Simulation and design of catalytic membrane reactor for hydrogen production via methylcyclohexane dehydrogenation

Simulation and design of catalytic membrane reactor for hydrogen production via methylcyclohexane dehydrogenation

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Simulation and design of catalytic membrane reactor for hydrogen production via methylcyclohexane dehydrogenation Yen-Ru Chen a, Toshinori Tsuru b, Dun-Yen Kang a,* a

Department of Chemical Engineering, National Taiwan University, Taipei 10617, Taiwan Department of Chemical Engineering, Hiroshima University, 1-4-1 Kagamiyama, Higashi-Hiroshima 739-8527, Japan

b

article info

abstract

Article history:

In this study, we sought to optimize the performance of catalytic membrane reactors for

Received 24 May 2017

the production of hydrogen through the dehydrogenation of methylcyclohexane. Finite

Received in revised form

element method was used to simulate the radial and axial distributions of velocity, tem-

21 August 2017

perature, and concentrations. We examined a number of design parameters and their ef-

Accepted 24 August 2017

fects on reactor performance, including the feed flow rate of methylcyclohexane, the mass

Available online xxx

of catalysts, and pressure on the permeation side of the hydrogen-selective membrane. € hler number and Pe clet number was also Dimensionless analysis using the Damko

Keywords:

employed in the optimization of the reactor. The catalytic membrane reactor optimized in

Catalytic membrane reactor

this work achieved a hydrogen production rate more than five times higher than that of

Finite element method

existing systems based on the same reactor volume. Simulations at the microscopic scale

Modeling

were also performed to investigate the effects of the pore size and the porosity of the

Hydrogen production

catalytic layer on hydrogen production.

Methylcyclohexane

© 2017 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.

dehydrogenation

Introduction Hydrogen is a zero-emission fuel regarded as an alternative energy source with outstanding potential. Unfortunately, a low liquefaction point under ambient pressure makes storage and transportation difficult. Over the past few decades, researchers have addressed the issues of hydrogen storage through hydrogen adsorption within a metal-organic framework [1e7], hydrogen storage in metal hydrides [8e10], and the direct production of hydrogen from liquid organic hydrides [11e15]. The production of hydrogen using liquid hydrides has environmental, economic, and technical

advantages in realizing the household use of hydrogen [14,16]. The liquid organic hydrides most widely used as a source of hydrogen include cyclohexane [12,17e19], methylcyclohexane (MCH) [11,14,16,20e27], and decalin [13,28e30]. The production of hydrogen from cyclohexane poses a number of problems associated with the production of carcinogenic benzene as a side product of the reaction. The reaction of decalin dehydrogenation produces highly condensable naphthalene, which makes its implementation in large-scale systems difficult [31]. Hydrogen production from methylcyclohexane also produces toluene (TOL), which is less toxic than the side products of dehydrogenation of cyclohexane. Compared to the two methods mentioned above, the production of

* Corresponding author. E-mail address: [email protected] (D.-Y. Kang). http://dx.doi.org/10.1016/j.ijhydene.2017.08.174 0360-3199/© 2017 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved. Please cite this article in press as: Chen Y-R, et al., Simulation and design of catalytic membrane reactor for hydrogen production via methylcyclohexane dehydrogenation, International Journal of Hydrogen Energy (2017), http://dx.doi.org/10.1016/j.ijhydene.2017.08.174

