mathematical simulation and optimization of methanol dehydration and cyclohexane dehydrogenation in...

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Mathematical simulation and optimization of methanoldehydration and cyclohexane dehydrogenation in a thermallycoupled dual-membrane reactor

M. Farsi, A. Jahanmiri*

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 7 March 2011

Received in revised form

3 August 2011

Accepted 7 August 2011

Available online 15 September 2011

Keywords:

DME

Benzene

Thermally coupled reactor

Dual-membrane reactor

Differential evolution

* Corresponding author. Tel.: þ98 711 230307E-mail address: [email protected] (A

0360-3199/$ e see front matter Copyright ªdoi:10.1016/j.ijhydene.2011.08.019

a b s t r a c t

Thermally coupling of endothermic and exothermic reactions in a membrane reactor

improves thermal efficiency and production rate in the processes, reduces the size of

reactors and decreases purification cost. This paper focuses on modeling and optimization

of a thermally coupled dual-membrane reactor for simultaneous production of hydrogen,

dimethyl ether (DME) and benzene. A steady state heterogeneous mathematical model is

developed to predict the performance of this novel configuration. The catalytic methanol

dehydration reaction takes place in the exothermic side that supplies the necessary heat

for the catalytic dehydrogenation of cyclohexane to benzene in the endothermic side.

Selective permeation of hydrogen and water vapor through the Pd/Ag and composite

membranes are achieved by co-current flow of sweep gas through the membrane wall. The

differential evolution method is applied to optimize the thermally coupled dual-membrane

reactor considering the summation of DME and benzene mole fractions from reaction sides

and hydrogen mole fraction in the permeation side as the main objectives. The optimi-

zation results are compared with corresponding predictions for an industrial methanol

dehydration adiabatic reactor operated at the same feed conditions. Methanol conversion

enhances about 5.5% in the optimized thermally coupled dual-membrane reactor relative

to the conventional DME reactor. The results suggest that coupling of these reactions in the

proposed configuration could be feasible and beneficial.

Copyright ª 2011, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights

reserved.

1. Introduction hydrogen, and the high energy density storage of liquid fuel. It

Significant commercial and regulatory developments world-

wide are driving large increases in dimethyl ether (DME)

production capacity, and demonstrating its remarkable

potential as an ultra clean, renewable, low-carbon fuel. It can

be stored in liquid phase at moderate pressure, and delivered

as a gas phase fuel in a pumpless operation. Therefore, DME

has the advantages of easy fuel delivery of pressurized

1; fax: þ98 711 6287294.. Jahanmiri).2011, Hydrogen Energy P

is a clean fuel with high cetane number, excellent combustion

characteristics and extremely low toxicity that does not

produce any particulate matter at burning. It can be produced

from various raw materials such as petroleum residues, coal

bed methane, and biomass as well as natural gas and coal [1].

DME is useful for a variety of applications such as power

generation, diesel engines, fuel cell and domestic household

[2]. Due to these properties, it is an attractive topic in academic

ublications, LLC. Published by Elsevier Ltd. All rights reserved.

mailto:[email protected]

http://www.sciencedirect.com

http://www.elsevier.com/locate/he

http://dx.doi.org/10.1016/j.ijhydene.2011.08.019



Pure DME

Product

Methanol fromStorage To Distillation Unit

Fig. 1 e A schematic diagram of a traditional adiabatic DME

reactor.

i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n en e r g y 3 6 ( 2 0 1 1 ) 1 4 4 1 6e1 4 4 2 7 14417

and industrial research. DME is commercially produced by

methanol dehydration in an adiabatic packed bed reactor

using acidic porous catalysts [3]. There are several articles in

the literature that discuss modeling of DME production in the

catalytic packed bed reactors. The advantages of fluidized bed

over fixed-bed or slurry reactorwere proved for DME synthesis

from syngas by Lu et al. [4]. Farsi et al. modeled and simulated

an industrial fixed-bed reactor in dynamic conditions for

methanol dehydration to DME [5]. They investigated control-

lability of DME process through dynamic simulation under

a conventional feedback PID controller. Farsi et al. proposed

an optimized isothermal reactor for large scale production of

DME from methanol [6]. The simulation results showed that

the isothermal reactor is more efficient than traditional

adiabatic reactor for methanol dehydration reaction. Fazlol-

lahnejad et al. investigated the methanol dehydration in

a bench scale fixed-bed reactor, experimentally [7]. The

reactor was packed with 1.5 mm g-Al2O3 pellets as catalyst

and operated at atmospheric pressure. They investigated the

effects of weight hourly space velocity and temperature on

methanol conversion.

Since most of reactions are endothermic or exothermic,

the heat transfer management is usually a key policy in

reaction engineering design. Thermally coupling of

exothermic and endothermic reactions, in one reactor, may

offer a new opportunity to broaden the reactor selection

possibilities. Thesemultifunctional reactorsmake the process

more efficient and compact and result in large savings in the

operational and capital costs [8]. A mathematical model for

thermally coupled hydrogen-permselective membrane

reactor that is composed of three sides is developed for

methanol and benzene synthesis by Khademi et al. [9,10]. In

this configuration, methanol synthesis takes place in the

exothermic side and supplies the necessary heat for the

endothermic dehydrogenation of cyclohexane reaction.

