Integrated Process Design and Control of Cyclic Distillation Columns

Proceedings, Proceedings, 10th 10th IFAC IFAC International International Symposium Symposium on on Proceedings, 10th of IFAC International Symposium on at www.sciencedirect.com Advanced Control Chemical Processes Available online Proceedings, 10th IFAC International Symposium on Advanced Control of Chemical Processes Advanced Control of Chemical Processes Proceedings, 10th IFAC International Symposium on Shenyang, Liaoning, China, July 25-27, 2018 Advanced of China, Chemical Processes Shenyang,Control Liaoning, July 25-27, 2018 Shenyang,Control Liaoning, July 25-27, 2018 Advanced of China, Chemical Processes Shenyang, Liaoning, China, July 25-27, 2018 Shenyang, Liaoning, China, July 25-27, 2018

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IFAC PapersOnLine 51-18 (2018) 542–547

Integrated Process Design and Control of Cyclic Distillation Columns Integrated Process Design and Control of Cyclic Distillation Columns Integrated Process Design and Control of Cyclic Distillation Columns Integrated Process Design and Control of Cyclic Distillation Columns Integrated Process Design and Control of Cyclic Distillation Columns Bastian B. Andersen, Rasmus F. Nielsen, Isuru A. Udugama, Emmanouil Papadakis,

