Novel Recuperative Configuration for Coupling of Methanol

Ind. Eng. Chem. Res. 2010, 49, 4633–4643

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Novel Recuperative Configuration for Coupling of Methanol Dehydration to Dimethyl Ether with Cyclohexane Dehydrogenation to Benzene Mohammad Farsi,† Mohammad H. Khademi,† Abdolhosein Jahanmiri,†,‡ and Mohammad Reza Rahimpour*,†,‡ Department of Chemical Engineering, School of Chemical and Petroleum Engineering, Shiraz UniVersity, Shiraz 71345, Iran, and Gas Refining Center of Excellence, Shiraz UniVersity, Iran

Coupling energy intensive endothermic reaction systems with suitable exothermic reactions improves the thermal efficiency of processes and reduces the size of reactors. One type of reactor suitable for such a type of coupling is the recuperative reactor. In this work, the catalytic methanol dehydration to dimethyl ether (DME) is coupled with the catalytic dehydrogenation of cyclohexane to benzene in a simulated integrated reactor formed of two fixed beds separated by a wall, where heat is transferred across the surface of tube. A steady state heterogeneous model of the two fixed beds predicts the performance of this novel configuration. The cocurrent mode is investigated, and the simulation results are compared with corresponding predictions for an industrial adiabatic methanol dehydration fixed-bed reactor operated at the same feed conditions. In this coupled reactor, benzene and hydrogen are also produced as additional valuable products in a favorable manner and autothermality is achieved within the reactor. This novel configuration can decrease the temperature of methanol dehydration reaction in the second half of the reactor and shift the thermodynamic equilibrium. Therefore, the methanol conversion and DME mole fraction increase by 1.82% and 1.6%, respectively. The influence of inlet temperature and the molar flow rate of exothermic and endothermic stream on reactor behavior is investigated. The results suggest that coupling of these reactions could be feasible and beneficial. An experimental proof-of-concept is needed to establish the validity and safe operation of the novel reactor. 1. Introduction The commitment to the production of any chemical product often depends on its profitability and environmental and economic factors such as pollution and resource. Dimethyl ether (DME) is a colorless gas at the ambient condition and easily liquefied under low pressure. Recently, DME is an attractive topic in academic and industrial research due to global environment pollution and energy supply problem. DME does not produce any particulate matter and toxic gases such as NOx at burning, when used as a fuel. It can be produced from a variety of feedstocks such as natural gas, crude oil, residual oil, coal, waste products, and biomass.1 It is useful for a variety of applications such as liquified petroleum gas (LPG) substitute, transportation fuel, propellant, chemical feedstock, and in fuel cells.2 DME production in the conventional process involves a methanol dehydration reaction as an indirect method. Currently, DME synthesize from syngas as a direct method is developed to produce it at low cost. DME production through direct synthesis from syngas using a dual catalyst system permits both methanol synthesis and dehydration in a single process, with no methanol purification. At present, DME is commercially produced by dehydration of methanol in the adiabatic packed bed reactor using acidic porous catalysts.3 There are several articles in the literature that discuss modeling of catalytic packed bed reactors. Nasehi et al.4 modeled and simulated DME synthesis in adiabatic fixed bed reactor and showed that difference between one-dimensional and two-dimensional modeling is negligible. Liu et al.5 modeled * To whom correspondence should be addressed. Tel.: +98 711 2303071. Fax: + 98 711 6287294. E-mail address: rahimpor@ shirazu.ac.ir. † School of Chemical and Petroleum Engineering. ‡ Gas Refining Center of Excellence.

and designed a three-phase bubble column reactor for direct synthesis of DME from syngas with considering the influence of inert carrier backmixing on transfer and the influence of catalyst grain sedimentation on reaction. Simulation of fluidizedbed reactor for DME synthesis from syngas has been performed by Lu et al.6 using a plug flow model, which shows the great advantage of fluidized-bed over fixed-bed or slurry reactors. Moradi et al.7 studied DME synthesis from synthesis gas in slurry reactor experimentally and determined the optimum operating conditions of DME synthesis. Omata et al.8 studied DME production from syngas in a temperature gradient reactor for overcoming both the equilibrium limit of the reaction at high temperature and low activity of the catalyst at low temperature. Then, they optimized the reactor for higher CO conversion by combined genetic algorithm and neural network. Multifunctional reactors integrate, in one vessel, one or more transport processes and a reaction system and are widely used in industries as process intensification tools.9,10 These multifunctional reactors make the process more efficient and compact and result in large savings in the operational and capital costs.11 A multifunctional reactor can be used, for example, for coupling exothermic and endothermic reactions. In this type of reactor, an exothermic reaction is used as the heat producing source to drive the endothermic reaction(s). In the last years promising concepts for the recuperative coupling of exothermic and endothermic reactions have been published. Hunter and McGuire12 were among the first to suggest the coupling of endothermic with exothermic reaction by means of indirect heat transfer. They considered heat exchangers where catalytic combustion or another highly exothermic reaction is used as a heat source for an endothermic reaction. Itoh and Wu13 investigated an adiabatic type of palladium membrane reactor for coupling endothermic and exothermic reactions. On one side of the membrane, dehydrogenation of cyclohexane takes place in the catalyst packed layer,

