Control and Profile Setting of Reactive Distillation Column for Benzene

Article pubs.acs.org/IECR

Control and Profile Setting of Reactive Distillation Column for Benzene Chloride Consecutive Reaction System Cuimei Bo,†,§ Jihai Tang,‡ Mifen Cui,‡ Kangkang Feng,† Xu Qiao,*,‡ and Furong Gao*,§ †

College of Automation and Electrical Engineering, Nanjing University of Technology, Nanjing Xinmofan Road No. 5, Nanjing, 210009 China ‡ State Key Laboratory of Materials-Oriented Chemical Engineering, College of Chemistry and Chemical Engineering, Nanjing University of Technology, Nanjing, 210009 China § Department of Chemical and Biomolecular Engineering, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong ABSTRACT: The purpose of this paper is to design and analyze the control structures of a consecutive reactive distillation process. On the basis of the optimal economic design, a systematic framework for the design of the decentralized control structure, controller parameter tuning, and setting profiles under uncertainty disturbances is proposed for benzene chloride production in a reactive distillation column. Its effectiveness and robustness are analyzed for disturbance resistance in terms of changes of the production rate and the feed composition. Simulations indicate that better control performance can be obtained by proper control loop pairing, tray location identification, and controller tuning. Furthermore, process performances are compared for the three different profile setting cases in the forms of one-step, multistep, and quadratic function changes of the product rate adjustment. The result shows that the process transient performance, such as overshoot, smoothness, and stability, can be greatly affected by the set-point transition form, indicating that it is necessary to study the relevant production rate setpoint adjustment strategy.

1. INTRODUCTION Traditionally, the two most important operations of chemical processes, reaction and separation, are carried out separately in different sections of a plant, using different equipment. Nowadays, the process intensification technology is increasingly practiced in the industry due to the economic and environmental considerations.1,2 Reactive distillation is such an example of process intensification. It is a process that combines reaction and multicomponent separation in a unit, offering advantages over the conventional multiunit processes in terms of catalyst usages, reactive heat utilization, and cost saving.3−5 As reaction and separation take place simultaneously in one column, the tray temperatures are determined by the vapor−liquid equilibrium of the process. A lower temperature results in a lower specific reaction rate; consequently, a large holdup will be required, while a higher temperature may promote undesirable side reactions. In such a reactive distillation, the interaction between the simultaneous reaction and distillation introduces a much more complex dynamic behavior compared to a conventional multiunit process, leading to challenges in design, optimization, and control of the process. Kaymak and Luyben6 quantitatively compared the dynamic controllability of a reactive distillation column against a conventional multiunit process, and they concluded that its control is more difficult and its operability region is smaller than that of a conventional multiunit process because the reactive distillation column has fewer degrees of control freedom. This is particularly true for the case of reactive distillation column with two feed streams. In this case, a ratio of the two reactants needs to be maintained for the column to satisfy the stoichiometry. Luyben7 defines this type of operation mode as “neat” operation mode. He suggested that it is necessary © 2013 American Chemical Society

to have a proper feedback control strategy to control the reactant flow rates inside the column.8,9 To do so, Al-Arfaj and Luyben proposed six alternative control structures, all of which use a composition controller in the reactive zone to satisfy the stoichiometric balance between the reactants.10 Decentralized linear controllers with multiloop PI/PID controllers are preferred in chemical processes not only because of their easy practical implementation but also because good performance can be obtained by appropriate control structure design and parameter tuning. Online composition analysis is expensive, difficult to maintain, and often plagued with a large dead time. On the other side, the temperature relevant information may be explored to infer composition with sufficient accuracy.11 Therefore, it is suggested that the product composition is to be controlled indirectly by controlling a suitable tray temperature as the temperature measurement is usually much cheaper, faster, and more reliable than concentration measurement. Owing to the complex dynamic interaction of reaction kinetics, mass transfer, and thermodynamics, the interaction often causes counteracting influences on the process; proper design and tuning of these controllers in a decentralized structure are very important to the process performance in face of a wide range of operating condition changes coupled with several uncertain disturbances. In this study, the key issues are the selection of a suitable tray temperature, the design of stable and robust decentralized PI/PID controller structure, and tuning of Received: Revised: Accepted: Published: 17465

March 8, 2013 October 5, 2013 October 16, 2013 October 16, 2013 dx.doi.org/10.1021/ie4007694 | Ind. Eng. Chem. Res. 2013, 52, 17465−17474

