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Optimal operating condition of membrane reactors to enhance isobutene production, selectivity and hydrogen production
Journal of Industrial and Engineering Chemistry 18 (2012) 1676–1682
Contents lists available at SciVerse ScienceDirect
Journal of Industrial and Engineering Chemistry journal homepage: www.elsevier.com/locate/jiec
Optimal operating condition of membrane reactors to enhance isobutene production, selectivity and hydrogen production M. Farsi, A. Jahanmiri *, M.R. Rahimpour Department of Chemical Engineering, School of Chemical and Petroleum Engineering, Shiraz University, Shiraz, Iran
A R T I C L E I N F O
Article history: Received 19 January 2012 Accepted 7 March 2012 Available online 16 March 2012 Keywords: Isobutane dehydrogenation Pd/Ag membrane reactor Heterogeneous model Genetic algorithm
A B S T R A C T
In the isobutene synthesis process, coupling reaction and separation improves isobutene production and selectivity, reduces operation cost and lets to produce hydrogen. This study focuses on the steady state optimization of the isobutane dehydrogenation in hydrogen-permselective Pd/Ag based membrane reactors. The membrane reactors have been modeled heterogeneously based on the mass and energy conservation laws at steady state condition. The Genetic algorithm has been considered to optimize the operating condition of membrane reactors. Optimization results of membrane reactors are compared with conventional adiabatic reactors at the same catalyst loading. This optimal configuration has enhanced isobutene mole fraction about 16.4%. ß 2012 The Korean Society of Industrial and Engineering Chemistry. Published by Elsevier B.V. All rights reserved.
1. Introduction Isobutene as one of the main unsaturated hydrocarbons is used as a feedstock to produce a variety of chemical components such as polybutene, methyl tert-butyle ether and ethyl tertiary butyl ether. The most common industrial method to produce isobutene is catalytic dehydrogenation of isobutane. Some of commercial technologies have been developed for dehydrogenation of light alkanes such as isobutane. The Catofin isobutane dehydrogenation technology is a continuous cyclic process to produce isobutene over chromia–alumina catalyst in the fixed-bed reactor [1,2]. The reactors operate adiabatically and to regenerate the catalyst, multiple reactors operate at a controlled sequence of reaction and regeneration. In the UOP process, dehydrogenation reaction occurs in the several adiabatic moving-bed reactors over modified Ptalumina catalyst considering continuous catalyst regeneration [3]. Although a large number of researches have been presented on the n-butane and n-butene dehydrogenation, few articles in the literature discuss about isobutane dehydrogenation and process modeling [4]. Korhonen et al. investigated the performances of zirconia, alumina, and zirconia/alumina supported chromia catalysts in the dehydrogenation of isobutane in order to elucidate the role of the support material in the dehydrogenation reaction [5]. They showed that activity of chromia catalysts, acidity of the support and the phase of zirconia are important in the dehydrogenation rate. Cortright et al. presented a rate equation
* Corresponding author. Tel.: +98 711 6133788; fax: +98 711 6287294. E-mail address: [email protected] (A. Jahanmiri).
for isobutane dehydrogenation over Pt–Sn catalyst over a wide range of temperatures [6]. Bakhshi et al. modeled a bench scale fixed bed reactor for selective dehydrogenation of isobutane at steady state condition, homogeneously [7]. Sahebdelfar et al. modeled the dehydrogenation of isobutane to isobutene in adiabatic radial-flow moving bed reactors without considering catalyst regeneration section [8]. They neglected from side reactions while the isobutene selectivity in the considered commercial process was about 90%. The integration of membrane separation and reaction in a vessel has attracted much attention in the recent years [9]. Simultaneous occurrence of reaction and separation in a membrane reactor leads to shift thermodynamic equilibrium limitations and reduces separation cost compared to conventional processes. Casanave et al. studied isobutane dehydrogenation over Pt–In catalyst in a packed-bed zeolite membrane reactor [10]. Higher dehydrogenation yield was observed due to the hydrogen removal from the reaction zone. Ciavarella et al. investigated isobutane dehydrogenation in a MFI membrane reactor [11]. The performance of membrane reactor was studied as a function of the feed and sweep gas flow rates. Liang and Hughes studied isobutene synthesis from isobutane in a membrane reactor over Pt/Al2O3 catalyst, experimentally [12]. Also, they modeled the considered Pd/Ag membrane reactor under similar operating conditions. In this work, the radial flow reactors in the UOP process have been substituted by membrane fixed bed reactor at the same catalyst loading. The object of this study is modeling and optimization of Pd/Ag hydrogen permselective membrane reactors to enhance isobutene selectivity, isobutane conversion and hydrogen production from isobutane dehydrogenation. The sum
1226-086X/$ – see front matter ß 2012 The Korean Society of Industrial and Engineering Chemistry. Published by Elsevier B.V. All rights reserved. doi:10.1016/j.jiec.2012.03.015
M. Farsi et al. / Journal of Industrial and Engineering Chemistry 18 (2012) 1676–1682
Nomenclature av Ac Cp Ci D Ep F hf k Keq L P Pi P0 Q QH r Re T u U yi z
specific surface area of catalyst pellet (m2 m3) cross section area of each tube (m2) specific heat of the gas at constant pressure (J mol1) molar concentration of component i (mol m3) tube diameter (m) activation energy of permeability (kJ mol1) total molar flow rate (mol s1) gas–solid heat transfer coefficient (W m2 K1) reaction rate constant (mol kg1 s1 bar1/2) equilibrium constant I (m3 mol1) reactor length (m) total pressure (bar) partial pressure of component i (bar) pre-exponential factor of hydrogen permeability (mol m2 s1 Pa1/2) volumetric flow rate (m3 s1) hydrogen permeation rate (mol m1 s1) rate of reaction for dehydrogenation (mol kg1 s1) Reynolds number temperature (K) superficial velocity of fluid phase (m s1) overall heat transfer coefficient (W m2 K1) mole fraction of component i (mol mol1) axial reactor coordinate (m)
Greek letters aH hydrogen permeation rate (mol m1 s1Pa1/2) h catalyst effectiveness factor r density of fluid phase (kg m3) e bed void fraction DP pressure difference (Pa) Superscripts g in bulk gas phase m in the sweep gas side particle p at surface catalyst s
constant
