Robust Control of Partially Heat-Integrated Pressure-Swing Distillation

Article Cite This: Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

pubs.acs.org/IECR

Robust Control of Partially Heat-Integrated Pressure-Swing Distillation for Separating Binary Maximum-Boiling Azeotropes Ye Li,§ Yanan Jiang,§ and Chunjian Xu* School of Chemical Engineering and Technology, Chemical Engineering Research Center and State Key Laboratory of Chemical Engineering, Tianjin University, Tianjin 300350, China

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S Supporting Information *

ABSTRACT: Previous studies of partially heat-integrated pressure-swing distillation (PHI-PSD) for separating the binary maximum-boiling azeotropes methanol/trimethoxysilane and ethylenediamine/water have demonstrated difficulties in dynamic control due to the complexity of these processes. In this paper, efforts are made to find new robust control structures to improve the dynamic controllability of these processes in three different types of PHI-PSD sequences. First, for the high-pressure column (HPC) → low-pressure column (LPC) sequence of PHI-PSD for separating the methanol/trimethoxysilane azeotrope, five new control structures are established and three of them are robust. Second, the dynamic controllability of the LPC → HPC sequence of PHIPSD for separating the methanol/trimethoxysilane azeotrope is investigated for the first time and four robust control structures are proposed. Finally, two new robust control structures are proposed for PHI-PSD for separating the ethylenediamine/water azeotrope. The crucial elements in establishing robust control of these processes are that the reboiler duty of the HPC should be manipulated to control the sump level of the HPC and the bottom flow rate of the HPC should be flow controlled. The feedforward control of the ratio of the recycling flow rate or the connecting bottom flow rate to the feed flow rate leads to worse results. In addition, the best control structure of the HPC → LPC sequence of PHI-PSD for separating the methanol/ trimethoxysilane mixture and the best control structure of PHI-PSD for separating the ethylenediamine/water mixture are compared with the robust control structures of the previous studies. All the robust control structures are valuable in practice for the control of PHI-PSD for separating maximum-boiling azeotropes.

1. INTRODUCTION

(PHI-PSD) with both a high-pressure column (HPC)→ lowpressure column (LPC) sequence and a LPC → HPC sequence.22 The controllability of the HPC → LPC sequence of this process was also investigated.23 Due to the complexity of the process, Luyben’s work mainly adopted composition control loops assisted by temperature control loops. However, online composition analyzers are expensive and have a longer time lag than temperature controllers, and a nonlinear controller was adopted to achieve robust control. In addition, the dynamic controllability of the LPC → HPC sequence has not been investigated.

Distillation has been widely applied to separate azeotropes. The controllability of processes for separating azeotropes by extractive distillation,1−8 heterogeneous azeotropic distillation,9−14 and pressure-swing distillation (PSD)15−21 has been widely investigated. For PSD for separating azeotropes, most studies have focused on minimum-boiling azeotropes, while only a few studies have addressed maximum-boiling azeotropes. Trimethoxysilane and methanol form a maximum-boiling azeotrope. Trimethoxysilane is used as a coupling agent. The process to produce trimethoxysilane involves the reaction of methanol with silicon. A mixture of unreacted methanol and trimethoxysilane is produced and requires separation so that the methanol can be recycled back to the reaction section.22 Luyben investigated the separation of the methanol/ trimethoxysilane mixture by partially heat-integrated PSD © XXXX American Chemical Society

Received: November 9, 2018 Revised: January 9, 2019 Accepted: January 14, 2019

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DOI: 10.1021/acs.iecr.8b05562 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

Article

Industrial & Engineering Chemistry Research

Figure 1. Temperature profiles of the (a) HPC and (b) LPC of the HPC → LPC sequence of PHI-PSD for separating the methanol/ trimethoxysilane mixture.

