Fixed bed membrane reactors for WGSR-based hydrogen production: Optimisation of modelling approaches and reactor performance

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 e n e r g y 3 7 ( 2 0 1 2 ) 4 9 9 7 e5 0 1 0

Available online at www.sciencedirect.com

journal homepage: www.elsevier.com/locate/he

Fixed bed membrane reactors for WGSR-based hydrogen production: Optimisation of modelling approaches and reactor performance Pablo Marı´n, Fernando V. Dı´ez, Salvador Ordo´n˜ez* Department of Chemical Engineering and Environmental Technology, University of Oviedo, Facultad de Quı´mica, Julia´n Claverı´a 8, E-33006 Oviedo, Spain

article info

abstract

Article history:

The production of high-purity hydrogen using the wateregas-shift reaction in both conven-

Received 26 July 2011

tional fixed bed reactor and hydrogen perm-selective membrane reactor at low to medium

Received in revised form

scale is studied in this work by developing and comparing models with different complexity

2 December 2011

levels. A two-dimensional rigorous reactor model considering radial and axial variations of

Accepted 5 December 2011

properties (including bed porosity), setting mass, energy and momentum differential

Available online 31 December 2011

balances, and nesting a rigorous model for mass transfer within the porous catalyst was considered as reference for comparison. Different simplifications of this model for taking into

Keywords:

account mass-transfer effects within the catalyst pellet (Thiele modulus, evaluation of

Pd composite membrane

apparent kinetic constants, empirical correlation for effectiveness factors or just neglecting

Hydrogen permeation

these effects) were tested, being observed that these effects are not negligible and that the first

Wateregas-shift reaction

two approaches are accurate enough for taking into account mass transfer within catalyst

Chemical reactor modelling

pellets. Regarding to the reactor model, it was observed that one-dimensional models are not

CFD

adequate, especially for the membrane reactor. Analogously, neglecting the momentum balances in the reactor (as made is most simulations reported in the literature) leads to important misspredictions in the behaviour of the membrane reactor performance. Finally, the influence of the main operation parameters (inlet temperature, pressure, space velocity, etc.) was studied using the detailed reactor model, concluding that space velocity and pressure are the most important parameters affecting reactor performance for membrane reactors. Copyright ª 2011, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved.

1.

Introduction

In the last decades, the interest for obtaining high-purity hydrogen as energy vector has increased considerably. Polymer electrolyte membrane fuel cells can produce electricity from hydrogen with extraordinary efficiency in comparison with the present energy conversion devices, and recent advances lead to important reductions in their investments costs. Therefore, hydrogen is likely to be a very

important clean energy vector in the next decades. However, hydrogen is a synthetic fuel that must be manufactured using another fuel or energy source. Today, the main raw materials for hydrogen manufacture are fossil fuels (natural gas and coal), although the interest for using renewable feedstocks (biomass, biogas, ethanol) has increased in the last years [1e4]. Gasification of solid fuels or reforming of methane and other organics lead to the formation of a syngas containing H2

* Corresponding author. Tel.: þ34 985 103 437; fax: þ34 985 103 434. E-mail address: [email protected] (S. Ordo´n˜ez). 0360-3199/$ e see front matter Copyright ª 2011, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.ijhydene.2011.12.027

4998

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 e n e r g y 3 7 ( 2 0 1 2 ) 4 9 9 7 e5 0 1 0

and CO. In the following stage, carbon monoxide is converted to H2 and CO2 by the reversible and exothermic wateregasshift reaction (WGSR): CO þ H2 O%CO2 þ H2

DHR ¼ 37:2 kJ=mol

(1)

Finally, hydrogen is purified: the remaining carbon monoxide is usually transformed into carbon dioxide by catalytic preferential oxidation. Traditionally, CO2 was removed by absorption or adsorption, leading to pure hydrogen that matches the requirements of the common polymer electrolyte membrane fuel cells [5e8]. At industrial scale, the wateregas-shift reaction is conducted in two intercooled separate reactors. The first reactor operates at high temperature (350e600  C) with a Fe2O4eCr2O3 catalyst, whereas the second one works with a CuO/ZnO catalyst at lower temperature (150e250  C), in order to shift the equilibrium. In the last years, new catalysts have been developed, especially tailored for different applications, i.e. if more active catalysts are used the two reactors can be replaced by one operating at an intermediate temperature [6,9]. Membrane reactors are integrated devices in which reaction and controlled mixing or separations take place in the same equipment. The use of membrane reactors with a hydrogenselective membrane can reduce considerably the stages required for the hydrogen manufacturing process described previously. Thus, the membrane removes hydrogen directly from the reaction medium, shifting the wateregas-shift reaction equilibrium towards hydrogen formation. In this way, high conversion can be achieved in one single reactor, even at relatively high temperatures (350e450  C) and with lower steam. In addition, hydrogen is recovered in the permeate side of the membrane reactor with high purity (depending on the membrane selectivity), so it is not necessary to use expensive stages for hydrogen purification. On the other hand, membrane reactors also enable the recovery of concentrated CO2 streams, enabling carbon sequestration options and yielding to low carbon footprint hydrogen production (when using fossil fuels) or even negative carbon footprints (if biomass is used as raw material). The membrane reactor usually consists of a multitubular device, where the catalytic bed can be situated inside or outside the tubes. The tubes are constructed in a composite material formed by different layers, one of them being selective for the permeation of hydrogen. The influence of the membrane nature and manufacture procedure has been extensively studied, concluding that Pd-based membranes are the most permeable and selective to hydrogen [3,4,7,10,11]. The wateregas-shift membrane reactor has been studied in several works, both experimentally and using numerical simulations. Simulation is a very powerful tool for studying these reactors, but the utility of the results obtained depends on the accuracy of the model used. Most models proposed in the literature are oversimplified or only valid for small devices, as recently stressed by different authors [4,8], no general guidelines for model selection being provided. Taking into account the number of space dimensions considered, One-dimensional (1D) models (only considering properties variation in the reactor axial coordinate) are the most commonly used in the modelling of membrane reactors [12e20], because they are mathematically simple and easy to solve. However, membrane reactors present non-negligible variation also in the radial axis because of the permeation of