10.1021/ie1000086  2010 American Chemical Society Published on Web 04/23/2010

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Ind. Eng. Chem. Res., Vol. 49, No. 10, 2010

and on the membrane surface of the other side, hydrogen permeated reacts in situ with oxygen. They simulated a simple mathematical model for analyzing the reaction process. Frauhammer et al.14 and Kolios et al.15,16 studied the process of methane steam reforming coupled with methane combustion both experimentally and theoretically, mainly in countercurrent configuration utilizing a ceramic honeycomb monolith with specially designed reactor heads. Elnashaie et al.17 and Moustafa and Elnashaie18 used a heterogeneous model to study the performance of the membrane catalytic reactor for the dehydrogenation of ethylbenzene to styrene. The mathematical model is extended to simulate a novel hybrid configuration which is composed of two catalytic sides separated by hydrogen-selective composite membrane for hydrogen separation. One side of the reactor is a dehydrogenation section in which ethylbenzene is dehydrogenated to styrene, while the other catalytic side is a hydrogenation section in which benzene is catalytically converted to cyclohexane. The effect of cocurrent and countercurrent flow patterns is investigated. A mathematical simulation and numerical method based on a two-dimensional model are developed by Fukuhara and Igarashi19 to analyze the operation of coupling methanol decomposition and methane combustion. They compared the performance of a wall-type reactor with a fixed-bed reactor in which exothermic and endothermic reactions proceed simultaneously. Ramaswamy et al.20 presented a one-dimensional pseudohomogeneous plug flow model to analyze and compare the performance of cocurrent and countercurrent heat-exchanger reactors. Ramaswamy et al.21 analyzed the steady state and the dynamic behavior of coupling exothermic and endothermic reactions in directly coupled adiabatic packed-bed reactors (DCAR) for the first order reactions using one-dimensional pseudohomogeneous plug flow model. Abo-Ghander et al.22 coupled the catalytic dehydrogenation of ethylbenzene to styrene with the catalytic hydrogenation of nitrobenzene to aniline in a simulated integrated reactor formed of two fixed beds separated by a hydrogen-selective membrane, where both hydrogen and heat are transferred across the surface of membrane tubes. Both cocurrent and countercurrent operating modes are investigated. A distributed mathematical model for a thermally coupled membrane reactor that is composed of three sides was developed for methanol and benzene synthesis by Khademi et al.23 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 cocurrent flow of sweep gas through the permeation side. This investigation focused on production of pure hydrogen from coupling of methanol and benzene synthesis in a hydrogen-permselective membrane reactor. Optimization of methanol synthesis and cyclohexane dehydrogenation in a thermally coupled reactor using differential evolution (DE) method is analyzed by Khademi et al.24 From these previous studies, coupling of endothermic and exothermic reactions may enable both the concentration and temperature profiles along the reactor to be manipulated, shifting the conversion of thermodynamically limited reactions to higher values, and efficiently using the heat liberated by an exothermic reaction side to provide the endothermic heat requirements of the other reaction side.25 It should be also mentioned that the recuperative coupling reactors have some disadvantages such

Figure 1. Schematic diagram of a traditional adiabatic DME reactor.

Figure 2. Schematic diagram of a thermally coupled reactor configuration.

as (i) difference in the catalyst life of two beds, and (ii) difficulty of replacement or recharge of the deactivated catalyst in the shell side. Figure 1 shows the schematic diagram of a conventional adiabatic methanol dehydration reactor. In the conventional adiabatic reactor, the catalyst is packed in the reactor. The methanol dehydration reaction is carried out over a commercial γ-Al2O3 catalyst. In a heat exchanger, the heat of product stream is used to preheat the feed stream. In the previous work,26 a shell and tube fixed bed reactor for DME production was modeled and optimized. DME production in the reactor was maximized based on two approaches which consist of a constant and variable temperature distribution along the shell of the reactor using genetic algorithm. In the first approach, the catalyst was packed in vertical tubes and surrounded by the boiling water. The boiling water entered the shell side at an optimal temperature. The heat of the DME synthesis reaction is transferred to the boiling water and steam is produced. In the present work, a catalytic dehydrogenation reaction in the shell side is used instead of the cooler-water in the methanol dehydration reactor proposed by Farsi et al.26 The dehydrogenation reaction chosen is the catalytic dehydrogenation of cyclohexane to benzene. Figure 2 shows a schematic diagram of thermally coupled reactor configuration. It consist a shell compartment surrounding tube compartments. Catalytic dehydrogenation of cyclohexane to benzene is assumed to take place in the shell, whereas methanol dehydration occurs inside the tube, with fixed bed of different catalysts on both sides. Heat is transferred continuously from the exothermic reaction to the endothermic reaction. The clear advantages of this integrated catalytic reactor include: achieving a multiple reactants multiple products configuration and possibility of achieving higher degree of in situ energy integration between the coupled endothermic dehydrogenation reaction and the exothermic DME synthesis reactions. Rigorous mathematical models are excellent tools for the exploration of the basic characteristics of such novel configurations. Such an exploration can achieve considerable savings in money and time during the expensive stage of pilot plant development. The continuous development of the model