Industrial & Engineering Chemistry Research

Article

controller parameters.27 Luyben and Kaymak proposed two alternative temperature control structures for a quaternary reversible reaction process to replace their early proposed composition control structures.12 Also recently, relevant process control has been investigated with respect to effectiveness of feed tray location,13,14 relative volatility ranking,18 multiplicity,19 controllability of control structure,15−17 and plant-wide control structure design.20,21 Furthermore, some nonlinear multivariable control methods were also investigated aiming at the complex interaction and nonlinear characteristic of reactive distillation. For example, Daoutidis and co-workers applied nonlinear multivariable control for ethyl acetate reactive distillation and ethylene glycol reactive distillation column.22,23 Venkateswarlu proposed a nonlinear model predictive control based on stochastic optimization for an ethyl acetate reactive distillation column with double-feed configuration involving an esterification reaction with azeotropism.24 All of the above works are confined to dynamic control for a quaternary or ternary reversible reaction process; no relevant work for the consecutive reaction process have been reported. In the consecutive reaction, the main reaction with some side reactions occur simultaneously. In the case where there are two reactants, one is involved in an undesirable series reaction (A + B → C + D and C + B → E + D). The higher selectivity of the desired product C may be achieved using reactive distillation technology, as the desired product C can be removed in a timely fashion from the column through vapor−liquid separation to restrain the production of the byproduct D.25 As the reaction kinetic in such cases is more complex than a reversible reaction process, dynamic control for consecutive reactions in the distillation column becomes a challenge when the selectivity as well as the conversion are both considered.27 In this work, the dynamic design and simulation of a decentralized control structure is studied for benzene chlorine consecutive reaction in a reactive distillation column based on the optimal economic design. The effectiveness of the proposed control structure is evaluated for the disturbance resistance of changes in the feed rate and composition. Production rate is often adjusted in response to changes of market, with three different profile settings in the forms of one-step, multistep, and quadratic parabola functions to represent changes of the product rate are tested and compared to evaluate the performance of the proposed control structure. The results show that the production rate set-point transition form has an important effect on the process dynamic performance.

side reaction

A+B→C+D C+B→E+D

(3)

⎛ −E ⎞ rE = −A 2 exp⎜ 2 ⎟CCC B ⎝ RT ⎠

(4)

where rC and rE are reaction rates of product C and E, respectively, A1 and A2 are preexponential factors, E1 and E2 are activation energy, R is the ideal-gas constant, and T is the reaction temperature. In a reactive distillation process, a large excess of reactant A should be used in the column, which will dilute the C and B concentrations to suppress the undesirable side reaction. A relatively higher selectivity to intermediate component C can be obtained by maintaining a high concentration of reactant A and low concentrations of reactants B and C in the reaction section. These recycle streams increase the difficulty of dynamic control about the reactive distillation process. 2.2. Benzene Chloride Production. The benzene chloride production in a reactive distillation column is used as the example of the consecutive reaction with two irreversible reactions. Chlorobenzene can be produced from the reaction of toluene and chlorine, while chlorobenzene will react further with chlorine to produce the byproduct dichlorobenzene (mainly o-dichlorobenzene, paracide). The chemical reaction is as follows: main reaction

Cl 2 + C6H6 → C6H5Cl + HCl

(5)

side reaction

C6H5Cl + Cl 2 → C6H4Cl 2 + HCl

(6)

The product chlorine hydride is as an inert gas, which will not affect the vapor−liquid equilibrium. The benzene chlorination kinetics with ferric trichloride as catalyst was discussed in refs 30 and 31. The kinetic equations for the benzene chloride consecutive reactions are shown in the following: ⎛ −75.01 × 103 ⎞ rC6H5Cl = −2.895 × 109 exp⎜ ⎟CC6H6C FeCl3CCl2 RT ⎝ ⎠ ⎛ −82.99 × 103 ⎞ + 8.686 × 109 exp⎜ ⎟CC6H5ClC FeCl3CCl2 RT ⎝ ⎠ ⎛ −82.99 × 103 ⎞ rC6H4Cl2 = −8.686 × 109 exp⎜ ⎟CC6H5ClC FeCl3CCl2 RT ⎝ ⎠

(7)

(8)