Ethylenediamine and water form a maximum-boiling azeotrope. Ethylenediamine is used to produce many industrial chemicals. Water is a common impurity in ethylenediamine. The mixture of ethylenediamine and water requires separation to get purified products.24,25 Li et al.26 investigated the design and control of PHI-PSD for separating the ethylenediamine/water mixture. In both HPC → LPC and LPC → HPC sequences of PHI-PSD for separating the methanol/trimethoxysilane mixture, the condenser duty of the HPC is totally utilized to supply the reboiler duty of the LPC. Thus, the operating pressure of the HPC cannot be controlled. However, in the process of separating ethylenediamine/water, the condenser duty of the HPC is partially utilized to supply the reboiler duty of the LPC. Thus, the operating pressure of the HPC can be controlled. Therefore, these processes represent three different types of PHI-PSD sequences for separating maximumboiling azeotropes. In this work, efforts are made to find new robust control structures for these processes to improve their dynamic controllability. First, five new control structures with temperature control loops are proposed for the HPC → LPC sequence of PHI-PSD for separating the methanol/trimethoxysilane mixture. Second, the dynamic controllability of the LPC → HPC sequence of PHI-PSD for separating the methanol/trimethoxysilane mixture is investigated for the first time, and four robust control structures are proposed. Finally, two new robust control structures are proposed for PHI-PSD for separating the ethylenediamine/water mixture. Meanwhile, the influence of the feedforward control of the ratio of the recycling flow rate or the connecting bottom flow rate to the feed flow rate is investigated for all these processes. In addition, the best control structure of the HPC → LPC sequence of PHI-PSD for separating the methanol/trimethoxysilane mixture and the best control structure of PHI-PSD for separating the ethylenediamine/water mixture are compared with the robust control structures of the previous studies.

Figure 3. Dynamic performances of CS1 of the HPC → LPC sequence of PHI-PSD for separating the methanol/trimethoxysilane mixture.

2. DYNAMIC CONTROL Aspen Plus V7.2 and Aspen Plus Dynamics V7.2 are used for simulations. For the methanol/trimethoxysilane mixture, UNIFAC model is selected, which is the same with the previous studies.22,23 The predicted normal boiling points, azeotropic composition, and azeotropic bubbling point of the methanol/ trimethoxysilane mixture are shown in Supporting Information Table S1. For the ethylenediamine/water mixture, the UNIQUAC model is selected, which is the same with the previous study.26 The binary interaction parameters of UNIQUAC model, predicted

Figure 2. Control structure CS1 of the HPC → LPC sequence of PHI-PSD for separating the methanol/trimethoxysilane mixture. B


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Figure 4. Control structure CS2 of the HPC → LPC sequence of PHI-PSD for separating the methanol/trimethoxysilane mixture.

reestablished with the same parameters of the previous study22 and shown in Supporting Information Figure S1. As the heat release of overhead vapor condensation of the HPC is not sufficient to supply the reboiler duty of the LPC, an auxiliary reboiler should be used to satisfy the remaining energy requirements.22,23 The pressure drop through each tray in the columns is set at 0.04 psi.22,23 The composition disturbances of this process are based on the methanol mole fraction. Feed flow rate disturbances of ±10% and feed composition disturbances of ±10% are introduced to test the dynamic controllability. For the HPC → LPC sequence, five different control structures are established. The temperature profiles of the HPC and the LPC are shown in Figure 1. The sensitive tray is selected by the “slope criterion” suggested by Luyben.27 The location of the stage with the greatest slope in the HPC is the third stage, while that in the LPC is the fifth stage. 2.1.1. Control Structure CS1 of the HPC → LPC Sequence. The control flowsheet is shown in Figure 2. The faceplate and flowsheet equations are shown in Supporting Information Figure S2. The controller tuning parameters are shown in Supporting Information Table S5. The control loops are listed below: (1) The fresh feed is flow controlled. (2) The pressure of the LPC is controlled by manipulating the heat removal rate of the condenser, while that of the HPC is not controlled. (3) The reciprocal of the reflux ratio of the LPC is fixed because the reflux ratio of the LPC is large, and in this situation it is suggested that the reflux flow rate can be manipulated to control the reflux drum level.23 (4) The reflux drum level of the HPC is controlled by manipulating the distillate flow rate, while that of the LPC is controlled by manipulating the reflux flow rate. (5) The base level of the LPC is controlled by manipulating the bottom flow rate. The reboiler duty of the HPC is proportional to the feed flow rate. This ratio is manipulated to control the base level of the HPC. (6) The bottom flow rate of the HPC is flow controlled at a constant initial value. (7) The third-stage temperature of the HPC (T3) is controlled by manipulating the reflux ratio. As the condenser duty of the HPC is totally supplied to the reboiler duty of the LPC, pressure-compensated temperature control is used in the HPC. The corresponding flowsheet equation can be seen in the Supporting Information. (8) The fifth-stage temperature of the LPC (T5) is controlled by manipulating the heat removal rate of the auxiliary reboiler.