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hydrogen through the dehydrogenation of MCH is considered eco-friendly. The dehydrogenation of MCH is generally achieved using a fixed-bed reactor, in which the MCH conversion is limited by thermodynamic equilibrium and high operating temperatures [14,32,33]. Researchers have developed catalytic membrane reactors (CMRs) capable of overcoming these thermodynamic limits as a means of improving MCH conversion. CMRs remove hydrogen continuously in order to promote complete dehydrogenation of MCH [21,34,35]. Palladium is widely used as a membrane in hydrogen separation, due to its extremely high selectivity for hydrogen and thermal resistance [21,34,36e38]. However, the high selectivity of Pd-type CMRs is limited to a temperature window of 573e623 K that ensures operation at high conversion level without catalyst deactivation, and the high cost of palladium makes industrial applications unfeasible [14,23,39,40]. Researchers have developed CMRs with catalysts supported by nanoporous silica membranes in order to reduce costs. CMRs with a Pt/g-Al2O3/a-Al2O3 bimodal catalytic layer combined with BTESE(bis(triethoxy-silyl)ethane)derived silica membrane have demonstrated excellent performance in the dehydrogenation of MCH [11,23,24]. Dimethoxydiphenylsilane (DMDPS)-derived silica membranes have also been combined with a Pt/a-Al2O3 catalytic layer to provide long-term stability in MCH dehydrogenation [41e44]. A variety of modeling tools have been developed for the prediction of reactor performance to facilitate the optimization of CMR [11,23,45e60]. A 1D plug-flow reactor is the simplest approach to modeling CMRs; however, this method does not take into account details pertaining to temperature, concentration, or velocity profiles [11,23]. More advanced 3D or 2D-axisymmetric models are capable of capturing more of the details associated with CMRs. For example, previous studies based on 2D-axisymmetric modeling with heat and mass transfer revealed that the pre-exponential factor for hydrogen permeation flux as a function of sweep gas flow rate is a critical parameter in the optimization of CMRs for watergas shift reactions [46,53]. 2D modeling using heat and mass transfer for steam reforming reactions has identified local heating and localized catalyst distributions as key parameters in enhancing reactor performance [56]. However, few studies have been conducted on the modeling of MCH dehydrogenation reactions involving CMRs. In this work, we employed 2D-axisymmetric modeling for a CMR used in the dehydrogenation of MCH. Many important phenomena are neglected in the existing 1D modeling, including the transport in the radial direction and the mass transfer in the porous catalytic layer of CMR. These critical phenomena were taken into account in our 2D axisymmetric model. Finite element method was used to solve the equation of change for heat and mass transfer, and the simulation results were compared with experimentally-derived data. We

r ε



. .

u $V

investigated a number of CMR design parameters, including temperature, pressure, feed flow rate, and reactor dimensions, with regard to their effects on MCH conversion and hydrogen production efficiency. Finally, we proposed design guidelines for the development of high-performance CMRs for use in the dehydrogenation of MCH.

Methods Specifications of reactor In this study, the reaction system for MCH dehydrogenation included two reactors operating in series, as shown in Fig. 1a. A tubular reactor with MCH conversion of 0.44 at its outlet was installed prior to the catalytic membrane reactor (CMR). As shown in Fig. 1b, the geometry of the proposed CMR model is based on the axial symmetry of a CMR reported in our previous study [11]. Fig. 1b also illustrates the two-layer structure of the CMR, wherein the inner layer is the catalytic layer and the outer layer comprises a hydrogen selective membrane. The catalytic layer actually comprises a catalyst supported within a porous media (eg. porous g-Al2O3 or porous a-Al2O3), in which MCH is converted into hydrogen and toluene via a catalytic reaction. According to the literature, the pore size of the catalytic support layer is approximately 1 mm [11]. Only hydrogen (as the product of the reaction) is allowed to permeate through the hydrogen selective membrane to the permeate side where it is collected.

Governing equations Fluid dynamics The proposed CMR system involves two types of flow: 1) bulk flow confined to the tubes and 2) flow passing through porous catalytic media. Bulk flow is simultaneously governed by the equation of continuity and the NaviereStokes equation. The steady-state equation of continuity is written as follows: .

rV$u ¼ 0

(1) .

where r and u are the density and the velocity of the fluid, respectively. The steady-state NaviereStokes equation is written as follows:    .T r  . . . r u $V u ¼ V$  pr I þ m V u þ V u

(2)

where pr is the pressure on the retentate side, I is the unit matrix, and T r is the transpose operation for a tensor. Viscosity of fluid, m, was set to 7.19  104 Pa$s. Flow through the catalytic support layer (Fig. 1b), whose pore size is of several micrometers, is governed by the equation of continuity (Eq. (1)) as well as the Brinkman equation:

"    .! T r ! #  . . . . u m .. 2m . . V $u I  mk1 u  V uþ V u ¼ V $  pI þ ε 3ε ε

(3)

Please cite this article in press as: Chen Y-R, et al., Simulation and design of catalytic membrane reactor for hydrogen production via methylcyclohexane dehydrogenation, International Journal of Hydrogen Energy (2017), http://dx.doi.org/10.1016/j.ijhydene.2017.08.174

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Fig. 1 e (a) Reaction system comprising a pre-reactor and catalytic membrane reactor (CMR); (b) layout of CMR for MCH dehydrogenation.

where ε and k are the porosity and permeability of the catalytic layer. ε was set to 0.5 [11] and k was set to 1.25  1013 m2 [61], respectively, according to the previous reports. Eq. (3) applies for the catalytic support layer, since its pore size is in several micrometers [62,63]. Eq. (3) does not apply for the hydrogen selective membrane on the top of the catalytic support layer, because the pore size of the hydrogen selective membrane is in several angstroms. Instead of describing the flow within the hydrogen selective membrane, we modeled it as a boundary condition for the mass transfer in the catalytic layer. The details are described in the subsequent section.

Mass transport Mass transport in the system, involving the bulk flow and the flow in the support catalytic layer, is governed by the mass balance equation taking into account diffusion as well as convection: .



.

.

V $  D i V ci þ u ci

 ¼ ri

(4)

where D i , ci, and ri are the diffusivity, concentration, and generation rate of species i, respectively. The transport diffusivity of the three species are set to 2.5  105 [57], 3.2  105 [64], and 2.4  104 [65] m2/s for MCH, TOL, and H2 respectively. For the bulk phase, transport diffusivity is used as D i in Eq. (4). For modeling the mass transport in the catalytic support layer, the effective diffusivity, derived from transport diffusivity with Millington and Quirk model [61], is used as D i in Eq. (4). ri in Eq. (4) for the three species in the system, MCH, TOL, and H2, is described as follows [11,23]:

 .  rMCH ¼ wcat $k$pMCH 1  pTOL $p3H2 pMCH $Keq

(5)

rTOL ¼ rMCH

(6)

rH2 ¼ 3 rMCH

(7)

where wcat is the catalyst loading in the catalytic layer, k is the rate constant, Keq is the equilibrium constant, and pMCH , pTOL , and pH2 are the pressure of MCH, TOL, H2, respectively. MCH, TOL, and H2 are considered ideal gasses in this work, and the gradient of total pressure on retentate side was disregarded. Thus, the partial pressure of species i (pi) on retentate side is calculated as follows: pi ¼ 

ci pr cMCH þ cTOL þ cH2

(8)

k and Keq in Eq. (5) are computed as follows [11,23]:   113000 k ¼ exp 11:4  RT   26200 Keq ¼ 6:237  1035  exp  T

(9)

(10)

where R is the gas constant in SI units. A constant flow of hydrogen was assigned to the sidewall of the CMR, comprising a hydrogen selective membrane. The molar flux of the hydrogen flow (FH2 ) is described as:   FH2 ¼ P  pH2  pp

(11)

Please cite this article in press as: Chen Y-R, et al., Simulation and design of catalytic membrane reactor for hydrogen production via methylcyclohexane dehydrogenation, International Journal of Hydrogen Energy (2017), http://dx.doi.org/10.1016/j.ijhydene.2017.08.174

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where P is the permeance of the hydrogen selective membrane, which was set to 8.2  107 mol/m2/s, and pp is the pressure on the permeate side. According to the previous report, the membrane can have a H2/toluene selectivity over 16,000 [11]. In our simulations, the membrane was assumed to only allow for the transport of hydrogen.

Heat transport Heat transport of the fluid in this study is governed by the following heat equation: . .