Here, R = 8.314 kJ/kmol/K. The reactions are highly exothermic and occur in a suitable temperature T = 365 K. Some important kinetic and vapor−liquid phase equilibrium parameters for the system are given in Table 1. The benzene chlorination system belongs to an easy separation system of the raw material from the product, which is ideal to use the reaction distillation configuration. 2.3. Reactive Distillation Configuration. The optimal steady state configuration parameters and operating parameters can be obtained on the basis of an optimal economic design to minimize the total annual cost, as reported in our previous research works.29,32 The optimal configuration of the reactive distillation column is given in Figure 1. In the configuration, the light product, chlorine hydride (HCl), is removed from the top, while the heavy products, chloride benzene (C6H5Cl) and dichlorobenzene (C6H4Cl2), are taken out from the bottom. The distillation column is divided into three sections: stripping section Ns = 10, reaction zone NRS = 5, and rectifying section NR = 1. The feed streams of chlorine and benzene are fed on the sixth tray and second tray, respectively. The column pressure is at atmospheric, the feed flow rates of benzene and chlorine are

2. REACTIVE DISTILLATION PROCESS 2.1. Consecutive Reaction. There are many important industrial examples of consecutive reactions: chlorination, oxidation, and nitration of a variety of hydrocarbons, etc.28 A common consecutive reaction with two irreversible reactions is the following: main reaction

⎛ −E ⎞ ⎛ −E ⎞ rC = −A1 exp⎜ 1 ⎟CAC B + A 2 exp⎜ 2 ⎟C BCC ⎝ RT ⎠ ⎝ RT ⎠

(1) (2)

The desired product is C, and the undesired byproduct is E; the desired product C is produced by the first reaction whose rate depends on the concentrations of A and B in reaction section, while C is consumed by the second reaction whose rate depends on the concentrations of C and B. The reaction rates rc and rE can be expressed by the following kinetic models 17466

dx.doi.org/10.1021/ie4007694 | Ind. Eng. Chem. Res. 2013, 52, 17465−17474


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Table 1. Kinetic and Vapor−Liquid Phase Equilibrium Parameters for System param

value

normal boiling temperature (K) ranking suitable reaction temperature reaction heat (kJ mol−1), main reaction reaction heat (kJ mol−1), side reaction heat of vaporization (kJ mol−1)

C6H6 (353.1) < C6H5Cl (405.2) < C6H4Cl2 (453.4) 350−365 K −123.78 (353 K) −98.01 (353 K) 45.90 (353 K) vapor pressure constants ln Ps = Avp − Bvp/(T + Cvp), Ps, bar; T, K

Avp Bvp Cvp

C6H6

C6H5Cl

C6H4Cl2

9.28 2788.5 55.6

9.45 3295.12 −55.6

9.66 3798.23 −59.84

Figure 1. Optimum design of the reactive distillation column for benzene chloride production. Figure 2. Parameter profile curves of the steady state simulation.

FC6H6 = 10.2 kmol/h and FCl2 = 10 kmol/h, respectively, and the reflux ratio of the column is R = 3. Figure 2 shows the vapor− liquid phase flow rate profiles, tray composition profiles, and temperature profiles for such optimally designed column. It is observed that the heavy product (chlorobenzene) profiles resemble the temperatures throughout the column. Therefore, it is reasonable to estimate the composition using the tray temperatures.

temperature profiles are established, the higher conversion and selectivity objectives can often be achieved. 3.1. Selection of Suitable Tray Temperatures. The key issue in the temperature control is the tray location selection and their pairing to control indirectly the composition. Singular value decomposition (SVD) and relative gain array (RGA) methods34 are used to determine the variable pairings of the controlled and manipulated variables. In the benzene chlorine process, there are three main input variables, namely, the two feed rates FC6H6, FCl2, and a vapor boilup, VS. While one of these three inputs is chosen as the product rate, the other two inputs are used to control the temperature of two trays. The relative gain array between these three inputs and the outputs (the tray temperatures) is calculated numerically on the basis of the optimal steady-state design. Figure 4 gives the RGA results and their related SVD. It is shown that the tray temperatures in the stripping section are sensitive to these inputs. The steady-state gains between the stripping tray temperature and the feed rate FC6H6 have the biggest negative magnitude, while the very small gain of the fresh feed stream FCl2 indicates small sensitivity to the changes in the FCl2.