Bastian Bastian B. B. Andersen, Andersen, Rasmus Rasmus F. F. Nielsen, Nielsen, Isuru Isuru A. A. Udugama, Udugama, Emmanouil Emmanouil Papadakis, Papadakis, Bastian B.V.Andersen, Rasmus Nielsen, Isuru A. Udugama, Emmanouil Papadakis, Krist Gernaey, Jakob K.F.Huusom, Seyed Soheil Mansouri, Jens Abildskov Krist Gernaey, Jakob Seyed Soheil Mansouri, Jens Bastian Nielsen, Isuru Udugama, Emmanouil Papadakis, KristB.V. V.Andersen, Gernaey, Rasmus Jakob K. K.F.Huusom, Huusom, SeyedA. Soheil Mansouri, Jens Abildskov Abildskov Krist V. Gernaey, Jakob K. Huusom, Seyed Soheil Mansouri, Jens Abildskov Krist V. Gernaey, Jakob K. Huusom, Seyed Soheil Mansouri, Jens Abildskov  Centre (PROSYS), of Chemical and Biochemical Engineering, Process and Engineering  Department Process and Systems Systems Engineering Centre (PROSYS), of Chemical and Biochemical Engineering,  Department Process Systems Engineering Centre (PROSYS), Department of Chemical and Biochemical Engineering, Process and and Systems Engineering Centre (PROSYS), Department of Chemical and Biochemical Engineering, Technical University of Denmark, Søltofts Plads, Building 229, DK-2800 Lyngby, Denmark Technical University of Denmark, Denmark, Søltofts Plads, Plads, Buildingof229, 229, DK-2800 Lyngby, Denmark Process and Systems Engineering Centre (PROSYS), Department Chemical and Lyngby, Biochemical Engineering, Technical University of Søltofts Building DK-2800 Denmark Technical University of Denmark, Søltofts Plads, Building 229, DK-2800 Lyngby, Denmark (E-mails: [email protected], [email protected], [email protected], [email protected], (E-mails: [email protected], [email protected], [email protected], [email protected], Technical University of Denmark, Søltofts Plads, Building 229, DK-2800 Lyngby, Denmark (E-mails: [email protected], [email protected], [email protected], [email protected], [email protected], [email protected], [email protected]) (E-mails: [email protected], [email protected], [email protected], [email protected], [email protected], [email protected], [email protected], [email protected], [email protected]) (E-mails: [email protected], [email protected], [email protected], [email protected], [email protected], [email protected], [email protected], [email protected]) [email protected], [email protected], [email protected], [email protected]) [email protected], [email protected], [email protected], [email protected]) Abstract: Integrated process and control design approach for cyclic distillation columns is proposed. The Abstract: Integrated process and control approach for distillation columns is The Abstract: Integrated is process and control design design approach for cyclic cyclic distillation columns is proposed. proposed. The design methodology based on application of simple graphical design approaches, known from simpler simpler Abstract: Integrated is process and control design approach for cyclic distillation columns is proposed. The design methodology based on application of simple graphical design approaches, known from Abstract: Integrated process and control design approach for cyclic distillation columns is proposed. The design methodology is based on application of simple graphical design approaches, known from simpler conventional distillation columns. Here, aa driving force approach and McCabe-Thiele type analysis is design methodology is based on application of simple graphical design approaches, known from simpler conventional distillation columns. Here, driving force approach and McCabe-Thiele type analysis is design methodology is based on application of simple graphical design approaches, known from simpler conventional distillation columns. Here, a driving force approach and McCabe-Thiele type analysis is conventional distillation columns. Here, a driving force approach and McCabe-Thiele type analysis is combined. It is demonstrated, through closed-loop and open-loop analysis, that operating the column at the combined. It is demonstrated, through closed-loop and open-loop analysis, that operating the column at the conventional distillation columns. Here, a driving force approach and McCabe-Thiele type analysis is combined. It is demonstrated, through closed-loop and open-loop analysis, that operating the column at the combined. It is demonstrated, through closed-loop and open-loop analysis, that operating the column at the largest available driving force results in an optimal design in terms of controllability and operability. The largest available driving force results in an optimal design in terms of controllability and operability. combined. It is demonstrated, through closed-loop and open-loop analysis, that operating the column atThe the largest available driving force results in an optimal design in terms of controllability and operability. The largest available force results in an designed optimal design in terms ofmaximum controllability andforce operability. The performance of aadriving cyclic distillation column to operate at the driving is compared performance of cyclic distillation column to operate at the driving is compared largest available force results in an designed optimal design in terms ofmaximum controllability andforce operability. The performance of aadriving cyclic distillation column designed to operate at the maximum driving force is compared driving force is less performance of cyclic distillation column designed to operate at the maximum driving force is compared to alternative sub-optimal designs. The results suggest that operation at the largest to alternative sub-optimal designs. The results suggest that operation at the largest driving force is less performance of a cyclic distillation column designed to operate at the maximum driving force is compared to alternative sub-optimal designs. The results suggest that operation at the largest driving force is less sensitive to disturbances in the feed and inherently has the ability to reject disturbances. to alternative sub-optimal designs. The results suggest that operation at the largest driving force is less efficiently sensitive to the and has ability to reject to alternative sub-optimalin results suggest that operation at the largest driving force is less sensitive to disturbances disturbances indesigns. the feed feed The and inherently inherently has the the ability to efficiently efficiently reject disturbances. disturbances. sensitive to Cyclic disturbances in theProcess feed andcontrol, inherently has the ability to efficiently reject disturbances. Keywords: distillation, Process design, Process intensification, Driving force sensitive to Cyclic disturbances in the feed andcontrol, has the ability to efficiently disturbances. © 2018, IFAC (International Federation ofinherently Automatic Control) Hosting by intensification, Elsevierreject Ltd. All rights reserved. Keywords: distillation, Process Process design, Process Driving force Keywords: Cyclic distillation, Process control, Process design, Process intensification, Driving force Keywords: Cyclic distillation, Process control, Process design, Process intensification, Driving force Keywords: Cyclic distillation, Process control, Process distillation design, Process intensification, Driving force columns with side draws (Udugama et al. 2017a, distillation columns with side (Udugama et distillation columns with intensified side draws drawsdistillation (Udugamasystems, et al. al. 2017a, 2017a, 2017b). In more complex such 1. INTRODUCTION distillation columns with intensified side drawsdistillation (Udugamasystems, et al. 2017a, 2017b). In more complex such 1. INTRODUCTION INTRODUCTION distillation columns with side draws (Udugama et al. 2017a, 1. 2017b). In more complex intensified distillation systems, such as reactive distillation, the sequential approach can be limiting 2017b). In more complex intensified distillation systems, such 1. INTRODUCTION Distillation has been the dominant separation process over as reactive distillation, the sequential approach can be limiting Distillation has been the dominant separation process over 2017b). In more complex intensified distillation systems, such 1. INTRODUCTION as reactive distillation, the sequential approach can be limiting Distillation has been the dominant separation process over as reactive distillation, the sequential approach can be limiting due to the lack of degrees of freedom as process design Distillation has been the dominant separation process over several decades in the chemical industry worldwide. However, due to the lack of degrees of freedom as process design several decades decades inbeen the industry worldwide. However, distillation, reactive the sequential approach can be limiting due to lack of of freedom as design Distillation has in the dominant separation process over as several the chemical chemical industry worldwide. However, due to the themight lack influence of degrees degrees ofprocess freedom as process process design decisions the control and operation several decadescosts in the chemical with industry worldwide. However, due the associated separation by decisions the control and operation the operating operating costs associated with separation by distillation distillation to themight lack influence of degrees ofprocess freedom as process design decisions might influence the process control and operation several decades in the chemical industry worldwide. However, the operating costs associated with separation by distillation decisions might influence the process control and operation (Mansouri et al. 2015, 2016a, 2016b, 2016c). Additionally, the account for substantial fractions of the total operational cost of the operating costs associated with separation by distillation (Mansouri et al. 2015, 2016a, 2016c). Additionally, the account for fractions of the total operational cost of might influence the2016b, process control and operation (Mansouri et al. 2015, 2016a, 2016b, 2016c). Additionally, the the operating costs associated separation by (Kiss distillation account for substantial substantial fractionswith ofenergy the total operational cost of decisions (Mansouri et al. 2015, 2016a, 2016b, 2016c). Additionally, the sequential approach does not guarantee a robust performance the industry due to the significant demands et al. account for substantial fractions ofenergy the total operational cost of (Mansouri sequential approach does not guarantee aa robust performance the industry due to the significant demands (Kiss et al. et al. 2015, 2016a, 2016b, 2016c). Additionally, the sequential approach does not guarantee robust performance due to the significant energy demands (Kiss et al. account for substantial fractions of the total operational cost of the industry sequential approach does not guarantee a robust performance due to its limitations related to dynamic constraint violations 2012, Kraller et al. 2016, Sholl et al. 2016). Therefore, it is the industry due significant demands (Kiss etital. due limitations related dynamic violations 2012, Kraller et to al.the 2016, Sholl et etenergy al. 2016). 2016). Therefore, is sequential approach does notto guarantee aconstraint robust performance due to toasits its operating limitations related to dynamic constraint violations the industry due to the significant energy demands (Kiss etital. et al. 2016, Sholl al. Therefore, 2012, Kraller is over-design, underdue its operating limitationspoints, related process to dynamic constraint or violations 2012, Kraller et al. 2016, Sholl et al.economic 2016). Therefore, it of is such desirable to improve the energy and efficiency suchto asits points, process over-design, or underdesirable to improve the energy and economic efficiency of due to limitations related to dynamic constraint violations such as operating points, process over-design, or under2012, Kraller et al. 2016, Sholl et al.economic 2016). Therefore, it of is performance to improve the energy and desirable efficiency (Seferlis and Georgiadis, 2004). One way to such as operating points, process over-design, or way underdesirable to processes. improve the energy and economic efficiency of performance distillation A substantial body of the literature (Seferlis and Georgiadis, 2004). One to distillation processes. A substantial body of the literature such as operating points, process over-design, or underperformance (Seferlis and Georgiadis, 2004). One way to desirable to processes. improve the energy and economic efficiency of overcome distillation A substantial body of the literature these limitations is to tackle design and control performance (Seferlis and Georgiadis, 2004). One way to distillation processes. A substantial body of the literature attempts to address this need for separations by introducing overcome these limitations is to tackle design and control attempts to address this need for separations by introducing performance (Seferlis and Georgiadis, 2004). One way to overcome these limitations is to tackle design and control distillation substantial body ofbytheintroducing literature issues to processes. address thisAneed attempts for separations overcome these limitations isTherefore, to tackle to design and control in an integrated fashion. assure that design attempts to address this need for separations by introducing intensified and highly integrated process design alternatives issues in an integrated fashion. Therefore, to assure that design intensified highly design these limitations isTherefore, to tackle to design and control issues in integrated fashion. that design attempts to and address thisintegrated need for process separations by alternatives introducing overcome intensified and integrated process alternatives issues in an angive integrated fashion. Therefore, to assure assure that design decisions the optimum operational and economic intensified and highly highly integrated diabatic process design design alternatives such reactive distillation, distillation, heatdecisions the optimum operational and economic such as as reactive distillation, diabatic distillation, heat- issues in angive integrated fashion. Therefore, to assure that design decisions