Ind. Eng. Chem. Res., Vol. 49, No. 10, 2010 Table 1. Reaction Rate Constant, the Adsorption Equilibrium Constant, and the Reaction Equilibrium Constant for the Methanol Dehydration Reaction

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Table 2. Reaction Rate Constant, the Adsorption Equilibrium Constant, and the Reaction Equilibrium Constant for Dehydrogenation of the Cyclohexane Reaction

k ) A exp(-E/RT)

A

E (J mol-1)

k ) A exp(B/T)

A

B (K)

k1 KCH3OH KH2O

3.7 × 1010 mol2 kg-1 s-1 m-3 7.9 × 10-4 m3 mol-1 0.84 × 10-1 m3 mol-1

-105000 70500 41100

k KB KP

0.221 mol m-3 Pa-1 s-1 2.03 × 10-10 Pa-1 4.89 × 1035 Pa3

-4270 6270 3190

in conjunction with the pilot plant optimal utilization can also achieve considerable benefits on the road toward the successful commercialization of such efficient novel configurations. The paper is organized as follows: reactions scheme and kinetics are shown in section 2. Mathematical model and numerical solution are explained in sections 3 and 4, respectively, followed by results and discussion (effect of different parameters on performance of the reactor) in section 5. Conclusions are drawn in section 6. 2. Reaction Scheme and Kinetics 2.1. Methanol Dehydration. The reaction of DME synthesis is mainly dehydration of methanol that is exothermic and equilibrium reaction. Many researches27-29 are focused on DME synthesis reaction. In the current work, the rate expressions have been selected from the work of Berc´ic´ and Levec.30 2CH3OH T CH3OCH3 + H2O

∆H298 ) -23.4 kJ mol-1 (1)

The following reaction rate equation for methanol dehydration, r1, is used30

r1 )

k1KCH3OH2(CCH3OH -

(CC2H6OCH2O) Keq

)

(1 + 2(KCH3OHCCH3OH).5 + KH2OCH2O)4

(2)

where the reaction equilibrium constant, Keq is as follows: ln(Keq) ) 0.86 log T +

3138 + 1.33 × 10-3T T 1.23 × 10-5T2 + 3.5 × 10-10T (3)

k1, KCH3OH, and KH2O are the reaction rate constant and the adsorption equilibrium constant for methanol and water vapor, respectively. These parameters are tabulated in Table 1. Commercially, γ-Al2O3 catalyst is used in the methanol dehydration reaction. 2.2. Cyclohexane Dehydrogenation. Hydrogen is an optimum large scale fuel for the future, although there remain some problems in transport and long-term storage. One has to develop the use of alternative fuels that are easily transformed into hydrogen and that can be stored in liquid form, and, thus, more safely and economically. One of these fuels is cyclohexane. The reaction scheme for the dehydrogenation of cyclohexane to benzene is as follows. C6H12 T C6H6 + 3H2

the adsorption equilibrium constant for benzene, and the reaction equilibrium constant that are tabulated in Table 2. pi is the partial pressure of component i in pascals. The reaction temperature is in the range of 423-523 K, and the total pressure in the reactor is maintained at 101.3 kPa. The catalyst for this cyclohexane dehydrogenation reaction is Pt/Al2O3.32 3. Mathematical Model Figure 3 shows a schematic diagram for the cocurrent mode of a heat-exchanger reactor configuration. A one-dimensional heterogeneous model, which is a conventional model for a catalytic reactor with heat and mass transfer resistances, has been developed for this reactor in order to determine the concentration and temperature distributions inside the reactor. In this model the following assumptions are used: • The gas mixture is an ideal gas in both catalytic reactor sections. • Both sections of the reactor are operated at steady state conditions. • Radial variations in both beds are negligible (onedimensional model). • With due attention to high gas velocity, axial diffusion of mass and heat are negligible in both sections. • Bed porosity in axial and radial directions is constant. • Plug flow is employed in both endothermic and exothermic sides. • The chemical reactions are assumed to take place only in the catalyst particles and homogeneous reactions are neglected. • Heat loss to surroundings is neglected. To obtain the mole balance equation and the energy balance equation, a differential element along the axial direction inside the reactor was considered. The balances typically account for convection, transport to the solid phase, and reaction. 3.1. Solid Phase. The mass and energy balances for the solid phase are expressed by g aVjcjkgi,j(yi,j - ysi,j) + ηjri,jFb ) 0

(6)

N

aVjhf(Tgj - Tsj ) + Fb

∑ηr

j i,j(-∆Hf,i)

)0

(7)

i-1

s where yi,j and Tjs are the solid-phase i-component mole fraction and temperature in the j side of reactor, respectively, and η is effectiveness factor (the ratio of the reaction rate observed to

∆H298 ) +206.2 kJ mol-1 (4)

The following reaction rate equation of cyclohexane, r2, is used:31 r2 )

-k(KPPC /PH23 - PB) 1 + (KBKPPC /PH23)

(5)

where k, KB, and Kp are, respectively, the reaction rate constant,

Figure 3. Schematic diagram of the cocurrent mode for a recuperative reactor configuration.