hydrogen and the heat transfer through the membrane. For this reason, the use of 1D models is rather questionable, as they can predict, for example, higher hydrogen permeation rates or lower maximum reactor temperatures (which can affect seriously catalyst stability). On the other hand, bi-dimensional models (2D) are accurate enough to model both axial and radial profiles inside the reactor, and this way the influence of the membrane on the reactor behaviour is fully modelled. The use of this type of model is scarcer [21e24], mainly due to the need of more sophisticated software tools to solve the set of partial differential equations. The highest complexity regarding space dimensions is obtained with the tri-dimensional (3D) models [25,26] that model the entire reactor geometry. These models take into account profiles in the angular direction, so their use is not justified unless they are applied to highly non-symmetrical reactors. The second point to be considered in the model is the number of conservation equations, corresponding to the transport phenomena considered, i.e. mass, energy and momentum balances. The use of the first two balances is common in most published studies, but the momentum balance has only been considered in a small number of works, regarding wateregasshift membrane reactor [21,27e30]. However, in membrane reactors flow rate changes along the reactor, due to permeation through the reactor wall. In addition, it is common that in membrane reactors ideal plug flow cannot be assumed, mainly because of two circumstances: the use of small reactor diameters in order to provide enough membrane area, and the use of a catalyst particle size high enough to avoid extremely high pressure drops in the reactor. In these situations, the porosity of the catalyst packed-bed is not uniform, increasing at the vicinity of the membrane wall. This produces a non-ideal flow pattern that can be modelled using the momentum balance. Other point rarely addressed in the simulation of this kind of reactors is the influence of intra-particle mass-transfer effects. Most reported works neglect these effects, although they can be important because of the fast kinetics of this reaction. It should be also noted that the common application of the Thiele modulus is not applicable because the WGSR kinetics cannot be considered as first order. In the present work, the adequacy of rigorous and simplified models for simulation of the wateregas-shift reaction in fixed bed and membrane reactor is analysed. The performance of different models is compared at the catalyst and reactor scales, and guidelines for the selection of models adequate for designing industrial scale reactors are given. The selected model, that best balances accuracy and complexity, is then used for studying the behaviour of the membrane reactor in detail; specifically, the influence of the most important operating conditions is studied using a systematic design of simulations.

2.

Methodology

2.1.

Reactor model

The multi-tubular fixed bed catalytic reactor is a complex device where different phenomena (chemical reaction, mass, heat and momentum transport) take place at different length

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 e n e r g y 3 7 ( 2 0 1 2 ) 4 9 9 7 e5 0 1 0

scales (e.g. reactor bed and catalyst particle). In addition, when this reactor is combined with a selective membrane wall, the complexity of the system, and hence the complexity of the model, increases. In this work, the catalyst is considered to be placed inside the reactor tubes, and for simplicity, only one tube is modelled. In addition, properties of the fluid in the shell side are considered to be uniform. These assumptions are commonly considered in the modelling of multi-tubular fixed bed reactors [31e33]. Fixed bed catalytic reactors contain fluid and catalyst solid particles. The modelling of each individual particle of the reactor bed is a very complicated and computing time consuming task [34,35]. For this reason, the bed is usually considered as a continuous medium, analogous to a single phase, with physical properties being also continuous. The behaviour of this pseudo-homogeneous bed is described by the conservation equations, obtained from mass, energy and momentum balances, as indicated in Table 1. In the mass and energy balances, the terms account, in this order, for convection, dispersion and generation. The meaning of the symbols is indicated in the notation section. For randomly and homogenously distributed packed-beds, physical properties rarely change in the angular direction of the bed, resulting in the socalled axi-symmetric bi-dimensional model, with only two independent variables at steady-state conditions: the radial (r) and axial (z) coordinates. The boundary conditions required to solve these equations are listed in Table 2. When applied to membrane reactors, the membrane is modelled through the boundary condition corresponding to the wall, r ¼ DR/2: in the mass balance using the component boundary flux (Ji) and in the momentum balance using the membrane surface velocity (um). This means that the membrane creates an additional coupling between mass and momentum balances. In 2D fixed bed reactor models, mass and heat effective dispersion coefficients are very important parameters, particularly the ones corresponding to the radial direction, which account for mass and heat transported thought the reactor wall/ membrane. These parameters must be determined accurately, using correlations specifically developed for 2D models, as shown in Table 3. Thus, mass transfer is modelled by means of Fick’s law (see Table 1), but using effective dispersion coefficients to account for turbulence and non-ideal flow. The component-mixture diffusion coefficients (Dim) are calculated from the binary diffusion coefficients (Dij) using the Wilke equation [36,37]. The binary diffusion coefficients (Dij) are determined using the correlation of Fuller; the equation and the physical properties needed are widely described in the literature

Table 1 e Conservation equations applied to the simulation of the fixed bed membrane reactor. Mass balance   0 Dier ; i ¼ 1.C  1 uVci þ VðDie Vci Þ þ aNip ¼ 0; Die ¼ 0 Diez Energy balance   ker 0 rG CPG uVT þ Vðke VTÞ þ aqP ¼ 0; ke ¼ 0 kez Momentum balance    m m Vu þ ðVuÞT u ¼ V$  pI þ KE εb Continuity equation VðrG uÞ ¼ 0

4999

[37]. The effective axial and radial thermal conductivities (Table 3) are calculated including two terms, one accounting for the bed thermal conductivity in the absence of flow (kb0), and another for the gas flow depending of the direction [21]. Table 3 also lists the correlations used to calculate gas to catalyst particle mass and heat transfer coefficients. Physical properties appearing in the equations in Tables 1and 3, such as viscosity, thermal conductivity and heat capacity, are determined using empirical correlations from the literature for the pure compounds and the mixture-average expressions to determine the property of the mixture [37]. Other geometrical and physical properties for the catalyst bed and membrane are listed in Table 4. Heat transferred through the reactor wall/ membrane depends on three heat transfer resistances, corresponding to the catalyst bed, membrane or reactor wall, and permeate on the shell side. The first is calculated using the radial heat effective dispersion coefficient of the 2D model; the second can be neglected when the membrane is made of a material with high thermal conductivity (e.g. stainless steel). The last one is modelled using a heat transfer coefficient (hw), which for a gas at the pressure and temperature range considered in this work, is found to be around 100 W/m2 K. The temperature of the shell/permeate side is considered to be equal to the corresponding tube inlet temperature. The momentum balance in Table 1 corresponds to the socalled Brinkman equation, which is a modification of the general NaviereStokes equation taking into account free flow and flow in porous media. The original Brinkman equation was formulated using the Darcy hydraulic permeability (KD), which for spherical randomly distributed particles can be calculated as follows: KD ¼

d2p ε3b

(2)

150ð1  εb Þ2

As the Darcy hydraulic permeability is only valid for the laminar region (Re < 10), it may overestimate friction losses at high flow rates. For this reason, the Ergun hydraulic permeability (KE), valid for both the laminar and turbulent regions, has been used instead. The following expression, derived from the Ergun equation, has then been used in the model [38]: KE ¼

1 ; 1 CE rG juj þ 1=2 KD KD m

1:75 1 CE ¼ pffiffiffiffiffiffiffiffi 2 150 εb

(3)

The use of the Brinkman equation in the 2D model allows the calculation of the friction losses caused both by the packed-bed and the reactor wall, the last one being only important at the vicinity of the wall. Moreover, in packed-bed reactors the bed porosity near the reactor wall is higher, which results in an increase in the local gas velocity. This effect is more marked in reactors with low reactor diameter to catalyst diameter ratio (DR/dp < 10); this is the case of the membrane reactor considered here. In these situations, the plug flow assumption (flat radial velocity profile), is not satisfied, and for this reason the use of Brinkman equation, instead of Darcy equation, is recommended. In order to determine the actual velocity radial profile, the Brinkman equation must be solved using an appropriate expression for the radial porosity distribution [39], where εb0 is the average bed porosity:

5000

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 e n e r g y 3 7 ( 2 0 1 2 ) 4 9 9 7 e5 0 1 0

Table 2 e Boundary conditions applied in the solution of the continuity equations for the fixed bed membrane reactor. Boundary

