Model Predictive Control of Reactive Dividing Wall Column for the

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Model predictive control of reactive dividing wall column for selective hydrogenation and separation of C3 stream in ethylene plant Xing Qian, Shengkun Jia, Sigurd Skogestad, Xigang Yuan, and Yiqing Luo Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.6b02112 • Publication Date (Web): 18 Aug 2016 Downloaded from http://pubs.acs.org on August 19, 2016

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Industrial & Engineering Chemistry Research

Model predictive control of reactive dividing wall column for selective hydrogenation and separation of C3 stream in ethylene plant Xing Qiana,b, Shengkun Jiaa, Sigurd Skogestadb, Xigang Yuana*, Yiqing Luoa School of Chemical Engineering and Technology, Chemical Engineering Research Center, Collaborative Innovation Center of Chemical Science and Engineering (Tianjin), State Key Laboratory of Chemical Engineering, Tianjin University, 300072, Tianjin, China; b Department of Chemical Engineering, Norwegian University of Science and Technology (NTNU), 7491, Trondheim, Norway

a

ABSTRACT Dividing wall column (DWC) is a promising process intensification technology of distillation. Researchers have been investigating different control structures of different DWC configurations. However, little research has been done on control, especially model predictive control, of reactive dividing wall columns (RDWC). The RDWC process of this paper combines a depropanizer, propylene distillation and selective hydrogenation into a single unit. The process is strongly interactive, which makes it difficult to achieve good control performance with traditional decentralized control strategies using PI control. The focus of this paper is to investigate the model predictive control (MPC) scheme, and compare the dynamic MPC responses with PI control. The dynamic responses of MPC are better than those of PI control. The maximum deviations are reduced, the oscillations are decreased and the required settling times are smaller. 1. INTRODUCTION Distillation is a significant and widely used separation technology in chemical industries. However, distillation is an energy-intensive process. Process intensification for distillation to improve its energy efficiency remains attractive for academic and industrial research.1 Dividing wall column (DWC), which has been successfully implemented in industry, provides a promising trend for process intensification technologies. It is a single shell, direct material coupling distillation column which demands much less energy, capital, and space.2-5 Compared with conventional configurations, the energy saving of DWCs is up to 30% in open literature.6, 7 Furthermore, DWCs can be applied to implement azeotropic, extractive, and reactive distillations, which lead to azeotropic dividing wall columns (ADWC), extractive dividing wall columns (EDWC) and reactive dividing wall columns (RDWC).8-20 In our previous work21, a process for C3 stream selective hydrogenation in ethylene plant is proposed. The proposed process integrates the propylene reactive distillation column with the depropanization column to achieve a direct material coupling distillation column configuration, which is thermodynamically equivalent to reactive dividing wall column (RDWC). The proposed RDWC configuration was proved to be promising and economically attractive for selective hydrogenation and separation of C3 stream, with its lower total annual cost (TAC) compared with the corresponding conventional reaction-and-distillation process.

*

To whom correspondence should be addressed. Email: [email protected]

ACS Paragon Plus Environment


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However, the control of the proposed RDWC is an issue that must be addressed for its effective application. The difficulties in the control of a DWC are owing to its inner complicated structure and interactions among different control loops. Dwivedi et al.22, 23 studied the control of three-product dividing wall column and four-product dividing wall column. Wu et al.13, 18 investigated the design and control of azeotropic dividing wall columns and extractive dividing wall columns. Xia et al.12, 24 studied the different control structures for extractive dividing wall columns. Buck et al.25 applied model predictive control (MPC) of dividing wall column. Kiss and Rewaged26 and Rewaged and Kiss27 investigated traditional PID control and advanced MPC of dividing wall column. Rodriguez Hernandez and Chinea-Herranz28 presented a decentralized control and its equivalent MPC schema. Control of reactive distillation has also been addressed in the literature29, 30. The dynamic behaviours of a RDWC is more complicated than a DWC, because it is determined by not only the fractionation process, which depends on thermodynamics and mass transfer rates, but also the chemical reactions, which depend on reaction kinetices of the chemical reaction system in the column. However, little research has been reported on control, especially model predictive control, of RDWCs. MPC is an advanced process control strategy, and offers a number of important advantages comparing with conventional multi loop PID control. MPC is based on the plant model and takes future states into account, and can anticipate future state of a process and take actions accordingly. MPC is thus well suited for difficult multi-input, multi-output (MIMO) control problems where there are significant interactions among different control loops. The objective of this paper is to investigate the MPC scheme of the RDWC for the selective hydrogenation and separation of C3 stream, and compare its dynamic responses with the traditional PI control.