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the real rate of reaction), which is obtained from dusty gas model calculations.33 The detail of such a dusty gas model is given in the Appendix. 3.2. Fluid Phase. The following mass and energy balances equations are written for the fluid phase: -

Fj dygi,j + aVjcjkgi,j(ysi,j - ygi,j) ) 0 Ac dz

(8)

Fj g dTgj πDi + aVjhf(Tsj - Tgj ) ( - Cpj U(Tg2 - Tg1) ) 0 (9) Ac dz Ac g where yi,j and Tjg are the fluid-phase i-component mole fraction and temperature in j side of reactor, respectively. The energy equation (eq 9) takes into account the heat transferred by convection, the heat exchanged between fluid phase and solid particles, and the heat transferred between two sides, respectively. In this equation, the positive sign is used for the exothermic side and the negative sign for the endothermic side. 3.3. Pressure Drop. The Ergun momentum balance equation is used to give the pressure drop along the reactor:

(1 - ε)2µug (1 - ε)ug2F dP ) 150 + 1.75 dz ε3dp2 ε3dp

(10)

where the pressure drop is in pascals. 3.4. Boundary Conditions. The boundary conditions applied to solve the model are discussed in this section. At the entrance of the reactor, the inlet temperature, the inlet pressure, and the inlet gas compositions of the reactant gas in the both sides are known. Therefore, the following boundary conditions are applied

z ) 0,

ygi,j ) ygi0,j,

Tgj ) Tg0j,

Pgj ) Pg0j

(11)

g g where yi0,j , T0j , and Pg0j are the fluid-phase mole fraction, temperature, and pressure at the entrance of j side of reactor, respectively. 3.5. Auxiliary Correlations. To complete the simulation, auxiliary correlations should be added to the model. In the heterogeneous model, because of transfer phenomena, the correlations for estimation of heat and mass transfer between two phases and estimation of physical properties of chemical species and overall heat transfer coefficient between shell and tube sides should be considered. The correlations used for physical properties, mass and heat transfer coefficient are summarized in Table 3. The heat transfer coefficient between the gas phase and reactor wall is applicable for the heat transfer coefficient between bulk gas phase and solid phase (hf) in the exothermic and endothermic side.

4. Numerical Solution The formulated model composed of eight ordinary differential equations and the associated boundary conditions lends itself to be an initial value problem. The algebraic equations in the model incorporate the initial conditions, the reaction rates, and the ideal gas assumption, as well as aforementioned correlations for the heat and mass transfer coefficients and the physical properties of fluids. These equations along with the discretized ordinary differential equations using backward finite difference form a set of nonlinear algebraic equations. The reactor length is then divided into 100 separate sections, and the Gauss-Newton method in the MATLAB programming environment is used to solve the nonlinear algebraic equations in each section.

Table 3. Physical Properties and Mass and Heat Transfer Correlations parameter

equation

ref

component heat capacity

Cp ) a + bT + cT2 + dT3

mixture heat capacity viscosity of reaction mixtures mixture thermal conductivity mass transfer coefficient between gas and solid phases

based on local compositions based on local compositions kgi ) 1.17Re-0.42Sci-0.67ug × 103 Re )

Sci )

34 35

2FRpug µ

µ FDim × 10-4 1 - yi yi Dij

Dim )

36

∑ i)j

Dij )

overall heat transfer coefficient

heat transfer coefficient between gas phase and reactor wall

10-7T3/2√1/Mi + 1/Mj 3/2

P(Vci

37

+ Vcj )

2/3 2

Ai ln(Do /Di) Ai 1 1 1 ) + + U hi 2πLKw Ao ho

( )

h Cpµ CpFµ K

2/3

)

( )

0.458 Fudp εB µ

-0.407

38

Ind. Eng. Chem. Res., Vol. 49, No. 10, 2010 Table 4. Operating Conditions for Methanol Dehydration Process (Exothermic Side) parameter

Table 6. Operating Conditions for Dehydrogenation of Cyclohexane to Benzene (Endothermic Side)

value

parameter

gas phase 0.936 0.055 0.009 0.1 535 18.18

catalyst particle density (kg m-3) particle diameter (m) specific surface area (m2 m-3) ratio of void fraction to tortuosity of catalyst particle length of reactor (m) bed void fraction density of catalyst bed (kg m-3) tube inner diameter (m) tube outer diameter (m) wall thermal conductivity (W m-1 K-1)

