PROCESS CONTROL
Chinese Journal of Chemical Engineering, 20(6) 1113—1120 (2012)
The Design and Control of Distillation Column with Side Reactors for
Chlorobenzene Production*
BO Cuimei (薄翠梅)1,2,**, TANG Jihai (汤吉海)2, BAI Yangjin (柏杨进)1, QIAO Xu (乔旭)2,
DING Lianghui (丁良辉)2 and ZHANG Shi (张湜)1
1
2
College of Automation and Electrical Engineering, Nanjing University of Technology, Nanjing 210009, China
State Key Laboratory of Materials-oriented Chemical Engineering, Nanjing University of Technology, Nanjing 210009,
China
Abstract The distillation column with side reactors (SRC) can overcome the temperature/pressure mismatch in
the traditional reactive distillation, the column operates at temperature/pressure favorable for vapor-liquid separation, while the reactors operate at temperatures/pressures favorable for reaction kinetics. According to the smooth
operation and automatic control problem of the distillation column with side reactors (SRC), the design, simulation
calculation and dynamic control of the SCR process for chlorobenzene production are discussed in the paper. Firstly,
the mechanism models, the integrated structure optimal design and process simulation systems are established, respectively. And then multivariable control schemes are designed, the controllability of SRC process based on the optimal steady-state integrated structure is explored. The dynamic response performances of closed-loop system against
several disturbances are discussed to verify the effectiveness of control schemes for the SRC process. The simulating results show that the control structure using conventional control strategies can effectively overcome feeding
disturbances in a specific range.
Keywords distillation column with side reactors (SRC), mechanism models, multivariable control schemes, simulation system, chlorobenzene production
1
INTRODUCTION
Economic and environmental considerations have
forced industry to focus on technologies based on
process intensification. Reactive distillation has received much attention in the past decade in both industry and academia [1]. It has several advantages in some
chemical systems, which may effectively reduce investment and operating costs, increase conversion and
selectivity comparing to conventional multi-unit flowsheets with separate reaction and separation sections
[2, 3]. There are two different kinds of integrated structure for reactive distillation process: One structure is
that reaction and distillation units are integrated in a
single column, namely the conventional reactive distillation; while the other is that the reactors are coupled
externally with a distillation column, namely the distillation column with side reactors (SRC). For conventional reactive distillation, the temperatures that are
good for reaction must match the temperatures that are
good for vapor-liquid separation. Therefore, traditional
reactive distillation is not effective in many chemical
systems because of a mismatch in temperatures [4].
The distillation column with side reactors can
not only effectively increase the conversion and selectivity, but also overcome the temperature or pressure
mismatch in the traditional reactive distillation [5, 6].
There are several papers in the literature dealing with
the design and dynamic control of traditional reactive
distillation. For example, Professor Luyben and his
partners gave eight different type control structures
(CS1-CS8) [7-9], which were widely used in traditional
reactive distillation control system design [10], while
the dynamic control of the SRC process was rarely
discussed in the recent literature [11, 12]. In this paper,
the mechanism model, structural design and dynamic
control of the SRC process for benzene chlorination
are explored, and the dynamic response performance
of closed-loop system against several disturbances are
discussed to verify the effectiveness of design for the
SRC process.
2
PROCESS DESCRIPTIONS
Chlorobenzene is widely used in dye and pharmaceutical industry to manufacture some organic intermediates such as phenol, aniline, nitro phenol. Chlorobenzene is produced from the reaction of benzene and
chlorine. The production is chlorobenzene and the byproduct is dichlorobenzene (mainly o-dichlorobenzene
and dichlorobenzene). Reaction equations are as follows:
(1)
Received 2012-05-28, accepted 2012-07-20.
* Supported by the National Natural Science Foundation of China (61203020, 21276126), the Natural Science Foundation of
Jiangsu Province (BK2011795), Jiangsu Province Higher Education Natural Science Foundation (09KJA530004), and China
Postdoctoral Science Foundation (20100471325).