Mass

z¼0 0 < r < DR/2 z ¼ LR 0 < r < DR/2 r¼0 0 < z < LR No membrane r ¼ DR/2 0 < z < LR Membrane r ¼ DR/2 0 < z < LR

Energy

u¼

n$ðDie Vci Þ ¼ 0

n$ðke VTÞ ¼ 0

p ¼ pout

n$ðDie Vci þ εb ci uÞ ¼ 0

n$ðke VT þ εb rG CPG T uÞ ¼ 0

n$u ¼ 0

n$ðDie Vci þ εb ci uÞ ¼ 0

n$ðke VTÞ ¼ hw ðT  Tsh Þ

n$u ¼ 0

n$ðDie Vci þ εb ci uÞ ¼ Ji

n$ðke VTÞ ¼ hw ðT  Tsh Þ

u¼



PC

i¼1 Ji =CGm ;

Ji ¼ 0;

(4)

The source terms of the mass and energy balances in Table 1 take into account chemical reaction in the bed. The rigorous calculation of these terms requires the determination of intraparticle concentration and temperature profiles, by solving the solid mass and energy balances in Table 5. These balances account for the external mass and heat transfer (using the gas to solid mass and heat transfer coefficients of Table 3, KGi and hG), the mass and heat diffusion inside the porous catalyst particle, and the reaction kinetics. The chemical reaction term corresponds to the intrinsic kinetics (rvc), calculated using the following expression obtained by Keiski et al. [40] for a Fe3O4eCr2O3 commercial wateregas-shift catalyst: the intrinsic kinetic parameters (A and B) obtained under diffusion

Table 3 e Transport properties used to solve the conservation equations of the bi-dimensional reactor model. Transport properties

Refs.

Mass transfer   pffiffiffiffiffiffiffiffiffiffiffiffiffi jujdp Diez ¼ 1  1  εb Dim þ 2   pffiffiffiffiffiffiffiffiffiffiffiffiffi jujdp Dier ¼ 1  1  εb Dim þ 8 1 Dim ¼ C X yj j¼1 Dij jsi   D 1=3 KGi ¼ im 2 þ 1:1 Re0:6 Sci dp

ker ¼ kb0 þ kG

  RePr 1:4 

um 0





isH2

Catalyst particle model

kez ¼ kb0 þ kG

0 u0

T ¼ Tin

 3  εb ¼ εb0 þ ð1  εb0 Þexp  ðDR  2rÞ dp

Heat transfer



ci ¼ yi, in CG,in

u0 ¼ GHSV$LR(Tin/273)(1.01/pin), um ¼

2.2.

Momentum

free experimental conditions are reported in Table 6. This kinetic expression is a general power-law equation, representative of the expressions commonly used for this reaction.   B ð1  bÞ; k ¼ expðAÞexp  rvc ¼ rS km cnCO cm (5) m H2 O T b¼

cCO2 cH2 ; cCO cH2 O Keq

Keq ¼ exp

  4577:8  4:33 T

(6)

The component-mixture effective diffusion coefficient (Diep) has been calculated considering bulk and Knudsen diffusion inside the catalyst pore network. The porous solid properties used in the calculations are those reported by Keiski et al. [40] (Table 4). Once concentration and temperature particle profiles have been determined from the equations in Table 5, the source terms of the conservation equations in Table 1 are determined using the following relationships: vcpi ; i ¼ 1.C (7) NiP ¼ Diep vx x¼dP =2 qP ¼ kep

vTP vx x¼dP =2

(8)

It should be noted that the equations Tables 1 and 5 are nested through the previous relationships. This means that

[27] [27] [36]

[37]

[21] 

RePr

[21]

2

8:65½1 þ 19:4ðdP =DR Þ       0:280:757logðεb Þ0:057log kS kS kG kb0 ¼ kG kG   kG hG ¼ 2 þ 1:1 Re0:6 Pr1=3 dP

[21]

[37]

Table 4 e Catalyst physical properties and membrane permeation model taken from the literature to solve the membrane reactor models. Catalyst properties [40] Active phase Fe3O4eCr2O3 Shape Spherical 2$103 m dP 0.4 εb0 1945 kg/m3 rS CPS 880 J/kg K 0.3 W/m K kS 9$109 m hdpore i 0.48 εint 4 sint Membrane properties [42] 8.6$106 m dPd Q 1.02$107 exp (8.2$103/RgT ) mol/m s Pa0.5

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 e n e r g y 3 7 ( 2 0 1 2 ) 4 9 9 7 e5 0 1 0

Table 5 e Solid particle model solved nested to the conservation equations of the reactor scale. Mass balance   1 v vc vc vc KGi ðC Cpi jx¼dP =2 Þ; x2 Diep Pi ¼vi rvc ; Pi ¼0; Pi ¼ 2 vx vx x¼0 vx x¼L Diep jx¼dP =2 i x vx i¼1.C Energy balance   1 v vTP vTP vTP hG ¼0; ¼ ðTTP jx¼dP =2 Þ ¼rvc DHR ; x2 kep vx vx x¼0 vx x¼L kep jx¼dP =2 x2 vx

a different set of solid balance equations must be solved at every point of the reactor 2D geometry.

2.3.

Membrane permeation model

Hydrogen permeation membranes usually consist of a composite material formed by different layers: a support (porous ceramic or stainless steel), an interphase (optional) to improve the surface properties of the support and avoid reaction or blending between the support and the active layer, and the active layer, responsible from the membrane selectivity (a thin dense layer of Pd or Pd alloy). Several studies have been carried out to improve the membrane preparation and performance [7,41]. In the present work, a PdeAg/ceramic membrane prepared by electroless plating has been considered. Membrane preparation, characterization, permeation experiments and modelling are described by Guo et al. [42]. They found that the main mass transfer resistance associated to hydrogen permeation was the diffusion in the Pd alloy layer. In this case, hydrogen flux can be modelled using Sievert’s law, where the fitted model parameters are listed in Table 4: JH2 ¼

QPd 0:5 ðp  p0:5 H2 ;shell Þ dPd H2 ;tube

2.4.

(9)

Model resolution

The described model is complex, because it requires solving the catalyst particle model nested within the reactor model, requiring high computer power and time. Because of this, it is common to use simplified models. In this work, the adequacy of different model simplifications for both catalyst particle and reactor is evaluated. Depending on the simplification considered, different numerical methods and software tools have been found to be appropriated for solving the model.

Table 6 e Parameters of the wateregas-shift reaction rate models: intrinsic from the literature and apparent obtained by simulation of the solid particle model. Intrinsic

Apparent 3

dP ¼ 1$10 A B (K ) n m SSE R2adj

8.22a 8008 0.54 0.10

m dP ¼ 2$103 m dP ¼ 3$103 m

2.20  0.05 4581  36 0.596  0.007 0.205  0.006 6.4$103 0.994

a SI units, different from [40].