3. CONTROL STRUCTURE DESIGN AND SIMULATION A poor control structure based on the optimal economic design may result in a plant with poor control properties. It is important to investigate the controllability, operability, and interaction among multiloop PI/PID controllers.33 In this section, a systematic approach is used to design the decentralized control structure for the benzene chlorine production in the reactive distillation. There are three main control objectives: (1) maintaining the product chlorobenzene purity higher than 0.96 kmol/ kmol; (2) keeping the selectivity of the product more than 0.99; (3) maintaining stoichiometric balance. When proper 17467



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tray are most sensitive to the changes in feed rate FCl2 and vapor boilup Vs, respectively. In this case, the T11/FCl2 controller is direct acting, while the T13/(V s) controller is reverse acting. 3.2. Design of Decentralized Control Structure. According to the T11/FCl2 and T13/(V s) variable pairings, a dualtemperature inferential control structure is proposed as shown in Figure 3. In this configuration, the ratio of the two feed rates (FCl2/FC6H6) is adjusted by tray temperature T11; tray temperature T13 and bottom vapor rate VS are controlled by a cascade control strategy. Thus, a correct ratio of the two feed streams can be maintained in the “neat” operation mode. By timely removing the product, chlorobenzene, from the column, the side reaction is kept small. The higher product composition (xB,C6H5Cl = 0.964 kmol/kmol) and the selectivity (more than 0.992) can be ensured by this dual-temperature inferential control structure. In addition to this major design, there are some other basic control loop designs, which are shown in Figure 3. The bottom level LB is controlled by manipulating bottom flow rate FB (LB/FB control loop), reflux drum level LR is controlled by reflux flow rate FR (LR/FR control loop), and top pressure Ps is controlled by hydrogen chloride gas recovery amount FD (Ps/FD control loop). 3.3. Controller Tuning. Multiloop PI/PID controllers with different tuning technique have been reported. Most of these tunings, such as the relay feedback tuning, Tyreus−Luyben tuning, BLT tuning, and iterative continuous cyclic tuning, rely on transfer functions to obtain response parameters as required in Ziegler−Nichols-type tuning rules to determine controller parameters.35 The dynamics of the reactive distillation exhibit severe nonlinearity and loop interaction; they cannot be presented in terms of transfer functions, and thus, the traditional tuning procedures are difficult to be applied to give satisfactory performance. Detuning techniques are often performed to preserve the system stability or to meet certain performance specification. Recently, new retuning techniques based on the stochastic search methods such as genetic algorithm (GA),36 or mixed integer dynamic optimization (MIDO),37 have been reported for applications in reactive distillation. In this section, a new retuning based on stochastic dynamic optimization against uncertainty disturbances is proposed for the robustness improvement of the above dual-temperature control structure, with the following optimization problem:

Figure 3. Dual-temperature control structure for the reactive distillation column.

min ϕ(x(t ), xa(t ), u(t ), y(t ), θ , p)

(9)

p

⎧ f (x(̇ t ), x(t ), xa(t ), u(t ), y(t ), θ , p) ∀ ⎪ d ⎪ f (x(t ), x (t ), u(t ), y(t ), θ , p) ∀ a ⎪ a ⎪ g (x(t ), x (t ), u(t ), y(t ), θ , p , t ) ≤ 0 ∀ ⎪ p k a k k k k s.t.⎨ ⎪ f (x(̇ t ), x(t ), u(t ), y(t ), θ , p) = 0 ∀ ⎪ c ⎪ g (p) ≤ 0 ⎪ c ⎪ ⎩θ ∈ Θ

t ∈ |t 0 , t f | t ∈ |t 0 , t f | t k ∈ |t 0 , t f | t ∈ |t 0 , t f |

(10)

Here, the objective function Φ(.) is a suitable statistical measure of the control system performance, fd(.) and fa(.) are differential algebraic equations modeling the process, gp(.) ≤ 0 represents a set of inequality constraints of the process, fc(.) is the dynamic equation for the dual-temperature controllers, gc(.) ≤ 0 represents inequality constraints for the controller parameters, x(t) and xa(t) are the vector of differential and algebraic variables, u(t) is the vector of manipulated variables, y(t) is the vector of output variables which are measured and to be controlled, and

Figure 4. Temperature RGA and SVD result for the benzene chloride production.

Therefore, the fresh feed stream of benzene FC6H6 is chosen as the production rate in the control structure. According to the SVD results of Figure 4, the temperatures of the 11th tray and the13th 17468



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p represents the time-invariant control parameters (kj,τi) in the vector form. θ is the uncertain disturbance assumed to follow a continuous probability density function with the mean of μ and the covariance of σ over the finite domain Θ. The dualtemperature PI controllers are considered with the following general equations: ⎛ 1 uj(t ) = Kcj⎜⎜ej(t ) + τ ⎝ j

∫0

t

⎞ ej(t ) dt ⎟⎟ + uj0(t ) ⎠

kj min ≤ kj ≤ kj max

no.