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of isobutane conversion and isobutene selectivity has been considered as the objective function that should be maximized using genetic algorithm. The performance of the optimized membrane reactors is compared with conventional reactors at the same catalyst loading. The clear advantages of this membrane reactor are: hydrogen production, improving isobutene productivity and selectivity and lower purification cost in the next stage. 2. Kinetics model The traditional method of isobutene synthesis is isobutane dehydrogenation over Pt–Sn/Al2O3 catalyst, which is an endothermic and equilibrium reaction. i-C4 H10 $ i-C4 H8 þ H2
DH298 ¼ 120 kJ kmol1
(1)
Use of high contact times or high temperatures causes isobutane cracking to methane and propane as the main side reaction: i-C4 H10 þ H2 $ i-C3 H8 þ CH4
DH298 ¼ 80 kJ kmol1
(2)
In this work, the rate expressions have been selected from the literature [13,14]. The rate equations for isobutane dehydrogenation and isobutane dissociation combined with the equilibrium constant provides enough information about kinetics of isobutene synthesis. 3. Process modeling 3.1. Reaction side The conventional dehydrogenation process consists of three series reactors. The inter heaters are take placed between reactors to increase the temperature of inlet streams. In this work, the conventional reactors have been substituted by Pd/Ag based hydrogen permselective membrane reactors at the same catalyst loading. Fig. 1 shows the schematic diagram of the considered process. A one-dimensional steady state heterogeneous model, based on mass and energy conservation laws, has been developed to simulate the hydrogen permselective membrane reactors. In this model the following assumptions are considered: The gas mixture is ideal. Radial diffusion of mass and energy is negligible. Axial diffusion of mass and heat are negligible duo to high gas velocity. The system is well isolated.
Fig. 1. The schematic diagram of the considered process.
M. Farsi et al. / Journal of Industrial and Engineering Chemistry 18 (2012) 1676–1682
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The chemical reactions take place on the catalyst surface. The membranes are completely selective. Subject to these assumptions, mass and energy balances for the gas phase in the reaction zone are expressed by: g 1 dðFyi Þ a pffiffiffiffi qffiffiffiffiffiffiffiffi þ av ct kgi ðysi ygi Þ i ð P i Pi;m Þ ¼ 0 Ac dz Ac
C gp dT g pD 1 g þ av h f ðT s T g Þ þ F UðTm Tg Þ Ac Ac Ac dz
Z
T
T0
(3)
Q H C p dT ¼ 0
Table 2 The used correlations for physical properties, mass and heat transfer coefficient. Parameter
Equation
Gas conductivity Mixture heat capacity Viscosity of reaction mixtures Mass transfer coefficient Binary diffusion coefficient Effective diffusion coefficient in pellet Permeation–exothermic side heat transfer coefficient Gas–catalyst heat transfer coefficient
Lindsay and Bromley [18] [19] [19] Cussler [20] Hirschfelder et al. [21] [22] [23] [24]
(4) where QH have been considered in the model duo to simultaneous heat and mass transfer through the membrane layer. Mass and energy balances for the solid phase are expressed by: X hri rb ¼ 0 (5) av ct kgi ðygi ysi Þ þ av h f ðT g T s Þ þ rb
N X
hri ðDH f ;i Þ ¼ 0
L
150 ð1 eÞ2 4:2 ð1 eÞ1:166 þ 1=6 3 Re e e3 Re
¼ f
dðF m ygi;m Þ dz
F m C p
The external mass transfer resistance in the gas phase has been inserted in the mathematical model using convective mass transfer between gas and catalyst phases. The both diffusion and convective mass transfer resistances in the catalyst phase have been considered in the model using effectiveness factor (h). The effectiveness factor is defined as actual reaction rate per particle to theoretical reaction rate in the absence of internal mass transfer. This parameter is calculated from dusty gas model along the reactor [15]. The pressure drop through the catalytic pack bed is calculated based on the Tallmadge equation that is usable for laminar and turbulent flow regimes [16].
DP
(6)
i1
f ¼
energy balance equations are written for hydrogen permselective side as follows:
(7)
u2 r Dp
(8)
pffiffiffiffi qffiffiffiffiffiffiffiffi þ ai ð P i Pi;m Þ ¼ 0
dT g g ðpDÞUðTm Tg Þ þ dz
Z
(9)
Tm T0
Q H C p dT ¼ 0
(10)
where the hydrogen permeation constant is calculated from [17]:
aH 2 ¼
2LpP¯ 0 exp ðE p =RTÞ lnðDo =Di Þ
(11)
3.3. Auxiliary equations To complete the considered mathematical model of the process, auxiliary correlations should be inserted to the model. In the heterogeneous model, heat and mass transfer coefficients between gas and solid phases, physical properties of chemical species and overall heat transfer coefficient should be estimated from proper correlations. The source of used correlations to calculate physical properties, mass and heat transfer coefficient are summarized in Table 2.
Feed specifications, reactor and catalyst characteristics of the commercial dehydrogenation reactors are shown in Table 1.
4. Optimization problem
3.2. Membrane side
Gradient based optimization methods suffer from trapping at local optimum related to the function complexity and considered initial guesses and do not guarantee global optimum of functions. Genetic algorithm (GA) is an adaptive heuristic search algorithm premised on the evolutionary ideas of natural selection and genetic [25]. It is a programming technique that mimics biological evolution as a problem-solving strategy such as inherence, mutation, selection and crossover. GA proceeds first by randomly generating an initial population of individuals, which contains a set of randomized strings of genes and should cover the domain to explore. Each string of genes, illustratively called a genome or chromosome, represents a series of traits. The size of this population remains constant along the procedure. At every generation, the genomes (individuals) in the population are tested according to some quality criterion that called fitness function. To form a new population in the next generation, individuals are selected according to their fitness. Selection alone cannot introduce new individuals into the population, which is necessary in order to make the solution as independent of the initial population as possible. New individuals in the search space are generated by crossover and mutation. Crossover concerns two selected individuals (parents) that exchange parts of their
Hydrogen mole flow rate increases in the sweep gas through the hydrogen permselective membrane due to hydrogen permeation from reaction zone to the sweep gas stream. Also, heat transfer between endothermic side and sweep gas stream results decreasing temperature of the sweep gas along the reactor. Mass and
Table 1 Feed and product specifications of the commercial dehydrogenation reactors.