normal boiling points, azeotropic composition, and azeotropic bubbling point of the ethylenediamine/water mixture are shown in Supporting Information Tables S2 and S3. The feeding conditions and the product purities of all the processes in this study are also the same as the previous studies.22,23,26 The feeding conditions of the HPC → LPC sequence of PHI-PSD for separating the methanol/trimethoxysilane mixture are 100 kmol/h with 50 mol % methanol and 50 mol % trimethoxysilane at a temperature of 50 °C. The feeding conditions of the LPC → HPC sequence of PHI-PSD for separating the methanol/trimethoxysilane mixture are 58.82 kmol/h with 15 mol % methanol and 85 mol % trimethoxysilane at a temperature of 50 °C. The product purities of both sequences for separating the methanol/trimethoxysilane mixture are 99 mol % methanol and 99 mol % trimethoxysilane. The feeding conditions of PHI-PSD for separating the ethylenediamine/water mixture are 100 kmol/h with 40 mol % ethylenediamine and 60 mol % water at a temperature of 30 °C. The product purities of PHI-PSD for separating the ethylenediamine/water mixture are 99.5 mol % ethylenediamine and 99.5 mol % water. For PHI-PSD to separate the methanol/trimethoxysilane mixture, the concentration of methanol in the feed depends on the methanol conversion back in the reaction section of the process. Thus, different feeding compositions result in different separating sequences. Higher conversion means lower methanol concentration in the feed and lower feed flow rate to the separating process. The HPC → LPC sequence has more energy demands than the LPC → HPC sequence.22 The column bases and reflux drums are sized to provide 10 min of liquid holdup when half full. All the controllers are PI controllers: the tuning constants of pressure controllers are the same with default values with a gain of 20 and an integral time of 12 min; the tuning constants of flow controllers are the conventional values with a gain of 0.5 and an integral time of 0.3 min; the tuning constants of level controllers are the conventional values with a gain of 2 and an integral time of 9999 min.27 The temperature and composition controllers are tuned by the Tyreus−Luyben method after relay-feedback tests. The dead times of the temperature controller and composition controller are 1 and 3 min, respectively.27 Except the temperature controller and composition controller, the abbreviations of other controllers in the control faceplate and their descriptions and units of set points are shown in Supporting Information Table S4. In the following diagrams, TMS denotes trimethoxysilane and EDA denotes ethylenediamine. 2.1. Dynamic Control of the HPC → LPC Sequence of PHI-PSD for Separating the Methanol/Trimethoxysilane Azeotrope. The steady-state flowsheet of this process is C


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Figure 5. Dynamic performance of CS2 of the HPC → LPC sequence of PHI-PSD for separating the methanol/trimethoxysilane mixture.


The most remarkable control loops are manipulating the reboiler duty of the HPC to control the base level of the HPC and flow-controlling the bottom flow rate of the HPC at a constant initial value. Usually, the reboiler duty is manipulated to control the temperature in a certain stage, and the bottom flow rate is manipulated to control the base level. However, for this process, if the bottom flow rates of both the HPC and the LPC are manipulated to control base levels, “snowballing” will happen.23 In Luyben’s paper, the auxiliary reboiler duty is manipulated to control the base level of the LPC and the bottom flow rate of the LPC is flow controlled and ratioed to the feed

flow rate. This control strategy is effective when mainly using composition control loops but does not work when mainly using temperature control loops, as verified in our previous simulation. Inspired by the manipulation of the auxiliary reboiler duty to control the base level of the LPC in Luyben’s work,23 we attempted to manipulate the reboiler duty of the HPC to control the base level of the HPC; thus, the bottom flow rate of the HPC is flow controlled, and the above control strategy has been established and tested. The results are shown in Figure 3. The product purities can be maintained very close to the specifications. However, under the −10% feed flow rate and

Figure 6. Control structure CS3 of the HPC → LPC sequence of PHI-PSD for separating the methanol/trimethoxysilane mixture. D