give the optimum operational and economic intensified and highly integrated process design alternatives such as reactive distillation, diabatic distillation, heatdecisions give the optimum operational and economic performance, operability and controllability issues are integrated distillation, divided wall columns and cyclic such as reactive distillation, distillation, heat- performance, and controllability are integrated distillation, divided diabatic wall columns columns and cyclic giveoperability the optimum operational and issues economic performance, operability and controllability issues are such as reactive distillation, diabatic distillation, heat- decisions and cyclic integrated distillation, divided wall performance, operability and controllability issues are preferably considered simultaneously with the process design distillation (Kiss et al. 2014). Here we focus on cyclic integrated distillation, divided wall columns and preferably considered simultaneously with the process design distillation (Kiss et al. 2014). Here we focus on cyclic performance, operability and controllability issues are preferably considered simultaneously with the process design et al. 2014). Here we focus on integrated distillation, divided wall columns and cyclic distillation (Kiss preferably considered simultaneously with the process design issues. distillation, which has shown promising results by lowering distillation (Kiss et al.shown 2014). Here we focusbyon cyclic preferably issues. distillation, which has promising results lowering considered simultaneously with the process design issues. distillation (Kiss et al.shown 2014). Here we focusbyon cyclic distillation, which has promising results distillation, whichcost has by shown promising results by lowering lowering issues. the operational 30-50% relative to conventional the operational 30-50% relative to conventional In this work, aa methodology for integrated process and control distillation, whichcost has by shown promising results by lowering issues. In this work, for integrated process and control the operational cost by 30-50% relative to conventional In this work, a methodology methodology for integrated process and control the operational cost by 30-50% relative to (Bîldea conventional distillation due to the lower energy requirement et al. distillation due to the lower energy requirement (Bîldea et al. In this work, a methodology for integrated process and control structure design for reactive distillation in conventional the operational cost by 30-50% relative to (Bîldea conventional structure design for reactive distillation in conventional distillation due to the lower energy requirement et al. In this work, a methodology for integrated process and control structure design for reactive distillation in conventional distillation due to the lower energy requirement (Bîldea et al. 2016). 2016). structure design for reactive distillation in conventional columns, proposed by Mansouri et al. (2016a) is used to distillation due to the lower energy requirement (Bîldea et al. structure columns, proposed Mansouri et al. (2016a) is used to 2016). design forby reactive distillation in conventional columns, proposed by Mansouri et al. (2016a) is used to 2016). columns, proposed by Mansouri et al. (2016a) is used to demonstrate the integrated process and control structure Cyclic distillation is a highly efficient method of separation, 2016). demonstrate the integrated process and control structure Cyclic distillation is a highly efficient method of separation, columns, proposed by Mansouri et al. (2016a) is used to demonstrate the integrated process and control structure Cyclic distillation is a highly efficient method of separation, design of cyclic distillation columns, also known as periodic demonstrate the integrated process and control structure Cyclic distillation is a highly efficient method of separation, with tray efficiencies substantially greater than those of design distillation also as periodic with tray efficiencies substantially those of demonstrate theapplicability integratedcolumns, process and known control design of of cyclic cyclic distillation columns, also known as structure periodic Cyclic distillation is a highly efficientgreater methodthan of separation, with tray efficiencies substantially greater than of The of the proposed methodology has design of cyclic distillation columns, also known as periodic with traytrays. efficiencies substantially greaterconcepts than those those of distillation. classical The underlying theoretical and the distillation. The applicability of the proposed methodology has classical trays. The underlying theoretical concepts and the design of cyclic distillation columns, also known as periodic distillation. The applicability of the proposed methodology has with traytrays. efficiencies substantially greaterconcepts than those of been classical The underlying theoretical and the highlighted in various cases involving binary reacting distillation. The applicability of the proposed methodology has classical trays. The underlying theoretical concepts and the engineering models of periodic cycling were developed been highlighted in various cases involving binary reacting engineering models of periodic cycling were developed distillation. The applicability of the proposed methodology has been highlighted in various cases involving binary reacting classical trays. The underlying theoretical concepts and the mixtures engineering models of periodic cycling were developed been highlighted inet various cases involving binary mixtures reacting (Mansouri al. 2016a) and ternary reacting engineering models of periodic cycling were developed sometime between 30’s and 50’s. However, practical results mixtures (Mansouri et al. 2016a) and ternary reacting mixtures sometime between 50’s. However, practical results been highlighted inetvarious cases involvingreacting binary mixtures reacting mixtures (Mansouri and engineering models30’s of and periodic cycling were developed sometime between 30’s 50’s. practical results mixtures (Mansouri et al. al. 2016a) 2016a) and ternary ternary reactingHere, mixtures one inert component (Mansouri et al. 2016b). first sometime between 30’s and and 50’s. However, However, practical results with leading realistic applications have much with one inert component (Mansouri et al. 2016b). Here, first leading towards towards realistic applications have been been much slower. slower. mixtures (Mansouri et al. 2016a) and ternary reacting mixtures with one inert component (Mansouri et al. 2016b). Here, first sometime between 30’s and 50’s. However, practical results leading towards realistic applications have been much slower. with one inert component (Mansouri et al. 2016b). Here, first cyclic distillation column design at the maximum driving force A significant body of both experimental and theoretical studies leading towards realistic applications have been much slower. cyclic distillation column design at the maximum driving force A significant body of both experimental and theoretical studies with one inert component (Mansouri etmaximum al. 2016b). Here,force first cyclic distillation column design at the driving leading towards realistic applications have been much slower. A significant body of both experimental and theoretical studies cyclic distillation column design at the maximum driving force is obtained using the method of Nielsen et al. (2017). Next, we have been made on cyclic distillation. Despite the significant A significant bodyonofcyclic both experimental and theoretical studies cyclic is using method of et Next, we have been made distillation. Despite the significant distillation column design at the maximum driving force is obtained obtained using the the method of Nielsen Nielsen et al. al. (2017). (2017). Next, we A significant body of both experimental and theoretical studies have been made on cyclic distillation. Despite the significant is obtained using method of Nielsen et al. (2017). Next, we demonstrate that the same concepts that are valid at maximum benefits over conventional distillation methods, its large-scale have been made on cyclic distillation distillation.methods, Despite the significant is demonstrate that the same concepts that are valid at maximum benefits over conventional its large-scale obtained using method of Nielsen et al. (2017). Next, we demonstrate that the same concepts that are valid at maximum have been made on cyclic distillation distillation.methods, Despite the significant driving benefits over conventional its large-scale force (for design and controllability) for conventional demonstrate that the same concepts that are valid at maximum benefits over conventional distillation methods, its large-scale implementation has not been as extensive as one might expect driving force (for design controllability) for conventional implementation has not been as extensive as oneits might expect demonstrate sameand concepts that are valid at maximum driving forcethat (forthe design and controllability) for conventional benefits over conventional distillation methods, large-scale implementation has been as might expect non-reactive distillation columns are also valid in driving forceand (forreactive design and controllability) for conventional implementation has not not Further been as as extensive extensive as one onein might expect (Bîldea et al. al. 2016). 2016). Further investigations relation to non-reactive and reactive distillation columns are also valid in in relation to (Bîldea et investigations driving force (for design and controllability) for conventional non-reactive and reactive distillation columns are also valid implementation has not Further been as extensive as oneinmight expect (Bîldea et al. 2016). investigations relation to case of non-reactive cyclic distillation columns. non-reactive and reactive distillation columns are also valid in in (Bîldea et al. 2016). Further investigations in relation to process control are needed to uncover the potential and reap case of non-reactive cyclic distillation columns. process control are needed to uncover the potential and reap and reactive distillation columns are also valid in case (Bîldea et al. 2016). Further investigations in relation to non-reactive process control are needed to uncover the potential and reap case of of non-reactive non-reactive cyclic cyclic distillation distillation columns. columns. process control are needed to uncover the potential and reap fully the benefits of the technique. fully thecontrol benefitsare of needed the technique. non-reactive cyclic distillation columns.DESIGN 2. CYCLIC DISTILLATION COLUMN process to uncover the potential and reap case of 2. fully 2. CYCLIC CYCLIC DISTILLATION DISTILLATION COLUMN COLUMN DESIGN DESIGN fully the the benefits benefits of of the the technique. technique. 2. CYCLIC DISTILLATION COLUMN DESIGN fully the benefits of the technique. Traditionally, process design and control have been considered Traditionally, process design and control have been considered 2. CYCLIC DISTILLATION COLUMN DESIGN Design of cyclic distillation columns, due to the separate vapor Design of cyclic distillation columns, due to the separate vapor Traditionally, process design and control have considered Design of cyclic distillation columns, due to the separate vapor tasks, with coming Traditionally, process design andprocess controldesign have been been considered separate sequential before separate sequential tasks, with process design coming before Design of cyclic distillation columns, due to the separate vapor and liquid flow periods during a cycle, is a more complex task Traditionally, process design andprocess controldesign have been considered and liquid flow periods during a cycle, is a more complex task separate sequential tasks, with coming before Design of cyclic distillation columns, due to the separate vapor and liquid flow periods during a cycle, is a more complex task system design. systems, separate sequential tasks, with process design coming before control In intensified separation this control system design. In intensified separation systems, this and liquid flow periods during a cycle, is a more complex task than design of conventional distillation columns, using separate sequential tasks, with processseparation design coming before thanliquid design ofperiods conventional distillation columns, using control system design. In intensified systems, this and flow during a cycle, is a more complex task than design of conventional distillation columns, using control system design. In intensified separation systems, this sequential approach can lead to controllability limitations and sequential approach can lead to controllability limitations and than design of conventional distillation columns, using graphical tools such as the McCabe-Thiele method. However, control system design. In intensified separation systems, this graphical toolsofsuch such as the the McCabe-Thiele McCabe-Thiele method. However, sequential approach can lead to controllability limitations and than design conventional distillation columns, using graphical tools as method. However, sequential approach can lead to controllability limitations require complex process control even in require unduly unduly complex process control structures, structures, evenand in graphical tools such as the McCabe-Thiele method. However, sequential approach can lead to controllability limitations and require unduly complex process control structures, even in graphical tools such as the McCabe-Thiele method. However, require unduly complex process control structures, even in Hosting 2405-8963 © 2018, complex IFAC (International Federation of Automatic Control) by Elsevier Ltd. All rights reserved. require unduly process control structures, even in Copyright © 2018 IFAC 536 Copyright 2018 responsibility IFAC 536 Peer review©under of International Federation of Automatic Control. Copyright 536 Copyright © © 2018 2018 IFAC IFAC 536 10.1016/j.ifacol.2018.09.368 Copyright © 2018 IFAC 536 Copyright © 2018 IFAC 536