Selective permeation of hydrogen through the Pd/Ag

membrane is achieved by co-current flow of sweep gas

through the permeation side. In the previous work, Farsi et al.

developed a mathematical model for thermally coupled

reactor that is composed of two sides for methanol dehydra-

tion and benzene synthesis [11]. Methanol synthesis takes

place in the exothermic side and supplies the necessary heat

for the endothermic dehydrogenation of cyclohexane reac-

tion. This novel configuration decreased temperature of

methanol dehydration reaction in the second half of the

reactor and shifted the thermodynamic equilibrium to

enhancemethanol conversion. Also, Khademi et al. optimized

DME synthesis reaction and cyclohexane dehydrogenation in

a thermally coupled reactor using differential evolution

method [12]. The results suggested that optimal coupling of

these reactions could be feasible and beneficial and improves

the thermal efficiency.

The application of membrane reactors has attracted much

attention in the recent years [13]. A membrane reactor is

a piece of chemical equipment that combines a reaction

sectionwith amembrane to add reactants or remove products

of the reaction. Simultaneous occurrence of reaction and

separation in a membrane reactor leads to lower cost of the

separation system for a process using membrane reactors

compared to conventional reactors. In addition, by removing

some product components from the reaction medium in

a membrane reactor, constraints of thermodynamic equilib-

rium can be overcome toward higher conversion. Product

removal increases residence time for a given volume of the

reactor and drives equilibrium-limited reactions toward

completion. Hydrophilic membranes such as zeolite and silica

were developed for water separation from organic mixtures.

Lee et al. utilized water-selective alumina-silica composite

membranes for design of a dehydrationmembrane reactor for

DME synthesis from methanol [14]. Also, Sea and Lee carried

out experimental studies on amembrane fixed-bed reactor for

methanol dehydration [15]. They proved the feasibility of

ceramic membranes for synthesis of DME from methanol

dehydration.

Recently, hydrogen energy has attracted much attention

due to its potential to reduce environmental burdens and the

viewpoint of energy security [16]. Hydrogen gas is highly

flammable and will burn in air at a very wide range of

concentrations. Hydrogen is produced from fossil fuels such

as natural gas, naphtha, and coal. The selection of reaction

system which generates high purity and cost efficient H2 is

a major challenge. One of the highly efficient systems for the

production of hydrogen is dehydrogenation of cyclic hydro-

carbons such as cyclohexane. The major advantage of this

system is that the involved reactions do not produce CO and

CO2 which causes global warming. In addition, cyclic hydro-

carbons have relatively high H2 contents compared to straight

chain hydrocarbons. Currently, large quantities of hydrogen

are used in the Haber process for production of ammonia,

hydrogenation of fats and oils, methanol production, hydro-

cracking and hydrodesulfurization. Itoh and Wu investigated

an adiabatic type of palladiummembrane reactor for coupling

endothermic and exothermic reactions and hydrogen

production [17].

The object of this study is modeling and optimization of

a thermally coupled dual-membrane reactor for DME,

benzene and hydrogen production. The performance of the

proposed dual-membrane reactor is compared with conven-

tional adiabatic DME reactor. The clear advantages of this

integrated catalytic reactor include: hydrogen production,

achieving a multiple reactants multiple products configura-

tion, improving DME productivity and DME catalyst life time.

Also, to verify the accuracy of the proposed model and

considered assumptions, results of steady state model for

conventional reactor are compared with design data of

Petrochemical Zagros Complex in Iran.



Table 1 e The characteristics of the catalyst pellet and thereactor design specifications for the conventional DMEsynthesis reactor.

Parameter Value

Gas phase

Feed composition (mole fraction)

CH3OH 0.936

DME 0.055

H2O 0.009

Inlet pressure (bar) 18.18

Inlet temperature (K) 533

Feed flow rate (mol s�1) 0.14

Catalyst particle

Density (kg m�3) 2010

Particle diameter (m) 0.3175 � 10�2

Specific surface area (m2 m�3) 673

Length of reactor (m) 8.08

Reactor diameter (m) 4


2. Process description

2.1. Conventional DME reactor

DME synthesis process consists of an adiabatic packed bed

reactor coupled with a shell and tube heat exchanger. The

tubes of reactor are packed with g-Al2O3 catalyst. Fig. 1 shows

Product

Methanol

Cyclohexane

Sweep gases

Sweep gas

CH3OH

C6H12

Ar

Sweep gas H2O Permeation side

H2 Permeation side

H2 Permeation side

Endothermic side

Endothermic side

Exothermic side

Exothermic side

a

b

Fig. 2 e (a) The schematic diagram of the proposed process, (b)

reactor.

a DME synthesis loop in Zagros Petrochemical Complex. The

inlet feed to the reactor is preheated with the outlet products

from the reactor in a shell and tube heat exchanger. The

characteristics of the catalyst pellet and the reactor design

specifications are summarized in Table 1.