2010 0.3175 × 10-2 673 0.066 8.08 0.5 1005 3.8 × 10-2 4.32 × 10-2 48

2457

plant data 2506

absolute error 1.95%

937.7

0.31%

652.2

644

1.27%

5. Results and Discussions 5.1. Model Validation. The model of methanol dehydration side is validated against conventional adiabatic DME synthesis reactor under the design specifications and input data listed in Table 4. It is observed that the model performed satisfactorily well under special case of industrial conditions and the observed plant data were in good agreement with simulation data. The comparison between steady state simulation results and plant data for the conventional adiabatic reactor is shown in Table 5. The plant data used for evaluation is taken from Zagros Petrochemical Complex. As it is seen, the maximum absolute error is about 1.95% which is acceptable. In this section, various steady-state behaviors observed in the cocurrent coupled reactor are analyzed and the predicted mole fraction, conversion, and temperature profiles are presented. The performance of the thermally coupled reactor is analyzed, using different operating variables, for methanol and cyclohexane conversion, as follows: FCH3OH,in - FCH3OH,out

cyclohexane conversion )

FCH3OH,in FC6H12,in - FC6H12,out FC6H12,in

(12)

(13)

An obvious measure for the performance of the reactor concept 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 Ψ: Ψ)

a Obtained from the work of Jeong et al.39 of Koukou et al.40

ξ)

940.6

methanol conversion )

feed compositiona (mole fraction) C6H12 C6H6 H2 Ar total molar flow rate (mol s-1) inlet temperature (K) inlet pressurea (Pa) particle diameterb (m) bed void fraction specific surface area (m2 m-3) shell inner diameter (m)

0.1 0.0 0.0 0.9 0.13 493 1.013 × 105 3.55 × 10-3 0.39 825 8.8 × 10-2 b

Obtained from the work

As efficiency of the reactor, we define

Table 5. Comparison between Steady State Simulation Results and Plant Data for the Conventional Adiabatic Methanol Dehydration Reactor

DME molar flow rate (kmol h-1) MeOH molar flow rate (kmol h-1) temperature (°C)

value gas phase

feed composition (mole fraction) CH3OH DME H2O total molar flow rate (mol s-1) inlet temperature (K) inlet pressure (bar)

simulation result

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available heat of exothermic reaction maximum required heat of endothermic reaction

(14)

heat actually consumed for endothermic reaction heat actually released for exothermic reaction

(15) Optimal conditions imply Ψ f 1+ and ξ f 1-. 5.2. Base Case. In order to establish a reference point, so that the influence of various parameters can be evaluated, calculations are first carried out for a “base case” and the operating conditions used for both sides of the reactor are given in Tables 4 and 6. Operating conditions for the methanol dehydration side are similar to those used by Farsi et al.26 The inlet composition of the methanol dehydration reaction is typical of industrial methanol dehydration process. On the endothermic side, the inlet mole fraction of cyclohexane that is diluted with argon is the same as that presented by Jeong et al.39 Thus, the base case aims to investigate the situation when the cyclohexane dehydrogenation is used to consume the generated heat from methanol dehydration and to cool down it, resulting in a higher temperature at the first parts of the exothermic side for higher kinetic constants and then reducing temperature gradually at the end parts of the reactor for increasing thermodynamic equilibrium which is not similar to the temperature profile along a tube filled with catalyst within a methanol dehydration adiabatic reactor. This allows comparison of the methanol dehydration process in the coupled reactor with adiabatic reactor for similar thermal behavior. The simulation results of the reactor in the endothermic side are not compared with any reference case. 5.2.1. Mole Balance Behavior. Figure 4a-c shows the comparison of the exothermic side of the coupled reactor with an adiabatic reactor. Figure 4a illustrates the mole fraction profile of methanol along the reactor, at steady state for the exothermic side and adiabatic reactor. Figure 4b and c presents similar results for DME and H2O, respectively, while Figure 4d is simultaneous plots of mole fraction for cyclohexane, benzene, and hydrogen in the endothermic side along the reactor axis. As shown, it is observed that there is not a considerable difference between the behavior of variables in the exothermic side and adiabatic reactor, that is, the profiles of mole fraction of components along the reactor have the same patterns in both reactors under steady-state conditions. This novel configuration can increase the mole fraction of DME by 1.6%. In Figure 5, cyclohexane and methanol conversion in adiabatic reactor and exothermic side along the reactor are shown. The profiles of methanol conversion along the reactor have the same patterns in the adiabatic reactor and exothermic side. Cyclo-

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Figure 4. Comparison of (a) methanol, (b) DME, and (c) H2O mole fraction along the reactor axis between exothermic side of coupled reactor and adiabatic reactor and (d) mole fraction of cyclohexane, benzene, and hydrogen in the endothermic side.

Figure 5. Cyclohexane and methanol conversion in adiabatic reactor and exothermic side along the reactor length.

hexane reaches 99.8% conversion in endothermic side, and methanol 83.5% and 82% conversion in the adiabatic reactor and exothermic side, respectively. 5.2.2. Thermal Behavior. Figure 6 shows axial temperature profiles in the adiabatic reactor, exothermic side, and endothermic side. In the adiabatic reactor, the temperature increases up to equilibrium temperature (652 K). After a certain position along the reactor (dimensionless length ) 0.2 in Figure 6), the temperature maintain constant. In addition, the highest temperature is observed at the exothermic side of coupled reactor, since this is where heat is generated. Part of this heat is used to drive the endothermic reaction and the rest to heat the reaction

Figure 6. Variation of temperature for adiabatic reactor, exothermic side, and endothermic side along the reactor for the base case.

mixtures in both sides. The temperature of the dehydrogenation side is always lower than that of the exothermic side in order to make a driving force for heat transfer from the solid wall. Along the exothermic side, temperature increases rapidly and a hot spot develops as demonstrated in Figure 6 and then decreases to 450 K. Also, the temperature pattern in endothermic side is the same as temperature pattern in exothermic side; at the entrance of dehydrogenation side, the temperature increases smoothly and a hot spot form and then the temperature decreases. Note that in the endothermic side, the outlet tem-


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Figure 8. Influence of inlet temperature of endothermic stream on the temperature profiles in exothermic and endothermic sides along the reactor length for thermally coupled reactor.