2018 IFAC ADCHEM Shenyang, Liaoning, China, July 25-27, Bastian 2018 Borum Andersen et al. / IFAC PapersOnLine 51-18 (2018) 542–547

a similar analysis using operating lines and the corresponding McCabe-Thiele constructions can be used for design of a cyclic column. To draw the operating lines of a cyclic column, ̅̅̅̅̅̅) the time-averaged vapor composition that enters tray 𝑛𝑛 (𝑦𝑦 𝑛𝑛+1 can be plotted against the liquid composition at the tray at the (𝑉𝑉) end of the vapor flow period (𝑥𝑥𝑛𝑛 ). The McCabe-Thiele diagram for conventional distillation columns assumes continuous internal and external flows. However, for the cyclic column, the internal and external flows are also constant when expressed in terms of amounts per cycle during steady operation. Therefore, the McCabe-Thiele steps for the cyclic system are different from the classical McCabe-Thiele steps, as the tray efficiency, ET, of a cyclic tray, 𝐸𝐸𝑇𝑇 =

̅̅̅ 𝑦𝑦𝑛𝑛+1 𝑦𝑦𝑛𝑛 − ̅̅̅̅̅̅

𝑦𝑦𝑛𝑛

(𝑉𝑉)

− ̅̅̅̅̅̅ 𝑦𝑦𝑛𝑛+1

Step 5: Run the design algorithm for NT stages and place the feed stage 𝑁𝑁𝑁𝑁 where 𝑥𝑥𝑁𝑁𝑁𝑁 ≈ 𝐷𝐷𝑥𝑥 , Step 6: If the distillate composition at the start of the vapor flow period matches the specified composition, the design has been obtained. If not, go to Step 3 and adjust 𝑉𝑉 ∙ 𝑡𝑡𝑣𝑣𝑣𝑣𝑣𝑣 accordingly. In this work, the design method of a cyclic distillation column is considered for a binary mixture of ethanol and water. In Table 1, the feed and product target compositions are given. Table 1. The feed and product molar fraction specifications. Component zF xB xD Ethanol 0.1500 0.0001 0.8300 Water 0.8500 0.9999 0.2700

(1)

The Wilson thermodynamic model was employed to predict liquid phase activity coefficients, and the vapor phase is assumed to behave ideally. Figure 1 shows the driving force diagram to perform the separation task by a cyclic distillation column together with the operating lines (SOL: stripper operating line, ROL: rectifying operating line). The corresponding operating lines and analogous McCabe-Thiele constructions are shown in Figure 2.