2.2. Thermally coupled dual-membrane reactor

Fig. 2(a) and (b) show the schematic diagram of the proposed

process and an elemental volume of thermally coupled dual-

membrane reactor, respectively. The considered configura-

tion is composed of four sides for methanol dehydration,

benzene synthesis, hydrogen production and water vapor

removal. Catalytic dehydrogenation of cyclohexane to

benzene is assumed to take place in the endothermic side and

methanol dehydration to DME occurs inside the exothermic

side. Heat is transferred continuously from the exothermic

side to the endothermic side and supplies part of required

heat for endothermic reaction. Selective permeation of

hydrogen and water vapor through the Pd/Ag and composite

membranes from endothermic and exothermic sides are

achieved by co-current flow of sweep gas through the

permeation sides. The water-permselective membrane tube

and endothermic side are surrounded with the exothermic

and hydrogen permeation sides, respectively. Require heat in

the endothermic reaction can be supplied from exothermic

and hydrogen permeation sides.

Pure DME

Benzene

Hydrogen

Hydrogen

To Distillation Unit

To separator

To separator

Sweep gas, H2

CH3OHDMEH2O

C6H12

C6H6

H2

Ar

Sweep gas, H2O

H2

H2O

an elemental volume of thermally coupled dual-membrane




3. Reactions schemes and kinetics

3.1. DME synthesis reaction

The reaction of DME synthesis is mainly dehydration of

methanol that is an exothermic and equilibrium reaction.

Many researches are focused on DME synthesis reaction

[18e20]. The reaction rate equation for methanol dehydration

and rate parameters are used from Bercic and Levec [21].

Commercially, g-Al2O3 catalyst is used in the methanol

dehydration reaction.

2CH3OH4CH3OCH3 þH2O DH298 ¼ �23:4 kJ=mol (1)

3.2. Benzene synthesis reaction

The selected endothermic reaction is cyclohexane dehydroge-

nation to benzene. Cyclohexane dehydrogenation is an

attractive alternative for hydrogen production because it has

essentially without CO and CO2 emission. Jeong et al. studied

the catalytic dehydrogenation of cyclohexane experimentally

and observed that no by-product except benzene and hydrogen

is produced in this system [22]. The reaction scheme for the

dehydrogenation of cyclohexane to benzene is as follows:

C6H124C6H6 þ 3H2 DH298 ¼ þ206:2 kJ=mol (2)

The temperature of this reaction is in the range of 423e523 K

and the total pressure in the reactor is maintained at 101.3 kPa.

The reaction rate equation for cyclohexane dehydrogenation

and rate parameters are selected from Itoh [23]. The rate of

Table 2 e The rate of reactions, reactions rate constantsand the adsorption equilibrium constants for DMEsynthesis and cyclohexane dehydrogenation reactions.

Definition Equation

DME synthesis reaction

Rate of reaction r1 ¼k1K2

CH3OH

�C2CH3OH � ðCC2H6OCH2OÞ=Keq

�

ð1þ 2ðKCH3OHCCH3OHÞ:5 þ KH2OCH2OÞ4

Reaction equilibrium

constant

ln ðKeqÞ ¼ 0:86log Tþ 3138T

þ 1:33� 10�3T

�1:23� 10�5T2 þ 3:5� 10�10T3

Reaction rate constant k1 ¼ 3:7� 1010exp ð�105000=RTÞMethanol adsorption

equilibrium constant

KCH3OH ¼ 7:9� 10�4exp ð70500=RTÞ

Water vapor adsorption


KH2O ¼ 0:84� 10�1exp ð41100=RTÞ

Cyclohexane dehydrogenation reaction

Rate of reaction r2 ¼ �kðKPPC=P3H2� PBÞ

1þ ðKBKPPC=P3H2Þ

Reaction rate constant k ¼ 0:221 exp ð�4270=TÞBenzene adsorption


KB ¼ 2:03� 10�10exp ð6270=TÞ

Reaction equilibrium

constant

KP ¼ 4:89� 1035exp ð3190=TÞ

reactions, reactions rate constants and the adsorption equilib-

rium constants for both reactions are given in Table 2.

4. Mathematical model

4.1. Process modeling

A one-dimensional heterogeneous model based on mass and

energy conservation laws has been developed to determine

the concentration and temperature profiles along the reactor

at the steady state condition. In this model the following

assumptions are made:

� The gas mixture is an ideal gas.

� Both sections of the reactor are operated at steady state

conditions.

� Radial variations in both reaction sides are negligible (one-

dimensional model).

� With due attention to high gas velocity, axial diffusion of

mass and heat are negligible in all sections.

� Bed porosity in axial and radial directions is constant.

� Plug flow is employed in all sides.

� The chemical reactions are assumed to take place only in

the catalyst particles.

� Heat loss to surrounding is neglected.

The mass and energy balances for all sides, hydrogen and

water vapor permeation rate through Pd/Ag and composite

membrane and pressure drop equation are summarized in

Appendix A.

4.2. Auxiliary correlations

To complete the simulation, auxiliary correlations should be

added to the model. In the heterogeneous model, the proper

correlations for estimation of heat and mass transfer coeffi-

cients and physical properties of chemical species should be

considered. The selected correlations for estimation of

Table 3 e Methods used for calculating the physicalproperties, heat and mass transfer coefficients.