Feed Temperature (8C) Flow rate (tonnes h1) Pressure (barg) Reactor and catalyst Catalyst loading (tonnes) Catalyst density (kg m3) Catalyst diameter (m) Reactor void fraction Catalyst specific surface area (m2 g1) Membrane inner diameter (cm)
Reactor 1
Reactor 2
Reactor 3
634 106 1.4
639 106 0.9
637 106 0.4
11.2
12 800 6 104 0.52 175 4.5
13.8
4.1. Genetic algorithm
M. Farsi et al. / Journal of Industrial and Engineering Chemistry 18 (2012) 1676–1682
genomes to form two new individuals (children). Mutation consists in flipping bits of individual’s strings at random. In practice, over successive generations, the population moves toward an optimal solution in the feasible domain. The main steps of the GA is given below: Initialization and randomly initialize population Repeat Evaluate the objective and fitness function Apply genetic operators o Selection o Crossover o Mutation Until stopping criteria
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Table 3 Comparison of simulation results and plant data for industrial reactor.
Total conversion Selectivity
Plant data
Model
40.5 90.4
40.7 90.9
5. Numerical solution
In this paper, GA is employed to obtain the global optimal condition of considered membrane reactors to enhance the overall isobutene selectivity and production capacity.
The mass and energy governing equations combined with the kinetic expressions and auxiliary correlations are comprised nonlinear algebraic, ordinary differential equations. The formulated model consists of some ordinary differential equations as an initial value problem, which isn’t solved analytically. This set of differential equations is solved numerically with 4th order RungeKutta method. At the end of this procedure it is possible to plot the concentration of components and temperature versus reactor length.
4.2. Objective function and constraints In this study, the sum of isobutane conversion and isobutene selectivity is considered as the objective function that should be maximized. Due to severe effect of temperature on reaction synthesis kinetics, optimal temperature policy is a key to optimal operation of reactors. Nine decision variables namely, feed temperature of reactors (T01, T02 and T03), inlet sweep gas temperature (T04, T05 and T06) and inlet composition of hydrogen permeation sides (y01, y02 and y03) are considered in the optimization problem. Because of thermodynamic equilibrium limitations, dehydrogenation of light alkanes such as propane and butane is conducted at temperatures around 600 8C to achieve reasonable commercial yields, hence an upper bound of 700 8C is chosen for inlet temperature of endothermic side [26,27]. The bounds of decision variables are: 30 C < T 0103 < 700 C
(12)
0 < yH2 0103 < 1
(13)
The environment temperature (30 8C) is selected as the lower bound for inlet temperature of the permeation sides and reactors feed. Also, three constraints are considered for optimization due to catalyst deactivation: 30 C < T 13 < 700 C
(14)
0:5 < yH2 < 1
(15)
Since hydrogen helps to reduce the coke formation on the catalyst surface, the hydrogen mole fraction in the reaction zone has been controlled using considered constraint. These constraints are incorporated into the objective function using penalty function. Penalty method is a class of optimization algorithms for solving constrained problems. The penalty method replaces a constrained problem by an unconstrained problem whose solution ideally converges to solution of the original constrained problem. The considered objective function for minimization, finally, is thus: P ¼ ðSC4 H8 þ X C4 H10 Þ þ s
3 X ðmaxð0; 30 T i ÞÞ2
6. Results and discussion The mathematical model of the process that is a set of nonlinear ordinary differential equations is solved numerically at steady state condition. To demonstrate the accuracy of the considered model and assumptions, the model of isobutene synthesis side is validated against conventional process at design specifications [28]. The comparison between simulation results and plant data for the industrial case is shown in Table 3. It is observed that the simulation results of the conventional process have a good agreement with the observed plant data. In this section, the optimal operating conditions of membrane reactors are analyzed and the predicted mole fraction, selectivity, conversion and temperature profiles are presented. Genetic algorithm is applied to determine the optimal reactor operating conditions of the process. The goal of optimization approach is to maximize the sum of isobutane conversion and isobutene selectivity. The calculated optimal value for decision variables has been summarized in Table 4. Fig. 2 shows the comparison of isobutene mole fraction along the optimized membrane and conventional reactors at steady state condition. According to this figure, isobutane mole fraction in the first, second and third optimized configuration is calculated about 0.099, 0.169 and 0.215. In the optimized process the isobutane mole fraction has been increased about 16.4% compared to the conventional process. This configuration leads to delay in thermodynamic equilibrium, while conventional reactors approach to the equilibrium in the second half of reactors. According to Le Chaˆtelier’s principle, when an independent variable of a system at equilibrium is changed, the equilibrium shifts in the direction that tends to reduce the effect of the change. Hydrogen transfer from tube side to the sweep gas decreases hydrogen concentration in the reaction zone, which shifts reaction to right side and higher isobutane is converted to isobutene. Also, the isobutane conversion and isobutene selectivity in the optimized and conventional reactors have been tabulated in Table 5. This table shows that the isobutane conversion in the optimized
Table 4 The optimal value for decision variables.
i¼1
þ ðmaxð0; T i 700ÞÞ2 þ
3 X ðmaxð0; 0:5 yi ÞÞ2 i¼1
þ ðmaxð0; yi 1Þ2
(16)
Feed temperature (8C) Sweep gas temperature (8C) Sweep gas composition
Reactor 1st
Reactor 2nd
Reactor 3rd
649.25 601.95 0.378
654.85 515.7 0.408
659.9 640.05 0.437
M. Farsi et al. / Journal of Industrial and Engineering Chemistry 18 (2012) 1676–1682
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Table 5 The isobutane conversion and selectivity in the membrane and conventional processes. Conventional process
Membrane process
Improvement (%)
40.7 90.9
44.8 93.4
10.1 3.3
0.21 0.18
C4H8 Mole Fraction
0.98
Selectivity
Conversion Selectivity
1
Conventional reactors Membrane reactors
0.96
0.94
0.15
0.92 0.12
0.9
0.09
0
.5
1
1.5
2
2.5
3
Dimensionless Catalyst Loading 0.06
data3 Membrane reactors
0.03
Conventional reactors
0
0
0.5
1
1.5
2
2.5
Fig. 4. Selectivity profile along the membrane and conventional reactors.