This efficiency is substantially greater than that of a classical tray. To calculate the ideal number of stages for cyclic operation, a backwards integration method, like the one of Toftegård and Jørgensen (1987) and extended by Pătruţ et al. (2014), can be utilized. The design algorithm requires a specified bottoms composition and knowledge about all the internal and external flows for the column. The algorithm integrates hereafter the mass-balances, for each stage, backwards in time, stage-by-stage. With this procedure, an approximate feed location is found together with the number of required stages for obtaining the specified separation. This design algorithm is however limited to only model saturated liquid feeds, which restricts the possibilities of operation. With an extended mass balance model, as suggested by Nielsen et al. (2017), the design algorithm can be used for mixed phase feeds (0 < q < 1). This makes it possible to obtain a driving force design for the cyclic distillation. The driving force, FDi, is defined as the difference in composition of a component i between the vapor phase and the liquid phase: 𝐹𝐹𝐹𝐹𝑖𝑖 = |𝑦𝑦𝑖𝑖 − 𝑥𝑥𝑖𝑖 |

543

Driving force, FD i = |yi – x i |

0.4

0.0

xB

Dx zF

xD

1.0

Liquid molar fraction at the end of the VFP, xn(V)

(2)

Fig. 1. Driving force diagram for the separation of ethanolwater mixture.

The driving force concept, based on identification of the largest driving force (see Figure 1), is used to find the optimal design target values of the process variables for separation systems. The algorithm for this combines the method of Pătruţ et al. (2014) with parts of the driving force procedure by BekPedersen and Gani (2004). The procedure is as follows:

Table 2 lists the operating parameters for the separation (outputs of the design approach). The optimal feed location is two trays above the reboiler, which is tray 12. Figure 2 shows that cyclic distillation requires far less trays, compared to a conventional distillation column with the same internal flows, due to the enhanced tray efficiency.

Step 1: Find the maximum driving force composition (𝐷𝐷𝑥𝑥 ) for the mixture,

Table 2. The operating parameters for the driving force based design of cyclic distillation column (RR is the reflux ratio, and RB is the boil-up ratio). V∙tvap/F q xF yF RR RB 0.778 0.837 0.093 0.441 4.212 0.950

Step 2: Specify product and feed compositions, all external flows, and the number of stages (𝑁𝑁𝑁𝑁), Step 3: Specify the internal vapor-flow rate (𝑉𝑉 ∙ 𝑡𝑡𝑣𝑣𝑣𝑣𝑣𝑣 ) and calculate the rest of the internal flow rates, Step 4: Adjust q, so the operating lines intersect at 𝑥𝑥 = 𝐷𝐷𝑥𝑥 , and calculate the corresponding molar fractions 𝑥𝑥𝐹𝐹 and 𝑦𝑦𝐹𝐹 ,

537

2018 IFAC ADCHEM 544 Bastian Shenyang, Liaoning, China, July 25-27, 2018 Borum Andersen et al. / IFAC PapersOnLine 51-18 (2018) 542–547

Condenser: 𝑑𝑑 ℎ = 𝐻𝐻2 − 𝑄𝑄𝐶𝐶 𝑑𝑑𝑑𝑑 1

1.0

8

54 7 6

321

Trays (𝑛𝑛 = [2 … 𝑁𝑁𝑁𝑁 − 2; 𝑁𝑁𝑁𝑁 … 𝑁𝑁𝑁𝑁 − 1]): 𝑑𝑑 ℎ = 𝐻𝐻𝑛𝑛+1 − 𝐻𝐻𝑛𝑛 𝑑𝑑𝑑𝑑 𝑛𝑛

Vapor molar fraction, yn+1

9 10

Tray above feed tray: 𝑑𝑑 ℎ = 𝐻𝐻𝑁𝑁𝑁𝑁 + 𝐻𝐻𝐹𝐹 − 𝐻𝐻𝑁𝑁𝑁𝑁−1 𝑑𝑑𝑑𝑑 𝑁𝑁𝑁𝑁−1

q-line

11

12 xB

0.0

(7)

xF

1.0

xD

Liquid molar fraction at the end of the VFP, xn(V)

Fig. 2. McCabe-Thiele constructions for the cyclic distillation (stage 12 is the reboiler).

Reboiler: 𝑑𝑑 ℎ = 𝑄𝑄𝐵𝐵 − 𝐻𝐻𝑁𝑁𝑁𝑁 𝑑𝑑𝑑𝑑 𝑁𝑁𝑁𝑁

(8)

(9)

(10)

Liquid flow period (LFP): 3. DYNAMIC PROCESS MODEL

a.

Here we employ the dynamic process model of Andersen (2016), based on the model of Lita et al. (2014). The purpose of this model is to describe the internal and external vapor and liquid flows, the temperature, the composition profiles and the energy requirements in a cyclic distillation column. The process model is developed under the following assumptions: (a) vapor-liquid equilibrium is reached instantaneously, (b) perfect mixing on each stage, (c) negligible vapor hold-up, (d) negligible pressure drop throughout the column, (e) negligible heat exchange with surroundings, (f) complete condensation of entering vapor, and (g) any boiling liquid will remain boiling throughout the VFP. Energy and mass balances are shown for the liquid and vapor flow periods. The notation uses capital H for vapor enthalpies and lower case h for liquid enthalpies, where M is the liquid hold up. Superscript (V) and (L) respectively denotes values at the end of the vapor and liquid flow period, where subscript j indicates the specific component. Q is the energy input for the condenser and reboiler and B, D and L are respectively the bottoms, distillate and reflux streams. The equations are as follows:

(11)