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+10% feed composition disturbances, both methanol and trimethoxysilane product purities fluctuate and it takes a long time to reach a new steady-state. This phenomenon is most probably the result of manipulating the auxiliary reboiler duty to control T5 because the temperature-controlled tray is far from the bottom. A modified control strategy is implemented in control structure CS2. 2.1.2. Control Structure CS2 of the HPC → LPC Sequence. The control flowsheet is shown in Figure 4. The faceplate and flowsheet equations are shown in Supporting Information Figure S3. The controller tuning parameters are shown in Supporting Information Table S6. The control loops that differ from those in CS1 are as follows: (1) The auxiliary reboiler duty is proportional to the feed flow rate. (2) The reciprocal of the reflux ratio of the LPC is manipulated to control T5. The results are shown in Figure 5. Slight fluctuations occur and it takes a short time to reach the new steady-state. Product purities very close to the specifications can be attained. 2.1.3. Control Structure CS3 of the HPC → LPC Sequence. The establishment of this control structure is aimed at determining whether manipulating the distillate flow rate of the LPC to control the reflux drum level of the LPC is effective. The control flowsheet is shown in Figure 6. The faceplate and flowsheet equations are shown in Supporting Information Figure S4. The controller tuning parameters are shown in Supporting Information Table S7. The control loops that differ from those in CS1 are as follows: (1) The reflux drum level of the LPC is controlled by manipulating the distillate flow rate. (2) The reflux ratio of the LPC is fixed. The results are shown in Figure 7. This control structure still works, but the results are almost the same as those of CS1. The product purities can be maintained very close to the specifications. However, under the −10% feed flow rate and +10% feed composition disturbances, both methanol and trimethoxysilane product purities fluctuate and it takes a long time to reach a new steady-state. A modified control strategy is implemented in control structure CS4. 2.1.4. Control Structure CS4 of the HPC → LPC Sequence. In the dynamic performance of CS3, fluctuations occur in the −10% feed flow rate and +10% feed composition disturbances, not in the +10% feed flow rate and −10% feed composition disturbances. The common element of the results of the −10% feed flow rate and +10% feed composition disturbances is a


decrease in the trimethoxysilane product flow rate. Therefore, if the flow rate input of the multiplier “RR2” is not changed under the −10% feed flow rate and +10% feed composition disturbances, fluctuations may not occur. This control strategy is implemented in control structure CS4. The modification of this control loop with respect to CS3 is that the output value of distillate of the LPC is first sent to the high-selector, whose output value is then sent to the multiplier “RR2”. The other input value of the high-selector is the initial value of the trimethoxysilane product flow rate, which is the compared object in the high-selector. The control flowsheet is shown in E


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Figure 8. The faceplate and flowsheet equations are shown in Supporting Information Figure S5. The controller tuning parameters are shown in Supporting Information Table S8. The results are shown in Figure 9. Slight fluctuations occur, and it takes a short time to reach the new steady-state. The product purities can be maintained very close to the specifications. 2.1.5. Control Structure CS5 of the HPC → LPC Sequence. This control structure is derived from CS2; the feedforward control of the ratio of the connecting bottom flow rate to the feed flow rate is added as the only difference. The establishment of this control structure is aimed at determining the influence of the feedforward control of the ratio of the connecting bottom flow rate to the feed flow rate. The control flowsheet is shown in Figure 10. The faceplate and flowsheet equations are shown in Supporting Information Figure S6. The controller tuning parameters are shown in Supporting Information Table S9. The results are shown in Figure 11. Compared with CS2, the feedforward control of the ratio of the connecting bottom flow