. 2

rCp u $V T þ kt V T ¼ rMCH $DH

(12)

where Cp and kt are the constant-pressure heat capacity and thermal conductivity of the fluid respectively, and DH is the change in enthalpy in the MCH dehydrogenation reaction. In our simulations, the heat transport in solid phase was not considered. Cp was averaged according to the heat capacities of the three species [66] and kt was set to 2.8  102 W/m$s. DH was calculated from the formation enthalpies of the three species at 543.15 K [66]. The inlet temperature and temperature on the permeate side of the CMR were identical, referred to as external temperature Te.

Numerical solution The equations for fluidic dynamics, mass transport, and heat transport were solved numerically using finite element method (FEM). The commercial software package COMSOL Multiphysics® was used for FEM, in conjunction with the PARDISO solver and the nested dissection multithreaded preordering algorithm to solve equations. Convergence tests were conducted to determine the required number of meshes. From these tests, we determined that the deviation of conversion when using more than 30,000 meshes was less than 0.0001. Nonetheless, we applied 60,000 of meshes in the FEM simulations.

Results and discussion Validation of simulated results Fig. 2a presents a typical set of simulation results obtained using a CMR model with a diameter of 8 mm and length of 100 mm. The specified conditions included the following: the Te of CMR was 543.15 K, the feed molar flow rate of MCH for the pre-reactor (NMCH; feed ) was 4  106 mol/s, catalyst loading in the catalytic layer (wcat) was 70.74 kg/m3, pr was 1.013 bar, and pp was 0.1 bar. The computed z-direction velocity profile revealed the parabolic distribution typical of laminar flow. The computed Reynolds number was below 1, and this suggested that turbulent effects do not need to be considered in this work. We observed a similar parabolic distribution in temperature along the radial direction. In the axial direction, the temperature presented an initial decrease of 5 K, which then increased to the entrance temperature. The initial decrease in temperature can be attributed to the fact that MCH dehydrogenation is endothermic. The subsequent increase in temperature can be attributed to the fact that the temperature on

the sidewall of the CMR (Te) was higher than the temperature inside the reactor. As for the concentration distributions of the three species (MCH, TOL, and H2), the concentration of the reactant, MCH, showed a monotonic decrease along the axial direction, whereas one of the products of this reaction, TOL, showed a monotonic increase. H2 was also produced in this reaction; however, the concentration of H2 decreased along the axial direction due to the extraction on the permeate side. These observations indicate that the simulation results qualitatively obey the physical rules. A typical set of simulation results obtained using a CMR model without hydrogen extraction is shown in the Supplementary Data (Fig. S1), in which high H2 concentration within the tubular reactor was observed. To quantitatively validate the simulation results, we conducted a comparison with empirical data presented in a previous report [11] (Fig. 2b). Two sets of experimental data were examined: one set involving the application of a vacuum on the permeate side of the hydrogen selective membrane (with H2 extraction) and one without the vacuum (without H2 extraction). The specifications and boundary conditions of the two sets of computed results were identical to those described in the preceding section, except that the entrance temperature was varied between 493.15 and 553.15 K. Our simulation results for the relationship between temperature and conversion are in good agreement with the experimental data in both cases (i.e., with and without H2 extraction). This validates the efficacy of our computational method in providing accurate results for this CMR system.

Effects of CMR design on hydrogen production In this section, we evaluate the hydrogen production performance of a CMR reactor based on MCH conversion and hydrogen production efficiency. MCH conversion was defined as follows: conversion ¼

NMCH;feed  NMCH;outlet NMCH;feed

(13)

where NMCH, outlet is the molar flow rate of MCH at the outlet. Hydrogen production efficiency was defined as H2 production efficiency ¼