Tray below condenser: (𝐿𝐿) (𝑉𝑉) 𝑀𝑀2,𝑗𝑗 = 𝐿𝐿𝑥𝑥1,𝑗𝑗

(12)

Trays (𝑛𝑛 = [3 … 𝑁𝑁𝑁𝑁 − 1; 𝑁𝑁𝑁𝑁 + 1 … 𝑁𝑁𝑁𝑁 − 1]): (𝐿𝐿) (𝑉𝑉) 𝑀𝑀𝑛𝑛,𝑗𝑗 = 𝑀𝑀𝑛𝑛−1,𝑗𝑗

(13)

Feed tray: (𝐿𝐿) (𝑉𝑉) 𝑀𝑀𝑁𝑁𝑁𝑁,𝑗𝑗 = 𝑀𝑀𝑁𝑁𝑁𝑁−1,𝑗𝑗 + 𝐹𝐹𝐿𝐿 𝑥𝑥𝐹𝐹,𝑗𝑗

(14)

Reboiler: (𝐿𝐿) (𝑉𝑉) (𝑉𝑉) (𝑉𝑉) 𝑀𝑀𝑁𝑁𝑁𝑁,𝑗𝑗 = 𝑀𝑀𝑁𝑁𝑁𝑁,𝑗𝑗 + 𝑀𝑀𝑁𝑁𝑁𝑁−1,𝑗𝑗 − 𝐵𝐵𝑥𝑥𝑁𝑁𝑁𝑁,𝑗𝑗

(15)

Energy balances for VFP:

Condenser: ℎ1 = ℎ1 (1 − (𝐿𝐿)

Mass balances for VFP:

Condenser: 𝑑𝑑 𝑀𝑀 = 𝑉𝑉2 𝑦𝑦2,𝑗𝑗 𝑑𝑑𝑑𝑑 1,𝑗𝑗

Condenser: (𝐿𝐿) (𝑉𝑉) (𝑉𝑉) 𝑀𝑀1,𝑗𝑗 = 𝑀𝑀1,𝑗𝑗 − (𝐷𝐷 + 𝐿𝐿)𝑥𝑥1,𝑗𝑗

b.

Vapor flow period (VFP): a.

Mass balances for LFP:

(𝑉𝑉)

𝐷𝐷 + 𝐿𝐿 𝑀𝑀1

(𝑉𝑉)

)

(16)

Tray below condenser: 𝐿𝐿 (𝑉𝑉) (𝐿𝐿) ℎ2 = (𝑉𝑉) ℎ1 𝑀𝑀1

(3)

(17)

Trays (𝑛𝑛 = [2 … 𝑁𝑁𝑁𝑁 − 2; 𝑁𝑁𝑁𝑁 … 𝑁𝑁𝑁𝑁 − 1]): 𝑑𝑑 𝑀𝑀 = 𝑉𝑉𝑛𝑛+1 𝑦𝑦𝑛𝑛+1,𝑗𝑗 − 𝑉𝑉𝑛𝑛 𝑦𝑦𝑛𝑛,𝑗𝑗 𝑑𝑑𝑑𝑑 𝑛𝑛,𝑗𝑗

(4)

Trays (𝑛𝑛 = [3 … 𝑁𝑁𝑁𝑁 − 1; 𝑁𝑁𝑁𝑁 + 1 … 𝑁𝑁𝑁𝑁 − 1]): (𝑉𝑉) (𝐿𝐿) ℎ𝑛𝑛 = ℎ𝑛𝑛−1

Tray above feed tray: 𝑀𝑀𝑁𝑁𝑁𝑁−1,𝑗𝑗 = 𝑉𝑉𝑁𝑁𝑁𝑁 𝑦𝑦𝑁𝑁𝑁𝑁,𝑗𝑗 + 𝐹𝐹𝑉𝑉 𝑦𝑦𝐹𝐹,𝑗𝑗 − 𝑉𝑉𝑁𝑁𝑁𝑁−1 𝑦𝑦𝑁𝑁𝑁𝑁−1,𝑗𝑗

(5)

Feed tray: (𝐿𝐿) (𝑉𝑉) ℎ𝑁𝑁𝑁𝑁 = ℎ𝑁𝑁𝑁𝑁−1 + ℎ𝐹𝐹

Reboiler: 𝑑𝑑 𝑀𝑀 = −𝑉𝑉𝑁𝑁𝑁𝑁 𝑦𝑦𝑁𝑁𝑁𝑁,𝑗𝑗 𝑑𝑑𝑑𝑑 𝑁𝑁𝑁𝑁,𝑗𝑗 b.

Reboiler:

ℎ𝑁𝑁𝑁𝑁 = ℎ𝑁𝑁𝑁𝑁 + ℎ𝑁𝑁𝑁𝑁−1 − (𝐿𝐿)

(6)

(𝑉𝑉)

(𝑉𝑉)

(18) (19)

𝐵𝐵

𝑀𝑀𝑁𝑁𝑁𝑁

(𝑉𝑉)

ℎ𝑁𝑁𝑁𝑁

(𝑉𝑉)

(20)

The liquid is assumed boiling at all times once it has reached its boiling point (see assumption (g) above). Therefore, during the VFP time derivatives of the tray temperatures can be

Energy balances for VFP:

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determined from chain-rule algebra when df = 0; thus, f = 1 ∑j xj Kj.

545

optimal solution for x (states) and y (outputs) is obtained at the maximum point of the driving force; see diagram in Figure 3, which is based on θ (the constitutive variables). By model analysis, the corresponding derivative information (with respect to x, y, u, d and θ) which satisfies controller design objectives, can be obtained.