0.974  0.04 4140  28 0.606  0.005 0.209  0.005 1.3$103 0.996

0.406  0.04 4003  27 0.609  0.005 0.209  0.005 5.75$104 0.996

5001

MATLAB: a code written in MATLAB (v. 7.10.0, R2010a) is able to solve the mass and energy balances of the reactor model (Table 1) in a 1D or 2D axi-symmetric geometry, together with the complete catalyst particle model (Table 5). The reactor model is solved using the ’method of lines’, with the help of the pdepe MATLAB function. This numerical method is based on the approximation of the reactor radial profiles in a grid of nodes (30 nodes was found to be enough to ensure a grid-independent solution), and then the resulting set of ordinary differential equations is solved for the reactor axial coordinate using a stiff solver. The catalyst particle model consists of a set of boundary value ordinary differential equations, solved at every point of the reactor scale geometry using the bvp4c MATLAB function. COMSOL: The software COMSOL Multiphysics (v. 4.0) is used when the reactor model is completed with the momentum balance, which is of particular interest for simulating the membrane reactor. This software solves the complete set of conservation equations of the reactor model (Table 1) by the ‘finite element method’. However, it is not possible to solve the nested equations corresponding to the catalyst particle model at the same time, and for this reason a simplified catalyst particle model will be used in this case. These software have been used to model membrane and fixed bed reactors with satisfactory results in previous works [6,33].

2.5.

Surface response model

Once the adequacy of different model simplifications has been determined, the optimised membrane reactor model is used for studying the influence of five of the main variables on the reactor performance. The simulation study has been performed systematically using the simulation cases proposed by a BoxeBehnken design of experiments. The surface response design is done in three levels, where the variables are evaluated at 3 equally-spaced values (lower, middle and upper). In a complete surface response design of three levels, the combination of all the levels creates 35 ¼ 243 simulation cases. Using the BoxeBehnken design, each pair of variables is combined at the lower and upper levels, whereas the rest of the variables are maintained in the middle level. This way, the number of simulation cases is highly reduced in comparison to the complete surface response design (to 40 simulations in this case), and the cross influence between variables is also taken into account. This study was conducted for both the fixed bed and the membrane reactor. Once the BoxeBehnken design was solved, the performance variable (CO outlet conversion) was fitted to a surface response model as a function of the study variables. The surface response model consisted of a second order polynomial with terms accounting for the effects of the pure variables and their interactions. All the possible terms were initially considered, but only the terms found statistically significant were considered in the final model.

3.

Results and discussion

3.1.

Analysis of simplified catalyst particle models

In this section, different simplified catalyst particle models are proposed in order to eliminate the need of solving the nested

5002

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 e n e r g y 3 7 ( 2 0 1 2 ) 4 9 9 7 e5 0 1 0

catalyst particle mass and energy balances (Table 5) together with the reactor model. The performance of these models for the case of the wateregas-shift reaction is evaluated by comparison with the rigorous catalyst particle model presented in the methodology section, and labelled here as model A. Depending on the adopted strategy, different simplified models, labelled from B to E, are considered, as explained as follows:

3.1.1.

Model B: generalized Thiele modulus

This model has been successfully applied for several reactions, such as the oxidation of SO2 or the synthesis of methanol [43]. Basically, the catalyst particle reaction term is substituted by the intrinsic reaction rate, evaluated at the catalyst surface conditions, and an effectiveness factor (h): NiP ¼ KGi ðCi  CSi Þ ¼ 

qP ¼ hG ðT  TS Þ ¼

vi h rvc jcSi ;TS aS

;

i ¼ 1/C

DHR h rvc jcSi ;TS

(10)

(11)

aS

The effectiveness factor is calculated using the analytical expression for first order reactions, but using a generalized Thiele modulus (f), defined as follows for spherical catalyst particles:   ðdP =6Þð  rvc jcsi Þ 1 1 1 (12)  ; f¼ h¼  1=2 Zcis f tanhð3fÞ 3f 2 Diep ðrvc Þ cieq

3.1.2.

Model C: simulated apparent reaction rate

This model uses an apparent reaction rate expression that takes into account the influence of mass and heat transfer resistances inside the catalyst particle [44]. Lim et al. [45] studied the mass transfer inside the catalyst pellets for the wateregas-shift reaction and a noble metal catalyst using this methodology. However, unlike intrinsic kinetic parameters, the apparent ones depend on the actual catalyst shape and size, and on the operating conditions. In the present work, the catalyst particle balances (Table 5) have been solved separately from the reactor model for different operating conditions: gas temperature (300e500  C), pressure, (1e3 bar), CO molar fraction (0.05e0.25, dry basis), and H2O to CO molar ratio (1e10). A total of five equally-spaced values within the previous ranges are considered for each variable, resulting by combination in 54 ¼ 625 simulation cases. The apparent reaction rate is determined from the simulations, and then fitted to a kinetic equation with the same mathematical form as the intrinsic one. This procedure is repeated for three different catalyst particle diameters (1, 2 and 3 mm), the resulting apparent kinetic parameters being listed in Table 6. It has been found that the fittings are very good in the three cases, with low standard square errors (SSE ) and adjusted regression coefficients higher than 0.99. For this reason, this procedure seems to be a reliable alternative to the rigorous catalyst particle model. However, extrapolation out from the range considered for the operating variables should be avoided.

3.1.3.

Model D: simulated effectiveness factor

In this case, the results of the catalyst particle balances performed in the previous section have been used to calculate the effectiveness factor. Then, the calculated effectiveness factor has been fitted to an empirical expression depending on the

most relevant operating variables, eq. (13). This methodology has been successfully used to model internal mass transfer by fitting experimental data by other authors [44]. h ¼ 1:955 þ 0:00540 cCO þ 0:00131 cH2 O  0:00199 TG  133:5 dP

3.1.4.

(13)

Comparison of the catalyst particle simplified models

The simplified catalyst particle models have been tested by including them in the reactor model. The reactor model considered includes the mass and energy balances in 2D axisymmetric geometry, and is solved in MATLAB for the operating conditions reported in Table 7. The wateregas-shift reaction is considered the only reaction taking place, and for simplicity, the reactor is considered as fixed bed with no membrane. Feed composition corresponds to that of a coal or biomass derived gas reforming [12,46]. For this reason, there is an important amount of hydrogen in the feed (40% dry basis, Table 7). A steam to carbon monoxide molar ratio of 2 has been selected, which is a good balance. Simulations results are summarized in Fig. 1. For comparison purposes, results corresponding to the absence of catalyst model have also been included, labelled as model E (intrinsic reaction rate obtained under diffusion free conditions) [40]. Results show that when using the intrinsic reaction rate, the mean CO conversion and temperature profiles are considerably over predicted. This means that the wateregasshift reaction, relatively fast, mass and heat transfer inside the catalyst particles cannot be neglected at the conditions considered, as it is sometimes done [16,21,47]. Differences between the simplified catalyst models (model B to D) and the rigorous one (model A) are rather slight. Thus, model B overlaps completely model A, which means that the model based on the generalized Thiele modulus can be used instead of the rigorous model, with no relevant discrepancies. Model C overpredicts slightly both CO conversion and temperature, but the discrepancies are within the error of the properties and correlations used in the simulation. Finally, the discrepancies observed for model D are higher. In our opinion, model C offers a good balance between precision and simplicity, as it is based on the use of a simulated apparent reaction rate, and for that reason is the one selected to model the catalyst particle in further studies.