3
Dimensionless Catalyst Loading Fig. 2. Isobutene mole fraction along the membrane and conventional reactors.
process has been increased about 10.1% compared to the conventional process. Fig. 3 shows the comparison of methane mole fraction along the optimized and conventional reactors at steady state condition. According to this figure, methane mole fraction as a undesired byproduct is decreased about 17.5% in the optimized membrane reactors compared to the conventional process. These results show that, hydrogen removal from reaction zone decreases isobutane dissociation and improves isobutene selectivity. According to Le Chaˆtelier’s principle, hydrogen removal from reaction zone shifts
the equilibrium limitations and results decreasing isobutane conversion to methane and propane. Fig. 4 shows the selectivity profile along the optimized membrane and conventional reactors. Selectivity as main parameters to investigate side reactions products is defined as the ratio of produced isobutene per consumed isobutane. The results show that the isobutene selectivity in the membrane process is approached to 93. 4 and it has been enhanced about 3.3% compared to the conventional process at the same catalyst loading. Fig. 5 shows the axial temperature profiles in the optimized and conventional reactors, respectively. In the processes, the temperature decrease along the reactor due to endothermic behavior of the dehydrogenation reaction. In the optimized membrane configuration, the reaction side is surrounded with hydrogen permselective tube. In the membrane configuration, higher isobutane conversion causes to the higher decreasing in the reactor temperature. Despite higher temperature in the membrane reactor, the selectivity in this
660 0.02 630
Temperature (C)
CH4 Mole Fraction
0.015
0.01
600
570
540
0.005
0
0
0.5
1
1.5
2
2.5
Conventional reactors Reactionside Sweepgas
510
Conventional reactors Membrane reactors 3
Dimensionless Catalyst Loading Fig. 3. Methane mole fraction along the membrane and conventional reactors.
480
0
0.5
1
1.5
2
2.5
3
Dimensionless Catalyst Loading Fig. 5. The axial temperature profiles in the membrane and conventional reactors.
M. Farsi et al. / Journal of Industrial and Engineering Chemistry 18 (2012) 1676–1682
0.68
H2 Mole Fraction
0.65
0.62
0.59
data3 data4 Conventional reactors Membrane reactors
0.56
0.53
0.5 0
0.5
1
1.5
2
2.5
3
Dimensionless Catalyst Loading Fig. 6. Hydrogen mole fraction profile in the membrane and conventional reactors.
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certain position along the reactor, the rate of isobutane dehydrogenation reaction decreases and hydrogen production rate is lower compared to the hydrogen permeation rate from reaction zone and consequently hydrogen mole fraction decreases along the reactor. While, there is a difference between hydrogen partial pressure in the reaction side and permeation side, hydrogen can continuously pass through the membrane layer into the sweep gas side. Hydrogen mole fraction profile in the sweep gas stream versus reactors length is shown in Fig. 7. Hydrogen permeation increases hydrogen content in the sweep gas stream. In this study, the hydrogen content in the inlet sweep gas stream to the each reactor has been chosen so that the hydrogen mole fraction in the reaction zone does not approach to the lower value compared to the fresh feed stream. At the last part of each reactor, the slope of hydrogen mole fraction profile decreases as a result of approaching the isobutane dehydrogenation to an equilibrium value and decreasing hydrogen partial pressure difference between the reaction side and permeation side. Also, this figure shows that, the rate of permeated hydrogen in the first reactor is more significant compared to the other reactors and in the third reactor is small due to higher isobutane conversion in the first reactor. 7. Conclusion
configuration is higher compared to conventional process. Also, sweep gas temperature approaches to the reactor temperature due to heat transfer with reaction side through the membrane layer. Hydrogen mole fraction profile in the reaction zone of the optimized and conventional reactors is shown in Fig. 6. Hydrogen permeation has a positive effect on the isobutane dehydrogenation and a negative effect on the isobutane dissociation. Hydrogen permeation from reaction zone to the sweep gas, through the membrane layer, results decreasing hydrogen mole fraction in the reaction zone and shifts dehydrogenation reaction to the right side and increases isobutane production. Also, it shifts dissociation reaction to the left side and decreases isobutane conversion to the methane and propane and increases isobutene selectivity. In the tube side of optimized membrane reactors, hydrogen mole fraction increases and then it decreases. Near the reactor entrance, the isobutane dehydrogenation reaction rate is fast and increases rapidly which is due to high temperature and reactant composition in the feed stream. Then, decreasing the temperature leads to decreasing the rate of isobutane dehydrogenation. Thus, after a
In this study, the dehydrogenation of isobutane to isobutene in Pd/Ag based hydrogen permselective membrane reactors was modeled and optimized at steady state condition. Genetic algorithm strategy was employed to determine the optimal operating conditions of the membrane reactors considering sum of isobutane conversion and isobutene selectivity as the objective function. The results of mathematical simulation for an industrial case were compared with the plant data and the accuracy of the proposed model is proved. Then, it was shown that isobutane conversion is enhanced about 10.1% in the optimized membrane process compared to the conventional process. Also, isobutene selectivity in the optimized membrane process was increased about 3.3%. This optimized configuration represents some important improvement in comparison to conventional reactors as follows: higher isobutene production rate and its selectivity, lower purification cost and hydrogen production. In general, the performance of optimized isobutane dehydrogenation membrane reactors was improved compared to the conventional process and this configuration can be feasible and beneficial.