L: C3H6 H2

F

H: C4H6 Depropanization

Hydrogenation

M: C3H8 Propylene distillation

Figure 1 The conventional reaction-and-distillation process

2. PROCESS DESCRIPTION The proposed RDWC process is based on the traditional front-end deethanization process which is shown in Figure 1. The feed F comes from a deethanizer’s bottom and comprises dozen of hydrocarbon components. To simplify the computation in our analysis, the components in the feed are represented by three main components (Light: C3H6, Medium: C3H8, Heavy: C4H6), which correspond to the three products of the process, and the two main impurities (methyl acetylene (MA) and propadiene (PD)), which are to be eliminated by the hydrogenation reaction, as given in Table 1. The distillate stream of the depropanizer goes into a selective hydrogenation reactor, and the outflow of the reactor is fed into the propylene


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distillation column to get the main product propylene. MAPD is a small proportion in the process of propylene purification in chemical industry. And MAPD is so small that it is not efficient to remove MAPD from propylene using distillation columns. The removal of MAPD in C3 stream is mandatory, and reactive distillation has been implemented in industry for the removal of MAPD. Therefore, selective hydrogenation is introduced. Selective hydrogenation not only removes MAPD, but also increases propylene productivity. The main reactions are hydrogenation of MA and PD to propylene, and the side reaction is the hydrogenation of propylene to propane. MAPD considerably reduced because of reactive distillation. As for the reactive distillation, it can simplify the process. Another important advantage of the reactive distillation for such a system is that the reaction temperature can be stabilized by eliminating hot spot on the catalysis and at the same time decrease the chance of deep hydrogenation, which may lead to the increase of by-product (propane) formation. Table 1 Feed data Variable names mole flux (kmol/hr) component mole fraction (L, M, H, MA, PD) temperature (K) pressure (atm)

Variable values 1000 zi=[0.32,0.32,0.32,0.02,0.02] 277.15 20.35

Table 2 Comparison of the conventional process and the RDWC process Cost (M$/yr) Capital cost Capital cost saving(%) Cold utility cost Hot utility cost Operating cost saving(%) TAC Saving(%)

The conventional process 12.19 6.64 16.35 26.65 -

The RDWC process 9.25 24.10 4.66 11.79 27.90 19.22 27.88

There are three types of configurations for three-product DWCs in terms of the position of the vertical partition. The first one’s vertical partition is in the middle of the column (DWCM) with top, side and bottom product, which is thermodynamically equivalent to fully thermally coupled system (FTCS). The second one’s vertical partition is at the bottom of the column (DWCL) with one top product and two bottom products, which is thermodynamically equivalent to partially thermally coupled system – side stripper (PTCS-SS). The third one’s vertical partition is at the top of the column (DWCU) with one bottom product and two top products, which is thermodynamically equivalent to partially thermally coupled system – side rectifier (PTCS-SR). The three main components are C3H6, C3H8 and C4H6. Usually, different carbon numbers are separated firstly in chemical industries because they are easy to split. Besides, the total number of the propylene distillation column is very large (165 theoretical stages). If fully thermally coupled system (or DWCM) is used here, the main column will be higher because the main column will complete sharp split of C3H6/C3H8 and C3H8/C4H6. Therefore, the partially thermally coupled system – side stripper (or DWCL) is used in this study. The RDWC process we proposed 21 is shown in Figure 2(a). It is thermodynamically equivalent to the thermally coupled reactive distillation configuration as shown in Figure 2(b) when there is no heat transfer occurs through the wall as shown in Figure 2(a). As shown in Table 2, comparing with the conventional process, the RDWC configuration gives encouraging results in both capital cost and operating cost. The partially thermally coupled distillations with all these equivalent configurations have been proved to be more economical than the conventional sequences, as the former have shown to have a lower minimum vapor flow rate than the latter 31. Another reason of lower energy demand by the RDWC configuration may consist in its ability of reducing the mid-component remixing



