−S, and TM7−R, in that order, with previously tuned loops on automatic. The composition controllers are PI and tuned individually by first setting the reset time to approximately the 2/3rd response completion time and the controller gain to the inverse of the process gain. These tuning parameters are then further refined for a slightly underdamped servo response. The two temperature profile downward curvature controllers (yTS1−VP/F and yTS5−xS,X) are PI and tuned by hit-and-trial for a fast and not-too-oscillatory regulatory response to the principal disturbances. The curvature offset, α, described previously, is chosen based on Figure 8 so that the y for the optimal conditions map to 0. To avoid a limit cycle due to the on−off nonlinearity in the definition of y, the α for yTS1

Figure 10. Quantifying curvature in a temperature profile.

Figure 11. TS1/TS5 curvatures for the different feed composition changes for fixed and reoptimized VP/F and xS,X.

CTS5, for the different feed composition changes with fixed or reoptimized VP/F and xS,X. The large negative curvatures in either CTS1 or CTS5 for fixed set point operation correlate to changes in the feed composition (except a xylene-rich feed). The absence of the large negative curvature in the corresponding optimum profiles implies that curvature may be used to infer suboptimality in QR and make appropriate adjustments in the available free set points to drive the operation toward optimality (QRMIN). The QR reduction control system then consists of manipulating the two free set points, VP/F and xS,X, to maintain yTS1 and K



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Figure 12. Petlyuk column control system for QR reduction.

middle-section split requiring the temperature profiles to shift, as in Figure 8, which is prevented by holding TP7 and TM16 constant. Quality deviations are also observed for throughput changes. This is attributable to variability in the column pressure profile at the altered internal flows so that the composition of the tray, whose temperature is controlled, is slightly different, implying a slightly altered split and hence product purity deviations. Because the column top pressure is controlled, the effect is naturally more pronounced toward the ends of the column, which show larger “local” tray pressure deviations. The product purity controllers in CSCC and CSEC should appropriately adjust the temperature set points for zero-offset in the product purities at the final steady state. The transient response of CSCC and CSEC to benzene, toluene, and xylene composition step changes in the fresh feed is shown in Figures 14, 15, and 16, respectively. The solid and dashed lines correspond to CSCC and CSEC responses, respectively, while the black and gray lines are for a composition increase and decrease, respectively. In all cases, the response completes in about 20 h with the final total impurity in each of the product streams settling at 1 mol % for on-target product purity of 99 mol % each. The QR responses show that the final steady-state QR using CSEC (dashed lines) is always less than CSCC, implying that the temperature profile curvature control helps improve the process

is relaxed a bit. The controller parameters of the salient loops used in this work are reported in Supporting Information. Closed Loops Results. Closed loop dynamic simulation results for the principal disturbances are now presented and discussed. To better appreciate the incremental improvement by the use of additional loops on top of the regulatory control system, results are presented for each of the three control structures CSR, CSCC, and CSEC. Figure 13 plots the transient response of salient process variables to the throughput and feed composition disturbances, obtained for the basic regulatory control system, CSR. The response curves suggest that the four-point temperature inferential control structure, CS R , robustly handles the throughput and feed composition changes in either direction with smooth changes in the manipulated process flow and the transient response is completed in about 6 h. Nonlinearity is evident in the response to feed composition changes with the total change in QR and LP, which set the column internal flows, exhibiting asymmetry. Table 2 reports the purity of the three product streams for the principal disturbances using CSR. Noticeable product purity deviations are evident for the feed composition change disturbances. This is expected because a change in the feed composition requires a readjustment in the prefractionator and L



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Figure 13. CSR transient response to (a) throughput disturbance and (b) feed composition disturbance.