** To whom correspondence should be addressed. E-mail: [email protected]; [email protected]
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Chin. J. Chem. Eng., Vol. 20, No. 6, December 2012
(2)
By using ferric chloride as a catalyst, the kinetic
equation for chlorobenzene is as follows [13]:
r1 = −
d[C6 H 6 ]
= k1[C6 H 6 ][Cl2 ]
dt
(3)
d[C6 H 4 Cl2 ]
(4)
= k2 [C6 H5 Cl][Cl2 ]
dt
where r1 and r2 are the reaction rate for monochloride
and dichloride; k1 and k2 are the reaction rate constants. The ratio of rate constants ω = k1 / k2 is about 8
at a reaction temperature of 55 °C. The physical properties of benzene (C6H6), chlorobenzene (C6H5Cl) and
dichlorobenzene (C6H4Cl2) are shown in the Table 1.
dichlorobenzene move to the column bottom, in which
there are two different zones: reaction zone and separation zone. The several trays in the reaction zone are
linked with three side reactors, respectively. The continuous chlorine with a certain proportion is introduced
to the bottom of three reactors, respectively, while fresh
benzene is given to the first reactor connected with the
top condenser. The hydrogen chloride generated in the
reactions will escape from the condenser of the column.
With continuous removal of the desired product chlorobenzene from the reaction zone, a higher selectivity may
be achieved.
r2 =
Table 1
benzene
Material related properties
Chemical
formula
Boiling point
/°C
Molar mass
/g·mol−1
C6H6
80.1
78.11
chlorobenzene
C6H5Cl
132.2
112.56
dichlorobenzene
C6H4Cl2
180.4
147
3
MODELING AND SIMULATING
The SRC process mechanism model contains two
parts: MESH equations of the column and chemical
kinetic model equations.
3.1
Reaction mechanism model
Each reactor was assumed to be a perfectly adiabatic mixed stirred tank reactor, and in the continuous
chlorination reaction system continuous reaction material equilibrium equations with the tray j are as follows Eqs. (5)-(13):
( y j ,1 − z j ,1 ) ⋅ FRj = V ⋅ k1 ⋅ z j ,1 = FCl ⋅ (a + b / 2) (5)
( z j ,2 − y j ,2 ) ⋅ FRj = V ⋅ ( k1 ⋅ z j ,1 − k2 ⋅ z j ,2 ) = FCl ⋅ a (6)
( z j ,3 − y j ,3 ) ⋅ FRj = V ⋅ k2 ⋅ z j ,3 = FCl ⋅ b / 2 (7)
2
Due to mismatch between reaction temperature
and the separation temperature in benzene chlorination
process, the SCR integrated structure for chlorobenzene production is designed, and the dynamic control
system is researched. The configuration of SRC for
chlorobenzene production is shown in Fig. 1. In Fig. 1,
the lighter component benzene moves toward the column top and the heavier component chlorobenzene and
Figure 1
2
2
where yj,1, yj,2, yj,3, zj,1, zj,2 and zj,3 are the inlet and
outlet mole compositions of benzene, chlorobenzene
and dichlorobenzene from the reactor which is connected with the j-th tray; FRj is the inlet liquid flow
rate to the reactor; FCl2 is chlorine feed flow rate; V is
Configuration of the SRC process for chlorobenzene production
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Chin. J. Chem. Eng., Vol. 20, No. 6, December 2012
the volume of the reactor; and a and b are the mole
fractions of chlorine used to form chlorobenzene and
dichlorobenzene, respectively. Dividing Eq. (7) by Eq.