0.49 References
H2 Mole Fraction
0.47
0.45
0.43
0.41
0.39
0.37
0
0.5
1
1.5
2
2.5
3
Dimensionless Catalyst Loading Fig. 7. Hydrogen mole fraction profile in the sweep gas stream versus reactors length.
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Contents lists available at SciVerse ScienceDirect
Journal of Industrial and Engineering Chemistry journal homepage: www.elsevier.com/locate/jiec
Optimal operating condition of membrane reactors to enhance isobutene production, selectivity and hydrogen production M. Farsi, A. Jahanmiri *, M.R. Rahimpour Department of Chemical Engineering, School of Chemical and Petroleum Engineering, Shiraz University, Shiraz, Iran
A R T I C L E I N F O
Article history: Received 19 January 2012 Accepted 7 March 2012 Available online 16 March 2012 Keywords: Isobutane dehydrogenation Pd/Ag membrane reactor Heterogeneous model Genetic algorithm
A B S T R A C T
In the isobutene synthesis process, coupling reaction and separation improves isobutene production and selectivity, reduces operation cost and lets to produce hydrogen. This study focuses on the steady state optimization of the isobutane dehydrogenation in hydrogen-permselective Pd/Ag based membrane reactors. The membrane reactors have been modeled heterogeneously based on the mass and energy conservation laws at steady state condition. The Genetic algorithm has been considered to optimize the operating condition of membrane reactors. Optimization results of membrane reactors are compared with conventional adiabatic reactors at the same catalyst loading. This optimal configuration has enhanced isobutene mole fraction about 16.4%. ß 2012 The Korean Society of Industrial and Engineering Chemistry. Published by Elsevier B.V. All rights reserved.
1. Introduction Isobutene as one of the main unsaturated hydrocarbons is used as a feedstock to produce a variety of chemical components such as polybutene, methyl tert-butyle ether and ethyl tertiary butyl ether. The most common industrial method to produce isobutene is catalytic dehydrogenation of isobutane. Some of commercial technologies have been developed for dehydrogenation of light alkanes such as isobutane. The Catofin isobutane dehydrogenation technology is a continuous cyclic process to produce isobutene over chromia–alumina catalyst in the fixed-bed reactor [1,2]. The reactors operate adiabatically and to regenerate the catalyst, multiple reactors operate at a controlled sequence of reaction and regeneration. In the UOP process, dehydrogenation reaction occurs in the several adiabatic moving-bed reactors over modified Ptalumina catalyst considering continuous catalyst regeneration [3]. Although a large number of researches have been presented on the n-butane and n-butene dehydrogenation, few articles in the literature discuss about isobutane dehydrogenation and process modeling [4]. Korhonen et al. investigated the performances of zirconia, alumina, and zirconia/alumina supported chromia catalysts in the dehydrogenation of isobutane in order to elucidate the role of the support material in the dehydrogenation reaction [5]. They showed that activity of chromia catalysts, acidity of the support and the phase of zirconia are important in the dehydrogenation rate. Cortright et al. presented a rate equation
* Corresponding author. Tel.: +98 711 6133788; fax: +98 711 6287294. E-mail address: [email protected] (A. Jahanmiri).
for isobutane dehydrogenation over Pt–Sn catalyst over a wide range of temperatures [6]. Bakhshi et al. modeled a bench scale fixed bed reactor for selective dehydrogenation of isobutane at steady state condition, homogeneously [7]. Sahebdelfar et al. modeled the dehydrogenation of isobutane to isobutene in adiabatic radial-flow moving bed reactors without considering catalyst regeneration section [8]. They neglected from side reactions while the isobutene selectivity in the considered commercial process was about 90%. The integration of membrane separation and reaction in a vessel has attracted much attention in the recent years [9]. Simultaneous occurrence of reaction and separation in a membrane reactor leads to shift thermodynamic equilibrium limitations and reduces separation cost compared to conventional processes. Casanave et al. studied isobutane dehydrogenation over Pt–In catalyst in a packed-bed zeolite membrane reactor [10]. Higher dehydrogenation yield was observed due to the hydrogen removal from the reaction zone. Ciavarella et al. investigated isobutane dehydrogenation in a MFI membrane reactor [11]. The performance of membrane reactor was studied as a function of the feed and sweep gas flow rates. Liang and Hughes studied isobutene synthesis from isobutane in a membrane reactor over Pt/Al2O3 catalyst, experimentally [12]. Also, they modeled the considered Pd/Ag membrane reactor under similar operating conditions. In this work, the radial flow reactors in the UOP process have been substituted by membrane fixed bed reactor at the same catalyst loading. The object of this study is modeling and optimization of Pd/Ag hydrogen permselective membrane reactors to enhance isobutene selectivity, isobutane conversion and hydrogen production from isobutane dehydrogenation. The sum
1226-086X/$ – see front matter ß 2012 The Korean Society of Industrial and Engineering Chemistry. Published by Elsevier B.V. All rights reserved. doi:10.1016/j.jiec.2012.03.015
M. Farsi et al. / Journal of Industrial and Engineering Chemistry 18 (2012) 1676–1682
Nomenclature av Ac Cp Ci D Ep F hf k Keq L P Pi P0 Q QH r Re T u U yi z
specific surface area of catalyst pellet (m2 m3) cross section area of each tube (m2) specific heat of the gas at constant pressure (J mol1) molar concentration of component i (mol m3) tube diameter (m) activation energy of permeability (kJ mol1) total molar flow rate (mol s1) gas–solid heat transfer coefficient (W m2 K1) reaction rate constant (mol kg1 s1 bar1/2) equilibrium constant I (m3 mol1) reactor length (m) total pressure (bar) partial pressure of component i (bar) pre-exponential factor of hydrogen permeability (mol m2 s1 Pa1/2) volumetric flow rate (m3 s1) hydrogen permeation rate (mol m1 s1) rate of reaction for dehydrogenation (mol kg1 s1) Reynolds number temperature (K) superficial velocity of fluid phase (m s1) overall heat transfer coefficient (W m2 K1) mole fraction of component i (mol mol1) axial reactor coordinate (m)
Greek letters aH hydrogen permeation rate (mol m1 s1Pa1/2) h catalyst effectiveness factor r density of fluid phase (kg m3) e bed void fraction DP pressure difference (Pa) Superscripts g in bulk gas phase m in the sweep gas side particle p at surface catalyst s
constant