Parameter Equation

Gas conductivity Lindsay and Bromley [24]

Mixture heat capacity Ideal [25]

Viscosity of reaction

mixtures

Lucas [25]

Mass transfer

coefficient

Cusler [26]

Binary diffusion

coefficient

Hirschfelder et al. [27]

Effective diffusion

coefficient in pellet

[28]

Permeationeexothermic

side heat transfer

coefficient

[29]

Gasecatalyst heat transfer

coefficient

[30]




physical properties, mass and heat transfer coefficients are

summarized in Table 3.

5. Optimization problem

5.1. Differential evolution

Differential Evolution (DE) is a stochastic direct search and

global Optimization algorithm, and is an instance of an evolu-

tionary algorithm from the field of evolutionary computation.

DE algorithm minimizes an objective function that can model

the problem’s objectives while incorporating constraints. The

algorithmmainly has three advantages; finding the true global

minimum regardless of the initial parameter values, fast

convergence, and using a few control parameters. The conver-

gence speed is one of the main issues indicating the perfor-

mance of a DE algorithm. The strategies can vary based on the

vector to be perturbed, number of difference vectors considered

for perturbation, and finally the type of crossover used.

Choosing population size, scaling factor and crossover constant

depends on the specific problemapplied, and are often difficult.

But some general guidelines are available. More details of

differential evolution, its strategies, and choosing of operating

parameters are reported by Storn and Price [31].

5.2. Objective function and constraints

In this study, the summation of the outlet DME and benzene

mole fractions from reaction sides and outlet hydrogen mole

fraction from the permeation side is considered as the objec-

tive function. The objective function is as follows:

J ¼ yDME þ yC6H6þ yH2

(3)

The inlet temperature of water permeation side T01, inlet

temperature of exothermic side T02, inlet temperature of endo-

thermic sideT03, inlet temperature of hydrogenpermeation side

T04, initial molar flow rate of exothermic side F02, initial molar

flow rate of endothermic side F03 are considered as the decision

variables in the optimization stage. For tubular and exothermic

reactors, temperature has a severe and direct effect on thermo-

dynamic equilibrium and catalyst activity. In order to thermally

couple the exothermic and endothermic reactions, the heat

productionand consumption in theselected reactions shouldbe

approximately same. The heat transferred from the exothermic

side to endothermic side is dependent on the ratio of the

exothermic-to-endothermic side flow rates and it can compen-

sate difference between heat production and consumption, if

there is a considerabledifferencebetween them.Thus, feedflow

rates are selected as decision variables. Jeong et al. reported that

the cyclohexane dehydrogenation reaction occurs in 101.3 kPa

[32]. The selected ranges for decision variables are:

298 < T01 < 650 K (4)

495 < T02 < 650 K (5)

423 < T03 < 523 K (6)

298 < T04 < 650 K (7)

0:01 < F02 < 0:3 mol=s (8)

0:01 < F03 < 0:3 mol=s (9)

The lower bound of inlet temperature in the exothermic

side is set at 495 K, to ensure that the temperature of inlet feed

stream to the reactor is not too low for the DME synthesis

reaction to occur. At high temperatures catalyst starts deac-

tivation, hence 550 K is chosen as an upper bound of inlet

temperature in the exothermic side [33]. While the activity of

the Pt/Al2O3 catalyst in the temperature range of 423e523 K

was evaluated in a conventional packed bed, the bounds for

the inlet temperature of endothermic side, T03 is chosen [23].

The lower and upper bounds for the initial molar flow rate of

exothermic and endothermic sides have been selected with

no prior intention. The environment temperature (298 K) is

selected as the lower bound for inlet temperature of perme-

ation sides, and their upper bound are the same as upper

bound for inlet temperature of exothermic side. Two

constraints are also considered in the optimization problem:

495 < T2 < 650 K (10)

423 < T3 < 523 K (11)

The optimization problem considered above is reformu-

lated and penalty function method employed for handling

constraints. A penalty method replaces a constrained opti-

mization problem by a series of unconstrained problems

whose solutions ideally converge to the solution of the orig-

inal constrained problem. The unconstrained problems are

formed by adding a term to the objective function that

consists of a penalty parameter and a measure of violation of

the constraints. Themeasure of violation is nonzero when the

constraints are violated and is zero in the region where

constraints are not violated. The objective function reformu-

lated as:

Minimize f ¼ �Jþ sX5

i¼1

G2i (12)

where

G1 ¼ maxf0; ð495� T2Þg (13)

G2 ¼ maxf0; ðT2 � 650Þg (14)

G3 ¼ maxf0; ð423� T3Þg (15)

G4 ¼ maxf0; ðT3 � 523Þg (16)

6. Numerical solution

The formulated model composed of 20 ordinary differential

equations and the associated boundary conditions lends itself

to an initial value problem. The algebraic equations in the

model incorporate the initial conditions, the reaction rates,

the ideal gas assumption, hydrogen permeation rate, as well



Table 5 e Operating conditions for methanol dehydrationto DME (exothermic side), dehydrogenation ofcyclohexane to benzene (endothermic side) andpermeation sides.