Figure 7. Variation of (a) rate of reaction for both sides and (b) generated and consumed heat flux and also transferred heat from solid wall along the reactor for the base case.

perature nearly is the same as the outlet temperature in exothermic side (450 K). Figure 7a shows the variation of rate of reaction for both sides. Near the reactor entrance, both the methanol dehydration and cyclohexane dehydrogenation reactions are fast. After a certain position along the reactor (dimensionless length ) 0.2 in Figure 7a), the rate of methanol dehydration reaction is zero. Figure 7b illustrates the variation of the generated and consumed heat flux from the exothermic and the endothermic reaction, respectively, and transferred heat from the solid wall along the reactor. At the reactor entrance, methanol dehydration reaction proceeds faster than dehydrogenation and as a result more heat is produced by the exothermic reaction than consumed by the endothermic one. The excess heat raises the temperature of the system in the first half of the reactor as illustrated by the temperature profile in Figure 6. In this region, the generated heat flux is higher than the consumed one. The system heats up and a peak in the generated heat flux is observed. Afterward, the generated heat flux decreases rapidly, mainly due to fuel depletion. The opposite situation occurs when the consumed heat flux is higher than the generated one. If the consumed heat flux is higher than the generated one, the system starts to cool down resulting to low temperature, which in turn decreases both reaction rates. Thus,

after a certain position along the reactor (dimensionless length ) 0.15 in Figure 7b), the generated heat flux becomes lower than the consumed one, which coincides with a hot spot development (see Figure 6). Along the reactor length, the heat consumed by the endothermic side and transferred from the solid wall are close to each other. This demonstrates the efficient thermal communication between the both sides, and which is due to high solid wall thermal conductivity and the relatively small shell diameter. At the reactor entrance, the transferred heat from the solid wall is higher than the consumed heat by the endothermic side. Almost maximum values in the reaction heat fluxes consumed and transferred from the solid wall are located at the same axial position, namely 0.15. After this position along the reactor, the consumed heat by the dehydrogenation side becomes larger than the transferred heat from the solid wall and the system starts to cool down (see Figure 6). Values of fuel ratio and reactor efficiency of the thermally coupled reactor for the base case are 0.91 and 1.2, respectively which are close to the optimal conditions. Overall, the operating and design parameters chosen for the base case lead to efficient coupling of the two reactions. 5.3. Influence of Inlet Temperature of Endothermic Stream. As it can be seen in Figure 6, there is a hot spot in the exothermic side. This may be attributed to the reasons such as dissimilar reaction rates and heats of exothermic and endothermic reactions. Decreasing the feed temperature of the endothermic stream leads to eliminate this hot spot. Figure 8 shows the influence of inlet temperature of endothermic stream on the temperature profiles in both sides along the reactor length. This is a case where the hot spot in exothermic side is not observed which is due to lower rate of DME synthesis reaction in the reactor entrance. Here, the inlet temperature of the endothermic stream (473 K) is lower than the exothermic stream in comparison with the base case. This arrangement requires the preheating of the exothermic stream by an external thermal source. Decreases in the inlet temperature of dehydrogenation stream from 493 to 473 K can decrease the methanol conversion from 83.5% to 29.4% and cyclohexane conversion from 99.8% to 50%, which is due to a lower rate of DME synthesis reaction in the reactor entrance and lower temperature of endothermic side.

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quence of the fact that the amount of catalyst on endothermic side is not enough for these higher flow rates. 5.5. Influence of the Molar Flow Rate of the Exothermic Stream. In this section, the reactor thermal behavior and performance are studied for different molar flow rate of exothermic stream. The variation range for molar flow rate of exothermic stream is 0.02-0.1 mol s-1. All other parameters are kept at their base case values. Figure 10a indicates the axial location where the maximum of the temperature in exothermic side moves down and toward the reactor exit as molar flow rate of exothermic stream increases, which is due to increasing the heat transferred from the solid wall and decreasing the space time, respectively. Figure 10b shows the effect of molar flow rate of exothermic stream on methanol and cyclohexane conversion. An increase in molar flow rate dose not affects significantly on exothermic side performance (see Figure 10b). In this case, the amounts of reactants going through the exothermic side increase per unit catalyst volume. Increasing molar flow rate of exothermic stream from 0.037 mol s-1 to base case (0.1 mol s-1) leads to decreasing methanol conversion from 84.2% to 83.5% which is due to lower residence time. Decreasing the molar flow rate from 0.037 to 0.02 mol s-1, reduces methanol conversion to 82%. As it can be seen in Figure 10b, methanol conversion is maximized in the molar flow rate of the exothermic side at 0.037 mol s-1. Therefore, the results show the optimum value of the molar flow rate of the exothermic side at the operating conditions of the base case is 0.037 mol s-1. Increasing molar flow rate of the exothermic side leads to increasing the cyclohexane conversion due to increasing the transfered heat flux from the solid wall (see Figure 10c). 6. Conclusion

Figure 9. Influence of molar flow rate of endothermic stream on (a) axial temperature profile in exothermic side and (b) methanol and cyclohexane conversion.