methanol product purity of CS5 has a slightly negative larger transient deviation than CS2. For CS4 and CS2, under the −10% feed flow rate and +10% feed composition disturbances, negative transient deviations in trimethoxysilane product purity can be observed for CS2, while they cannot be observed for CS4. Meanwhile, trimethoxysilane product purity of CS4 can be maintained at the initial specification after reaching a new steady-state, while that of CS2 is slightly less than the initial specification. The robust control structure of Luyben’s previous study is control structure CS5 with nonlinear controller in the previous paper, which handles feed flow rate disturbances of ±20% and feed composition disturbances of ±20%.23 To further compare CS2 and CS4 and compare with Luyben’s previous study simultaneously, feed flow rate disturbances of ±20% and feed composition disturbances of ±20% are introduced to CS2 and CS4. The results are shown in Figures 12 and 13. It can be found that under the −20% feed flow rate and +20% feed composition disturbances, large negative transient deviations in trimethoxysilane product purity can be observed for CS2, while they cannot be observed for CS4. Meanwhile, trimethoxysilane product purity of CS4 can be maintained at the initial specification after reaching a new steady-state, while that of CS2 is slightly less than the initial specification. Therefore, CS4 is better than CS2. The most significant difference between CS4 of this study and CS5 with nonlinear controller of Luyben’s previous study is that, all the product purities can return back to the initial specifications for CS5 with nonlinear controller of Luyben’s previous study because composition controllers are used, while those of CS4 of this study can be just maintained close to the initial specifications. Second, under the −20% feed flow rate disturbance, trimethoxysilane product purity of CS5 with nonlinear controller of Luyben’s previous study has a negative transient deviation, while it does not happen for CS4 of this study. Third, under the −20% feed composition disturbance, methanol product purity of CS4 of this study has a large negative transient deviation, while it does not happen for CS5 with nonlinear controller of Luyben’s previous study. Finally, under the +20% feed composition disturbance, trimethoxysilane product purity of CS5 with nonlinear controller of Luyben’s previous study has a transient deviation, while this does not happen for CS4 of this study. Generally speaking, CS2, CS4 of this study, and CS5 with a nonlinear controller of Luyben’s previous study are all robust control structures.


rate to the feed flow rate does not influence the results under composition disturbances, so only the results under feed flow rate disturbances are shown. The only obvious difference from CS2 is the slightly larger negative transient deviation in methanol product purity under the −10% feed flow rate disturbance. 2.1.6. Comparison. For CS1 and CS3, fluctuations occur. For CS5 and CS2, under the −10% feed flow rate disturbance, F


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Figure 13. Dynamic performance of CS4 of the HPC → LPC sequence of PHI-PSD for separating the methanol/trimethoxysilane mixture under large feed flow rate and composition disturbances.

Figure 12. Dynamic performance of CS2 of the HPC → LPC sequence of PHI-PSD for separating the methanol/trimethoxysilane mixture under large feed flow rate and composition disturbances.

2.2. Dynamic Control of the LPC → HPC Sequence of PHI-PSD for Separating the Methanol/Trimethoxysilane Azeotrope. The steady-state flowsheet of this process is reestablished with the same parameters of the previous study22 and shown in Supporting Information Figure S7. As the heat release of overhead vapor condensation of the HPC is not sufficient to supply the reboiler duty of the LPC, an auxiliary reboiler should be used to satisfy the remaining energy requirements.22,23 The pressure drop through each tray in the columns is set at 0.04 psi.22,23 The composition disturbances of this process are based on the methanol mole fraction. Feed flow rate disturbances of ±10% and feed composition disturbances of ±10% are introduced to test the dynamic controllability. For the LPC → HPC sequence, four different control structures are established. The temperature profiles of the LPC and the HPC are shown in Figure 14. The sensitive tray is selected by the “slope criterion” suggested by Luyben.27 The location of the stage with the greatest slope in the LPC is the fourth stage, while that in the HPC is the third stage. 2.2.1. Control Structure CS1 of the LPC → HPC Sequence. The control flowsheet is shown in Figure 15. The faceplate and flowsheet equations are shown in Supporting Information Figure S8. The controller tuning parameters are shown in Supporting Information Table S10. The control loops are listed as follows:

Figure 14. Temperature profiles of the (a) LPC and (b) HPC of the LPC → HPC sequence of PHI-PSD for separating the methanol/ trimethoxysilane mixture.

(1) The fresh feed is flow controlled. (2) The pressure of the LPC is controlled by manipulating the heat removal rate of the condenser, while that of the HPC is not controlled. (3) The reflux drum level of the LPC is controlled by manipulating the distillate flow rate, while that of the HPC is controlled by manipulating the reflux flow rate. (4) The base level of the LPC is controlled by manipulating the bottom flow rate. The reboiler duty of the HPC is proportional to the feed flow rate. This ratio is manipulated to control the base level of the HPC. G


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Figure 15. Control structure CS1 of the LPC → HPC sequence of PHI-PSD for separating the methanol/trimethoxysilane mixture.