Parameter Value


as proper correlations for the heat and mass transfer coeffi-

cients and the physical properties of fluids. The governing

equations of the model are solved numerically. The model

equations cannot be solved analytically. The set of ODE is

solved by using Runge-Kutta (4,5) formula, the Dormand-

Prince pair [34].
Exothermic side

CH3OH 0.936

DME 0.055

H2O 0.009

Inlet pressure (bar) 18.18

Catalyst particle



Length of reactor (m) 8.08

Density of catalyst bed (kg m�3) 1005

Tube inner diameter (m) 4.5 � 10�2

Tube outer diameter (m) 5.1 � 10�2

Endothermic side


C6H12 0.1

C6H6 0.0

H2 0.0

Ar 0.9

Inlet pressure (Pa) 1.013 � 105


Bed void fraction 0.39


Tube inner diameter (m) 6.6 � 10�2

Hydrogen permeation side

Total molar flow rate (mol s�1) 0.13

Inlet pressure (Pa) 1 � 105

Hydrogen permeation

tube inner diameter (m)

8.4 � 10�2

Pre-exponential factor for hydrogen

permeability (mol m�2 s�1 Pa�1/2)

6.33 � 10�8

Activation energy for

hydrogen permeability (kJ mol�1)

15.7

Water permeation side

Total molar flow rate (mol s�1) 0.13

Inlet pressure (Pa) 18 � 105

Water permeation tube

inner diameter (m)

2.54 � 10�2

Water permeation rate

constant (mol m�2 s�1 Pa�1)

1.14 � 10�7

7. Results and discussions

7.1. Model validation

The model of methanol dehydration side is validated against

conventional adiabatic DME reactor under the design data

listed in Table 1. It is observed that the simulation results have

a good agreement with observed plant data from Zagros

Petrochemical Complex in Iran. The comparison between

steady state simulation results and plant data for the

conventional adiabatic reactor is shown in Table 4. As it is

seen, the maximum absolute error is about 1.95% which is

acceptable and proves accuracy of the considered correlations

and considered mathematical model.

7.2. Considered base case

Optimization is carried out for a “base case” and the operating

conditions used for all sides of the reactor are given in Table 5.

Operating conditions for the methanol dehydration side are

similar to those used by Farsi et al. [6]. The inlet composition

of the methanol dehydration and cyclohexane dehydrogena-

tion reaction is typical of industrial dehydrationmethanol and

cyclohexane dehydrogenation processes. The considered base

allows investigating the process performance when the

cyclohexane dehydrogenation and methanol dehydration

occur simultaneously in a membrane reactor. Also, the

comparison of the methanol dehydration process in the

thermally coupled dual-membrane reactor with conventional

adiabatic reactor is attainable. The simulation results of the

proposed reactor in the endothermic side are not compared

with any reference case.

7.3. Simulation results

In this section, the simulation results of the proposed ther-

mally coupled dual-membrane reactor are analyzed and the

predicted mole fractions and temperature profiles are

Table 4 e Comparison between steady state simulationresults and plant data for the conventional adiabaticmethanol dehydration reactor.

Simulation Plantdata

Absoluteerror

Outlet DME molar

flow rate (kmol/hr)

2457 2506 1.95%

Outlet MeOH molar

flow rate (kmol/hr)

940.6 937.7 0.31%

Outlet Temperature (K) 652.2 644 1.27%

presented. The simulation of thermally coupled dual-

membrane reactor is carried out using the data presented in

Table 5. The performance of the dual-membrane thermally

coupled reactor is analyzed for methanol and cyclohexane

conversion and hydrogen recovery yield as follows:

Methanol conversion ¼ FCH3OH;in � FCH3OH;out

FCH3OH;in(17)

Cyclohexane conversion ¼ FC6H12 ;in � FC6H12 ;out

FC6H12 ;in(18)

Hydrogen recovery yield ¼ FH2

FC6H12 ;in(19)



0 0.2 0.4 0.6 0.8 10

0.65

1.3

1.95

2.6

H2 r

ecov

ery

yiel

d

0

0.25

0.5

0.75

1

Con

vers

ion

Dimensionless length

Conventional reactorExothermic sideEndothermic side

Fig. 3 e Comparison of methanol conversion in exothermic

side of OTCDMR and CADR and also, cyclohexane

conversion in endothermic side and hydrogen recovery

along the OTCDMR.

0.4

0.48

0.56

0.64

ctio

n


An obvious measure to investigate the reactor performance

is how much heat has to be supplied through the exothermic

reaction to maintain the endothermic reaction. The relative

heat supply is defined by the fuel ratio j:

J ¼ available heat of exothermic reactionmaximum required heat of endothermic reaction

(20)

As efficiency of the reactor is defined by:

x ¼ heat actually consumed for endothermic reactionheat actually released for exothermic reaction

(21)

With attention to subjects of Section 5, the feed temperature

of all sides and feed flow rate of exothermic and endothermic

sides are considered as decision variables to maximize DME,

benzene and hydrogen mole fractions using differential

evolution method. The results of the optimization are

summarized in Table 6.