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effect. In the conventional distillation sequence, the remixing may take place at the upper part of the depropanizer, where the concentration of propane is getting lower toward the top of the column because the concentration of butylene is getting extremely lower toward the top of the column. To reduce such a remixing in the traditional distillation sequence, more propane must be allowed to come out with the top product of the depropanization column, but the butylene contamination in the propane product in the propylene distillation column may violate a specification. In the thermally coupled configuration however, a double higher concentration of butylene in the top product of the depropanizer is allowed because half of the butylene that goes out will come back to the column via the liquid stream from the propylene distillation column to the depropanizer (if the liquid split is by half and half) as shown in Figure 2. Ho et al. 32 have given a similar explanation. In our case, the degree of remixing effect is measured by a remixing ratio defined by − ,

= where and , represent respectively the maximum and the column top concentrations of propane of the depropanizer, and it is estimated from our simulation reported in our previous work21 that the is 5.94% for the conventional configuration and 4.90% for the RDWC, showing that the thermodynamic efficiency of RDWC is higher than that of the conventional configuration. C3H6

Liquid split F Reaction section H2

C3H8 C4H6

(a) RDWC configuration

C3H6

F

H2

Reaction section

C3H8

C4H6 Depropanization column

Propylene distillation column

(b) direct material coupling distillation Figure 2 Illustration of the direct material coupling design and the equivalent RDWC configuration


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The selective hydrogenation reactions include hydrogenation of methyl acetylene to propylene, hydrogenation of propadiene to propylene and hydrogenation of propylene to propane, and can be represented as the following. CH3CCH (MA) + H2→C3H6 (1) (2) CH2CCH2 (PD) + H2→C3H6 C3H6 + H2→C3H8 (3) The kinetics used in the present work come from Yu33 and are given by: rMA = 0.19666e

rPD = 0.19666e

−

12053 RT

12053 − RT

rC 3 H 6 = 8.1539 × 10−4 e

0.8 0.5 C MA CH 2

(4)

0.8 0.5 C PD CH 2

(5)

11249 − RT

C H1.922

(6)

where rMA , rPD and rC 3 H 6 are the rates of hydrogenation of MA, PD to propylene and of propylene to propane, respectively; and C MA , C PD , and C H 2 are concentrations of MA, PD, and hydrogen, respectively. Note that reaction (3) reduces the recovery of the propylene product and so should be restricted. For such a purpose, the concentration of hydrogen at the entrance of the reaction section (the hydrogen feeding stage) in the column should be controlled, considering the kinetics of equation (6). As explained in our previous study21, MAPD is less volatile than the heavy key component propane of the propylene distillation column, so MAPD is concentrated at the bottom of the propylene distillation column. Therefore, the hydrogenation reaction section is placed at the bottom of the reactive distillation column. The product purity specifications of the three products in this paper are 99.5% mole fraction of butadiene, 93% mole fraction of propane and 99.6% mole fraction of propylene. The process parameters of the RDWC are shown in Table S1 in the Supporting Information. This work was implemented by joint simulation of Aspen Dynamics and Simulink in Matlab. The steady state simulation of the RDWC is performed by simulating its equivalent configuration given in Figure 2(b). A short-cut method based on the Winn-Underwood-Gilliland approach is used to provide initial designs for the distillation columns. After determining the recoveries for light and heavy key components, the results of total stage numbers, feed stage numbers and reflux ratios for the distillation columns are achieved using the short-cut model DSTWU in Aspen Plus (property method: RK-Soave). With the initial values given by the short-cut method, the traditional reaction-and-distillation process as shown in Figure 1 is simulated rigorously. With the initial values given by the traditional process simulation, the RDWC process as shown in Figure 2(b) is simulated rigorously employing Aspen Plus. Then, the Tray Sizing feature for the distillation column in Aspen Plus is used to determine the sizes of the column sections before the results are exported to Aspen Dynamics. The reflux drum and the sump of each column are sized to provide 10 min holdup with 50% liquid level34, 35. The model predictive control is achieved by using Matlab MPC toolbox.