(5) The bottom flow rate of the HPC is flow controlled at a constant initial value. (6) The auxiliary reboiler duty is proportional to the feed flow rate. (7) The third-stage temperature of the HPC (T3) is controlled by manipulating the reciprocal of the reflux ratio. Note that, as the condenser duty of the HPC is totally supplied to the reboiler duty of the LPC, pressurecompensated temperature control is used in the HPC. The corresponding flowsheet equation can be seen in the Supporting Information. (8) The fourth-stage temperature of the LPC (T4) is controlled by manipulating the reflux ratio. For the control of the LPC → HPC sequence, it is also necessary to manipulate the reboiler duty of the HPC to control the base level of the HPC and make the bottom flow rate of the HPC flow controlled at a constant initial value. The attempt to manipulate both bottom flow rates to control both sump levels shows failure. Another attempt to manipulate the auxiliary reboiler duty to control the sump level of the LPC and flowcontrol the bottom flow rate of the LPC also shows failure. This “failure” means that the process cannot be controlled. The attempt to manipulate the auxiliary reboiler duty to control T4 also shows failure. Therefore, the auxiliary reboiler duty is set to be proportional to the feed flow rate. The results are shown in Figure 16. It takes a short time to reach a new steady-state, and the product purities can be maintained very close to the specifications. The only problem with this control structure is that the sump level of the LPC (LC2) increases slowly over a long time under the +10% flow rate and +10% composition disturbances. As time goes on, the rate of increase in LC2 decreases and becomes almost unchanged at 30 h. Although the value of LC2 does not reach the maximum and the valve is not fully opened at 30 h, this trend is thought to indicate that the system does not completely reach stability. The ultimate parameters of LC2 under the +10% flow rate and +10% composition disturbances are shown in Supporting Information Figure S9. The reason for the observed results is assumed to be related to the control of T4. The rather flat temperature profile of the LPC suggests that controlling T4 may be ineffective. A modified control strategy is implemented in control structure CS2.

Figure 16. Dynamic performance of CS1 of the LPC → HPC sequence of PHI-PSD for separating the methanol/trimethoxysilane mixture.

2.2.2. Control Structure CS2 of the LPC → HPC Sequence. To overcome the drawback of CS1, the difference between the fourth-stage temperature and the 27th-stage temperature is controlled in control structure CS2, with the hope that the large stage span will help the system stabilize under disturbances. The control flowsheet is shown in Figure 17. The item “Com” and H


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“DT” represent the comparator of the fourth-stage temperature and the 27th-stage temperature and the corresponding temperature controller, respectively. The faceplate and flowsheet equations are shown in Supporting Information Figure S10. The controller tuning parameters are shown in Supporting Information Table S11. The results are shown in Figure 18. The trimethoxysilane product purity drops more than that of CS1 under the +10%

flow rate and +10% composition disturbances. A slow increase in LC2 is not observed, and the other results are rather good. To overcome the drawbacks, control structure CS3 is established. In addition, an attempt to manipulate the auxiliary reboiler duty to control differential temperature is also implemented, but the results show failure. Therefore, for the LPC → HPC sequence, the auxiliary reboiler duty can only be selected to be proportional to the feed flow rate, not to control the stage temperature. 2.2.3. Control Structure CS3 of the LPC → HPC Sequence. In control structure CS3, composition/temperature cascade control is used. The trimethoxysilane mole fraction of the trimethoxysilane product is measured and then sent to the composition controller, whose output value is the remote set point of the temperature controller. The control flowsheet is shown in Figure 19. The faceplate and flowsheet equations are shown in Supporting Information Figure S11. The controller tuning parameters are shown in Supporting Information Table S12. The results are shown in Figure 20. Both product purities quickly reach values close to the specifications. 2.2.4. Control Structure CS4 of the LPC → HPC Sequence. This control structure is derived from CS3; the feedforward control of the ratio of the recycling flow rate to the feed flow rate is added as the only difference. The establishment of this control structure is aimed at determining the influence of the feedforward control of the ratio of the recycling flow rate to the feed flow rate. The control flowsheet is shown in Figure 21. The faceplate and flowsheet equations are shown in Supporting Information Figure S12. The controller tuning parameters are shown in Supporting Information Table S13. The results are shown in Figure 22. Compared with CS3, the feedforward control of the ratio of the recycling flow rate to the feed flow rate does not influence the results under composition disturbances, so only the results under feed flow rate disturbances are shown. The only obvious difference from CS3 is the much larger negative transient deviation in methanol product purity under the −10% feed flow rate disturbance. 2.2.5. Comparison. For CS1, the system does not completely reach stability until almost 30 h. For CS2 and CS3, under the +10% feed flow rate and +10% feed composition disturbances, trimethoxysilane product purity of CS3 is much closer to the initial specification than that of CS2 after reaching new steadystate. For CS4 and CS3, under the −10% feed flow rate disturbance, a large negative transient deviation in methanol