(6) and introducing the rate-constants ratio ω = k1 / k2 ,
Eq. (8) can be obtained.
z j ,2 − y j ,2
z j ,3 − y j ,3
=
k1 ⋅ z j ,1 − k2 ⋅ z j ,2
k2 ⋅ z j ,3
=
ω ⋅ z j ,1 − z j ,2
z j ,3
MESH equations include the material balance
equations, phase equilibrium equations, the mole fraction
of the normalized equation and heat balance equation
[14]. MESH equations of tray j are shown as follows:
M j ,i = I j FR z j ,i + (1 − I j ) L j −1 x j −1,i −
2a
=
(8)
b
L j x j ,i + V j +1 y j +1,i − V j y j ,i
When the reaction temperature is 55 °C, ω = 8 .
zj,1, zj,2 and zj,3 can be evaluated by shifting Eqs. (5-7)
as follows:
z j ,1 = y j ,1 − FCl2 FRj ⋅ a + y j ,2
(9)
z j ,2 = FCl2 FRj ⋅ a + y j ,2
(10)
z j ,3 = ( FCl2 FRj ) ⋅ (b / 2) + y j ,3
(11)
ω ⋅ y j ,1 − ω ⋅ ( FCl FRj ) ⋅ (a + b / 2) −
2
} ⎡⎣( F
2a
FRj ) ⋅ a + y j ,2 ⎤ =
⎦ b
(12)
a + b =1
(13)
When the reactor feeding conditions are known
( FCl2 , FR, yj,1, yj,2), we calculate the selectivity of the
chlorine on the chlorobenzene and dichlorobenzene.
The materials mole distribution of the reactor outlet
can be calculated by Eqs. (9-11). For liquid phase
reactions, the above Eqs. (5-13) can be used to calculate the liquid mole fraction and the distribution rate
of material chlorine on product.
⎡( FCl2 FRj ) ⋅ a + y j ,2 ⎤
⎣
⎦
3.2
Cl2
Column MESH model
The mechanism model of the distillation column
can be built as a column with several side streams.
The activity coefficients of the liquid phase are calculated using the Wilson model. A schematic diagram of
equilibrium tray is shown in Fig. 2.
(a) Ij = 0
Figure 2
c
S xj = ∑ xi , j − 1
i =1
Substituting zj,1, zj,2, zj,3 described by Eqs. (9) and
(10) to Eq. (8), Eqs. (12) and (13) can be obtained.
{
E j = y j ,i −
rj ,i PjS,i
P
x j ,i
c
S yj = ∑ yi , j − 1
(14)
(15)
(16)
i =1
H j = I j FRj H Rj + I j FHClj H HClj + (1 − I j ) L j −1 H Lj −1 −
L j H Lj + V j +1 H Vj +1 − V j H Vj +
VGj +1 H VGj +1 − VGj H VGj
(17)
where j = 1, 2," , N means the number of the column
tray; i = 1, 2, 3 means benzene, chlorobenzene and
dichlorobenzene, respectively. x j ,i and y j ,i are liquid
phase and vapor phase molar composition of component i in the tray j ; L j and V j , represent liquid and
vapor flow rate of the tray j; H Lj and H Vj are liquid
and vapor enthalpies of the tray j; FRj is the flow rate
from the reactor into the tray j; z j ,i is the molar composition from the reactor into the tray j; H Rj is the liquid enthalpy from the reactor into the tray j. The product hydrogen chloride get into the distillation column
system, and its influence on the vapor-liquid equilibrium is very little. It only affects the pressure and energy balance of the column. FHClj and H HClj represent
hydrogen chloride vapor phase flow rate and enthalpy
from reactor into tray j; and VGj and H VGj are hydrogen chloride liquid flow rate and enthalpy of tray j.