3.2.

Analysis of simplified reactor models

In this chapter, we will focus on the different reactor models that can be used to simulate the membrane reactor. The

Table 7 e Main simulation parameters used to solve the conservation equations. LR DR GHSV Tin pout H2O:CO dry yCO dry

0.5 m 0.0127 m 30 000 h1 (n.t.p) 400  C 3 bar 2 0.20 0.20

dry

0.40

dry

0.20

yCO2 yH2

yN2

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 e n e r g y 3 7 ( 2 0 1 2 ) 4 9 9 7 e5 0 1 0

Fig. 1 e Comparison of different catalyst particle models A, B, C, D and E) for simulations obtained ( with reactor model 2. (a) Mean CO conversion axial profile. (b) Mean temperature axial profile.

influence of the number of dimensions and conservation equations considered in the model is analysed by comparing the results of three different models (labelled from 1 to 3). Model 1 is the most complex, formed by the equations in Table 1 solved in 2D using COMSOL software. A first simplification of model 1 consists of neglecting the momentum balance, which results in model 2. Model 3 is obtained if model 2 is solved in 1D geometry, instead of 2D. Models 2 and 3 are solved using the MATLAB code described in the methodology section. For comparison purposes, the simulations have been performed also for a conventional fixed bed reactor (with no membrane), and using the catalyst particle model C. The operating conditions and physical properties are reported in Table 4 and Table 7. Fig. 2 compares the models using as measure of the reactor performance the calculated mean CO conversion and temperature profiles. The higher discrepancies are found in the temperature profile. Model 3 clearly underpredicts temperature with respect to the other two. The wateregas-shift reaction is exothermic, so the heat released in the reactor bed is transported in the radial direction thorough the catalyst bed and reactor wall to the shell side of the multi-tubular reactor, which is at lower temperature. As model 3 is 1D, it assumes uniform temperature in the radial coordinate, neglecting the bed heat transfer resistance and resulting in a lower bed temperature. The discrepancies between 1D and 2D models increase as reaction enthalpy increases. Besides this, 1D models cannot predict the higher temperature attained at the reactor axis. Then, using 1D models is particularly dangerous for highly exothermic reactions, where unpredicted hot spots can damage the catalyst or the reactor [33]. The discrepancies between 1D and 2D models may also be important for endothermic reactions; Oyama et al. [48], who studied the methane steam reforming reaction, concluded that in membrane reactors radial gradients become relevant within a wider range of

5003

Fig. 2 e Comparison of different reactor models ( 1, 2 3) for the simulations obtained using the apparent and reaction rate simplified catalyst model C. (a) Mean CO conversion axial profile. (b) Mean temperature axial profile.

operating conditions than in non-membrane reactors, and they proposed a general criterion to identify this situation. Model 2 slightly overpredicts temperature with respect to model 1, the most rigorous. Since both models are 2D, the observed differences are due to the momentum balance. Thus, model 1 calculates the “exact” radial and axial velocity profiles, taking into account not only pressure drop, but also the higher bed porosity near the reactor wall. As explained in the methodology section, for fixed bed reactors with small diameter the radial velocity profile is far from plug flow. The influence of this phenomenon on the reactor performance is more marked when the diameter of the reactor is small, which is usually the case for membrane reactors. When the reactor wall is a membrane, the momentum balance is also required to take into account the effect of permeation on the axial velocity. Summarizing, on one hand, the use of a 1D model underpredicts reactor temperature, which can be a problem with highly exothermic reactions. On the other hand, the use of the momentum balance in 2D models is necessary to model accurately all the transport processes taking place, especially for membrane reactors of small diameter. For this reason, the complete 2D axisymmetric model (model 1) is used in the present work. This and other similar models have been validated with experimental data for various reactions (in same cases for membrane reactors): wateregas-shift reaction [18,32], steam reforming of methane [48] and methanol [49], or butane partial oxidation [33], among others. It should be noted that only a few authors [21] consider the momentum balance in the modelling of the membrane reactor for the case of the wateregas-shift reaction. For this reason, the results obtained with this model in the present work and discussed in the following section, are very interesting in order to understand the behaviour of these reactors.

5004

3.3.

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 e n e r g y 3 7 ( 2 0 1 2 ) 4 9 9 7 e5 0 1 0

Analysis of the membrane reactor

In the previous sections, it was concluded that a 2D axisymmetric model for the reactor, consisting of the mass, energy and momentum balances, together with a simplified catalyst particle model based on the simulated apparent reaction rate (model 1C), presents a good balance between complexity and accuracy for the simulation of the wateregas shift reaction taking place in membrane reactors. In this section this model is used for comparing the performance of a membrane reactor (MR) and conventional fixed bed (FB). Operating conditions and physical properties used for this study are listed in Table 4 and Table 7. Surfaces in Figs. 3 and 4 depict, respectively, the temperature and hydrogen molar fraction profiles for the MR (left graph) and FB (right graph). The importance of radial profiles for the membrane reactor can be clearly observed in these plots, supporting the adequacy of using 2D models. Fig. 5 shows the variation of the conversion, temperature, gas velocity and parameter b average axial profiles. Parameter b, defined in eq. (6), measures the approach to the equilibrium of the system, and depends on the concentrations of reactant and products and temperature (the higher the value of b the closer to equilibrium, b ¼ 1 corresponding to equilibrium). It can be observed that the membrane reactor clearly exhibits a better performance in terms of CO conversion (99% and 59%, respectively, for the reactor with and without membrane). In both reactor configurations, temperature exhibits a maximum a little before the middle of the reactor in the axial direction (z ¼ 0.20 m). The maximum temperature is quite different in both reactors, 450  C with membrane and 436  C without membrane. This maximum is a consequence of the balance between the heat evolved by the exothermic reaction

and the heat transported through the reactor wall. Conversion up to the point of maximum temperature is higher for the membrane reactor (75% for the MR and 40% for the FB, see Figure 5-a), and for this reason the maximum temperature is higher for this reactor. At the end of the reactor (z > 0.4 m), it is observed that the average temperature of the membrane reactor decreases below that of the fixed bed reactor (Figure 5-c). In this region, the heat released by the reaction is very little for the membrane reactor (conversion changes from 97% to 99%), and the heat transferred through the membrane is enough to decrease the temperature to 409  C by the end of the reactor. Fig. 4 shows the surface plots corresponding to the hydrogen molar fraction; the differences between the reactor with and without membrane are very important. Thus, in the MR hydrogen molar fraction decreases along the bed length, due to the permeation through the membrane, no maximum being observed. This means that the average permeation rate (80.6 mol H2/m3bed s) is higher than the average reaction rate (20.4 mol H2/m3bed s). The reactor has been designed this way, as the reactor feed contains 40% mol (dry basis) hydrogen that should be recovered by permeation through the membrane. In the reactor without membrane, hydrogen molar fraction increases gradually, as corresponds to a reaction product. This difference is responsible of the higher conversion achieved in the membrane reactor (Figure 5-a), due to the positive effect of removing hydrogen in the equilibrium of the wateregas-shift reaction equilibrium. Figure 5-d shows that b is lower for the membrane reactor, decreasing as hydrogen permeation increases, and increasing as temperature increases. The observed behaviour results of the opposing effect of both factors. It is also important to consider that hydrogen