NH2 ;permeate V reactor

(14)

where NH2, permeate is the molar flow rate of hydrogen through the hydrogen selective membrane on the side wall of the CMR, and V reactor is the volume of the reactor. The influence of MCH feed flow flux (FMCH, feed) on hydrogen production performance is illustrated in Fig. 3. FMCH, feed is defined as the MCH molar flow rate feeding to the pre-reactor divided by the cross-section area of the CMR. This set of simulations was obtained under Te at 543.15 K, pr at 1.013 bar, and pp at 0.1 bar. The reactor had a diameter of 8 mm, and length of 100 mm with wcat of 70.74 kg/m3. As FMCH, 2 feed was increased from 0.01 to 0.76 mol/s/m , we observed a tradeoff between MCH conversion and hydrogen production efficiency. Specifically, the conversion decreased from approximately 1.00 to 0.57, and hydrogen production efficiency increased from 0.29 to 11.54 mol/s/m3 in the tested

Please cite this article in press as: Chen Y-R, et al., Simulation and design of catalytic membrane reactor for hydrogen production via methylcyclohexane dehydrogenation, International Journal of Hydrogen Energy (2017), http://dx.doi.org/10.1016/j.ijhydene.2017.08.174

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Fig. 2 e (a) Profiles of velocity, temperature, and concentration in CMR derived from simulations. The specified conditions for this simulation included the following: the Te of CMR was 543.15 K, the feed molar flow rate of MCH for the pre-reactor (NMCH; feed ) was 4 £ 10¡6 mol/s, catalyst loading in the catalytic layer (wcat) was 70.74 kg/m3, pr was 1.013 bar, and pp was 0.1 bar. (b) Comparison of simulation and experiment results [11].

range of FMCH, feed. The decrease in conversion when FMCH, feed was increased can be attributed to the fact that the fast feed flow limited the residence time for the MCH dehydrogenation reaction. However, increasing FMCH, feed led to an increase in hydrogen production efficiency, due to the fact that the increase in FMCH, feed was more pronounced than the decrease in conversion. The effects of catalyst loading in the catalytic layer (wcat) on conversion and hydrogen production performance are summarized in Fig. 4. In this work, the catalyst loading was used as a measure of catalytic activity. In most practical CMRs, the catalytic layer comprises a catalyst supported by a porous media, in which catalyst loading is adjusted during the fabrication of the CMRs. This set of simulations was obtained under the same conditions described in the preceding section, except that FMCH, feed was fixed at 0.08 mol/s/ m2 and wcat was varied between 3.54 and 212.21 kg/m3.

Conversion and hydrogen production efficiency increased with wcat, when wcat was below 70 kg/m3. When wcat exceeded 80 kg/m3, conversion and hydrogen production efficiency both remained nearly constant, which suggests the existence of an optimal catalyst loading. For this set of simulations, we designated the optimal wcat as 75 kg/m3, wherein the addition of more catalyst would not enhance CMR performance. The results shown in Figs. 3 and 4 suggest that the further increase of catalyst loading or feed flow rate did not further improve the hydrogen production. This indicate that the system is diffusion control. In the subsequent sections, we describe the results of how the reduction of mass transfer resistance improved the performance of CMR. Specifically, we investigated the effects of reducing the permeate pressure (increasing the driving force of mass transfer) and reducing € hler number on the CMR performance. the Damko

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Fig. 3 e Variations in MCH feed and effects on CMR performance. This set of simulations was obtained under Te at 543.15 K, pr at 1.013 bar, and pp at 0.1 bar. The reactor had a diameter of 8 mm, and length of 100 mm with wcat of 70.74 kg/m3.

Fig. 5 e Pressure on permeate side and effects on CMR performance. This set of simulations was obtained under Te at 543.15 K, pr at 1.013 bar, and FMCH, feed at 0.08. The reactor had a diameter of 8 mm, and length of 100 mm with wcat of 70.74 kg/m3.

