Proportional-Integral Control and Model Predictive Control of

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Proportional-Integral Control and Model Predictive Control of Extractive Dividing-Wall Column Based on Temperature Differences Zemin Feng, Weifeng Shen, Gade Pandu Rangaiah, and Lichun Dong Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.8b02729 • Publication Date (Web): 13 Jul 2018 Downloaded from http://pubs.acs.org on July 20, 2018

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Industrial & Engineering Chemistry Research

Proportional-Integral Control and Model Predictive Control of Extractive Dividing-Wall Column Based on Temperature Differences Zemin Feng,a,b Weifeng Shen,a G.P. Rangaiah,b,* Lichun Donga,c,* a

School of Chemistry and Chemical Engineering, Chongqing University, Chongqing 400044, PR China

b

Department of Chemical and Biomolecular Engineering, National University of Singapore, Singapore

117585 c

Key Laboratory of Low-grade Energy Utilization Technologies & Systems of the Ministry of Education,

Chongqing University, Chongqing, 400044, PR China

* Corresponding authors: G.P. Rangaiah, Email: [email protected] Lichun Dong, Email: [email protected]

Abstract: Extractive dividing-wall column (EDWC) was proved to be a promising energy-saving technique for the separation of multiple azeotropes or closing-boiling mixtures; however, its controllability is very challenging due to its intensified structure with smaller physical space and strong interactions. While most studies on the EDWC control focused on evaluating the performance of temperature or composition control using proportional-integral (PI) control, nevertheless, significant steady-state offsets and overshoots are present in the control of two product purities of EDWC under different disturbances. In this paper, the performance of single temperature control (TC), temperature difference control (TDC) and double temperature control (DTDC) schemes for PI control of EDWC was firstly examined. The results show that the steady-state offsets in product purities of TDC scheme are much smaller than those of TC and DTDC schemes. Subsequently, the offset-free model predictive control (MPC) based on temperature differences was proposed to improve the operation of EDWC. The results indicate that this MPC scheme can achieve much better control performance than PI control in terms of maximum transient deviation, amplitude of oscillations and setting time. Keywords: Extractive distillation; Extractive dividing-wall column; Temperature difference control; Proportional-integral control; Offset-free model predictive control

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1 INTRODUCTION Extractive distillation (ED) is the predominant technology for the separation of liquid mixtures with azeotrope and/or low relative volatility in the chemical and pharmaceutical industries, which cannot be realized by the conventional distillation.1,2 An additional entrainer (also known as solvent) is added to alter the relative volatility of liquid mixtures in ED, and two pure components can then be obtained at the top of two columns together with entrainer at the bottom of the second column.3 However, the thermal efficiency of ED based on conventional two-column sequence is low at 5 to 20%.4,5 Various approaches have been developed to intensify and improve the ED process, e.g. extractive dividing-wall column (EDWC),6-8 ED with varying pressure,9 and heat-integrated ED.10-12 As an improved ED process, the fully thermally coupled EDWC (Figure 1a) integrates the extractive distillation and entrainer recovery columns of conventional ED sequence into one single shell, leading to lower energy and capital cost requirement. However, the operation of EDWC is very challenging due to the integrated structure with small physical internal space and strong interactions between the two sections on both sides of the dividing wall. Although many previous studies on the control of EDWC using conventional proportional-integral (PI) control demonstrated that most EDWCs can be operated smoothly for the desired product purities via temperature or composition control schemes, they also shown significant steady-state offsets in the control of two product purities of EDWC under the feed composition disturbances when temperature control scheme is used.13-19 The reason is that the composition profile in the column changes when the feed composition changes; this leads to changes in the required setpoints of the temperature controllers and significant steady-state offsets in product purities. On the other hand, composition control scheme can regulate the two product purities of EDWC at their desired values without any offset after the system reaches a new steady state but it shows slower dynamic response compared to temperature control scheme. Moreover, the measurement required by composition controller has large time-lags than the temperature measurement, and it also needs large investment and high maintenance; further, on-line measurement of product purity is not always possible in industrial practice. Therefore, inferential temperature control (TC) scheme is preferred for composition control due to its faster response, lower investment and higher reliability, while temperature difference control (TDC) scheme can 2