control loop

target

Kc

τ (min)

1 2 3 4

LR/FRR LB/FB PS/FD T11/R (case 1) T11/R (case 2) T13/Vs (case 1) T13/Vs (case 2)

0.32 m 1.12 m 1 atm 362.5 K 362.5 K 380.3 K 380.3 K

10 10 20 3 10.5 8 3.5

60 60 12 35 30 45 30

5

∀ j = 1, ..., Nu

ej(t ) = ysp , j − yj (t )

Table 2. Control Structure Description of the Consecutive Reactive Distillation Process

(11)

∀ j = 1, ..., Nu

(12)

τj min ≤ τj ≤ τj max

(13)

Here, kj and τj are controller parameters to be searched; k , kmax, τmin, τmax are the upper and lower bounds of the controller parameters, respectively. The statistical objective function of the system performance has the following form: min

ϕ = E[J(p , θ , t )] + ω V [J(p , θ , t )]

J=

∫0

tf

(14)

[(ysp − y(t ))T Q (ysp − y(t ))

+ (usp − u(t ))T R(usp − u(t ))] dt

(15)

Here, E and V are the expectation and variance of the performance index, respectively, and ω is weighting factor between the two terms; y(t) represents the measurements of both tray temperatures; ysp is the set points, and u(t) represents the vector of manipulated variables, vapor boil-up rate Vs, and feed stream ratio Rf. usp is the expected values of manipulated variable at the steady state; Q and R are positive definite weighting matrices for scaling purposes. The expectation and variance of the performance index are estimated using a sample average approach based on sigma point method.39 The set of sigma points have the following forms: set of sigma points: ⎧ θ0 = μ ⎪ ⎪ ⎨ θi = μ + ( (n + λ) ∑ )i ∀ i = 1 , ..., n ⎪ ⎪ θ = μ − ( (n + λ) ∑ ) ∀ i = n + 1 , ..., 2n i ⎩ i

Figure 5. Open response of dual-temperature control for reactive distillation column.

(16)

weight:

2n

⎧ λ ⎪ ω0 = ⎪ n+λ ⎨ λ ⎪ω = ∀ i = 1 , ..., n ⎪ i 2( n + λ) ⎩

V [J ] =

i=0

(17)

2n

∑ wJi (θi) i=0

(19)

The stochastic dynamic optimization problem may be converted to a deterministic one, which is solved by the deterministic algorithms using a sequential approach. Also, the lagrange multipliers for the point constraints and other constraints may be used to solve the optimization problem. All optimization computations are performed by the MATLAB optimization program. All controllers are tuned first using the Tyreus−Luyben tuning method. Two cases are studied: in case 1, the tunings of controllers are obtained by directly using the Tyreus−Luyben tuning, and in case 2, the parameters of the dual-temperature controllers are retuned using the proposed stochastic

Here, μ and Σ represent the mean and covariance of a random disturbance condition θ, λ is a scaling parameter, and n is the number of uncertain disturbances. The expectation and the variance of the performance index are given by E[J ] =

∑ wi(E[J ] − J(θi))(E[J ] − J(θi))T

(18) 17469



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Figure 6. System response: ±10% step changes in the feed stream of benzene (case 1, Tyreus−Luyben tuning; case 2, stochastic optimization retuning).

composition change 5%, in which the product composition maintains a new steady state of 0.95 kmol/kmol after about 11 h. Simulations are conducted for the designed control structure with the different parameters as stated in case 1 and case 2. In both cases, the process reaches steady-state with 1 h. Disturbances of changes ±10% step in the fresh stream of benzene are introduced. The responses of the two manipulated variables (FCl2 and Vs), the two controlled variables (T11 and T13), and the bottom product compositions (xB,C6H5Cl, xB,C6H6) are shown in Figure 6. The left curves show the responses of the control system with the Tyreus−Luyben tuning parameters (case 1), while the right curves show that of the control system with the optimal parameters by the proposed retuning (case 2). It shows that, with the increased feed rate of benzene FC6H6, the feed rate of chlorine also increases to 12.2 kmol/h by the ratio control strategy. A greater amount of energy is required to maintain vapor−liquid equilibrium in the column, and the vapor boilup VS also is increased from 2.19 to 2.26 GJ/h. This result shows that the ±10% step disturbances can be handled well and the purity of the product chlorobenzene (xB,C6H5Cl) can be maintained at the desired value of 0.964 kmol/kmol. Moreover, the temperatures of sensitive plate T11 and T13 can also recover to the ideal steady state. At the same time, Figure 6 shows that the dynamic responses of case 2 have been greatly improved as compared to those of case 1 for the feed disturbance handling, with faster response (as shown taking about 1 h for case 2 while almost 8 h for case 1 for the bottom product composition to recover), a smaller overshoot for tray temperatures T11, fdT13, and product compositions xB,C6H5Cl, and a higher accuracy.