Note also that the LFP is non-dynamic because all liquid holdup on each tray dumps down to the stage below with no back mixing or any other interaction with the rest of the process. This is justified by the assumption of each tray having a sluice chamber, allowing for plug flow. The model is applicable for cases of multiphase feed, though the parameter q does not explicitly appear in the model equations. Its effect is incorporated by flashing the feed prior to introducing it to the column, thereby separating the feed flow F in a liquid and vapor fraction, respectively FL and FV. Thereby the vapor feed fraction is continuously supplied during the VFP to stage NF – 1 as shown in equation 5. The liquid fraction is transferred to stage NF during the LFP, as shown by equation 14. A pressure-enthalpy flash calculation evaluates the separation of the feed mixture. In order to implement this feature, the previous definition of the feed tray was altered, where the liquid feed would previously drop to stage NF + 1, meaning the designated feed stage differs by a single stage with this definition. Similarly, the mass and energy balances were modified, by splitting the feed into two individual stages. Inclusion of energy balances means that a non-constant vapor flow profile is obtained for the column. This means that one of the controlled variables (RR or BR) will deviate slightly from the pseudo-steady-state design based on models not employing energy balances.

d

y

u

Process Model Balance Equations

Ө

Constraint Equations

Constitutive Equations

T, P, x

Fig. 3. Dynamic process system representation (Mansouri et al., 2016a)

As shown in section 2, selecting the design targets at the maximum driving force when designing the cyclic distillation column, the optimal design objectives are obtained. Furthermore, these design targets achieve the best controllability and operability of the process from a controller point of view. This means that, the derivative of the controlled variables y with respect to disturbances in the feed, d (dy/dd) and manipulated variables, u (dy/du) will determine the process sensitivity and influence of the control structure selection. Accordingly, dy/dd and dy/du are defined as (Russel et al., 2002):

4. OPTIMAL DESIGN-CONTROL SOLUTION The development of an integrated approach can be achieved by taking into consideration key process variables and their target values that influence process-controller design. The solution to this optimization problem must balance the tradeoffs between opposing process design and control requirements. As such, a systematic analysis needs to be performed to identify optimal design together with designmanipulated variables u, process-controlled variables y, and their target set points. It is important to note that their pairing significantly contributes to the integration of process design, operation and control. A systematic analysis in this context may provide additional or innovative options to address the conflicting trade-offs between process design, control and operation of an intensified distillation process such as cyclic distillation.

dy  dy  d  dx      dd  d  dx  dd 

(21)

dy  dy  d  dx      du  d  dx  du 

(22)

The values for dθ/dx can be obtained from the process (dynamic and/or steady state) constraints: dx (23)  f  x, y, u, d , , Y , t  dt and values for dy/dθ, dx/dd and dx/du can be obtained from constitutive (thermodynamic) constraints:

From a process design point of view, a set of process design objectives (specifications) needs to be determined at the maximum driving force that also satisfy the specified inputs, u, and disturbances, d, values for states, x, and outputs, y. In this case x and y also represent some of the operational conditions for the process. From a controller design point of view values of u need to be determined that are able to recover the process to its optimal designed condition at the maximum driving force, for any changes in d and/or set point values in y. It is also important to note that x and y are directly influenced by θ (the constitutive variables such as reaction rate or equilibrium constant). This concept is illustrated through representation of a dynamic process system in Figure 3. The

0  g  u, x, y   

(24)

It must be noted that at the maximum driving force, the sensitivity of controlled variables, y, to disturbances, d, is minimum while the sensitivity of y variables to manipulated variables, u, is maximum. This has been demonstrated in detail by Mansouri et al. (2016a, 2016b). Interested readers are referred to that work for further details and analytical analyses. Dynamic simulations were conducted in MATLAB on a system defined by the design parameters through the method by Nielsen (2017) – see section 2. The reboiler duty was approximated from the overall vapor flow for a total cycle, as the dynamic model simulates a dynamic and altering vapor 539

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flow. The system was allowed to reach pseudo-steady state under these conditions, where the combined mass and energy model’s response to the design decisions was obtained. The reboiler duty was gradually altered as to obtain the exact averaged vapor flow, where the reflux ratio differs. Perturbations of ±10% were introduced in the feed flow rate as to evaluate the open loop response of this. This was applied to different systems, where all parameters were unchanged except the feed stage.

rate is observed. All these designs use the same process control strategy and process tuning parameters and the results shown are these closed-loop responses. Analyzing the all-important reboiler duty variable, which is the manipulated variable in this control structure, illustrates that the optimal design has a noticeably lower reboiler duty usage for both feed flow perturbations.

The condenser’s liquid hold-up, the reflux flow and the distillate flow are constrained, leaving only a single control variable as stated by Matsubara (1982). This may be the vapor flow duration, reboiler duty or changes in the feed. Easy controllability was provided by the reboiler duty, which was altered to achieve the desired purities of the products, meaning the reflux ratio changed as well as to retain a constant condenser hold-up. This clearly illustrated that the smallest disturbance in both top and bottom composition was obtained while operating at a feed stage corresponding to the optimal driving force, as expected. A simple discrete PI controller was introduced as stated by Matsubara (1982), of the following form (𝜃𝜃𝑣𝑣 )𝑖𝑖+1 = (𝜃𝜃𝑣𝑣 )𝑖𝑖 − 𝐾𝐾𝑃𝑃 (𝑒𝑒𝑖𝑖 − 𝑒𝑒𝑖𝑖−1 ) − 𝐾𝐾𝐼𝐼 𝑒𝑒𝑖𝑖 .

(25)

The manipulated value 𝜃𝜃𝑣𝑣 was chosen as the reboiler duty, 𝑄𝑄𝐵𝐵 , and 𝑒𝑒 is the control error of the bottom product concentration. It was chosen to monitor the offset in the ethanol concentration. In this case, the controller was tuned relatively aggressively as the inherent cyclic nature of the process coupled with relatively long column time constants required aggressive control actions to keep the column within specification. The fastest response time for the closed loop simulations was obtained while operating as close to the maximum driving force as possible. Not only is the fastest response time observed, but generally the magnitude of the fluctuations is smaller, though there are exceptions. To test the ability of the proposed optimal design to reject disturbances, the optimal cyclic distillation column design was compared with two suboptimal designs. Critical process parameters of these three designs are recorded in the table below, Where B = 245.8 (bottom flow rate), D = 54.2 (distillate flow rate) and F = 300 (feed flow rate) are recorded in moles per cycle. The design alternatives are considered by altering the feed location.