controllers, cause the appropriate “shift” in the prefractionator and middle section temperature profiles for QR reduction. This is evident in the mostly large differences between the final steady-state TP7 and TM16 values for CSEC (dashed lines) and CSCC (solid lines). For a quantitative comparison of the energy savings resulting from using the temperature profile downward curvature controllers,

energy efficiency. The savings in QR are particularly significant for a benzene-rich (Figure 14, black dashed line) and a toluene-lean feed (Figure 15, gray dashed line) with marginal savings for the other feed composition changes. The transient responses also show that the curvature controllers, through their manipulation of VP/FSP and TP7SP and the consequent nested action of the product purity M



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which alters the prefractionator top xylene spillover and hence the side-draw purity. The deviation in the side-draw purity is detected by its purity controller, which would adjust TM16SP. It is then expected that the final steady state at which the column settles would have an altered impurity mix in the side-draw. Thus, for example, for the benzene-rich feed composition disturbance, at the final steady state with only yTS5 regulated, xS,X changes from 0.92 mol % to 0.88 mol % (xS,X + xS,B = 1 mol % for 99 mol % pure toluene side product). This readjustment of the product impurity distribution corresponds to QR reducing from 1859 kW to 1652 kW, which is quite close the QRMIN value of 1600 kW. Even as the absolute change in the benzene and toluene impurity mole fractions appears small, the relative change in the impurity distribution is quite substantial with the xS,B:xS,X ratio changing from 0.087 to 0.133. This then suggests that the side-product impurity distribution (which is constrained by the side-product purity target) is a key determinant of the reboiler energy consumption. Its proper adjustment with feed composition is then critical toward energy efficient operation, and any meaningful control strategy must necessarily address the same to realize the energy efficiency benefit of the complex column configuration, particularly when large changes in the feed composition are expected.

Table 2. Purity of the Three Product Streams for Principal Disturbances to CSR disturbance (mol %)

xD,B

xS,T

xB,X

B 27 B 39 T 27 T 39 X 27 X 39 F −20 F +20

0.9928 0.9859 0.9875 0.9916 0.9885 0.9912 0.9921 0.9885

0.9869 0.9758 0.9866 0.9863 0.9831 0.9936 0.9961 0.9739

0.9893 0.9910 0.9891 0.9909 0.9917 0.9882 0.9916 0.9879

Table 3 compares QR for CSCC, CSEC, and CSEC with the yTS1 (TS1 downward curvature) controller on manual (i.e., VP/FSP kept fixed at base-case value) and CSEC with yTS5 (TS5 downward curvature) controller on manual (i.e., xS,XSP is kept fixed at base-case value with xS,X controller manipulating TP7SP). The quantitative data shows that the two curvature controllers together help significantly reduce QR toward QRMIN for the benzene-rich and toluene-lean feed composition disturbances with marginal improvement for the other feed composition disturbances. The results also suggest that a substantial fraction of the QR reduction benefit can be attained from only the yTS5 controller with the yTS1 controller achieving only marginal improvements in QR. For the system studied, downward curvature in the temperature profile of the middle tray section below side-draw product (TS5) thus appears to have a more significant impact on QR reduction. To explain the results, consider regulating only yTS5 by directly adjusting TP7SP while holding VP/FSP constant. A large negative yTS5 indicates substantial suboptimality in QR. To bring yTS5 back toward zero, the direct acting yTS5 controller would reduce TP7SP,

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DISCUSSION On the basis of the results presented, some comments on the operability of a ternary Petlyuk column vis-à-vis a conventional direct or indirect sequence are in order. The basic argument in favor of a Petlyuk column is that an optimized design for a given throughput and feed composition is significantly more energy efficient and less capital intensive than an optimized direct or

Figure 14. CSCC and CSEC transient response to benzene composition disturbance. N



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Figure 15. CSCC and CSEC transient response to toluene composition disturbance.