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of isobutane conversion and isobutene selectivity has been considered as the objective function that should be maximized using genetic algorithm. The performance of the optimized membrane reactors is compared with conventional reactors at the same catalyst loading. The clear advantages of this membrane reactor are: hydrogen production, improving isobutene productivity and selectivity and lower purification cost in the next stage. 2. Kinetics model The traditional method of isobutene synthesis is isobutane dehydrogenation over Pt–Sn/Al2O3 catalyst, which is an endothermic and equilibrium reaction. i-C4 H10 $ i-C4 H8 þ H2
DH298 ¼ 120 kJ kmol1
(1)
Use of high contact times or high temperatures causes isobutane cracking to methane and propane as the main side reaction: i-C4 H10 þ H2 $ i-C3 H8 þ CH4
DH298 ¼ 80 kJ kmol1
(2)
In this work, the rate expressions have been selected from the literature [13,14]. The rate equations for isobutane dehydrogenation and isobutane dissociation combined with the equilibrium constant provides enough information about kinetics of isobutene synthesis. 3. Process modeling 3.1. Reaction side The conventional dehydrogenation process consists of three series reactors. The inter heaters are take placed between reactors to increase the temperature of inlet streams. In this work, the conventional reactors have been substituted by Pd/Ag based hydrogen permselective membrane reactors at the same catalyst loading. Fig. 1 shows the schematic diagram of the considered process. A one-dimensional steady state heterogeneous model, based on mass and energy conservation laws, has been developed to simulate the hydrogen permselective membrane reactors. In this model the following assumptions are considered: The gas mixture is ideal. Radial diffusion of mass and energy is negligible. Axial diffusion of mass and heat are negligible duo to high gas velocity. The system is well isolated.
Fig. 1. The schematic diagram of the considered process.
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The chemical reactions take place on the catalyst surface. The membranes are completely selective. Subject to these assumptions, mass and energy balances for the gas phase in the reaction zone are expressed by: g 1 dðFyi Þ a pffiffiffiffi qffiffiffiffiffiffiffiffi þ av ct kgi ðysi ygi Þ i ð P i Pi;m Þ ¼ 0 Ac dz Ac
C gp dT g pD 1 g þ av h f ðT s T g Þ þ F UðTm Tg Þ Ac Ac Ac dz
Z
T
T0
(3)
Q H C p dT ¼ 0
Table 2 The used correlations for physical properties, mass and heat transfer coefficient. Parameter
Equation
Gas conductivity Mixture heat capacity Viscosity of reaction mixtures Mass transfer coefficient Binary diffusion coefficient Effective diffusion coefficient in pellet Permeation–exothermic side heat transfer coefficient Gas–catalyst heat transfer coefficient
Lindsay and Bromley [18] [19] [19] Cussler [20] Hirschfelder et al. [21] [22] [23] [24]
(4) where QH have been considered in the model duo to simultaneous heat and mass transfer through the membrane layer. Mass and energy balances for the solid phase are expressed by: X hri rb ¼ 0 (5) av ct kgi ðygi ysi Þ þ av h f ðT g T s Þ þ rb
N X
hri ðDH f ;i Þ ¼ 0
L
150 ð1 eÞ2 4:2 ð1 eÞ1:166 þ 1=6 3 Re e e3 Re
¼ f
dðF m ygi;m Þ dz
F m C p
The external mass transfer resistance in the gas phase has been inserted in the mathematical model using convective mass transfer between gas and catalyst phases. The both diffusion and convective mass transfer resistances in the catalyst phase have been considered in the model using effectiveness factor (h). The effectiveness factor is defined as actual reaction rate per particle to theoretical reaction rate in the absence of internal mass transfer. This parameter is calculated from dusty gas model along the reactor [15]. The pressure drop through the catalytic pack bed is calculated based on the Tallmadge equation that is usable for laminar and turbulent flow regimes [16].
DP
(6)
i1
f ¼
energy balance equations are written for hydrogen permselective side as follows:
(7)
u2 r Dp
(8)
pffiffiffiffi qffiffiffiffiffiffiffiffi þ ai ð P i Pi;m Þ ¼ 0
dT g g ðpDÞUðTm Tg Þ þ dz
Z
(9)
Tm T0
Q H C p dT ¼ 0
(10)
where the hydrogen permeation constant is calculated from [17]:
aH 2 ¼
2LpP¯ 0 exp ðE p =RTÞ lnðDo =Di Þ
(11)
3.3. Auxiliary equations To complete the considered mathematical model of the process, auxiliary correlations should be inserted to the model. In the heterogeneous model, heat and mass transfer coefficients between gas and solid phases, physical properties of chemical species and overall heat transfer coefficient should be estimated from proper correlations. The source of used correlations to calculate physical properties, mass and heat transfer coefficient are summarized in Table 2.
Feed specifications, reactor and catalyst characteristics of the commercial dehydrogenation reactors are shown in Table 1.
4. Optimization problem
3.2. Membrane side
Gradient based optimization methods suffer from trapping at local optimum related to the function complexity and considered initial guesses and do not guarantee global optimum of functions. Genetic algorithm (GA) is an adaptive heuristic search algorithm premised on the evolutionary ideas of natural selection and genetic [25]. It is a programming technique that mimics biological evolution as a problem-solving strategy such as inherence, mutation, selection and crossover. GA proceeds first by randomly generating an initial population of individuals, which contains a set of randomized strings of genes and should cover the domain to explore. Each string of genes, illustratively called a genome or chromosome, represents a series of traits. The size of this population remains constant along the procedure. At every generation, the genomes (individuals) in the population are tested according to some quality criterion that called fitness function. To form a new population in the next generation, individuals are selected according to their fitness. Selection alone cannot introduce new individuals into the population, which is necessary in order to make the solution as independent of the initial population as possible. New individuals in the search space are generated by crossover and mutation. Crossover concerns two selected individuals (parents) that exchange parts of their
Hydrogen mole flow rate increases in the sweep gas through the hydrogen permselective membrane due to hydrogen permeation from reaction zone to the sweep gas stream. Also, heat transfer between endothermic side and sweep gas stream results decreasing temperature of the sweep gas along the reactor. Mass and
Table 1 Feed and product specifications of the commercial dehydrogenation reactors.