Figure 18. Dynamic performance of CS2 of the LPC → HPC sequence of PHI-PSD for separating the methanol/trimethoxysilane mixture. I


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shown in Figure 23, which reveals that robust control can be achieved. 2.3. Dynamic Control of PHI-PSD for Separating the Ethylenediamine/Water Azeotrope. The steady-state flowsheet of this process is reestablished with the same parameters of the previous study26 and shown in Supporting Information Figure S13. As the heat release of overhead vapor condensation of the HPC is sufficient to supply the reboiler duty of the LPC, an auxiliary condenser should be used to condense the remaining overhead vapor.26 The pressure drop through each tray in the columns is set at 0.04 psi.26 In this process, the condenser duty of the HPC is greater than that required to supply the reboiler duty of the LPC, so the operating pressure of the HPC can be controlled by the auxiliary condenser duty. This approach is different from the processes for separating the methanol/ trimethoxysilane mixture. The composition disturbances of this process are based on the ethylenediamine mole fraction. Feed flow rate disturbances of ±20% and feed composition disturbances of ±20% are introduced to test the dynamic controllability. Two control structures are established. The temperature profiles of the HPC and the LPC are shown in Figure 24. The sensitive tray is selected by the “slope criterion” suggested by Luyben.27 The location of the stage with the greatest slope in the HPC is the third stage, while that in the LPC is the fourth stage. 2.3.1. Control Structure CS1 of the Ethylenediamine/Water System. The control flowsheet is shown in Figure 25. The faceplate and flowsheet equations are shown in Supporting Information Figure S14. The controller tuning parameters are shown in Supporting Information Table S14. The control loops are listed as follows: (1) The fresh feed is flow controlled. (2) The pressure of the LPC is controlled by manipulating the heat removal rate of the condenser, while that of the HPC is controlled by manipulating the heat removal rate of the auxiliary condenser. (3) The reflux drum level of the LPC is controlled by manipulating the distillate flow rate, while that of the HPC is controlled by manipulating the reflux flow rate. (4) The base level of the LPC is controlled by manipulating the bottom flow rate. The reboiler duty of the HPC is proportional to the feed flow rate. The ratio is manipulated to control the base level of the HPC.


product purity can be observed for CS4. Therefore, CS3 is the best one. To further investigate the dynamic performances of CS3 under large disturbances, feed flow rate disturbances of ±20% and feed composition disturbances of ±20% are introduced to CS3. The feed composition disturbances are also based on the methanol mole fraction. The results are J


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(5) The bottom flow rate of the HPC is flow controlled at a constant initial value. (6) The third-stage temperature of the HPC (T3) is controlled by manipulating the reciprocal of the reflux ratio. (7) The fourth-stage temperature of the LPC (T4) is controlled by manipulating the reflux ratio. The results are shown in Figure 26. The product purities can be maintained very close to the specifications. However, a large negative transient deviation in water product purity can be observed under the +20% feed composition disturbance. When the bottom flow rate of the HPC is manipulated to control the sump level of the HPC, there are other two control structures. The first makes the reboiler duty of the HPC proportional to the feed flow rate, and the other control loops are the same as in the above control structure. The second manipulates the reboiler duty of the HPC to control T3 with a fixed reciprocal of the reflux ratio of the HPC, and the other control loops are the same as in the above control structure. Both control structures show failure because “snowballing” happens. 2.3.2. Control Structure CS2 of the Ethylenediamine/Water System. The only difference between this control structure and CS1 is the addition of the feedforward control of the ratio of the

Figure 23. Dynamic performance of CS3 of the LPC → HPC sequence of PHI-PSD for separating the methanol/trimethoxysilane mixture under large feed flow rate and composition disturbances.

connecting bottom flow rate to the feed flow rate. The establishment of this control structure is aimed at determining the influence of the feedforward control of the ratio of the connecting bottom flow rate to the feed flow rate. The control flowsheet is shown in Figure 27. The faceplate and flowsheet equations are shown in K


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Figure 24. Temperature profiles of the (a) HPC and (b) LPC of PHI-PSD for separating the ethylenediamine/water mixture.