3. CONTROL STRATEGIES 3.1 PI control The structure of PI control is illustrated in Figure 3. The typical DBB/LVV control strategy is adopted. The compositions of product butadiene, propane, and propylene are controlled using the reboiler duty of the depropanizer, the reboiler duty, and the reflux flow rate of the propylene distillation column, respectively. The liquid split ratio (RL) is the fraction of liquid



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that remains in the main section, while the other fraction (1-RL) of liquid flows to the depropanization section from the main section. During the dynamic simulation, the liquid split ratio is set to be fixed as suggested by Chien et al 13. There is a ratio controller for the fixed ratio (1-RL). The input of the ratio controller is the liquid flow rate in the main section before liquid splits. The output of the ratio controller is the thermally coupled liquid flow rate back to the depropanization section. Therefore, the liquid split ratio remains the same regardless of feed flow rate changes and internal flow rate changes. The pressure of the propylene distillation column is controlled by the corresponding condenser duty. The level controllers use the flow rates of product streams as manipulated variables. In addition to the distillation control loops, the hydrogen concentration on the hydrogen feed stage is controlled by the hydrogen feed flow rate. Segovia-Hernandez et al.36 investigated the sensitivity of thermally coupled distillations under uncertainties in process parameters and modeling errors, and found thermally coupled distillations show different controllability at different operating conditions under feedback control. As derivative (D) control is sensitive to measurement noise, D control is not used in this system. PI controllers are used in this paper, except the P controllers for the controls of the levels. The values of gains and integral times of pressure controller and level controllers are taken as suggested in Luyben’s book34. The values of step changes in the manipulated variables are obtained in open loop tests. The values for the gains and integral times for the other loops are obtained based on SIMC tuning rules37. As the process is interactive, manual tuning is used after parameters calculated with the tuning rules. The tuning results for the composition controllers of PI control are listed in Table 3. LC

PC

D2 XA CC Fixed RL F CC

XH2

LC

LC

B2 B1

XC

XB CC

CC

Figure 3 Control structure of PI control Table 3 Controller tuning parameters of PI control Control loop

Controlled variable

Manipulated variable

Controller gain

Controller integral time (min)

CCB1

x H ,B 1

QR1

0.08

40

CCB2

x M ,B 2

QR2

0.3

30

CCD2

x L ,D 2

R

0.2

20

CCH2

xH 2

FH2

0.1

4

The maximum deviation of C4H6 in B1 stream is relatively large when +20% feed flow rate disturbance occur. This is mainly due to the slow response of the reboiler duty of the


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depropanizer. To increase the response speed of PI control, three feed forward controllers are employed. The three feed forward controllers include the ratio of the reboiler duty of the depropanizer to the feed flow rate (QR1/F), the ratio of the reboiler duty of the propylene distillation column to the feed flow rate (QR2/F), and the ratio of the reflux of the propylene distillation column to the feed flow rate (R2/F). The control structure of PI with feed forward control (PIFF) is illustrated in Figure 4. LC

PC

D2 XA CC

(R/F)S

Fixed RL

F

CC

XH2

LC

LC

CC

B2 B1 XC

XB CC (QR/F)S

(QR/F)S

Figure 4 Control structure of PI with feed forward control (PIFF)

3.2 Model predictive control Model predictive control (MPC) is based on three operations: 1. prediction of process future outputs, 2. optimization of process outputs and inputs, 3. adjustment of the prediction. State space model is usually used as the linear time invariant (LTI) model, which can be expressed by:

x' (k ) = Ax(k ) + Bu(k ) y(k ) = Cx(k ) + Dd (k )

(6) (7)

where x(k) is the plant state, u(k) represents the vector of manipulated variables, y(k) indicates the vector of controlled variables, and d(k) collects the vector of disturbances. The model matrices A, B, C, and D are obtained through linearizing the nonlinear plant models. Based on the state space model, the optimization problem, at every sampling time k is formulated as:   ny   y 2   ∑ | wi +1, j ( y j (k + i + 1| k ) − rj (k + i + 1)) |     j =1    p −1  nu   min ∆u 2 2   + | w ∆ u ( k + i | k ) | + ρ ε ∑ ∑ i , j j  ε ∆u (k | k ),L , ∆u (m − 1 + k | k ), ε  i =0  j =1      nu    + ∑ | wiu, j u j (k + i | k ) − u jtarget (k + i | k ) |2       j =1  (8)

where the subscript j denotes the j component of a vector, and (k+i|k) represents the predicted value for time k+i when time is at k. r(k) is the current set point of the controlled variables.