Fig. 3 e Reactor simulated (model 1C) temperatures profiles. (a) Membrane reactor. (b) Conventional fixed bed 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 e n e r g y 3 7 ( 2 0 1 2 ) 4 9 9 7 e5 0 1 0

5005

Fig. 4 e Reactor simulated (model 1C) hydrogen molar fraction profiles. (a) Membrane reactor. (b) Conventional fixed bed reactor.

permeation concentrates all the other compounds in the mixture, which also decreases the value of b parameter. At the end of the reactor (z > 0.4 m), CO conversion is very high (>95%) and CO concentration is very low, which results in a steep increase in b, even matching the b obtained for the reactor

without membrane. This means that at the end of both reactor types the fractional approach to the equilibrium is the same, but with very different conversion. The performance of the membrane is analysed in Fig. 6. Hydrogen flux (Figure 6-a) decreases from the reactor inlet to

Fig. 5 e Comparison of reactor average axial profiles for: conversion (a), velocity (b), temperature (c), and b (d). ( reactor. ( ) Conventional fixed bed reactor.

) Membrane

5006

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 e n e r g y 3 7 ( 2 0 1 2 ) 4 9 9 7 e5 0 1 0

a

b

ðRj ¼ ðDpH2 Þj =JH2 Þ. At the beginning of the bed, where the total driving force is high and hence the hydrogen flux, the most important mass transfer resistance is the one corresponding to the membrane. Along the reactor, hydrogen flux decreases and the relative weight of the mass transfer resistances reverses. Results indicate that both mass transfer resistances are relevant and that the bed mass transfer resistance will influence negatively the hydrogen flux even if a membrane with high permeability is used. Bed resistance depends mainly on the radial effective dispersion coefficient and the reactor diameter, being more relevant for reactors with large diameters. This issue should be taken into account in the reactor design, requiring the use of 2D models, as the one considered in the present work.

3.4.

c

Fig. 6 e Membrane performance for the simulated membrane reactor (model 1C). (a) Hydrogen flux axial profile ( ). (b) Hydrogen partial pressure axial profiles in the centreline ( ), in the membrane surface ( ) and in the permeate side (e e). Hydrogen partial pressure driven force: (1) bed and (2) membrane. (c) Mass transfer ) and total ( ). resistances: Bed ( ), membrane (

the outlet, as a consequence of the decrease in the driving force (hydrogen partial pressure). Figure 6-b depicts hydrogen partial pressure axial profiles at different radial positions (centreline, r ¼ 0, membrane surface, r ¼ DR/2, and permeate side). The presence of radial hydrogen concentration gradients, also evidenced in Figure 4-a, suggests that the resistance associated to the gas phase hydrogen mass transfer in the bed is important, and cannot be neglected in the modelling of this membrane reactor at the considered operating conditions. Figure 6-c illustrates the two mass transfer resistances: the corresponding to the gas phase mass transfer in the catalytic bed (labelled as 1), and to the membrane (labelled as 2). The resistances have been calculated using the hydrogen flux and the corresponding driven force

Surface response study

In the previous sections, the optimum membrane reactor model was identified (model 1C), and studied in detail at fixed operating conditions. In the present section, this model is used to study the reactor performance when varying five important variables, selected within the most relevant for the reactor operation, and affecting both the catalytic reaction and the reactor performance, namely: feed inlet temperature, outlet pressure, space velocity, hydrogen partial pressure in the permeate side, and catalyst particle diameter. As indicated in the methodology section, the variable study has been carried out systematically using a BoxeBehnken design of experiments to determine the most appropriate simulations. The levels considered for each of the study variables are indicated in Table 8. The simulations proposed by the design of experiments have been carried out for the membrane and fixed bed reactors. The results from the simulations have been compared in terms of CO outlet conversion, taken as performance variable. By fitting CO outlet conversion to a surface response model as a function of the study variables, the statistical weight of each one of the selected study variables is quantified. Since three levels were considered for each study variable, a second order polynomial surface response model with all the interaction terms can be fitted. Table 9 summarizes the terms found to be statistically significant (95% confidence) and the corresponding regression coefficients. Thus, all the first order terms (e.g. Tin, pout, GHSV, pH2 permeate , and dp) and most second order pure terms were found to be important (e.g. T2in , .) for both the membrane and fixed bed reactors. Regarding the interactions, only four were found to be significant enough for the models, and, remarkably two of them (Tin$GHSV and Tin$dP) are common for the membrane and fixed

Table 8 e Variables selected to study the reactor performance using the BoxeBehnken and cross designs. Variable Tin pout GHSV pH2 permeate dP

Units

Lower value (1)

Middle value (0)

Upper value (1)

C bar h1 @ s.t.p. bar mm

350 1 15 000 0.02 1

400 3 30 000 0.06 2

450 5 45 000 0.1 3



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 e n e r g y 3 7 ( 2 0 1 2 ) 4 9 9 7 e5 0 1 0

Table 9 e Simplified model parameters obtained by fitting the simulations from the BoxeBehnken design. Membrane reactor Term

Fixed bed reactor

Coefficient

Constant Tin pout GHSV dP (Tin)2 ( pout)2 (dP)2 Tin $GHSV Tin $dP pH2 permeate (GHSV)2 SE R2adj

1

1.045$10 4.51$103 2.33$101 8.99$106 1.64$101 8.14$106 2.74$102 2.11$102 4.26$108 5.71$104 5.70$102 1.61$1010 0.067 0.929

Term

Coefficient

Constant Tin pout GHSV dP (Tin)2 ( pout)2 (dP)2 Tin$GSHV Tin$dP Tin$dout pout$GSHV SE R2adj

1.006 9.47$103 5.09$101 4.45$105 3.61$101 1.40$105 3.08$102 2.10$102 7.23$108 9.65$104 7.95$104 2.74$106 0.0285 0.940

* SE: standard error.

bed reactor. This is explained because these interactions depend mainly on the reaction, rather than on the membrane. Despite its simplicity, the proposed surface response models were found to fit reasonably well the results of the simulations with the rigorous model (adjusted regression coefficient higher than 0.9, error always well below 10%). The residuals and parity plots of Fig. 7 show that the surface response model corresponding to the fixed bed reactor model provides a better fitting. This type of surface response models is recommended to predict the reactor behaviour within the range of variables, i.e. for preliminary reactor design or optimization purposes. The use of the rigorous model is recommended for the final design.

3.5.

Analysis of the main reactor variables

In this section, the variable study is extended with additional simulations of the rigorous model for the same levels of Table 8. The study variables are first evaluated at the middle level, and then the levels are varied one variable each time, while maintaining the rest of variables in the middle level. The aim is to obtain a new design of experiments with cross shape, easier to compare graphically, and to provide additional simulations to which compare the performance of the surface response model fitted in the previous section.