3.3
Solution and simulation of mechanism model
For the calculation of strong nonlinearity and
(b) Ij = 1
Column equilibrium schematic of the tray j (Ij is the signs for reactor site, Ij = 1 mean tray j linked with side reactor)
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Chin. J. Chem. Eng., Vol. 20, No. 6, December 2012
coupled relation between thermodynamic equilibrium
and the kinetic equations of non-ideal system, the solution of mechanism model is more complex. Since
the simulating convergence of model is rather difficult,
a good initial value to ensure reliable convergence is
needed. In this paper, it is firstly assumed that the capacity of the reactor is large enough to promise chlorine to be consumed completely, and the feeding flow
rates of chlorine ( FCl2 ) are defined as the independent
reaction amount. Therefore, the mechanism model may
be equivalent to distillation column simulation problem
with multi-stream inlet and outlet. After distillation
column calculating convergent, the material properties
of the reactor can be obtained, which is connected
with the tray j. According to reaction kinetics model,
the sizes of reactors are calculated. This solution has
greatly improved the convergence speed of the model
of the SCR process [15]
The SRC simulation process is that the above reactors equations and MESH equations are simultaneously calculated. The algorithm block diagram of the
SCR process is shown in Fig. 3. In this paper, NewtonRaphson method with numerical evaluation of the
Jacobian matrix is used to the steady-state solution of
the MESH equations. In addition, the initial values of
V j and L j are generated from the constant molar flow
assumption. The initial column composition profile
x j ,i is guessed according to the distribution rule of the
Figure 3
components. The initial tray temperature ( T j ) is set to
be the boiling point of benzene at the given pressure.
The simulation of the SRC process is completed using
MATLAB software.
3.4
Simulation results
The optimal steady-state design of the SCR
process for Chlorobenzene production are obtain by
the economic optimal design procedures based on sequential quadratic programming (SQP) algorithmic in
the literature [15, 16]. The optimization structural parameters and operating parameters are as follows: the
column tray numbers N = 12 ; the reactors numbers
N R = 3 ; the tray numbers between reactors N RS = 1 ;
the vapor boilup in column bottom Vn = 30 kmol·h−1;
the fresh feeding flow rates of chlorine FCl2 = 9.95
kmol·h−1; and the chlorine proportion to three reactors
fb(i) = [0.41 0.31 0.28]. In the simulations, the fresh
feeding flow rates of benzene are excess to guarantee
the complete reaction of chlorine, and thus, the optimal feeding flow rates of benzene is calculated by the
reaction terms. Fig. 4 shows the simulating results. Fig.
4 (a) is the composition distribution of liquid material
in the bottom column, Fig. 4 (b) is the temperature
distribution of the bottom tray; and Fig. 4 (c) is the
flow rate distribution of the column bottom.
Algorithm block diagram of the SCR process
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Chin. J. Chem. Eng., Vol. 20, No. 6, December 2012
(a) The composition distribution
■ C6H6; ● C6H4Cl2; ▲ C6H5Cl
(b) The temperature distribution
(c) The flow rate distribution
■ liquid; ● vapour
Figure 4 Simulating results of the steady-state optimal design
Figure 5
Multivariable control schemes of the SRC process for chlorobenzene production
When the feeding flow rates of chlorine is 9.95
kmol·h−1, the feeding flow rates of benzene calculated
by the reaction terms is FB = 9.58 kmol·h−1. In the
simulated results, the purity of chloride production is
0.9683, the purity of benzene is 0.099%, and the selectivity is 0.968/(1−0.0309) = 99.88%.
Comparing the experimental data, i.e., the chlorobenzene in column bottom is about 96% with various
kinds of catalysts, the conversion rate of benzene is 99%,
and the selectivity of chlorobenzene is about 97%, it
demonstrates that the simulated results are closed to
the experimental results. Thus, the simulated results can
be used in the guidance of chlorobenzene production.
4 DESIGN AND ANALYSE OF CONTROL SYSTEM
The dynamic control of the SRC process is the
significant element during the engineering application
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Chin. J. Chem. Eng., Vol. 20, No. 6, December 2012
design of integrated technology [17]. Comparing with
the conventional distillation, the dynamic characteristics
of the SRC process are more complicated. As a result
of the interaction between the reaction and the separation, the SRC process has strong nonlinear, coupling
and multi steady-stable characteristics [18]. The above
characteristics make the dynamic operation and control for the SRC process become bottleneck problems.