Fig. 5 illustrates the influence of permeate pressure (pp) associated with the hydrogen selective membrane on hydrogen production performance. This set of simulations was conducted under the same conditions described in the preceding section, except that wcat was fixed at 70.74 kg/m3 and pp was varied between 0.001 and 0.500 bar. We observed that conversion and hydrogen production efficiency both decrease with pp. According to Eq. (11), lower pressure on the permeate side accelerates the removal of hydrogen from the retentate side, thereby lowering the partial pressure of hydrogen on that side and accelerating the hydrogen diffusion in r-direction. The low partial pressure of hydrogen provides a strong driving force for the MCH dehydrogenation reaction, in accordance with Le Chatelier's principle. Although reducing pp appears to

be an effective way to improve CMR performance, it leads to an increase in operating costs due to the need to apply a vacuum on the permeate side. It is worth pointing out that when pp was below 0.05 bar, only marginal improvements in conversion and hydrogen production efficiency were observed.

Optimizing design of a CMR for MCH dehydrogenation € hler number We used two dimensionless groups, Damko  clet number (Pe), as design parameters to (Da) and Pe investigate the optimization of a CMR for MCH dehydrogenation, due to the generality and simplicity of dimen€ hler number represents the sionless analysis. The Damko ratio between the reaction rate and rate of convective mass transport. In the CMR system discussed in this study, Da was computed as follows: Da ¼

rMCH;inlet  V reactor cMCH;inlet  vinlet

(15)

where rMCH;inlet is the reaction rate at the inlet, cMCH; inlet is the concentration of MCH at the inlet, and vinlet is the volumetric flow rate at the inlet. clet number refers to the ratio between the rate of The Pe convective mass transport and diffusive mass transport. In this work, Pe was computed as follows: Pe ¼

Fig. 4 e Catalyst loading in catalytic layer and effects on CMR performance. This set of simulations was obtained under Te at 543.15 K, pr at 1.013 bar, pp at 0.1 bar, and FMCH, 2 feed at 0.08 mol/s/m . The reactor had a diameter of 8 mm, and length of 100 mm.

d  uavg;inlet D MCH

(16)

where d is the diameter of the reactor and uavg; inlet is the average velocity at the inlet. Fig. 6 summarizes the effects of Da and Pe on conversion and hydrogen production efficiency for MCH dehydrogenation at 543.15 K. It is worth noting that the velocity used for the calculation of Pe was the free flow (bulk) velocity, instead of the velocity in the porous catalytic media. In the free flow region both convective and diffusive mass transport were important, whereas in the porous catalytic media

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Fig. 6 e Dimensionless analysis of MCH conversion using (a) 2D axial symmetric model and (b) 1D model; dimensionless analysis of hydrogen production efficiency using (c) 2D axial symmetric model and (d) 1D model. This set of simulations was obtained under Te at 543.15 K.

diffusion dominated the mass transport (Pe in the porous media was as low as 107 to 106). To highlight how concentration and temperature distribution in the radial direction can affect CMR performance, we compared our results from simulations obtained using the 2D axial symmetric model with those obtained using 1D models in previous studies [11,23]. Fig. 6a shows that an increase in Da or a decrease in Pe can enhance the conversion associated with MCH dehydrogenation. This suggests that the reaction rate and diffusive mass transport rate should exceed convective mass transport in order to achieve high conversion. From a quantitative perspective, if (Pee0.56  Da) < 0.66, then the overall conversion would exceed 0.97. The qualitative results obtained using 1D models presented the same trend as that of the 2D axial symmetric model; however, the predicted conversion values were higher (Fig. 6b). In other words, the 1D model provided somewhat optimistic predictions with regard to conversion in the dehydrogenation of MCH. 2D axial symmetric simulations indicate that low Da and low Pe are beneficial to hydrogen production

efficiency (Fig. 6c). The results from simplified 1D simulations suggest that hydrogen production efficiency is affected primarily by Da and almost entirely unaffected by Pe. This can be explained by the fact that the 1D model assumed a constant concentration in the radial direction, thereby erroneously diminishing the contribution of Pe. The fact that low Da are beneficial to hydrogen production efficiency might be counterintuitive. This is because for most simulations presented in Fig. 6c, in which the parameters were obtained from experiments [11], the MCH depleted in the middle of the reactor. In these cases, smaller reactors make the hydrogen production more efficiently. Based on the analysis in Fig. 6, we further optimized the hydrogen production efficiency of the CMR with the conversion fixed at 0.97 (Fig. 7a). Five cases involving different values for FMCH feed and pr were investigated. In each of the five cases, pp was set at 0.1 bar and Te was set at 543.15 K. Each data point in the five cases in Fig. 7a referred to a reactor of different dimensions, the details of which are outlined in the Supplementary Data (Table S1). We determined that a smaller reactor