5.4. Influence of the Molar Flow Rate of the Endothermic Stream. The influence of the flow rates could be considered through variation of the average inlet velocities. When reactor geometric, inlet operating conditions and catalyst loading are fixed, then variations of flow rates result in corresponding variations of fluid velocities and residence times. Figure 9a shows the influence of molar flow rate of endothermic stream on the temperature profile of the exothermic side along the reactor length. With increase of the flow rate of the dehydrogenation stream, axial temperature variation becomes lower which is due to higher transferred heat from the solid wall. Figure 9b illustrates how the methanol and cyclohexane conversion behave when the flow rate of the endothermic stream increases from 0.12 to 0.16 mol s-1. Cyclohexane conversion significantly decreases from 100% to 53%, and methanol conversion, from 83.2% to 41.6%. Methanol conversion is maximized in the molar flow rate of the endothermic side 0.126 mol s-1. This means that the optimum molar flow rate of the endothermic side is 0.126 mol s-1, in the operating conditions of the base case. In this point, the values of fuel ratio and reactor efficiency are 0.91 and 1.2, respectively. Decreasing of methanol yield after 0.126 mol s-1 is due to the lower axial temperature profile (see Figure 9a) and consequently lower rate of reaction. Decreasing of cyclohexane conversion is an obvious conse-

DME synthesis reaction coupled with dehydrogenation of cyclohexane to benzene by means of indirect heat transfer in a catalytic heat-exchanger reactor was studied by a onedimensional model. The reactor consists of two separated sides for exothermic and endothermic reactions. A base case was generated considering similar operating conditions to industrial adiabatic methanol dehydration reactor. It is shown that a suitable amount of feed in both sides can provide the necessary heat to heat up the mixtures and to drive the endothermic process at the same time. The short distance between the heat sink and transferred heat increases the efficiency of heat transfer. This new configuration represents some important improvement in comparison to the conventional adiabatic methanol dehydration reactor as follows: it reduces the size of the reactors; the lower outlet temperature of the product stream leads to a shift the thermodynamics equilibrium; hydrogen and benzene are also produced as an additional valuable product; and autothermality is achieved within the reactor. The effect of the inlet temperature and molar flow rate of the endothermic stream on the temperature profile of the exothermic side and methanol and cyclohexane conversion along the reactor length are shown. The higher flow rate of the endothermic stream results in lower methanol conversion due to the lower temperature profile in the exothermic side and also lower cyclohexane conversion due to the fact that the amount of catalyst on the endothermic side is not enough for these higher flow rates. The results show that the optimum molar flow rate of the endothermic side is 0.126 mol s-1, in the operating conditions of the base case. In this point, the values of fuel ratio and reactor efficiency are 0.91 and 1.2, respectively, which are close to the optimal conditions. The influence of molar flow rate of exothermic stream on reactor thermal behavior and performance was also studied. At the base


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increase the cyclohexane conversion which is due to increasing the transferred heat flux from solid wall. 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: Dusty Gas Model When reactants diffuse into the pores to react and form products, bulk, Knudsen, and surface diffusion may take place simultaneously, depending on the size of the pores, the molecules involved in the diffusing stream, the operating conditions, and the geometry of the pores.41 In the dusty gas model which is based on Stefan-Maxwell equations, both diffusional and convective mass transport terms are considered, and this includes the description of pressure drop over the catalyst particle resulting from the stoichiometry of reaction and accompanying convective transport of molecules.42 The results of sensitivity analysis show that at low pressures (up to 10 bar), Knudsen diffusion is the most important diffusing term, while at high pressures (100 bar) bulk diffusion predominates.33 In this model, it is assumed that pore walls consist of giant molecules (“dust”) which are uniformly distributed in the space. These dust molecules are considered to be dummy, or pseudospecies in the mixture.43 The dusty gas flux relations can be offered as follows, with a small change in the notation as to avoid conflicting with other notations used in the model:44 Ni Deff i

N

+

∑ i*j

(

yjNi - yiNj Deff ij

)

)-

(

)

yi B0P dP P dyi 1+ RT dr RT dr µDeff i (A.1)

In the above equation, B0 is permeability of catalyst pellet, Dieff is effective Knudsen diffusion coefficient, and Dijeff is the effective binary diffusion coefficient which are presented by eqs A.2 and A.3 below, respectively:45,46 Deff i ) aP

[ ]

εs 2 8RT τ 3 πMi

Deff ij )