In Fig. 3, the comparison of methanol conversion in the

exothermic side of optimized thermally coupled dual-

membrane rector (OTCDMR) and conventional adiabatic

DME reactor (CADR), cyclohexane conversion in the endo-

thermic side along the OTCDMR are shown. Cyclohexane

conversion is 99.2% in the endothermic side. Also, methanol

conversion reaches 86.5% and 82% in the exothermic side of

OTCDMR and CADR, respectively. The comparison of meth-

anol conversion in OTCDMR and CADR shows that the

methanol conversion in output of OTCDMR increased about

5.5%. The important point in this figure is that the exothermic

reaction is under kinetic control at the reactor entrance and in

the other section, the rate of DME synthesis reaction has

decreased to its equilibrium value and reaction is under

equilibrium control. The reaction scheme for cyclohexane

dehydrogenation indicates that the hydrogen recovery

approaches the value of three if all cyclohexane is converted

to benzene. The right-hand side of Fig. 3 illustrates the

hydrogen recovery profile along the reactor axis for endo-

thermic side of OTCDMR. This reactor configuration leads to

hydrogen recovery yield 2.4. Overall, the optimized operating

parameters for this configuration lead to efficient coupling of

these two reactions for hydrogen production.

Fig. 4 shows the comparison of DME mole fraction in the

exothermic side of OTCDMR with CADR. Since reaction is

catalytic and takes place on the catalyst surface, the mole

fraction of DME along the reactor in solid and gas phase pre-

dicted by the heterogeneous model has been presented in this

figure. As shown, it is observed that there is a considerable

difference between the DMEmole fraction in the ODMTCR and

Table 6 e The optimized parameters for the membranethermally coupled reactor.

Parameter Value

T01, K 514.2

T02, K 457.0

T03, K 500.6

T04, K 557.7

F02, mol s�1 0.068

F03, mol s�1 0.028

CADR under steady state conditions. The difference is much

higher for the upper section of the reactor which is due to

delay in the thermodynamics equilibrium and water vapor

removal from exothermic side through water vapor-

permselective membrane. Since water vapor is catalyst

poisoning agent in DME process, water vapor removal

increases catalyst life time. As it can be seen in Fig. 4, the

comparison of DME mole fraction in exothermic side of

OMTCR with CADR shows that the DME mole fraction in

output of OMTCR is increased by 38%. While there is a differ-

ence between water vapor partial pressure in the exothermic

and permeation side, water vapor can penetrate from the

0 0.2 0.4 0.6 0.8 10

0.08

0.16

0.24

0.32

Mol

e fr

a


Adiabatic reactor Exo. side, Gas phaseExo. side, Satalyst surface

Fig. 4 e Comparison of DME mole fraction profiles in the

exothermic side of OTCDMR with CADR.



0 0.2 0.4 0.6 0.8 10

0.02

0.04

0.06

0.08

0.1

0.12M

ole

frac

tion


C6H12

H2

C6H6

Fig. 5 e Mole fraction profile of cyclohexane, benzene and

hydrogen along the reactor axis.

0 0.05 0.1 0.15 0.20

20

40

60

80

100

120

140


Rat

e of

rea

ctio

n fo

r D

ME

syn

thes

is, m

ol m

-3 s

-1

0

0.3

0.6

0.9

1.2

1.5

1.8

2.1

Rea

ctio

n ra

te f

or C

6H12

, mol

m-3

s-1

Fig. 7 e Variation of reaction rate in exothermic and

endothermic sides.


reaction zone into the permeation side through composite

membrane layer.

Fig. 5 illustrates the mole fraction profile of cyclohexane,

benzene and hydrogen along the reactor axis, at steady state

for endothermic side of OTCDMR. Hydrogen permeation

from endothermic side to separation side results shifting

the dehydrogenation reaction to right and increases

hydrogen and benzene mole fractions. While there is

a difference between hydrogen partial pressure in the

endothermic and permeation side, hydrogen can continu-

ously pass from the endothermic side into the permeation

0 0.1 0.2 0.3 0.4 0.5430

470

510

550

590

630

660

Tem

pera

ture

, K


Adiabatic reactor

Exothermic side

H 2 O perm. side

Endothermic side

Hydrogen perm. side

Fig. 6 e Comparison of axial temperature profiles in the

exothermic side of OTCDMR with CADR and also,

temperature profiles of endothermic and permeation sides.

side. Thus, decreasing hydrogen partial pressure in the

permeation side causes higher decreasing hydrogen level in

the endothermic side.

Fig. 6 shows the temperature profiles in the exothermic

side, endothermic and permeation sides in OTCDMR

(dimensionless 0e0.5). In the CADR, the temperature profile

increases up to equilibrium temperature and after a certain

position along the reactor the temperature remains constant.

Thus, DME is not produced after equilibrium point in the

CADR and dehydration reaction rate approaches to zero. The

highest temperature in the OTCDMR is observed at the

exothermic side due to heat generation. The temperature of

0 0.05 0.1 0.15 0.2-5

0

5

10

15

20

25

30


Hea

t flu

x, W

Gene. heat in exothermic sideCons. heat in endothermic sideTran. heat from solid wallTran. heat from H2 membrane

Tran. heat from H2O membrane

Fig. 8 e Generated and consumed heat flux in exothermic

and endothermic side and transferred heat from solid

walls.