optimization method, in which the parameters of case 1 are set as the initials. For illustration purposes, disturbances are assumed to be the step functions, whose magnitude is described by the normal probability distribution function (PDF), N(μj, σj), j = 1,2, where j represents the disturbance variable of the product rate or the feed composition. Assuming these two disturbances are independent, the joint normal PDF is N(μ, Σ), where μ is the mean vector and Σ is the covariance matrix. The covariance matrix is diagonal. There are four sigma points (ΔF = ±10%,Δz = ±5%) when the number of uncertain disturbances n is set to 2. The optimal parameters of these controllers are shown in Table 2. 3.4. Simulation and Discussion. The dynamic simulation for the benzene chlorine process is simulated by the Aspen Plus software with Aspen Dynamic modules. The effectiveness of the proposed dual-temperature control structure is analyzed by the uncertain disturbance resistance in terms of changes in the production rate (ΔFC6H6) and the feed compositions (ΔzC6H6 and ΔzCl2). Before implementing the dual-temperature control structure in simulation system of the benzene chlorine reaction, the openloop responses are tested first through introducing a flow rate change 10% in the benzene feed and a composition change 5%. Also, three based control loops, such as LB/FB, LR/FR, and Ps/FD loops, are implemented in the dynamic simulation in order to maintain the system steadily running. The open-loop responses of the process are shown in the Figure 5. Figure 5a shows the responses of composition and tray 11th temperature against the flow rate change 10%, in which product composition is greatly reduced until it maintains a new steady state of 0.88 kmol/kmol after about 5 h. Figure 5b shows their responses against the 17470



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Figure 7. System response: 5% step changes in feed stream composition ΔzCl2,ΔzC6H6 (case 1, Tyreus−Luyben tuning; case 2, stochastic optimization retuning).

Table 3. Comparison of Dynamic Performance Indexes of Product Composition in Both Casesa case 1

case 2

N

disturbances

σ%

Ts

ess

IAE

σ%

Ts

ess

IAE

1

FC6H6 = 10%

0. 18

7

1.705 × 10−4

0.0112

0. 06

2.4

1.76 × 10−4

0.0037

2

FC6H6 = −10%

0. 07

7

1.002 × 10−4

0.0137

0. 02

2.15

1.57 × 10−4

0.0036

−4

−4

3

zC6H6 = 5%

0.033

9

8.560 × 10

0.0149

0.000

1.2

8.560 × 10

0.0164

4

zCl2 = 5%

0.027

7

1.023 × 10−4

0.0082

0.003

0.4

9.831 × 10−5

0.0019

5 6 7

one-step profile three-step profile parabola profile

0. 39 0. 32 0. 29

8 8.5 8.5

3.330 × 10−4 3.302 × 10−4 3.257 × 10−4

0.02018 0.0197 0.0194

0. 07 0.027 0.003

1.4 1.3 1.4

3.413 × 10−4 3.413 × 10−4 3.408 × 10−4

0.0071 0.0068 0.0065

a Case 1: Tyreus−Luyben tuning. Case 2: stochastic optimization retuning. σ: overshoot. Ts: stabilization time. ess: steady state error. IAE: the integral performance index of absolute value of error.

Other process performance tests are conducted with the feed composition disturbances. A 5% impurity of chlorobenzene in the feed of benzene (ΔzC6H6) and a 5% impurity of chlorine hydride (ΔzCl2) in the feed of chlorine are introduced, respectively. Figure 7 shows the responses rejecting these composition disturbances. For a 5% composition disturbance in the benzene feed, the process settles dynamically to the ideal steady state, and the bottom product composition reaches the stable desired value of 0.965 kmol/kmol. Production rate is decreased in response to the impurity changes in the feed stream of benzene, the feed of FCl2 is also decreased to 9.7 kmol/h by the feed ratio control, and the vapor boilup Vs is increased to 2.26 GJ/h to maintain the product composition at the expected value. For the case of 5% impurity introduced in the feed of chlorine, the feed rate FCl2 is increased to 10.62 kmol/h to satisfy the stoichiometry of the column, and the vapor boilup Vs maintains at the steady-state of 2.22 GJ/h as

production rate FC6H6 remains unchanged. The bottom product composition xB,C6H5Cl is kept at the desired value 0.964 kmol/kmol. Similarly, the dynamic performance of case 2 has been greatly improved when compared to those of case 1 under the feed composition disturbances against a dynamic response (about 1 h for case 2 while almost 5 h for case 1 for product composition to recover), smaller overshoot, and higher control accuracy. These simulation results in Table 3 show that the feed rate disturbances as well as the composition disturbances can be better handled by the proposed retuning of the controller parameters.