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reactor volume. We also performed the same analysis of the optimization of hydrogen production efficiency calculated based on the same volume of catalytic layer, instead of the reactor volume (Fig. 7b). The hydrogen production efficiency is thus defined as: H2 production efficiency  ¼

NH2 ;permeate V cat

(17)

where V cat is the volume of catalytic layer. The results shown in Fig. 7b exhibited a very similar trend with those shown in Fig. 7a. Quantitatively speaking, system optimization based on the same volume of the catalytic layer led to a three-fold improvement in hydrogen production efficiency [11].

Microscopic model of CMR

Fig. 7 e (a) Optimization of hydrogen production efficiency based on the same reactor volume with MCH conversion fixed at 0.97. (b) Optimization of hydrogen production efficiency based on the same volume of the catalytic layer. The details of the conditions for each curve were summarized in Supplementary Data (Table S1).

is more efficient with regard to hydrogen production. This provides an important rule of thumb for optimizing the performance of CMRs; i.e., smaller reactors operating in parallel outperform a single reactor of equivalent volume. Case 5 presented the optimal reaction conditions, in which FMCH, feed was set at 0.24 mol/s/m2 and pr was set at 3.039 bar in a reactor with volume of 1.18  106 m3. Based on this optimal reactor design, the operation of four CMRs in parallel for a total reactor volume of 4.72  106 m3 would produce hydrogen at a rate of 5.4  105 mol/s. In experiment results obtained prior to optimization, a CMR with the same total reactor volume achieved a hydrogen production rate of only 1.1  105 mol/s [11]. Thus, system optimization led to a five-fold improvement in hydrogen production efficiency. The analysis presented above was deduced from the hydrogen production efficiency calculated based on the same

The analysis presented in the preceding sections focused on the macroscopic properties of CMRs and their effects on performance. In this section, we discuss the microscopic properties of CMRs, including the effects of pore size and porosity (in the catalytic layer) on hydrogen production. Fig. 8a presents the microscopic-scale CMR model used in the simulations. To make the pore size and porosity easily defined and controlled, interconnected cylinders were used to model the pores of the catalytic layer. The length along x direction of this model was set to be 1 mm, which is identical to the thickness of the entire catalytic layer. The length along y and z direction ranged from 0.5 to 5 mm. The x axis in the microscopic model coincided with the r axis in the macroscopic CMR model, and the hydrogen selective membrane was located at x ¼ 0. The mass and heat transfer in the microscopic modeling was modeled governed by Eqs. (4) and (12) respectively. The convective mass and heat transfer in Eqs. (4) and (12) were neglected, because that our calculations for macroscopic modeling suggest that Pe in the catalytic layer was extremely low (approximately 107 to 106). The materials properties used for the microscopic modeling were identical to the macroscopic modeling. In this set of simulations, Te was 543.15 K, catalyst loading per unit surface area was 2.25  10e5 kg/m2, and pr was 1.013 bar. Fig. 8b presents the concentration profiles obtained for the three species in the system, showing a clear concentration gradient in the radial direction. Microscopic modeling was used to investigate the effects of porosity and pore size on the production of hydrogen, which was quantified in terms of the hydrogen flux. We found that under a fixed porosity of 0.57, increasing the size of pores had no effect on the production of hydrogen (Fig. 8c). In this set of simulations, an increase in pore size from 0.31 to 3.13 mm resulted in a remarkable decrease in the pore surface area to pore volume from 9.00  106 to 0.90  106 1/m. The compensation between pore size and specific pore surface area might be the cause of the invariability in hydrogen production. In the other set of simulations with fixed pore size of 1.25 mm, we observed a pronounced improvement in hydrogen production following an increase in porosity (Fig. 8d). When porosity was increased from 0.24 to 0.75, the pore surface area per pore volume dropped marginally from 2.86 to 1.91 1/m. From this, we can deduce that hydrogen production is dominated by porosity.