0 0.2 0.4 0.6 0.8 10

0.02

0.04

0.06

0.08

0.1

0.12

H2 m

ole

frac

tion

in m

embr

ane

Dimensionless lengthFig. 9. e Hydrogen mole fraction in permeation side.


the dehydrogenation side is always lower than that of the

exothermic side due to heat consumption and it makes

a driving force for heat transfer from the solid walls. Along

the exothermic side, temperature increases rapidly and a hot

spot develops as demonstrated in Fig. 5 and then decreases to

480 K. Higher temperature at the entrance of exothermic side

causes increasing reaction rate constant and consequently

higher DME production capacity. According to Le Chatelier’s

principle, temperature reduction in the exothermic reversible

reactions leads to shift the reaction in the exothermic

direction. Thus, temperature reduction in the second half of

the OTCDMR leads to shift thermodynamic equilibrium and

higher DME production. Also, in the endothermic side the

temperature increases smoothly and a hot spot forms and

then the temperature decreases. The consumed heat in the

endothermic side is supplied from heat of exothermic and

hydrogen permeation sides.

Fig. 7 shows the variation of reaction rate for both sides of

OTCDMR. Near the reactor entrance, both the methanol

dehydration and cyclohexane dehydrogenation reactions are

fast, and increase rapidly which is due to increase in

temperature of both sides (see Fig. 6). After a certain position

along the reactor, rate of methanol dehydration reaction

decreases rapidly due to thermodynamic limitations. This

figure shows that the exothermic reaction is under kinetic

control at the entrance of exothermic side and in the other

section, the rate of DME synthesis reaction is under equilib-

rium control. DME reaction rate and DME production capacity

increase due to high temperature at the reactor entrance,

lower temperature at the other section of reactor and water

vapor removal from reaction zone.

Fig. 8 illustrates the variation of the generated and

consumed heat flux in the exothermic and endothermic

reaction, respectively, and transferred heat from the walls

along the reactor for OTCDMR. At the reactor entrance DME

reaction proceeds faster than dehydrogenation and more

heat is produced by the exothermic reaction. The excess heat

raises the temperature of the system in the first section of the

reactor as illustrated by the temperature profile in Fig. 6. In

this region, the generated heat flux in the exothermic side is

higher than the consumed one. The system heats up and

a peak in the generated heat flux is observed. If the

consumed heat flux is higher than the generated one, the

system starts to cool down which results in decreasing

reaction rates in both sides. Thus, after a certain position

along the reactor (dimensionless length ¼ 0.05), the

consumed heat by the dehydrogenation side becomes larger

than the transferred heat from the solid wall and the system

starts to cool down. At the entrance of reactor, consumed

heat in the endothermic side is supplied from exothermic

side and hydrogen permeation side. Also, the calculated

values for fuel ratio and reactor efficiency of OTCDMR are

0.98 and 0.87, respectively.

Fig. 9 shows the hydrogen mole fraction in the hydrogen

permeation side of OTCDMR. Hydrogen permeation through

the membrane layer increases hydrogen mole fraction in the

permeation side. Higher sweep gas flow rates in permeation

side decreases hydrogen partial pressure and mole fraction in

the permeation side and leads to higher hydrogen permeation

through membrane. Also, decreasing hydrogen partial pres-

sure in the permeation side causes higher decreasing in

hydrogen level in endothermic side.

8. Conclusions

In this study, DME synthesis reaction coupled with dehydro-

genation of cyclohexane to benzene was modeled one-

dimensionally in a dual-membrane reactor at steady state

condition. The reactor consists of four separated sides for

selected reactions and hydrogen and water permeation. A

base case was generated considering similar operating

conditions to industrial adiabatic methanol dehydration

reactor. This new configuration represents some important

improvement in comparison to conventional reactors as

follows: improving catalyst life time in DME process; lower

outlet temperature of product stream which results higher

DME production rate; lower purification cost and hydrogen

production. The differential evolution as a stochastic global

optimization method was applied to optimize thermally

coupled dual-membrane reactor with manipulation of

selected decision variables. The summation of DME and

benzene mole fractions and hydrogen in the permeation side

was considered as the objective function. It was shown that

methanol conversion and DME mole fraction enhances about

5.5% and 38% in the optimized thermally coupled dual-

membrane reactor. The results indicate that DME synthesis

reaction and cyclohexane dehydrogenation in a heat

exchanger reactor is feasible provided that initial molar flow

rates and inlet temperatures are properly designed.

Appendix A

Themass and energy balances and pressure drop equation for

solid and fluid phases are summarized in Table 7. In these

equations h is effectiveness factor (the ratio of the reaction

rate observed to the real rate of reaction), which is obtained

from a dusty gas model calculations [35].



Table 7 e The mass and energy balances and pressure drop equation for solid and fluid phases.