Feed Temperature (8C) Flow rate (tonnes h1) Pressure (barg) Reactor and catalyst Catalyst loading (tonnes) Catalyst density (kg m3) Catalyst diameter (m) Reactor void fraction Catalyst specific surface area (m2 g1) Membrane inner diameter (cm)
Reactor 1
Reactor 2
Reactor 3
634 106 1.4
639 106 0.9
637 106 0.4
11.2
12 800 6 104 0.52 175 4.5
13.8
4.1. Genetic algorithm
M. Farsi et al. / Journal of Industrial and Engineering Chemistry 18 (2012) 1676–1682
genomes to form two new individuals (children). Mutation consists in flipping bits of individual’s strings at random. In practice, over successive generations, the population moves toward an optimal solution in the feasible domain. The main steps of the GA is given below: Initialization and randomly initialize population Repeat Evaluate the objective and fitness function Apply genetic operators o Selection o Crossover o Mutation Until stopping criteria
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Table 3 Comparison of simulation results and plant data for industrial reactor.
Total conversion Selectivity
Plant data
Model
40.5 90.4
40.7 90.9
5. Numerical solution
In this paper, GA is employed to obtain the global optimal condition of considered membrane reactors to enhance the overall isobutene selectivity and production capacity.
The mass and energy governing equations combined with the kinetic expressions and auxiliary correlations are comprised nonlinear algebraic, ordinary differential equations. The formulated model consists of some ordinary differential equations as an initial value problem, which isn’t solved analytically. This set of differential equations is solved numerically with 4th order RungeKutta method. At the end of this procedure it is possible to plot the concentration of components and temperature versus reactor length.
4.2. Objective function and constraints In this study, the sum of isobutane conversion and isobutene selectivity is considered as the objective function that should be maximized. Due to severe effect of temperature on reaction synthesis kinetics, optimal temperature policy is a key to optimal operation of reactors. Nine decision variables namely, feed temperature of reactors (T01, T02 and T03), inlet sweep gas temperature (T04, T05 and T06) and inlet composition of hydrogen permeation sides (y01, y02 and y03) are considered in the optimization problem. Because of thermodynamic equilibrium limitations, dehydrogenation of light alkanes such as propane and butane is conducted at temperatures around 600 8C to achieve reasonable commercial yields, hence an upper bound of 700 8C is chosen for inlet temperature of endothermic side [26,27]. The bounds of decision variables are: 30 C < T 0103 < 700 C
(12)
0 < yH2 0103 < 1
(13)
The environment temperature (30 8C) is selected as the lower bound for inlet temperature of the permeation sides and reactors feed. Also, three constraints are considered for optimization due to catalyst deactivation: 30 C < T 13 < 700 C
(14)
0:5 < yH2 < 1
(15)
Since hydrogen helps to reduce the coke formation on the catalyst surface, the hydrogen mole fraction in the reaction zone has been controlled using considered constraint. These constraints are incorporated into the objective function using penalty function. Penalty method is a class of optimization algorithms for solving constrained problems. The penalty method replaces a constrained problem by an unconstrained problem whose solution ideally converges to solution of the original constrained problem. The considered objective function for minimization, finally, is thus: P ¼ ðSC4 H8 þ X C4 H10 Þ þ s
3 X ðmaxð0; 30 T i ÞÞ2
6. Results and discussion The mathematical model of the process that is a set of nonlinear ordinary differential equations is solved numerically at steady state condition. To demonstrate the accuracy of the considered model and assumptions, the model of isobutene synthesis side is validated against conventional process at design specifications [28]. The comparison between simulation results and plant data for the industrial case is shown in Table 3. It is observed that the simulation results of the conventional process have a good agreement with the observed plant data. In this section, the optimal operating conditions of membrane reactors are analyzed and the predicted mole fraction, selectivity, conversion and temperature profiles are presented. Genetic algorithm is applied to determine the optimal reactor operating conditions of the process. The goal of optimization approach is to maximize the sum of isobutane conversion and isobutene selectivity. The calculated optimal value for decision variables has been summarized in Table 4. Fig. 2 shows the comparison of isobutene mole fraction along the optimized membrane and conventional reactors at steady state condition. According to this figure, isobutane mole fraction in the first, second and third optimized configuration is calculated about 0.099, 0.169 and 0.215. In the optimized process the isobutane mole fraction has been increased about 16.4% compared to the conventional process. This configuration leads to delay in thermodynamic equilibrium, while conventional reactors approach to the equilibrium in the second half of reactors. According to Le Chaˆtelier’s principle, when an independent variable of a system at equilibrium is changed, the equilibrium shifts in the direction that tends to reduce the effect of the change. Hydrogen transfer from tube side to the sweep gas decreases hydrogen concentration in the reaction zone, which shifts reaction to right side and higher isobutane is converted to isobutene. Also, the isobutane conversion and isobutene selectivity in the optimized and conventional reactors have been tabulated in Table 5. This table shows that the isobutane conversion in the optimized
Table 4 The optimal value for decision variables.
i¼1
þ ðmaxð0; T i 700ÞÞ2 þ
3 X ðmaxð0; 0:5 yi ÞÞ2 i¼1
þ ðmaxð0; yi 1Þ2
(16)
Feed temperature (8C) Sweep gas temperature (8C) Sweep gas composition
Reactor 1st
Reactor 2nd
Reactor 3rd
649.25 601.95 0.378
654.85 515.7 0.408
659.9 640.05 0.437
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Table 5 The isobutane conversion and selectivity in the membrane and conventional processes. Conventional process
Membrane process
Improvement (%)
40.7 90.9
44.8 93.4
10.1 3.3
0.21 0.18
C4H8 Mole Fraction
0.98
Selectivity
Conversion Selectivity
1
Conventional reactors Membrane reactors
0.96
0.94
0.15
0.92 0.12
0.9
0.09
0
.5
1
1.5
2
2.5
3
Dimensionless Catalyst Loading 0.06
data3 Membrane reactors
0.03
Conventional reactors
0
0
0.5
1
1.5
2
2.5
Fig. 4. Selectivity profile along the membrane and conventional reactors.