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Model predictive control (MPC) strategy is shown in Figure 5. The MPC schematic is shown in Figure 5(a). The controlled process is RDWC. , , and represent the controlled variables, the manipulated variables, the disturbances and the set points, respectively. The prediction model calculated values of process outputs at time k and at time k+j are calculated at time k on the basis of the prediction model. And the actual values of process outputs at time k are detected according to detectors. Then, adjustment of the prediction at time k will be made. The prediction value + | will be achieved according to the adjustment and the prediction model calculated values. And the differences between the prediction values and the set points are calculated. Then online optimization will be made to achieve the optimal manipulated variables. The control structure of MPC is illustrated in Figure 5(b). There are eight controlled variables: the composition of product butadiene x H ,B 1 , the composition of product propane x M ,B 2 , the composition of product propylene x L ,D 2 , the hydrogen composition on the feed stage of hydrogen x H 2 , the pressure of the propylene distillation column P, the sump level of the depropanizer LB1, the sump level of the propylene distillation column LB2 and the reflux drum level of the propylene distillation column LD2. There are eight manipulated variables: the reboiler duty of the depropanizer QR1, the reboiler duty of the propylene distillation column QR2, the reflux flow rate of the propylene distillation column R2, the feed flow rate of hydrogen FH2, the condenser duty of the propylene distillation column QC2, the product flow rate of the bottom of the depropanizer B1, the product flow rate of the bottom of the propylene distillation column B2, and the product flow rate of the top of the propylene distillation column D2. The prediction horizon and control horizon are determined to keep the system stable with less numbers of oscillations. The weights of manipulated variables and controlled variables are determined to reduce the maximum deviations. The tuning of MPC can be defined as a multi-objective optimization problem, which can be solved by different methods to achieve a discrete set of the Pareto optimum solution. Then, a final solution can be selected. In this paper, genetic algorithm (GA) is used for the multi-objective optimization of MPC tuning to obtain Pareto optimum solutions38, 39 for weights of controlled variables and manipulated variables variations ( and ∆ ). The sum of the squared differences between controlled variables and set points and the sum of the squared variations of the manipulated variables are considered as two objective functions as shown below: min 1 = ∑[ − ]! (9)

min 2 = ∑[∆ ]!

(10)

The Pareto optimum solutions set are shown in Figure 6. Considering the importance of the objective functions, the hollow point among the solid points is chosen as the final solution. And the corresponding tuning parameters of MPC are listed in Table 4. The controller stability of MPC is an important aspect for theoretical investigation. The stability of the MPC was extensively discussed by Mayne et al.40 and Maciejowski41. For the state space model, the optimization problem Equation (8) with finite time horizon and terminal constraints can be used as Lyapunov function, and the stability of MPC can be proved according to Lyapunov stability. If the norm length of each eigenvalue of the A matrix for the the unconstrained controller's state space realization is less than 1, the controller can be known as internal stable. Figure 7 shows the distribution of all the eigenvalues generated by Matlab for the MPC, where the x-axis and the y-axis are for the real and the imaginary parts respectively of the eigenvalues. It can be found in Figure 7 that all the points of the eigenvalues are within the unit circle, suggesting the stability of the MPC.


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+

Online optimization

−

+ | +

+

$ + |

RDWC

Prediction Model $ |

−

Feedback correction

+

(a) MPC schematic P LD2 D2

P1

XA Fixed RL

F

MPC

XH2 LB2 B2

B1 XB XC

LB1

(b) Control structure for MPC Figure 5 Model predictive control (MPC) strategy

Table 4 Controller tuning parameters of MPC Manipulated variables Weights

wy wu w∆u

QR1 QR2

Controlled variables

R2

FH2

QC2

B1

B2

D2

x H ,B 1 x M , B 2 x L , D 2

xH 2

-

-

-

-

-

-

-

-

9.663

0

0

0

0

0

0

0

0

-

-

-

-

-

-

-

-

0.349 0.208 0.074 0.077 0.095 0.081 0.047 0.089 Prediction horizon p 50

P

LB1

LB2

LD2

8.016 11.704 1.536 2.354 1.062 0.376 2.003

Control horizon m 4


-

-

-

-

-

-

-

-

Sampling time △k 0.01 h


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Figure 6 The Pareto optimum solutions set