Definition Equation

Mass and energy balances for solid phase

(exothermic and endothermic side)avCjkgi;j

�ygi;j � ys

i;j

�þ hjri;jrb;j ¼ 0 (22)

avhf

�Tgj � Ts

j

�þ rb;j

XNi�1

hjri;j��DHf ;i

� ¼ 0 (23)

Mass and energy balances for fluid phase (exothermic side) �Fj

Ac

vygi;j

vzþ avCjkgi;j

�ysi;j � yg

i;j

�� bðpDÞ JH2O

Ac¼ 0 (24)

�Fj

AcCgpj

vTgj

vzþ avhf

�Tsj � Tg

j

�� pDi

AcU1�2

�Tg2 � Tg

1

�

�bðpDÞ JH2O

Ac

ZT2

T1

Cp;jdT� pDi

AcU2�3

�Tg2 � Tg

3

� ¼ 0(25)

Mass and energy balances for fluid phase (endothermic side) �Fj

Ac

vygi;j

vzþ avCjkgi;j

�ysi;j � yg

i;j

�� b

JH2

Ac¼ 0 (26)

�Fj

AcCgp;j

vTgj

vzþ avhf

�Tsj � Tg

j

�þ pDi

AcU2�3

�Tg2 � Tg

3

�

�bJH2

Ac

ZT4

T3

Cp;jdTþ bpDi

AcU3�4

�Tg3 � Tg

4

� ¼ 0(27)

Mass and energy balances for hydrogen permeation side �F4

vygi;4

vzþ b JH2

¼ 0 (28)

�F4Cgp4

vTg4

vzþ b JH2

ZT4

T3

Cp;4dTþ

pDiU3�4

�Tg3 � Tg

4

� ¼ 0

(29)

Hydrogen permeation in Pd/Ag membraneJH2

¼2LpP0exp

��Ep

RT

�

ln

�Do

Di

� � ffiffiffiffiffiffiffiffiffiffiPH2 ;2

p � ffiffiffiffiffiffiffiffiffiffiPH2 ;3

p �(30)

Mass and energy balances for water permeation side �F1

vygi;1

vzþ b ðpDÞJH2O ¼ 0 (31)

�F1Cgp;1

vTg1

vzþ b ðpDÞJH2O

ZT2

T1

Cp;1dT

þpDiU1�2

�Tg1 � Tg

2

� ¼ 0

(32)

Hydrogen permeation in Pd/Ag membrane JH2O ¼ pi

�PH2 ;1 � PH2 ;2

�(33)

Pressure drop (Tallmadge equation [36]) f ¼ 150Re

ð1� εÞ2ε3

þ 4:2

Re1=6

ð1� εÞ1:166ε3

(34)

DPL

¼ fu2r

Dp(35)





Nomenclature

av Specific surface area of catalyst pellet, m2 m�3

Ac Cross section area of each tube, m2

C Total concentration, mol m�3

Ci Molar concentration of component i, mol m�3

Cp Specific heat of the gas at constant pressure,

J K�1 mol�1

dp Particle diameter, m

Di Tube inside diameter, m

Dij Binary diffusion coefficient of component i in j, m2 s�1

Dim Diffusion coefficient of component i in the mixture,

m2 s�1

Do Tube outside diameter, m

Ep Activation energy of permeability, J mol�1

F Total molar flow rate, mol s�1

hf Gas-solid heat transfer coefficient, W m�2 K�1

DHf,i Enthalpy of formation of component i, J mol�1

J Objective function

JH2 Hydrogen permeation rate in Pd/Ag membrane,

mol m�1 s�1

JH2O Water vapor permeation rate in composite

membrane, mol m�2 s�1

k Rate constant of dehydrogenation reaction,

mol m�3 Pa�1 s�1

k1 Rate constant for the rate of methanol dehydration

reaction, mol kg�1 s�1

kg Mass transfer coefficient for component i, m s�1

K Conductivity of fluid phase, W m�1 K�1

KB Adsorption equilibrium constant for benzene, Pa�1

Keq Reaction equilibrium constant for methanol

dehydration reaction, �Ki Adsorption equilibrium constant for component i

(CH3OH and H2O) in methanol dehydration reaction,

m3 mol�1

Kp Equilibrium constant for dehydrogenation reaction,

Pa3

Kw Thermal conductivity of reactor wall, W m�1 K�1

L Reactor length, m

N Number of components

P Permeability of hydrogen through Pd/Ag membrane,

mol m�2 s�1 Pa�1/2

P0 Pre-exponential factor of hydrogen permeability,

mol m�2 s�1 Pa�1/2

P Total pressure (for exothermic side: bar; for

endothermic side: Pa)

Pi Partial pressure of component i, Pa

r1 Rate of reaction for DME synthesis, mol kg�1 s�1

r2 Rate of reaction for dehydrogenation of cyclohexane,

mol m�3 s�1

R Universal gas constant, J mol�1 K�1

Re Reynolds number

Sci Schmidt number of component i

T Temperature, K

u Superficial velocity of fluid phase, m s�1

ug Linear velocity of fluid phase, m s�1

U Overall heat transfer coefficient between exothermic

and endothermic sides, W m�2 K�1

yi Mole fraction of component i, mol mol�1

z Axial reactor coordinate, m

Greek letters

aH Hydrogen permeation rate constant,

mol m�1 s�1 Pa�1/2

pi water permeation rate constant, mol m�2 s�1 Pa�1

m Viscosity of fluid phase, kg m�1 s�1

h Effectiveness factor

b Switch for component permeation from membrane

layer (0 and 1)

rb Density of catalytic bed, kg m�3

Superscripts

g In bulk gas phase

s At surface catalyst

0 Inlet conditions

i Chemical species

j Side of the coupled reactor (1: water-permselective

side, 2: exothermic side, 3: endothermic side, 4:

hydrogen-permselective side)

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