4. PROFILE SETTING OF PRODUCTION RATE Production rate is often changed in response to market demand. Reactive distillation has inherent strong nonlinearity and coupling; its operation is more difficult than that of a conventional multiunit processes for the adjustment of production 17471



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parabola function profile: ⎧ F0 0 ≤ t < t0 ⎪ ⎪ F −F Fset = ⎨ F0 + 0 2 new (t − t 0 − T )2 t 0 ≤ t < t 0 + T T ⎪ ⎪F t > t0 + T ⎩ new

Here, F0 and Fnew are the original value and adjusted value of the product rate, respectively, N is the step length of the multistep profile, T1 is duration of each step, and T is the total transition duration. The lengths of duration time T and T1 may be chosen on the basis of the system dynamic characteristics, such as the desired rise time, overshoot, and attenuation ratio, or may be determined on the basis of certain form optimization. In this section, these three set-point transition forms of a 20% increase (ΔFC6H6 = 2.04 kmol/h) in production rate are introduced 1 h after the system reaches the steady-state. After another 5 h, the process reaches again the new steady-state; the production is decreased back to the original value through the same three set-point transition forms, which are shown in Figure 8. In the multistep profile setting form, the step length N is set as 3 steps, and the duration time T1 is set as 1 h. While in the quadratic parabola function profile form, the transition duration T is set as 4 h. 4.2. Simulation and Discussion. The above profile setting forms of production rate change are implemented, respectively, into the simulation of the benzene chlorine process controlled with the above dual-temperature control structure. Changes in production rate typically result in changes in product compositions with a poor control structure or the inappropriate parameter tuning, especially for reactive distillation. For a good control structure and control tuning, with the product rate increasing, the feed rate of chlorine FCl2, vapor boilup Vs, and reflux flow FR should also be increased accordingly to maintain the material balance and energy balance; consequently, the product compositions can maintain the optimal value. A 20%

Figure 8. Three profile setting forms of the production rate FC6H6.

rate. It may result in loss of product quality, even lead to safety issues if it is not properly operated.38,39 In this section, three different set-point transition forms of the production rate adjustment are tested and compared to evaluate the performance of the proposed control structure. 4.1. Production Rate Set-Point Transition Forms. Three profile setting forms of the changes of benzene chlorine production in the reactive distillation column are constructed with a one-step, multistep, or quadratic parabola function. They are tested in the following simulation. The profile setting forms are given as the following: one-step profile: ⎧ F0 0 ≤ t < t0 Fset = ⎨ ⎩ Fnew t ≥ t0 ⎪

⎪

(20)

multistep profile: ⎧ F0 0 ≤ t < t0 ⎪ ⎪ ⎛ F − F0 ⎞ ⎟ t + (k − 1)T ≤ t < t + kT Fset = ⎨ F0 + k ⎜ new 1 0 1 ⎝ ⎠ 0 N ⎪ ⎪ t > t 0 + NT1 ⎩ Fnew k = 1, 2 , ..., N

(22)

(21)

Figure 9. Comparison with process transient performance of three profile setting forms (case 1, Tyreus−Luyben tuning; case 2, stochastic optimization retuning). 17472