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effectively handle changes in column composition profiles due to feed composition disturbances and results in smaller steady-state offsets in product purities compared to those in conventional TC scheme.20 This is because, when the feed composition disturbances occur, changes in temperature difference between various trays in the distillation column are much smaller and are approximately constant. Accordingly, the employment of TDC to improve the operation of dividing-wall columns (DWCs) has recently attracted considerable attention. Halvorsen and Skogestad21 firstly discussed the concept of TDC for the optimal operation of DWC through analyzing the steady-state behavior. Ling and Luyben22 compared the control performance of TC and TDC schemes for the operation of DWC, demonstrating that TC scheme can handle large feed flowrate disturbances but fails to handle feed composition disturbances. On the contrary, TDC scheme can effectively handle large disturbances in both feed flowrate and composition, exhibiting much better control performance than TC scheme. Wu et al.23 and Yuan et al.24 proposed the double temperature difference control (DTDC) scheme for improved operation of DWC, and showed that it is capable of handling severe disturbances of as much as 30% in feed composition with acceptably small steady-state offsets in the purities of the three products. Model predictive control (MPC) is an advanced strategy of process control that can handle multivariable control problems by taking into account constraints and interactions among controlled variables, manipulated variables and measured disturbances.25 It has been widely used in the process control of chemical plants since 1980s, and is particularly suitable for control of integrated, strongly coupled processes like DWCs. In a pioneering study on the control of a pilot DWC, Adrian et al.26 demonstrated that MPC shows considerably improved control behavior than PI control in terms of maximum deviations in the controlled variables and time to reach the new steady state. Buck et al.27 proposed a systematic procedure for implementing MPC on a pilot DWC plant, starting from the definition of controlled variables and manipulated variables, and the identification of linear model to the setting of controller parameters; the developed MPC shows outstanding control performance than PI control for the operation of DWC in terms of negligible oscillations and smaller setting time. Rewagad and Kiss28,29 explored the dynamic optimization and MPC-based advanced control of DWC for separating benzene-toluene-xylene mixture, demonstrating that MPC leads to significant increase

in

performance,

as

compared

to 3

the

previously


reported

conventional


proportional-integral-derivative (PID) controllers in the multi-loop framework. Hernández and Chinea-Herranz30 presented a decentralized control scheme of a DWC and its equivalent MPC scheme, in which, the dynamic step test using pseudo random binary sequence as the test signals was implemented in Aspen Dynamics to identify the linear prediction model; they demonstrated that MPC scheme shows superior performance in eliminating control-loop coupling in the decentralized control scheme. Qian et al.31 compared the control performance of MPC and PI control for reactive DWC operation; they showed that the performance of MPC is better than PI control in terms of setting time, amplitude of maximum transient deviation and oscillations. Even though the above studies have demonstrated the advantages of MPC over the conventional PI and PID controllers for the operation of DWC, similar studies on the application of MPC in EDWC are very few. EDWC is a typical process with strong interactions due to the thermal coupling between the two sections on both sides of the dividing wall; from this point of view, MPC is a very suitable control strategy to improve EDWC operation. Rodríguez et al.32 proposed a MPC strategy for the operation of EDWC, but the detailed control performance and control structures were not presented. Hence, in the present study, an advanced offset-free control scheme by integrating MPC with temperature differences is proposed for improved operation of EDWC; this integration can synergize the advantages of MPC and temperature difference control strategy in terms of process stability and improved control performance (i.e., smaller steady-state offsets in TDC scheme and smaller transient overshoots and faster dynamic responses in MPC scheme) for the operation of EDWC. The proposed scheme is applied and tested on the EDWC for separating toluene and 2-methoxyethanol (2-MEA) mixture using dimethyl sulfoxide (DMSO) as the entrainer.33 The remainder of this manuscript is organized as follows. Section 2 describes the steady-state process of EDWC for separating toluene and 2-MEA. In Section 3, the conventional PI control with TC, TDC and DTDC schemes for the operation of EDWC is presented, and the performance of these control strategies is investigated. In Section 4, the advanced control strategy based on MPC together with temperature differences is proposed and evaluated. Finally, in Section 5, the main findings of this work are summarized.

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2 STEADY-STATE FLOWSHEET OF EDWC The EDWC process for separating toluene and 2-MEA mixture using DMSO as the entrainer was reported by Li et al,33 wherein the feed is an equimolar mixture of toluene and 2-MEA, and the make-up DMSO is assumed to be pure. The desired product purity of both toluene and 2-MEA products is 99.5 wt% whereas purity of recycled DMSO is set as 99.8 wt%. In the present study, the steady-state simulation of EDWC was implemented in Aspen Plus 9.0 through its thermodynamically equivalent model shown in Figure 1b. The non-random two liquid (NRTL) model along with the binary parameters in Li et al.33 was chosen to calculate activity coefficients and describe the vapor-liquid equilibrium. The extractive section (C1) of the EDWC has 40 ideal stages including the condenser, and the reflux ratio of 1.2957. On the other side of the dividing wall, the rectifying section (C2) has 12 ideal stages including the condenser, and the reflux ratio of 0.3347; while the stripping section (C3) at the bottom has 10 ideal stages including the reboiler. The stage pressure drop is set as 0.0068 atm. The fresh feed enters on the 28th stage of C1 column, at a flowrate of 100 kmol/h. The recycled DMSO (99.8 wt% DMSO and 0.2 wt% 2-MEA), after being cooled to 378.10 K by cooling water and mixed with a small amount make-up, is fed on the 6th stage of C1 column at 69.95 kmol/h. The molar flowrate ratio of entrainer-to-feed (S/F) is 0.7, and the flowrate split ratio of the vapor stream from the top of C3 (βv, refers to the vapor flowrate fraction going to the bottom of C1) is 0.65. The condenser temperatures of C1 and C2 are respectively 383.59 K and 403.04 K that are high enough for using cooling water as the coolant. In order to balance the pressure at the bottom of C1 and C2 sections, the pressure at the top of C1 is set as 1 atm while that at the top of C2 is set as 1.19 atm.