3
Dimensionless Catalyst Loading Fig. 2. Isobutene mole fraction along the membrane and conventional reactors.
process has been increased about 10.1% compared to the conventional process. Fig. 3 shows the comparison of methane mole fraction along the optimized and conventional reactors at steady state condition. According to this figure, methane mole fraction as a undesired byproduct is decreased about 17.5% in the optimized membrane reactors compared to the conventional process. These results show that, hydrogen removal from reaction zone decreases isobutane dissociation and improves isobutene selectivity. According to Le Chaˆtelier’s principle, hydrogen removal from reaction zone shifts
the equilibrium limitations and results decreasing isobutane conversion to methane and propane. Fig. 4 shows the selectivity profile along the optimized membrane and conventional reactors. Selectivity as main parameters to investigate side reactions products is defined as the ratio of produced isobutene per consumed isobutane. The results show that the isobutene selectivity in the membrane process is approached to 93. 4 and it has been enhanced about 3.3% compared to the conventional process at the same catalyst loading. Fig. 5 shows the axial temperature profiles in the optimized and conventional reactors, respectively. In the processes, the temperature decrease along the reactor due to endothermic behavior of the dehydrogenation reaction. In the optimized membrane configuration, the reaction side is surrounded with hydrogen permselective tube. In the membrane configuration, higher isobutane conversion causes to the higher decreasing in the reactor temperature. Despite higher temperature in the membrane reactor, the selectivity in this
660 0.02 630
Temperature (C)
CH4 Mole Fraction
0.015
0.01
600
570
540
0.005
0
0
0.5
1
1.5
2
2.5
Conventional reactors Reactionside Sweepgas
510
Conventional reactors Membrane reactors 3
Dimensionless Catalyst Loading Fig. 3. Methane mole fraction along the membrane and conventional reactors.
480
0
0.5
1
1.5
2
2.5
3
Dimensionless Catalyst Loading Fig. 5. The axial temperature profiles in the membrane and conventional reactors.
M. Farsi et al. / Journal of Industrial and Engineering Chemistry 18 (2012) 1676–1682
0.68
H2 Mole Fraction
0.65
0.62
0.59
data3 data4 Conventional reactors Membrane reactors
0.56
0.53
0.5 0
0.5
1
1.5
2
2.5
3
Dimensionless Catalyst Loading Fig. 6. Hydrogen mole fraction profile in the membrane and conventional reactors.
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certain position along the reactor, the rate of isobutane dehydrogenation reaction decreases and hydrogen production rate is lower compared to the hydrogen permeation rate from reaction zone and consequently hydrogen mole fraction decreases along the reactor. While, there is a difference between hydrogen partial pressure in the reaction side and permeation side, hydrogen can continuously pass through the membrane layer into the sweep gas side. Hydrogen mole fraction profile in the sweep gas stream versus reactors length is shown in Fig. 7. Hydrogen permeation increases hydrogen content in the sweep gas stream. In this study, the hydrogen content in the inlet sweep gas stream to the each reactor has been chosen so that the hydrogen mole fraction in the reaction zone does not approach to the lower value compared to the fresh feed stream. At the last part of each reactor, the slope of hydrogen mole fraction profile decreases as a result of approaching the isobutane dehydrogenation to an equilibrium value and decreasing hydrogen partial pressure difference between the reaction side and permeation side. Also, this figure shows that, the rate of permeated hydrogen in the first reactor is more significant compared to the other reactors and in the third reactor is small due to higher isobutane conversion in the first reactor. 7. Conclusion
configuration is higher compared to conventional process. Also, sweep gas temperature approaches to the reactor temperature due to heat transfer with reaction side through the membrane layer. Hydrogen mole fraction profile in the reaction zone of the optimized and conventional reactors is shown in Fig. 6. Hydrogen permeation has a positive effect on the isobutane dehydrogenation and a negative effect on the isobutane dissociation. Hydrogen permeation from reaction zone to the sweep gas, through the membrane layer, results decreasing hydrogen mole fraction in the reaction zone and shifts dehydrogenation reaction to the right side and increases isobutane production. Also, it shifts dissociation reaction to the left side and decreases isobutane conversion to the methane and propane and increases isobutene selectivity. In the tube side of optimized membrane reactors, hydrogen mole fraction increases and then it decreases. Near the reactor entrance, the isobutane dehydrogenation reaction rate is fast and increases rapidly which is due to high temperature and reactant composition in the feed stream. Then, decreasing the temperature leads to decreasing the rate of isobutane dehydrogenation. Thus, after a
In this study, the dehydrogenation of isobutane to isobutene in Pd/Ag based hydrogen permselective membrane reactors was modeled and optimized at steady state condition. Genetic algorithm strategy was employed to determine the optimal operating conditions of the membrane reactors considering sum of isobutane conversion and isobutene selectivity as the objective function. The results of mathematical simulation for an industrial case were compared with the plant data and the accuracy of the proposed model is proved. Then, it was shown that isobutane conversion is enhanced about 10.1% in the optimized membrane process compared to the conventional process. Also, isobutene selectivity in the optimized membrane process was increased about 3.3%. This optimized configuration represents some important improvement in comparison to conventional reactors as follows: higher isobutene production rate and its selectivity, lower purification cost and hydrogen production. In general, the performance of optimized isobutane dehydrogenation membrane reactors was improved compared to the conventional process and this configuration can be feasible and beneficial.
0.49 References
H2 Mole Fraction
0.47
0.45
0.43
0.41
0.39
0.37
0
0.5
1
1.5
2
2.5
3
Dimensionless Catalyst Loading Fig. 7. Hydrogen mole fraction profile in the sweep gas stream versus reactors length.
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