Figure 7 Distrbution of the eigenvalues of the MPC


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4. RESULTS AND DISCUSSION In order to demonstrate the performance of the proposed MPC method and compare it with those of PI and PIFF controls, four types of disturbances are used, namely, ±20% changes in fresh feed flow rate and ±20% changes in fresh feed composition. The changes for each of the three components: butadiene (Heavy), propane (Medium) and propylene (Light) are used in the feed composition disturbances. Figure 8 to 11 give dynamic responses of the MPC vs those of the PI control to disturbances in feed flow rate and feed composition, respectively. The figures show that both methods can drive the purities of the products to their set points. The MPC can give much better control qualities in terms of both number and amplitude of the oscillations of the dynamic responses in most cases than the PI control, and behave extremely well under the feed composition disturbances. With PI control, in addition to the interaction between the loops of D/L and B/V for a traditional distillation, the thermally coupling scheme shown in Figure 3 interlinks an additional B/V loop into the interaction. The maximum transient deviations of the three products compositions when feed flow rate disturbances occur are relatively larger than those when the feed composition disturbances occur. As shown in Figure 8, the B1_C4H6 product purity has the largest deviation from its set point and shortest settling time under the feed flow rate disturbances. This is because that the impact of the feed flow rate change is the most immediate on this product than on the others for a saturated liquid feed, given the smallest number of stages from the feed stage, and thus less hydraulic lags34, than the other products. The maximum deviations of C3H8 are larger than those of C3H6 and C4H6 when feed composition disturbances occur, as the steady state designed composition of C3H8 (93%) is much lower than C3H6 (99.6%) and C4H6 (99.5%).



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(a)

(b)

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(c)

Figure 8 MPC vs PI control: dynamic responses to ±20% feed flow rate disturbances

(a)

(b)

(c)

Figure 9 MPC vs PI control: dynamic responses to ±20% feed composition of C3H6 (Light) disturbances

(a)

(b)

(c)

Figure 10 MPC vs PI control: dynamic responses to ±20% feed composition of C3H8 (Medium) disturbances

(a)

(b)

(c)

Figure 11 MPC vs PI control: dynamic responses to ±20% feed composition of C4H6 (Heavy) disturbances


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(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

Figure 12 MPC vs PI control: Dynamic responses of manipulated variables when ±20% feed flow rate disturbances occur



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(a)

(b)

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(c)

Figure 13 MPC vs PI control: Dynamic responses of manipulated variables when ±20% feed flow rate disturbances occur (zoomed in from 0 to 2 h)

Dynamic responses of some manipulated variables of MPC vs PI control when ±20% feed flow rate disturbances occur at 0.5 h are shown in Figure 12. And, Figure 13 shows a zoomed-in plot of Figure 12 for the time period from 0 to 2 h. The manipulated variables of PI and MPC settle to the same steady state as shown in Figure 12. However, the changes of the variable values given by MPC are much smoother than by the PI controllers. This explains why the MPC can improve the control quality significantly as suggested in Figure 8 to 11. The difference between the MPC and PI control is that the former gives quick response of the manipulated variable to the disturbances as shown in Figure 13. To test the influence of the response speed, feed forward controls are integrated into the PI controls. Figures 13 to 17 give dynamic responses of MPC vs PIFF control to disturbances in feed flow rate and feed composition, respectively. Using PIFF, the dynamic performances of C4H6 composition in B1 stream is appreciably improved while the dynamic performances of the other two change slightly as shown in Figure 14 to 17. (a)

(b)

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Figure 14 MPC vs PIFF control: dynamic responses to ±20% feed flow rate disturbances (a)

(b)

(c)

Figure 15 MPC vs PIFF control: dynamic responses to ±20% feed composition of C3H6 (Light) disturbances


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(a)

(b)

(c)

Figure 16 MPC vs PIFF control: dynamic responses to ±20% feed composition of C3H8 (Medium) disturbances (a)

(b)

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Figure 17 MPC vs PIFF control: dynamic responses to ±20% feed composition of C4H6 (Heavy) disturbances (a)

(b)

(c)

Figure 18 MPC vs PIFF control: Dynamic responses of manipulated variables when ±20% feed flow rate disturbances occur (zoomed in from 0 to 2 h)

A common performance evaluation index is the integral of squared error (ISE). ISE compromises both overshooting and settling times. ISE is defined as ,