εs D τ ij

1/2

(A.2)

(A.3)

where ap is the mean pore radius. The dusty gas flux relations (eqs A.1-A.3) contain three parameters: the mean pore radius, a, the ratio of porosity and tortuosity factors, εs/τ, and the permeability parameter, B0. Using Darcy’s law combines the two parameters of permeability and the mean pore radius and gives a two-parameter model using the following correlation:45,46 B0 ) Figure 10. Influence of molar flow rate of exothermic stream on (a) axial temperature profile in exothermic side, (b) methanol and cyclohexane conversion, and (c) transferred heat from the solid wall.

case, alteration of the molar flow rate of the exothermic side in the range 0.02-0.1 mol s-1 does not introduce significant differences in DME synthesis performance. Rather some differences in axial temperature profile of the exothermic side are observed. The methanol conversion is maximized in molar flow rate of exothermic stream of 0.037 mol s-1, and this is the optimum value of flow rate. Increasing molar flow rate leads to

aP2 8

(A.4)

The reader should note that the flux relations (eq A.1) could be rewritten for distinct components to form a set of ordinary differential equations, yielding expressions for dyi/dr.44 Knowing that the summation of all components equals 1 (i.e., ΣN1 yi ) 1), N -1 ordinary differential equations should be written for the flux relations. To complete the mathematical modeling of dusty gas model, the material balances and the stoichiometric relations have to be added in order to be able to describe the multicomponent reaction-diffusion problem. Since we have used the detailed

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Graaf kinetics for the system of the methanol synthesis process, which is based on three independent reactions,33 and cyclohexane dehydrogenation reaction, four material balances are needed to add to flux relations. For a spherical and isothermal particle, this yields44 dΩk ) r2rk dr

k ) 1, 2, 3, 4

3 5 dyi 1 ) - 2( Ωk VkjFij), dr r k)1 j)1

∑ ∑

(A.5)

i ) 1, 2, ..., N - 1

(A.6) Fii )

(

RT 1 + P Deff i

Fij ) -

5

yi

∑

-

eff j)1,j*i Dij

(

yi Deff i

))

(

B0P 1 w µDeff i

1+

(

))

yi B 0P 1 RT yi + eff 1 + eff P D w Dj µDeff i i w)1+

B 0P µ

N

yi

∑D

(A.8)

(A.9)

eff i

i)1

(A.7)

Where, Fii, Fij, w, and Ωk are auxiliary parameters and V is the stoichiometric coefficient. The pressure drop in radial coordinate is given by dP 1 RT )- 2 dr r w

(

N

∑ i)1

1 Deff i

∑V Ω ik

k

k

)

(A.10)

The boundary conditions for the set of ordinary differential equations are given by Ωk ) 0

at

r)0

(A.11)

yi ) ysi

at

r ) RP

(A.12)

P ) Ps

at

r ) RP

(A.13)

The effectiveness factor for reaction k is given by

∫

Rp

ηk )

0

rk dr

Rprsk

hi ) heat transfer coefficient between fluid phase and reactor wall in exothermic side (W m-2 K-1) ho ) heat transfer coefficient between fluid phase and reactor wall in endothermic side (W m-2 K-1) ∆Hf,i ) enthalpy of formation of component i (J mol-1) k ) rate constant of dehydrogenation reaction (mol m-3 Pa-1 s-1) k1 ) rate constant for the rate of methanol dehydration reaction (mol2 kg-1 s-1 m-3) 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 (mol m-3) Ki ) adsorption equilibrium constant for component i 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) Mi ) molecular weight of component i (g mol-1) N ) number of components (N ) 3 for both dehydration and dehydrogenation reaction) 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) ri ) reaction rate of component i (for exothermic reaction mol kg-1 s-1; for endothermic reaction mol m-3 s-1) R ) universal gas constant (J mol-1 K-1) Rp ) particle radius (m) 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) Vci ) critical volume of component i (cm3 mol-1) yi ) mole fraction of component i (mol mol-1) z ) axial reactor coordinate (m) Greek Letters

(A.14)

µ ) viscosity of fluid phase (kg m-1 s-1) F ) density of fluid phase (kg m-3) Fnb ) density of catalytic bed (kg m-3) τ ) tortuosity of catalyst

Nomenclature

Superscripts

aV ) specific surface area of catalyst pellet (m2 m-3) Ac ) cross-sectional area of each tube (m2) Ai ) inside area of inner tube (m2) Ao ) outside area of inner 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 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) Dsh ) shell inside diameter (m) F ) total molar flow rate (mol s-1) G ) mass velocity (kg m-2 s-1) hf ) gas-solid heat transfer coefficient (W m-2 K-1)

g ) in bulk gas phase s ) at surface catalyst Subscripts 0 ) inlet conditions B ) benzene C ) cyclohexane i ) chemical species j ) reactor side (1 exothermic side, 2 endothermic side) K ) reaction number index

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ReceiVed for reView January 2, 2010 ReVised manuscript receiVed February 22, 2010 Accepted March 21, 2010 IE1000086

Novel Recuperative Configuration for Coupling of Methanol

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