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Figure 1. (a) EDWC structure along with potential manipulated variables; and (b) thermodynamically equivalent model of EDWC with stream data

3 TEMPERATURE CONTROL SCHEME FOR EDWC According to the recommendations by Luyben,34 column diameters are calculated by the tray sizing in Aspen Plus with a default tray spacing of 0.6096 m. The reflux drums and column base for all three sections are sized to give 10 min liquid holdup with 50% liquid level. After adding the required pumps, valves and compressor into the steady-state flowsheet, Aspen Plus model is exported to Aspen Dynamics 9.0 to obtain the dynamic responses of EDWC using pressure driven model. 3.1 Selection of Sensitive Tray Temperatures and Basic Temperature Control Scheme In addition to level and pressure control loops, EDWC has 5 degrees of freedom that can be chosen as manipulated variables (Figure 1a), i.e. reflux ratios of C1 (RR1) and C2 (RR2), vapor split ratio (βv), reboiler duty (QR) and molar flowrate ratio of recycle entrainer to feed (S/F). Among these, βv, which is determined by the hydrodynamic conditions of the column (i.e. the dividing wall placement, pressure drop and flow resistance),35 is commonly not a manipulated variable for the operation of DWC; however, several studies show that the control structure with βv as a manipulated variable can achieve better control performance for rejecting feed composition disturbances than that without manipulating βv for the operation of EDWC.13,15 Tututi-Avila et al.16 6


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compared PI control performance of a EDWC for ethanol dehydration using temperature control with and without manipulating βv, demonstrating that the product purities can be controlled for ±20% feed flowrate disturbances without manipulating βv. However, the same control strategy is not able to handle ±10% feed composition disturbances, where the desired product purities cannot be achieved, and large setting times and poor control performances were observed. On the contrary, the control strategy with manipulating βv can effectively reject both the feed flowrate and feed composition disturbances. Recently, Luyben36 presented an alternative method to indirectly manipulate βv by adjusting the condenser duty (and consequently pressure) at the top of the rectifying section (C2). In the present study, a four-point temperature control scheme is presented for the operation of EDWC, in which, βv is directly manipulated to enhance the control performance of EDWC to reject feed composition disturbances. The four manipulated variables used in the stage temperature control loops of the control scheme are the reflux ratios of C1 (RR1) and C2 (RR2), βv and QR, while S/F is fixed at 0.7. Sensitive trays for temperature control in the three sections are selected by employing the open-loop sensitive analysis, which is implemented by giving ±0.1% step change in each manipulated variable while keeping the others at their nominal values. Singular value decomposition (SVD), a popular method for selecting sensor locations for multivariable control from steady-state gain matrix,37 is used to choose control pairs for C1 having 40 ideal stages. The steady-state gain matrix (K) with 40 rows and 2 columns (one for RR1 and another for βv), can be

∆ ∆

calculated by:

=

(1)

Here, ∆ is the change in stage temperatures and ∆ is the step change in manipulated

variables. Subsequently, the obtained gain matrix can be decomposed using SVD analysis according to Eq. 2 using the SVD function in Matlab.37

=

(2)

Here, the steady-state gain matrix is decomposed into three unique component matrices: the

∈ ℝ × and ∈ ℝ× are, respectively, the left and right and singular vectors of the gain

matrix, ∈ ℝ × , and ∈ ℝ × is a diagonal matrix of singular values. The 1st and 2nd

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columns of U related to RR1 and βv respectively, are plotted against stage numbers of C1 as shown

in Figure 2f.