Figure 16. CSCC and CSEC transient response to xylene composition disturbance. O



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Table 3. Comparison of QR for Different Operating Strategies CSCC

CSEC

CSEC: yTS1 manual

CSEC: yTS5 manual

disturbance (mol %)

QR

% sub optimality

QR

% sub optimality

QR

% sub optimality

QR

% sub optimality

B 39 B 27 T 39 T 27 X 39 X 27

1859 1740 1736 1758 1651 1798

16.2 3.0 1.9 11.5 2.2 8.1

1652 1690 1712 1608 1650 1735

3.3 0.0 0.5 2.0 2.2 4.3

1652 1740 1736 1608 1650 1735

3.3 3.0 1.9 2.0 2.2 4.3

1863 1690 1714 1760 1650 1800

16.4 0.0 0.6 11.7 2.2 8.2

control performance degradation. We also highlight that differential temperature measurements would also mitigate inadvertent changes in the tray section splits due to variability in the column pressure profile.

indirect sequence. However, the energy efficiency of the optimized high-purity Petlyuk column design deteriorates significantly (up to 16% for the example case study) unless the two free set points (unconstrained degrees of freedom) are readjusted to appropriately rebalance the prefractionator and middle section splits toward minimum energy consumption. This rebalancing in an automated feedback arrangement is, however, not a straightforward task. For the commonly applied constant set point operating policy in the industry (CSCC for the studied example), the Petlyuk column energy efficiency may then deteriorate significantly because of large feed composition changes. Because the split rebalancing readjusts the impurity distribution in the side draw, the deterioration in energy efficiency may be mitigated if small deviations in the side-draw product purity from its target are allowed, i.e., the side-draw product purity is allowed to float. From the operational standpoint, it then stands to reason that a high-purity Petlyuk column would be preferable over a conventional distillation train when (a) large changes in the feed composition are not expected or (b) relatively “loose” side-draw product purity control is acceptable. Alternatively, the Petlyuk configuration may also be preferred when the side-draw product purity target is not too stringent (e.g., 90 mol % pure instead of 99 mol %). We note that the current study has considered a conventional Petlyuk column where the liquid and vapor flow rate to the prefractionator is directly adjustable. In the DWC arrangement, however, typically only the liquid split ratio (and not flow rate) is adjustable with the vapor split ratio not being adjustable because it is fixed by the dividing wall partitioning of the column crosssectional flow area. Control system design for optimal operation with on-target product purity control of a DWC must then account for the loss in a control dof. In particular, the feasibility of the desired product impurity targets becomes an issue, which is also referred to as the black-hole problem.22 We are currently researching control strategies for on-target product purity control with reboiler duty reduction for the ternary Petlyuk DWC arrangement and hope to report the findings shortly. Lastly, we highlight the fact that the prefractionator and middle section temperature profiles shift quite a bit for handling the feed-composition disturbances (see Figure 8, for example). If the product composition measurements are very infrequent (e.g., once per shift or day), the composition-based updates in the temperature set points would be very infrequent. The column would then, in-effect, operate at constant temperature set points for prolonged durations (until the next update). Holding a prefractionator or middle section tray temperature constant necessarily prevents the respective profiles from shifting. This would significantly degrade product purity and reboiler duty reduction control. In such situations, we recommend the use of differential temperature difference in temperature of two trays in a section17 or double differential temperature,23 instead of absolute temperature, to infer the tray section splits to mitigate the economic

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CONCLUSION This work has systematically developed and evaluated the performance of a control system for energy efficient on-target product purity operation of a high-purity BTX Petlyuk column. Results show that maintaining the four principal impurities (toluene in distillate and bottoms; xylene and benzene in side draw) in the product streams at constant prefractionator vapor to feed ratio (as in CSCC) results in significant energy inefficiency. For feed composition changes, the reboiler duty is noticeably higher than the minimum duty possible with on-target product purities. The suboptimality is particularly severe (∼16%) for a benzene-rich feed. It is shown that large downward curvature in the temperature profile of the prefractionator enriching section and the middle section below the side draw can be used to infer the suboptimality. Preventing large downward curvature in these profiles by manipulating the vapor to the prefractionator and the prefractionator control tray temperature set point, as in CSEC, significantly mitigates the suboptimality. The worst-case reboiler energy consumption penalty is then only 4.26% more than the minimum possible. The work highlights the need for innovative control solutions for realizing the energy-efficiency benefit of the ternary Petlyuk column for large disturbances.