Fig. 4. The closed loop process response of the optimal process design and suboptimal process designs to ±10% change in feed flow rate. Closer inspection reveals that the two suboptimal controllers continue to have a process offset for a relatively long duration. Thus, it can be concluded that the optimal process design has better disturbance rejection characteristics as the integral absolute error (IAE) is two times smaller than for the competing suboptimal designs. If a design is able to quickly return the controlled process variable to its steady state value it illustrates the design’s ability to stabilize the column during process disturbances. In this instance, the superior controllability is associated with the optimal process design, which swiftly is able to bring the bottom ethanol concentration back to its set point with a smaller absolute offset than the suboptimal designs. The variation in the controller variable is also smaller, illustrating that operating at the optimal driving force ensures economic optimization as well. It should be stressed that the objective was not to optimize the controller, but to exemplify the principle of optimized controllability, where further tuning of the controller would increase the efficiency vastly. Long settling times are observed in the top, however

Table 3. Operating parameters for optimal design and alternative sub-optimal designs Design Optimal (FD Design) Suboptimal 1 Suboptimal 2

𝐍𝐍𝐅𝐅 12 10 9

𝐍𝐍𝐓𝐓 13 13 13

𝐭𝐭 𝐕𝐕𝐕𝐕𝐕𝐕 [s] 9.41 9.41 9.41

𝐐𝐐𝐁𝐁 [kW] 1019 1136 1460

Based on the results in Table 1, it can be expected that the optimal distillation column design should have a lower reboiler duty on average. In Figure 4, the response of the optimal cyclic distillation column design along with two suboptimal designs for a ±10% disturbance in the feed flow 540

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due to the control structure this response is the system’s natural response, on which the controller performance cannot be evaluated where the relative offset is furthermore low.

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distillation processes. IFAC-PapersOnLine, 48 (8), 10201025. Mansouri, S. S., Huusom, J. K., Gani, R. and Sales-Cruz, M. (2016a). Systematic integrated process design and control of binary element reactive distillation processes. AIChE J., 62, 3137–3154. Mansouri S.S., Sales-Cruz M., Huusom J.K., and Gani R. (2016b). Systematic integrated process design and control of reactive distillation processes involving multielements, Chem. Eng. Res. Des., 115, 348-364 Mansouri S.S., Sales-Cruz M., Huusom J.K., and Gani R. (2016c). Integrated process design and control of multielement reactive distillation processes. IFACPapersOnLine 49 (7), 735–740. Matsubara, M., Nishimura, Y., Watanabe, N. and Onogi, K. (1982). Relay feedback periodic control of plate columns. Chemical Engineering Science, 37, 753-758. Nielsen, R.F., Huusom, J.K., Abildskov, J. (2017). Driving force based design of cyclic distillation, Ind. Eng. Chem. Res., 56, 10833–10844. Russel, B. M., Henriksen, J. P., Jørgensen, S. B., Gani, R. (2002). Integration of design and control through model analysis. Comput. Chem. Eng., 26, 213-225. Seferlis, P. and Georgiadis, M. C. (2004). The integration of process design and control, Elsevier B. V., Amsterdam. Sholl, D. S. and Lively, R. P. (2016). Seven chemical separations to change the world. Nature, 532, 435-437. Patrut, C., Bîldea, C. S., Lit ̧ A.I., Kiss, A. A. (2014). Cyclic distillation. Design, control and applications. Sep. Purif. Technol., 125, 326-336. Toftegård, B. and Jørgensen, S. B. (1987). Design Algorithm for Periodic. Cycled Binary Distillation Columns. Ind. Eng. Chem. Res., 1987, 26, 1041-1043. Toftegård, B., Clausen, C. H., Jørgensen, S. B. and Abildskov, J. (2016). New Realization of Periodic Cycled Separation. Ind. Eng. Chem. Res., 55, 1720-1730. Udugama. I.A., Wolfenstetter, F. Kirkpatrick, R., Yu, W., and Young B. R. (2017). A comparison of a novel robust decentralized control strategy and MPC for industrial high purity, high recovery, multicomponent distillation. ISA Trans., 69, 222-233 Udugama, I.A., Zander, C., Mansouri, S.S., Kirkpatrick, R., Young, B.R. (2017). A novel back-up control structure to manage non-routine steam upsets in industrial methanol distillation columns. Comput. Aided Chem. Eng., 40, 1597–1602.

Overall, based on this evidence it can be concluded that the optimal cyclic distillation column design based on the maximum driving force has the best controllability. In terms of process controllability and potential operational optimization, this means that designing a cyclic distillation column at its maximum driving force would allow for relatively tight and very responsive process control. As such, in comparison to the two suboptimal designs presented, the optimal design would possess much better disturbance rejection characteristics. This in turn would allow industrial operators to operate an optimally designed column much closer to hard product specifications. 5. CONCLUSIONS In this work, for the first time an integrated process design and control approach based on the driving force has been explored for cyclic distillation columns. The approach has been applied to design a cyclic distillation column for separation of a binary mixture of water and ethanol. For comparison, two suboptimal process designs (that are not operating at the maximum driving force) were also considered. The controller performance of the design at the maximum driving force (optimal design) and suboptimal design alternatives were then fitted with a standard process control scheme proposed by Matsubara (1982) with identical process tuning parameters. These design alternatives were then tested against feed flow disturbances where it was clearly demonstrated that the optimal process design at the maximum driving force provides better process controllability, column stability as well as energy efficiency. REFERENCES Andersen, B.B. (2016) Model Development for Cyclic Distillation. B.Sc. Thesis. Technical University of Denmark. Bek-Pedersen, E. and Gani, R. (2004). Design and synthesis of distillation systems using a driving-force-based approach, Chem. Eng. Process., 43, 251–262. Bîldea, C. S., Patrut, C., Jørgensen, S. B., Abildskov, J. and Kiss, A. A. (2016). Cyclic distillation technology - a minireview. J. Chem. Technol. Biotechnol., 91, 1215-1223 Kiss, A. A., Flores Landaeta, S. J. and Zondervan, E. (2012). Cyclic distillation - towards energy efficient binary distillation. Compt. Aid. Chem. Eng., 30, 697-701. Kiss, A. A. (2014). Distillation technology - still young and full of breakthrough opportunities. J. Chem. Technol. Biotechnol., 89, 479-498. Kraller, M. A., Udugama, I.A., Kirkpatrick, R., Yu, W., and Young B. R. (2016). Side draw optimization of a highpurity, multi-component distillation column. Asia-Pacific J. Chem. Eng., 11, 958–972. Lita̧, I., Bîldea, C. S. and Kiss, A. (2012). Modeling, Design and Control of Cyclic Distillation Systems. Procedia Eng., 42, 1202-1213. Mansouri S.S., Sales-Cruz M., Huusom J.K., and Gani R. (2015). Integrated process design and control of reactive

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