&'( = ) [* +]! + -

Comparison of performance of MPC vs PIFF control in terms of integral of squared error (ISE) is shown in Table 5. The dynamic performances using MPC with low values of ISE are improved a lot than those with PIFF control. Compared with the PIFF performances, the MPC performances are stable and superior. Table 5 Comparison of performance of MPC vs PIFF control in terms of integral of squared error (ISE) Disturbance D2_C3H6_PIFF D2_C3H6_MPC B2_C3H8_PIFF B2_C3H8_MPC B1_C4H6_PIFF B1_C4H6_MPC +10%L 1.21E-05 7.10E-07 2.86E-03 6.98E-07 5.48E-05 2.81E-08 -10%L 1.01E-05 1.17E-06 2.46E-03 4.04E-08 5.08E-05 1.33E-07 +10%M 2.23E-06 7.47E-07 4.14E-04 4.15E-07 1.51E-05 3.98E-07 -10%M 1.77E-06 7.81E-07 3.66E-04 1.00E-06 1.41E-05 7.00E-09 +10%H 9.18E-06 7.57E-08 2.04E-03 4.28E-07 4.74E-05 5.60E-08 -10%H 1.10E-05 1.02E-07 2.19E-03 7.59E-08 4.77E-05 1.30E-07 +10%F 2.10E-05 3.12E-05 6.82E-03 1.42E-06 4.46E-04 8.73E-07 -10%F 6.16E-05 1.66E-05 1.71E-02 7.72E-07 1.43E-03 2.22E-07



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Dynamic responses of manipulated variables of MPC vs PIFF control for the time period from 0 to 2 h when ±20% feed flow rate disturbances occur at 0.5 h are shown in Figure 17. The responses of manipulated variables of PIFF are faster than those of PI and as early as those of MPC, as shown in Figure 17. The reboiler duties and the reflux flow rate change immediately when the feed flow rate change. Although the dynamic performances of PIFF are better than those of PI, the improvement is not significant comparing to those of MPC as shown in Figure 13 to 16. The dynamic responses of all manipulated variables using MPC or PI control or PIFF control when ±20% feed flow rate disturbances occur (zoomed in from 0 to 2 h) are shown in Figure S1 to S2 in the Supporting Information. The advantage of MPC over PI control is that not only one manipulated variable is used to settle down the controlled variable. MPC is able to oversee the entire process and make proper adjustment accordingly, and this is very advantageous in a strongly interactive process, as reflected in the control of the RDWC in the present paper. The RDWC configuration is a highly nonlinear system, but the performances of the linearized model derived from the nonlinear RDWC system and used for predictions in MPC in the present paper are fantastic. As shown in Figure 11, the dynamic responses of manipulated variables of MPC are more stable than those of PI control. With MPC, the optimized manipulated variables reduce effectively the oscillations in the dynamic responses of product compositions. Besides, the optimized manipulated variables reduced the maximum deviations of the product compositions. The improved performance of the MPC can also be proved by compare the results of the present study with some previously published ones. Sharma and Singh42 investigated MPC and neural network predict control for RD control. In their published results, the ISE values for the control of 92.5% mole fraction TAME product with ±10% feed flow rate changes are roughly 0.03 for PID and 0.012 for MPC. In the present work, according to Figure 14 (a), the ISE values for 99.6% mole fraction propylene product with ±20% feed flow rate changes can be estimated as 4.64E-5 for PID and 1.88E-5 for MPC. The comparison indicates that the performance of the MPC in the present work is compatible with the previous study even with doubled stronger disturbances in the feed flowrate. In the RDWC control, the changes in the manipulated variable values will affect the chemical reaction via the kinetics given by equatins (4), (5), and (6), and the changes in the reaction rates would affect in turn the controled vriables. Thus, the dynimic behaviours of the RDWC are the result of coupled-effect of both the thermodymics for distillation and chemical reaction kinetics. The linear time invariant (LTI) model is simple and easy to implement, and therefore is used in this paper for preliminary investigation. However, nonlinear models are worthy of investigations in the future.

5. CONCLUSIONS This paper proposes an advanced control strategy, model predictive control (MPC), for the control of reactive dividing wall columns (RDWC) for selective hydrogenation and separation of C3 stream in ethylene production. The dynamic responses of the controlled and some manipulated variables demonstrate that the performance of the MPC is significantly better than that of the PI control in the presence of ±20% disturbances of either the feed flow rate or its composition. The highest oscillation of dynamic response for the PI control occurs at the C4H6 purity of B1 product under the disturbance of the feed flow rate. The introduction of feed forward control into the PI control (PIFF) can reduce the amplitude of such an oscillation by increase the reacting speed of the manipulated variable to the disturbance, but give little improvement for the rest loops. With the MPC, the maximum deviations of the responses are remarkably reduced, the oscillations are even unappreciable in many of the cases. Therefore,