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production rate adjustment is used as an example for the benzene chloride reactive distillation to evaluate the process performances under the above three set profile forms. The production rate setpoint transitions are, respectively, implemented and tested in simulation system for the two cases with different tuning parameter. In case 1, the parameters of the controllers keep the same as the previous case, Loop T11/R: K = 3, τ = 35 min, and Loop T13/(V s): K = 8, τ = 45 min, using the Tyreus−Luyben tuning. Responses of the process under these three different setting profiles are shown in the left curves of Figure 9. The results show that, with the product rate FC6H6 increasing, the feed rate of chlorine FCl2 is increased accordingly to 10.2835 kmol/h to maintain the material balance in the column, while vapor boilup Vs is increased to 2.285 kmol/h to the energy balance. Consequently, the product compositions can maintain the optimal value of 0.964 kmol/kmol within 8 h for the three profile forms. However, in the one-step profile case, the responses of the tray temperature T13 and the bottom product composition xB,C6H6 have obvious fluctuations with the bigger overshoot, which are likely to cause the damage of the plates in industry operation. The dynamic performances of the three-step profile form have been improved greatly. In quadratic parabola function form, the best process performance with the smallest overshoot and best smoothness can be achieved. In case 2, the parameters for the dual-temperature controllers are retuned using the proposed optimization based on the new optimal steady-state parameters which are achieved by the economic optimum design. The parameters of case 1 serve as the initials for the parameters optimization of case 2. The responses under these three different setting profiles are shown in the right curves of Figure 9. The system responses have improved significantly as compared to these of case 1. For the one-step profile, the output response curves of tray temperature T11, T13 and production composition xB,C6H5Cl have smaller overshot and better stability than those of case 1. For the three-step profile and parabola profile, the process responses are excellent with good stability and precision. By comparing the performance indexes (Tr, ess, and IAE of the composition response) of these different profile forms under cases 1 and 2, as shown in Table 3, we conclude that the close-loop dynamics are improved significantly by the propose retuning. They are strong functions of setting profiles.

production set-point transition strategy can be an important study.

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected] (X.Q.). Phone: 86-25-83172298 (X.Q.). Fax: 86-25-83172298 (X.Q.). *E-mail: [email protected] (F.G.). Phone: 852-23587139 (F.G.). Fax: 852-23580054 (F.G.). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work is supported, in part, by the National Natural Science Foundation of China (61203020, 21276126), Jiangsu Province Natural Science Foundation (BK2011795), National Key Technology Research and Development Program of the Ministry of Science and Technology of China (2011BAE18B01), and Jiangsu Province Six Domain Talent Peak Program.

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5. CONCLUSION A framework for design of a decentralized control structure, and controller parameter tuning, has been proposed. The proposed framework was successfully demonstrated and tested in simulation control of benzene chloride consecutive reaction system. It has been shown that the proposed control structure with proposed selection of tray temperatures and their pairing is very effective and has good robustness against the production rate and the feed composition disturbances. Further, retuning of the dual-temperature controllers by the proposed stochastic dynamic optimization can result in superior control performance even under several uncertainty disturbances. Three different setpoint transition forms for the production rate adjustment have been tested in the simulation to evaluate the process control performances. The results indicated that the different profile setting forms have an important effect on the transient performance of the proposed control structure. Therefore, the 17473

NOMENCLATURE ki = reaction rate constant of the reaction i Avp,j = Antoine constant of component j Bvp,j = Antoine constant of component j Cvp,j = Antoine constant of component j rC = reaction rate of product C (kmol/s) rE = reaction rate of product E (kmol/s) A1, A2 = pre-exponential factors E1, E2 = activation energy (kJ/kmol) FCl2 = feed flow rate of chlorine (kmol/h) FC6H6 = feed flow rate of benzene (kmol/h) Vs = vapor boilup (kJ/h) zj = feed mole fraction of component j Δzj = change in feed mole fraction of component j xB,j = composition of component j in bottom product xD,j = composition of component j in top product PS = vapor pressure on tray i (atm) FR = reflux flow rate (kmol/h) Kp = steady-state gain of temperature ΔKp = steady-state gain of temperature difference relate Ti = temperature of tray i (K) U = left singular vector matrix E = expectation of the performance index ei = error between set-points and output variable i J = performance index n = number of uncertain disturbances Nu = number of potential manipulated variables Nc = number of control loops P = vector of continuous controller parameters Q, R = weighting matrixes V = variance of the performance index x(t) = vector of differential state variables xa(t) = vector of algebraic variables u(t) = vector of manipulated variables y(t) = vector of measurements/output variables ysp = set-points for output variables R = covariance matrix Kc = controller gain F0 = original value of the product rate (kmol/h) Fnew = expected value of the product rate (kmol/h) N = the step length of multistep profile k = the step number of multistep profile dx.doi.org/10.1021/ie4007694 | Ind. Eng. Chem. Res. 2013, 52, 17465−17474


Article

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T = the regulating time of every step (h) T1 = the regulating time of (h) Greek Symbols

τ = reset time (min) λ = parameters in the sigma point method θ = vector of uncertain disturbances μ = mean of the random disturbances σ = standard deviation of the random disturbances Φ = statistical objective function ω = weighting factor between the expectation and the variance

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Control and Profile Setting of Reactive Distillation Column for Benzene

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