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Fig. 8 e (a) Illustration of microscopic model; (b) concentration profiles obtained from a set of typical simulation results; effects of (c) pore size and (d) porosity of catalytic layer on hydrogen production as well as pore size per pore volume. In this set of simulations, Te was 543.15 K, catalyst loading per unit surface area was 2.25 £ 10¡5 kg/m2, and pr was 1.013 bar.

Conclusions A 2D axial symmetric model was developed for the evaluation of catalytic membrane reactors (CMRs) used in the production of hydrogen through methylcyclohexane (MCH) dehydrogenation. The profiles of fluid velocity, temperature, and the concentrations of various species within CMRs were simulated using finite element method, and the accuracy of the simulation results was verified through comparisons with experimental data. We examined reactor performance from the perspectives of methylcyclohexane feed flow, the mass of catalysts, and pressure on the permeate side of the CMRs. We also performed dimensionless analysis using the € hler number and Pe clet number for the optimization Damko of the reactor. In comparison to 1D model, the 2D axial symmetric model used in this work can show the effects of clet number on hydrogen production efficiency. It was Pe determined that several small reactors operating in parallel

outperform a single reactor with the same total volume. The optimized CMRs were shown to produce hydrogen at a rate more than five times higher than that of existing CMRs based on the same reactor volume (three times higher than that of existing CMRs based on the same volume of the catalytic layer). Finally, simulations at the microscopic-scale were performed to evaluate the effects of pore size and the porosity of the catalytic layer on hydrogen production. Our results suggest that the porosity of the catalytic layer plays a far greater role than does pore size in the performance of CMRs.

Acknowledgment This work was supported by the Ministry of Science and Technology (MOST) of Taiwan (MOST 104-2628-E-002-009MY3 and MOST 105-2923-E-002 -002 -MY2).

Please cite this article in press as: Chen Y-R, et al., Simulation and design of catalytic membrane reactor for hydrogen production via methylcyclohexane dehydrogenation, International Journal of Hydrogen Energy (2017), http://dx.doi.org/10.1016/j.ijhydene.2017.08.174

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Appendix A. Supplementary data Supplementary data related to this article can be found at http://dx.doi.org/10.1016/j.ijhydene.2017.08.174.

Nomenclature ci concentration of species i cMCH;inlet concentration of MCH at inlet of MCR constant-pressure heat capacity Cp € hler number Da Damko effective diffusivity of species i Di d diameter of CMR hydrogen molar flux FH2 FMCH;feed MCH molar flux at inlet of pre-reactor I unit matrix equilibrium constant for MCH dehydrogenation Keq k reaction rate constant thermal conductivity of fluid kt NH2 ;permeate molar flow rate of hydrogen flowing to permeate side NMCH;inlet molar flow rate of MCH at inlet of CMR NMCH;feed molar flow rate of MCH in pre-reactor NMCH;outlet molar flow rate of MCH at outlet of CMR P permeance of hydrogen-selective membrane  clet Number Pe Pe pressure of H2 pH2 pi partial pressure of species i pressure of MCH pMCH total pressure on permeate side pp total pressure on retentate side pr pressure of TOL pTOL R gas constant reaction generation rate of species i ri rMCH;inlet generation rate of MCH at inlet of CMR r density of fluid T temperature inside CMR temperature on permeate side as well as inlet side of Te CMR transpose operation for matrix T r . velocity of fluid u uavg; inlet averaged velocity of fluid at inlet of CMR V cat volume of catalytic layer V reactor volume of reactor volumetric flow rate at inlet of CMR vinlet catalyst loading in catalyst layer of CMR wcat DH heat of reaction involved in MCH dehydrogenation ε porosity of catalytic layer m viscosity of fluid k permeability of catalytic layer

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