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the overall dynamic performances of MPC are much better than those of traditional PI control structure. With DWC being one of the promising distillation configurations for process intensifications, dynamic and operation research of different structures of the RDWC configuration should be investigated. This work demonstrates that both MPC and PI control are able to handle disturbances inserted into reactive dividing wall columns, which is an encouraging result for industrialization of reactive dividing wall columns. And the MPC is recommended to the strongly interactive reactive dividing wall columns. It should be pointed out that the liquid split ratio of the RDWC we studied is optimized during the column design and is kept constant in the process control. This causes no problem for the cases of control with feed flow rate disturbances, because the feed flow rate change does not demand to shift the value of optimal liquid split ratio. But for the feed composition disturbances, the offset in the optimal value for the liquid split ratio should be taken into consideration. In this sense, the MPC discussed in the present work is not strictly an optimum control. However, this does not prevent us from demonstrating effectively the advantageous of MPC in stabilizing the RWDC operation.

ACKNOWLEDGMENTS The authors acknowledge the National Basic Research Program of China (973 Program: 2012CB720500), the National Supporting Research Program of China (Grant 2013BAA03B01), the National Natural Science Foundation of China (No. 21176178) and China Scholarship Council (CSC File No. 201506250011) for supporting this research. Supporting Information In the Supporting Information, the process parameters of the RDWC are shown in Table S1. The dynamic responses of all manipulated variables using MPC or PI control or PIFF control when ±20% feed flow rate disturbances occur (zoomed in from 0 to 2 h) are shown in Figure S1 to S2. This material is available free of charge via the Internet at http://pubs.acs.org. REFERENCES 1. Kiss, A. A., Distillation technology-still young and full of breakthrough opportunities. J. Chem. Technol. Biot. 2014, 89, (4), 479-498. 2. Dejanovic, I.; Matijasevic, L.; Olujic, Z., Dividing wall column-A breakthrough towards sustainable distilling. Chem. Eng. Pro. 2010, 49, (6), 559-580. 3. Yildirim, O.; Kiss, A. A.; Kenig, E. Y., Dividing wall columns in chemical process industry: A review on current activities. Sep. Purif. Technol. 2011, 80, (3), 403-417. 4. Staak, D.; Gruetzner, T.; Schwegler, B.; Roederer, D., Dividing wall column for industrial multi purpose use. Chem. Eng. Pro. 2014, 75, 48-57. 5. Chu, K. T.; Cadoret, L.; Yu, C. C.; Ward, J. D., A New Shortcut Design Method and Economic Analysis of Divided Wall Columns. Ind. Eng. Chem. Res. 2011, 50, (15), 9221-9235. 6. Emtir, M.; Rev, E.; Fonyo, Z., Rigorous simulation of energy integrated and thermally coupled distillation schemes for ternary mixture. Appl. Therm. Eng. 2001, 21, (13-14), 1299-1317. 7. Hernandez, S.; Pereira-Pech, S.; Jimenez, A.; Rico-Ramirez, V., Energy efficiency of an indirect thermally coupled distillation sequence. Can. J. Chem. Eng. 2003, 81, (5), 1087-1091. 8. Kiss, A. A.; Pragt, J. J.; van Strien, C. J. G., Reactive dividing-wall column show to get more with less resources? Chem. Eng. Commun. 2009, 196, (11), 1366-1374. 9. Sun, L. Y.; Chang, X. W.; Qi, C. X.; Li, Q. S., Implementation of Ethanol Dehydration Using Dividing-Wall Heterogeneous Azeotropic Distillation Column. Separ. Sci. Technol. 2011, 46, (8), 1365-1375. 10. Kiss, A. A.; Ignat, R. M., Innovative single step bioethanol dehydration in an extractive dividing-wall column. Sep. Purif. Technol. 2012, 98, 290-297. 11. Kiss, A. A.; Suszwalak, D., Enhanced bioethanol dehydration by extractive and azeotropic distillation in dividing-wall columns. Sep. Purif. Technol. 2012, 86, 70-78. 12. Xia, M.; Yu, B. R.; Wang, Q. Y.; Jiao, H. P.; Xu, C. J., Design and Control of Extractive Dividing-Wall



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Stability and optimality. Automatica 2000, 36, (6), 789-814. 41. Maciejowski, J. M., Predictive control: with constraints. Pearson education: 2002. 42. Sharma, N.; Singh, K., Model predictive control and neural network predictive control of TAME reactive distillation column. Chemical Engineering and Processing: Process Intensification 2012, 59, 9-21.



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Model Predictive Control of Reactive Dividing Wall Column for the

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