4.1
Design of multivariable control schemes
Based on the above economic optimal design and
simulation analysis of the SRC process for chlorobenzene production, the multivariable control schemes
are developed with the conventional control strategies
as shown in Fig. 5.
The control schemes include several control loops,
such as the liquid level control loops (LIC-100, LIC-101),
the pressure control loop (PIC-100), the feed flow rate
control loops (FIC-101, FIC-102), outlet flow rates
control loops of the three reactors (FIC-103, FIC104,
FIC105), the temperature cascade control loop (TIC-100),
etc., which are given in Table 2. For the composition
analyzers have higher cost, require more maintenance,
and can introduce dead-time into the control loop, the
temperature cascade control loop is proposed. The
temperature control of column bottom is the main loop
(TIC-100), and the control of the steam flow rate is
sub-loop (FIC-100), which are shown in Fig. 5.
4.2 The performance analysis of the close-loop
control system
The dynamic simulation of the SRC process for
chlorobenzene production with the above designed control structures are explored with chemical simulation
software HYSYS. Through reasonable setting control
system parameters and operating parameters, the
closed loop control system of the SRC process can run
smooth and attain the expected control goals. To check
Table 2
Control loop
the effectiveness of this control structure, the disturbances of feed flow rates, the feed composition and
the steam calorific value disturbances are applied to
the system, respectively.
4.2.1 Change of temperature set-value
The temperature set-value Tsp of the column bottom temperature is adjusted respectively ±5 °C. Fig. 6
shows the dynamic response of the control structure to
set-value change.
As seen in Fig. 6, the temperature controlled variables track to the new set-value for both positive and
negative changes in a short time. The chlorobenzene
composition of the product can be settled down smoothly
to steady-state values within specification values of
92%-93.5%.
4.2.2 Change of production rate handle
To check the effectiveness of this control structure,
the ±5% step changes of the production rate (the feed
flow rate of chlorine FCl2 ) are applied to the system.
The feed flow rate of benzene is growing with increasing feed flow rate of chlorine under the ratio control
structure. Fig. 7 shows the dynamic response of the
control structure to these disturbances. As seen in Fig.
7, the fluctuation range of the temperature is within
about 0.5 °C range. The chlorobenzene composition of
the production is also maintained in the fluctuation
range within about 0.2% range.
4.2.3 The 5% impurities in fresh-feed stream
The 5% impurities of nitrogen in fresh-feed
stream FCl2 are applied to the system. Fig. 8 gives the
responses of control structure to 5% impurities of nitrogen in fresh-feed stream FCl2 . The control structure
keeps the temperature within range of about 1 °C and
product purities within 1.5% of their specified values
for the 5% feed stream impurity.