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ASSOCIATED CONTENT

S Supporting Information *

Variation in prefractionator bottom benzene spillover for feed composition disturbances with xD,T, xS,T, xB,T, VP, and xS,T constant and salient controller parameters including tuning. This material is available free of charge via the Internet at http:// pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: +91-512-2597513. Fax: +91-512-2590104. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Financial support from the Ministry of Human Resource and Development, Government of India, is gratefully acknowledged. The support from Mr. Vivek Kumar in revising the manuscript is also gratefully acknowledged. P



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(14) Wolff, E. A.; Skogestad, S. Operation of Integrated Three-Product (Petlyuk) Distillation Columns. Ind. Eng. Chem. Res. 1995, 34, 2094− 2103. (15) Halvorsen, I. J.; Skogestad, S. Optimal Operation of Petlyuk Distillation: Steady-State Behaviour. J. Process Control 1999, 9, 407−424. (16) Luyben, W. L.; Ling, H. New Control Structure for Divided-Wall Columns. Ind. Eng. Chem. Res. 2009, 48, 6034−6049. (17) Luyben, W. L.; Ling, H. Temperature Control of the BTX Divided-Wall Column. Ind. Eng. Chem. Res. 2010, 49, 189−203. (18) Dwivedi, D.; Strandberg, J. P.; Halvorsen, I. J.; Skogestad, S. Steady State and Dynamic Operation of Four-Product Dividing-Wall (Kaibel) Columns: Experimental Verification. Ind. Eng. Chem. Res. 2012, 51 (48), 15696−15709. (19) Caballero, J. A.; Grossmann, I. E. Optimal Synthesis of Thermally Coupled Distillation Sequences Using a Novel MILP Approach. Comput. Chem. Eng. 2014, 61, 118−135. (20) Antonio, C. G.; Ramirez, A. B.; Gutierrez, A. J. Optimization of Petlyuk Sequences using a Multi Objective Genetic Algorithm with Constraints. Comput. Chem. Eng. 2011, 35, 236−244. (21) Luyben, W. L. The Concept of Eigenstructure in Process Control. Ind. Eng. Chem. Res. 1988, 27 (1), 206−208. (22) Wang, Y.; Huang, K.; Luan, S.; Chen, W.; Wang, S.; Wong, D. S. H. Circumventing the Black-Hole Problem in Design and Control of Dividing-Wall Distillation Columns. Ind. Eng. Chem. Res. 2012, 51, 14771−14792. (23) Luyben, W. L. Feedback Control of Distillation Columns by Double Differential Temperature Control. Ind. Eng. Chem. Fundam. 1969, 8 (4), 739−744.

NOMENCLATURE CTSi = Temperature profile curvature of tray section i; i = 1 to 6 (°C) F = Feed rate (kmol/h) LM = Liquid rate to main column (from prefractionator) LP = Liquid rate to prefractionator (from main column) QR = Reboiler duty R = Reflux rate (kmol/h) S = Side-draw rate (kmol/h) TMk = Temperature of kth tray in main column (top down numbering) TPk = Temperature of kth tray in prefractionator (top down numbering) VM = Vapor rate to main column (from prefractionator) (kmol/h) VP = Vapor rate to prefractionator (from main column) (kmol/h) xD,i = Mole fraction of component i in distillate; i = B, T, X xS,i = Mole fraction of component i in side draw; i = B, T, X yTSi = Downward curvature of temperature profile in tray section i; i = 1 to 6

Superscripts

MIN = Minimum SP = Set point

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REFERENCES

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Control System Design for Energy Efficient On-Target Product Purity

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