5007

Fig. 8 shows, in terms of CO outlet conversion, the results of the additional simulations (symbols) and the corresponding predictions of the surface response model (lines). Considering that the surface response model was fitted using only the simulations of the BoxeBenhken design of experiments, Fig. 8 can be used to illustrate the accuracy of the model against additional simulations. As shown, the surface response model exhibits good performance for all the additional simulations, except for the lowest outlet pressure. The influence of temperature, relevant in reversible exothermic reactions, like the wateregas-shift reaction, is illustrated in Figure 8-a. In our case, the effect of temperature on conversion in the range studied is not very marked. For the conventional fixed bed reactor, there is an optimum temperature (400  C) at which conversion is slightly higher. For the membrane reactor the optimum is even less marked, and similar conversions are reached in the range 400e450  C. This is explained by the effect of the membrane, which shifts the equilibrium allowing reaching higher conversions. The outlet pressure is in our case very close to the pressure inside the reactor, since pressure drop is low for all the simulations (typically lower than 1 bar). On increasing the outlet pressure, conversion increases, so the optimum value is set by mechanical and economic restrictions. Space velocity (GHSV) relates reactor performance and productivity. This variable is calculated considering the inlet gas flow rate, measured at normal conditions (273 K, 1 atm), in order to compare membrane and non-membrane reactors at different inlet conditions (e.g. temperature and pressure) but the same total feed rate. As shown, the behaviour of both reactors is very similar, showing the expected decrease in conversion as space velocity increases, although conversion is consistently higher for the membrane reactor (except the difference in the conversion scale, which was expected because the space velocity is strongly related to the reaction). Hydrogen partial pressure in the permeate side affects negatively conversion, due to the resulting reduction in the hydrogen flux through the membrane. However, this effect is very small within the range considered. Fig. 6, where the performance of the membrane is studied, explains this behaviour: as in the first half of the reactor the driven force for transport through the membrane is high, changes in the hydrogen partial pressure in the permeate side have little effect. Anyway, this variable is particularly important at the end of the reactor, because determines the hydrogen outlet

Fig. 7 e Accuracy of the surface response model fitted with the simulations proposed by the BoxeBehnken design of experiments: residuals (a) and parity plots (b). ( ) Membrane reactor. ( ) Fixed bed reactor.

5008

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 e n e r g y 3 7 ( 2 0 1 2 ) 4 9 9 7 e5 0 1 0

a

b

c

d

e

Fig. 8 e Comparison of reactor performance at different operating conditions with membrane reactor ( ) and fixed bed reactor ( ). Symbols: rigorous model (cross design). Lines: fitted model.

concentration of the reactor, and hence the maximum conversion. For this reason, the permeate side is recommended to work at the lowest economically suitable pressure. Finally, the influence of the catalyst particle diameter, which determines the internal mass transfer resistance in the catalyst particles, is analysed. As expected, for a fast reaction as the wateregas-shift reaction, this effect is relevant, and on increasing the particle size, the observed reaction rate decreases, and hence conversion (Figure 8-e). However, very low particle diameters are not adequate for industrial reactors because they cause high pressure drops. The performances of the reactors with and without membrane exhibit a similar trend, but in different conversion ranges.

4.

Conclusions

The performance of both fixed bed and membrane reactors (fixed bed catalytic reactor with hydrogen-selective membrane) has been studied by simulation, several

modelling approaches of different complexity being compared. The most complex model considered is bidimensional, taking into account mass, energy and momentum balances, and nesting a rigorous model for mass transfer within the porous catalyst. Several simplifications were considered for the reactor model (not including the momentum balance or the radial coordinate), being observed that both simplifications lead to misspredictions of the reactor performance. Concerning to the catalyst effectiveness, it was concluded that intra-particle mass transfer effects are not negligible (as many reported works considered), and simplified models for taking into account these effects, such as generalised Thiele modulus, use of apparent kinetic parameters or empirical fitting of the external efficiency are proposed. A model (bi-dimensional with momentum balance and using the apparent kinetic parameters for accounting for intra-particle mass transfer effects), was selected and used for a statistic sensitivity analysis of the effect of different operation variables, for both reactor configurations, concluding that the variables most affecting the reactor performance are outlet pressure and space velocity.

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 e n e r g y 3 7 ( 2 0 1 2 ) 4 9 9 7 e5 0 1 0

Acknowledgements This work was financed by the Spanish Ministry for Science and Innovation (contract CIT-120000-2008-4, Applied Collaborative Research Program 2008).

Nomenclature Abbreviations CFD computational fluid dynamics SSE sum of square errors WGSR wateregas-shift reaction Latin symbols a geometric surface area per unit of bed volume, 6 ð1  εb Þ ; m2 dP aS geometric surface area per unit of solid volume, 6 ; m2 dP c molar concentration, mol/m3 Cp heat capacity, J/kg K D, d diameter, m diffusion coefficient, m2/s Dij catalyst mean pore size, m hdpore i GHSV gas-hourly space velocity at the inlet flow rate measured at normal conditions, h1 h heat transfer coefficient, W/m2 K I unitary matrix, e J membrane flux, mol/m2 s k thermal conductivity, W/m K K hydraulic permeability, m2 K mass transfer coefficient, m/s kinetic constant per unit of catalyst mass, km mol1-nm (m3)nþm/kgcat s equilibrium constant, e Keq L length, m N molar flux, mol/m2 s n normal unitary vector, e p pressure, Pa Pr Prandlt number, CPG m/kG, e q heat flux, W/m2 Q membrane permeability, mol/m s Pa0.5 r radial coordinate, m adjusted regression coefficient R2adj reaction rate, mol/m3cat s rvc mass transfer resistance, m2 s bar/mol Rj ideal gas constant, 8.314 J/mol K Rg Re particle Reynolds number, dP jujrG =m,  Sc Smidt number, m/rG Dim,  T temperature, K pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u surface velocity, juj ¼ u2z þ u2r , m/s x particle coordinate, m X conversion,  y molar fraction,  z axial coordinate, m Subscripts b bed D Darcy

e eq E G i, j in int m out P R S sh w

5009

effective equilibrium Ergun gas components inlet internal mixture outlet particle reactor solid shell wall

Greek symbols b approaching to equilibrium, ε porosity, e palladium thickness, m dPd reaction enthalpy, J/mol DHR f Thiele modulus,  h internal effectiveness factor, e m viscosity, kg/m s stoichiometric coefficient, e vi r density, kg/m3 s tortuosity, e

references

[1] Gallucci F, Basile A. PdeAg membrane reactor for steam reforming reactions: a comparison between different fuels. Int J Hydrogen Energy 2008;33(6):1671e87. [2] Muradov NZ, Veziroglu TN. “Green” path from fossil-based to hydrogen economy: an overview of carbon-neutral technologies. Int J Hydrogen Energy 2008;33(23):6804e39. [3] Augustine AS, Ma YH, Kazantzis NK. High pressure palladium membrane reactor for the high temperature wateregas shift reaction. Int J Hydrogen Energy 2011;36(9): 5350e60. [4] Falco MD, Marrelli L, Iaquaniello G. Membrane reactors for hydrogen production processes. Springer; 2011. [5] Gallucci F, Van Sintannaland M, Kuipers JAM. Theoretical comparison of packed bed and fluidized bed membrane reactors for methane reforming. Int J Hydrogen Energy 2010; 35(13):7142e50. [6] Marin P, Ordonez S, Diez FV. Performance of reverse flow monolithic reactor for wateregas shift reaction. Catal Today 2009;147:S185e90. [7] Dolan MD, Dave NC, Ilyushechkin AY, Morpeth LD, McLennan KG. Composition and operation of hydrogenselective amorphous alloy membranes. J Membr Sci 2006; 285(1e2):30e55. [8] Babita K, Sridhar S, Raghavan KV. Membrane reactors for fuel cell quality hydrogen through WGSR e review of their status, challenges and opportunities. Int J Hydrogen Energy 2011;36(11):6671e88. [9] Ruettinger W, Ilinich O, Farrauto RJ. A new generation of water gas shift catalysts for fuel cell applications. J Power Sources 2003;118(1e2):61e5. [10] Tosti S. Overview of Pd-based membranes for producing pure hydrogen and state of art at ENEA laboratories. Int J Hydrogen Energy 2010;35:12650e9.