Supporting Information Figure S15. The controller tuning parameters are shown in Supporting Information Table S15. The results are shown in Figure 28. Compared with CS1, the feedforward control of the ratio of the connecting bottom flow rate to the feed flow rate does not influence the results under composition disturbances, so only the results under feed flow rate disturbances are shown. The obvious differences with CS1 are the larger negative transient deviations in both the water and ethylenediamine product purities under the −20% feed flow rate disturbance. Therefore, CS1 is better than CS2. 2.3.3. Comparison. The robust control structure of Li’s previous study is control structure CS2 in the previous paper.26 First, a large negative transient deviation in water product purity under the +20% feed flow rate disturbance can be observed for CS1 of this study, while it does not happen for CS2 of the previous study. Second, water product purity has a large negative transient deviation under the +20% feed composition disturbance for CS1 of this study, while it has a large negative transient deviation under the −20% feed composition disturbance for CS2 of the previous study. Third, ethylenediamine product purity has a large negative transient deviation under the −20% feed composition disturbance for CS2 of the previous study, while it does not happen for CS1 of this study. Generally speaking, CS1 of this study and CS2 of the previous study are both robust control structures.

Figure 26. Dynamic performance of CS1 of PHI-PSD for separating the ethylenediamine/water mixture.

Finally, two new robust control structures are proposed for PHI-PSD for separating the ethylenediamine/water mixture. The crucial elements to establish robust control of these processes are that the reboiler duty of the HPC should be manipulated to control the sump level of the HPC, and the bottom flow rate of the HPC should be flow controlled. Meanwhile, the influence of the feedforward control of the ratio of the recycling flow rate or the connecting bottom flow rate to the feed flow rate is investigated for all these processes. The results show that CS4 is the best for the HPC → LPC sequence of PHI-PSD for separating the methanol/trimethoxysilane

3. CONCLUSION In this study, robust control strategies are investigated for PHIPSD for separating the maximum-boiling azeotropes methanol/ trimethoxysilane and ethylenediamine/water. First, five new control structures of the HPC → LPC sequence of PHI-PSD for separating the methanol/trimethoxysilane mixture are established and the results show that three of them are robust. Second, the dynamic controllability of the LPC → HPC sequence of PHIPSD for separating the methanol/trimethoxysilane mixture is investigated for the first time with four robust control structures.

Figure 25. Control structure CS1 of PHI-PSD for separating the ethylenediamine/water mixture. L


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Figure 27. Control structure CS2 of PHI-PSD for separating the ethylenediamine/water mixture.

ORCID

Chunjian Xu: 0000-0002-2263-144X Author Contributions §

These authors contributed equally.

Notes

The authors declare no competing financial interest.

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Figure 28. Dynamic performance of CS2 of PHI-PSD for separating the ethylenediamine/water mixture.

mixture; CS3 is the best for the LPC → HPC sequence of PHIPSD for separating the methanol/trimethoxysilane mixture; CS1 is the best for PHI-PSD for separating the ethylenediamine/water mixture. The feedforward control of the ratio of the recycling flow rate or the connecting bottom flow rate to the feed flow rate leads to worse results. In addition, CS4 of the HPC → LPC sequence of PHI-PSD for separating the methanol/ trimethoxysilane mixture and CS1 of PHI-PSD for separating the ethylenediamine/water mixture are compared with the robust control structures of the previous studies. All the robust control structures are valuable in practice for the control of PHI-PSD for separating maximum-boiling azeotropes.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.iecr.8b05562. (1) Thermodynamic data, (2) description of the abbreviations of the control faceplate, (3) process steady-state flowsheet, (4) control faceplate, (5) flowsheet equations of the control structure, (6) parameters of temperature and composition controllers (PDF)

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Robust Control of Partially Heat-Integrated Pressure-Swing Distillation

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