4.3
Analysis of the system performance indexes
The performance indexes of the SRC process for
Loop structure description of multivariable control schemes
Controlled variable
Manipulated variable
Control target
LIC-101
liquid level of condenser
flow rates of reflux
50%
LIC-100
liquid level of column bottom
outlet flow rates
50%
PIC-100
pressure of column top
emission of HCl
101.3 kPa
FIC-101
feed flow rates of Cl2
feed flow rates of Cl2
9.95 kmol·h−1
FIC-102
feed flow rates of C6H6
feed flow rates of C6H6
9.58 kmol·h−1
FIC-103
outlet flow rate of reaction 1
outlet flow rates of reaction 1
10 kmol·h−1
FIC-104
outlet flow rate of reaction 2
outlet flow rates of reaction 2
24 kmol·h−1
FIC-105
outlet flow rate of reaction 3
outlet flow rates of reaction 3
25 kmol·h−1
FIC-106
inlet flow rate of reaction 1
inlet flow rate of reaction 1
fb(1)
FIC-107
inlet flow rate of reaction 2
inlet flow rate of reaction 2
fb(2)
FIC-108
inlet flow rate of reaction 3
inlet flow rate of reaction 3
fb(3)
cascade control
temperature of column bottom
steam flow rate of reboiler
135 °C
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Chin. J. Chem. Eng., Vol. 20, No. 6, December 2012
(a)
Figure 6 Dynamic response under the temperature set value Tsp changes
Tsp + 5 °C;
Tsp − 5 °C
(b)
(a)
Figure 7 Dynamic response under step change (±5%) in production rate handle
flow +5% ;
flow −5%
(b)
(a)
Figure 8
(b)
The dynamic response under the 5% impurities in fresh-feed stream
Table 3
Analysis of the system performance indexes
Temperature response
Disturbance
Disturbance
amplitude
ts/min
Tsp change
+5℃
−5℃
production rate handle ΔFCl2
5% impurities in feed stream FCl2
Composition response
IAE
e(∞)
ts/min
IAE
e(∞)
30
76.42
0.5
30
0.04
0.001
75
183.66
0.3
75
0.06
0.002
+5%
3.4
0.22
0.5
3.4
0.001
0.002
−5%
3.4
0.28
0.3
3.4
0.001
0.002
5%
2.87
43
0.12
2.87
1.22
0.015
chlorobenzene production, such as the settling time ts,
the absolutely integral error IAE and the steady-state
error e(∞) are calculated further under the above disturbances conditions. The calculating results are given
in Table 2. Through the analysis of the performance
indexes of the control system in Table 3, the recommended multivariate control structure can overcome
effectively the above different type disturbances within
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Chin. J. Chem. Eng., Vol. 20, No. 6, December 2012
a certain range.
5
REFERENCES
1
CONCLUSIONS
The distillation column with side reactors can not
only effectively increase the conversion and selectivity,
but also can overcome the temperature or pressure
mismatch in the traditional reactive distillation. In this
paper, the mechanism model, the optimizing design
and dynamic control of the SRC process for chlorobenzene production are discussed. The effectiveness
of control structure is demonstrated using disturbances
in production rate and fresh-feed compositions.
The simulating results show that the control structure using conventional control strategies can effectively
overcome various disturbances in a specific range.
However, owing to the nonlinear and coupling characteristics, the system will probably deviate from the
ideal condition and even cause the instability when the
disturbance with larger range is added. The dynamic
intelligent control methods and the multivariate predictive control will be researched in future work to
solve the problems about the on-line optimizing operation and synergy control for the SRC process.
2
3
4
5
6
7
8
9
10
NOMENCLATURE
11
FCl2
FRj
fb
HLj
HRj
HVj
i
j
k
Lj
N
NR
NRS
NS
r
Tj
Vj
xj,i
yj,c
yj,i
zj,c
ω
−1
chlorine feeding flow rate, kmol·h
inlet liquid flow rate of reactor, kmol·h−1
distributed ratio of chlorine to reactor
liquid enthalpies of tray j, MJ·kmol−1
liquid enthalpy from the reactor into tray j, MJ·kmol−1
vapor enthalpies of tray j, MJ·kmol−1
number of components
number of trays
reaction rate constant, h−1
liquid flow rate of tray j, kmol·h−1
number of trays in the column
number of the side reactors
number of trays between adjacent reactors in the reaction zone
number of stripping trays
reaction rate, kmol·L−1·h−1
column temperature on tray j, K
vapor flow rate of tray j, kmol·h−1
mole compositions of component i in liquid on tray j
inlet mole compositions of reactor, kmol·L−1
mole compositions of component i in vapor on tray j
outlet mole compositions of reactor, kmol·L−1
rate-constants ratio
12
13
14
15
16
17
18
Harwardt, A., Kraemer, K., Rüngeler, B., “Conceptual design of a
butyl-levulinate reactive distillation process by incremental refinement”, Chin. J. Chem. Eng., 19 (3), 371-379 (2011).