Figure 2. Open-loop test results: temperature change profile in C1 (plots a and d), C2 (plot b), and C3 (plot c); stage temperature gains of C1 for changes in RR1 and βv (plot e), and SVD analysis for C1 for RR1 and βv (plot f) Figures 2a and 2d show the results of open-loop sensitive analysis for ±0.1% step changes in RR1 and βv, respectively, in which, two similar peaks that are sensitive to changes in RR1 and βv appear on the 13th and 34th stages. Figures 2e and 2f are the plots of steady-state gains and SVD results for changes in RR1 and βv. The temperature on the 13th stage (T13) of C1 has the largest steady-state gain for the change in RR1, and it should be used to maintain the top product purity by manipulating RR1 since 13th stage is near the top of C1 and so has a small time lag. The temperature on the 34th stage (T34) of C1 gives the largest steady-state gain to the change in βv, and hence it should be selected to adjust βv. The singular values of the steady-state gain matrix are:

= 2480 and = 608, which gives the condition number, = / = 4.07 indicating that

the two selected sensitive tray temperatures, T13 and T34, are entirely independent and the dual-temperature control scheme should be feasible.38 Relative gain array (RGA) can also be used to select control pairings according to Eq. 3.39,40

RGA = % ⊗ '%( )*

(3)

8


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Here, G is the gain matrix with two rows (referring to T13 and T34) and two columns (referring to

RR1 and βv), (G-1)T is the transpose of the inverse of the gain matrix, and ⊗ denotes element-by-element multiplication of two matrices. The steady-state gains of this dual-point control

,−452.727 .=/ ,- 1078.503

are shown in Eq. 4, and the calculated RGA results are given in Eq. 5.

+

1.658 RGA = / −0.658

−198.254 661 5+ . 1190.080 78

(4)

−0.658 5 1.658

(5)

It can be seen that RGA analysis gives the same controller parings of T13-RR1 and T34-βv as the SVD analysis. Figure 2b shows the plots of open-loop sensitive results for ±0.1% changes in RR2 of C2. The temperature on the 9th stage (T9) has largest change, and can be used as the controlled variable to maintain 2-MEA product purity at the top of C2. The open-loop sensitive analysis for ±0.1% changes in QR (Figure 2c) shows that the temperature on the 43th stage (T43) has largest change, and it can be selected as the sensitive tray temperature to maintain recycled DMSO purity at the bottom of C3 by adjusting QR. 3.2 Reference Temperature Selection for TDC and DTDC Schemes The feed composition changes with fixed S/F affect the molar ratio of entrainer to the heavy component (2-MEA) on all column stages of C1 and C2. Hence, composition on all stages of C1 and C2 (Figure 1a) changes, and consequent temperature changes on all stages of C1 and C2 cause the failure to handle the feed composition disturbances by controlling selected stage temperatures at their specified values. However, temperature differences of two stages in each section are approximately constant, and so they can be used as the controlled variables (instead of stage temperatures) to handle feed composition disturbances.

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Figure 3. Variation of required tray temperatures with changes in toluene feed composition: for C1 (plots a and b), for C2 (plot c), and for C3 (plot d); zT refers to mol% of toluene in the feed steam Figure 3 shows the steady-state temperature profiles on various stages in the column versus the changes in toluene composition in feed stream, while maintaining the purity of two products and the recycled DMSO, and the toluene mole fraction in the bottom liquid stream of C1 at their desired values. As shown in Figure 3a, T13 decreases by about 3℃ as the toluene mole fraction in the feed stream (zT) increases from 45% to 55%, which makes the setpoint of TC1 controller 1.5℃ higher or lower than that required to maintain the product purity in the face of ±10% changes in zT. Therefore, if the setpoint of TC1 controller is not updated when the toluene mole fraction in the feed stream increases by 10%, more 2-MEA will go up to the top of C1, thus decreasing the toluene purity, since the required temperature of TC1 for maintaining toluene product purity is lower than its setpoint. This is the reason for the relatively large offsets in the two product purities in the dynamic responses of TC scheme for feed composition disturbances (Figure 6). Similar to T13 variation for feed composition disturbances, T34 of C1 and T9 of C2 vary (Figures 3b and 3c), which also affect the performance of TC2 and TC3 controllers. However, Figure 3d shows that T43 of C3 for TC4

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controller is not much affected by feed composition changes, and thus the single temperature controller, TC4, can maintain recycled DMSO purity at the desired value. One and two reference stages are required for each temperature control loop in the TDC and DTDC schemes, respectively. In this study, the average absolute variation (AAV) method proposed by Yuan et al.41 is used to select the reference temperatures for the TDC and DTDC schemes. The AAV for the nth stage is defined as in Eq. 6, which calculates the mean of temperature differences between the sensitive stage and the nth stage for a specified control loop under the assumption of completely rejecting all the encountered feed composition disturbances. BC

1 AAV; = = >? |∆',; − ,AA )? | 2

Proportional-Integral Control and Model Predictive Control of

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