Kaymak, D.B., Luyben, W.L., “Optimum design of a column/side
reactor process”, Ind. Eng. Chem. Res., 46, 5175-5185 (2007).
Sundmacher, K., Kienle, A., “Reactive distillation: status and future
directions”, Wiley-VCH, Weiheim, Germany (2003).
Kaymak, D.B., Luyben, W.L., “Design of distillation columns with
external side reactors”, Ind. Eng. Chem. Res., 43 (25), 8049-8056
( 2004).
Baur, R., Krishna, R., “Distillation column with reactive pump
arounds: an alternative to reactive distillation”, Chem. Eng. and
Process., 43 (3), 435-445 (2004).
Radulescu, G., Gangadwala, J., Paraschiv,N., “Dynamics of reactive
distillation processes with potential liquid phase splitting based on
equilibrium stage models”, Computers and Chemical Engineering,
33 (3), 590-597 (2009).
Al-Arfaj, M.A., Luyben, W.L., “Comparison of alternative control
structures for an ideal two-product reactive distillation column”, Ind.
Eng. Chem. Res., 39 (9), 3298-3307 (2000).
Al-Arfaj, M.A., Luyben, W.L., “Comparative control study of ideal
and methy acetate reactive distillation”, Chem. Eng. Sci., 57 (24),
5039-5050 (2002).
Kaymak, D.B., Luyben, W.L., “Comparison of two types of
two-temperature control structures for reactive distillation columns”,
Ind. Eng. Chem. Res., 44 (13), 4625-4640 (2005).
Wang, S.J., Yu, C.C., Huang, H.P, “Plant-wide design and control of
DMC synthesis process via reactive distillation and thermally coupled extractive distillation”, Computers and Chemical Engineering,
34 (3), 361-373 (2010).
Kaymak, D.B, Luyben, W.L., “Dynamic control of a column/sidereactor process”, Ind. Eng. Chem. Res., 47 (22), 8704-8712 (2008).
Tsai, R.C., Cheng, J.K., Huang, H.P., Yu, C.C., “Design and control
of the side reactor configuration for production of ethyl acetate”, Ind.
Eng. Chem. Res. , 47 (23), 9472-9484 (2008).
Cui, M.F. Huang, X.Z., Qiao, X., “Study on process of chlorination
of benzene in the three-phase catalytic-distillation column with vapor diffluence”, Journal of Chemical Engineering of Chinese Universities, 18 (6), 696-700 (2004).
Ye, J.C., Huang, J.C., Lin, H., “Kinetic-thermodynamic analysis of
the reactive distillation process of the cyclohexene hydration using
the zeolite catalyst”, Chin. J. Chem. Eng., 19 (5), 808-814 (2011).
Ding, L.H., Tang, J.H., Cui, M.F., Bo, C.M., Qiao, X., “Optimum
design and analysis based on independent reaction amount for distillation column with side reactors: production of benzyl chloride”, Ind.
Eng. Chem. Res., 50 (19), 1143-1152 (2011).
Bo, C.M., Tang, J.H., Qiao, X., Ding, L.H., Cui, M.F., “The optimization method and simulating system of distillation column with side
reactors for benzene chloride production”, Journal of Shanghai
Jiaotong University, 45 (8), 1157-1162 (2011). (in Chinese)
Suresh Babu, K., Pavan Kumar, M.V., Kaistha, Nitin, “Controllable
optimized designs of an ideal reactive distillation system using genetic algorithm”, Chem. Eng. Sci, 64, 4929-4942 (2009).
Lin, Y.D., Huang, H.P., Yu, C.C., “Relay feedback tests for highly
nonlinear processes: reactive distillation”, Ind. Eng. Chem. Res., 45
(12), 4081-4092 (2006).