5010

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 e n e r g y 3 7 ( 2 0 1 2 ) 4 9 9 7 e5 0 1 0

[11] Sanz R, Calles JA, Alique D, Furones L, Ordo´n˜ez S, Marı´n P, et al. Preparation, testing and modelling of a hydrogen selective Pd/YSZ/SS composite membrane. Int J Hydrogen Energy 2011;36(24):15783e93. [12] Brunetti A, Caravella A, Barbieri G, Drioli E. Simulation study of water gas shift reaction in a membrane reactor. J Membr Sci 2007;306(1e2):329e40. [13] Huang J, El-Azzami L, Ho WSW. Modeling of CO2-selective water gas shift membrane reactor for fuel cell. J Membr Sci 2005;261(1e2):67e75. [14] Ma DH, Lund CRF. Assessing high-temperature wateregas shift membrane reactors. Ind Eng Chem Res 2003;42(4):711e7. [15] Zou J, Huang J, Ho WSW. CO2-selective water gas shift membrane reactor for fuel cell hydrogen processing. Ind Eng Chem Res 2007;46(8):2272e9. [16] Adrover ME, Lo´pez E, Borio DO, Pedernera MN. Simulation of a membrane reactor for the WGS reaction: pressure and thermal effects. Chem Eng J 2009;154(1e3):196e202. [17] Gosiewski K, Warmuzinski K, Tanczyk M. Mathematical simulation of WGS membrane reactor for gas from coal gasification. Catal Today 2010;156(3e4):229e36. [18] Adams Ii TA, Barton PI. A dynamic two-dimensional heterogeneous model for water gas shift reactors. Int J Hydrogen Energy 2009;34(21):8877e91. [19] Abdollahi M, Yu J, Liu PKT, Ciora R, Sahimi M, Tsotsis TT. Hydrogen production from coal-derived syngas using a catalytic membrane reactor based process. J Membr Sci 2010;363(1e2):160e9. [20] Piemonte V, De Falco M, Favetta B, Basile A. Counter-current membrane reactor for WGS process: membrane design. Int J Hydrogen Energy 2010;35(22):12609e17. [21] Markatos NC, Vogiatzis E, Koukou MK, Papayannakos N. Membrane reactor modelling e a comparative study to evaluate the role of combined mass and heat dispersion in large-scale adiabatic membrane modules. Chem Eng Res Des 2005;83(A10):1171e8. [22] Chiappetta G, Clarizia G, Drioli E. Theoretical analysis of the effect of catalyst mass distribution and operation parameters on the performance of a Pd-based membrane reactor for wateregas shift reaction. Chem Eng J 2008; 136(2e3):373e82. [23] Basile A, Paturzo L, Gallucci F. Co-current and countercurrent modes for water gas shift membrane reactor. Catal Today 2003;82(1e4):275e81. [24] Falco MD. Pd-based membrane steam reformers: a simulation study of reactor performance. Int J Hydrogen Energy 2008;33(12):3036e40. [25] Byron Smith RJ, Muruganandam L, Murthy Shekhar S. CFD analysis of water gas shift membrane reactor. Chem Eng Res Des 2011;89(11):2448e56. [26] Di Carlo A, Dell’Era A, Del Prete Z. 3D simulation of hydrogen production by ammonia decomposition in a catalytic membrane reactor. Int J Hydrogen Energy 2011;36(18): 11815e24. [27] Tiemersma TP, Patil CS, Annaland MV, Kuipers JAM. Modelling of packed bed membrane reactors for autothermal production of ultrapure hydrogen. Chem Eng Sci 2006;61(5):1602e16. [28] Chen W-H, Lin M-R, Jiang TL, Chen M-H. Modeling and simulation of hydrogen generation from high-temperature and low-temperature water gas shift reactions. Int J Hydrogen Energy 2008;33(22):6644e56. [29] Zhai X, Ding S, Cheng Y, Jin Y, Cheng Y. CFD simulation with detailed chemistry of steam reforming of methane for hydrogen production in an integrated micro-reactor. Int J Hydrogen Energy 2010;35(11):5383e92. [30] Irani M, Alizadehdakhel A, Pour AN, Hoseini N, Adinehnia M. CFD modeling of hydrogen production using steam reforming of methane in monolith reactors: surface or

[31]

[32]

[33]

[34]

[35]

[36] [37] [38] [39]

[40]

[41]

[42]

[43] [44] [45]

[46]

[47]

[48]

[49]

volume-base reaction model? Int J Hydrogen Energy 2011; 36(24):15602e10. De Falco M, Nardella P, Marrelli L, Di Paola L, Basile A, Gallucci F. The effect of heat-flux profile and of other geometric and operating variables in designing industrial membrane methane steam reformers. Chem Eng J 2008; 138(1e3):442e51. Ding OL, Chan SH. Wateregas shift reaction e a 2-D modeling approach. Int J Hydrogen Energy 2008;33(16): 4325e36. Marı´n P, Hamel C, Ordo´n˜ez S, Dı´ez FV, Tsotsas E, SeidelMorgenstern A. Analysis of a fluidized bed membrane reactor for butane partial oxidation to maleic anhydride: 2D modelling. Chem Eng Sci 2010;65(11):3538e48. Kolaczkowski ST, Chao R, Awdry S, Smith A. Application of a CFD code (FLUENT) to formulate models of catalytic gas phase reactions in porous catalyst pellets. Chem Eng Res Des 2007;85(11):1539e52. Dixon AG, Ertan Taskin M, Hugh Stitt E, Nijemeisland M. 3D CFD simulations of steam reforming with resolved intraparticle reaction and gradients. Chem Eng Sci 2010; 62(18e20):4963e6. Bird RB, Stewart WE, Lightfoot EN. Transport phenomena. 2nd ed. John Wiley; 2002. Green DW, Perry RH. Perry’s chemical engineers’ handbook. 8th ed.; 2008. Teng H, Zhao TS. An extension of Darcy’s law to non-Stokes flow in porous media. Chem Eng Sci 2000;55(14):2727e35. Hunt ML, Tien CL. Non-Darcian flow, heat and mass transfer in catalytic packed-bed reactors. Chem Eng Sci 1990;45(1): 55e63. Keiski RL, Desponds O, Chang YF, Somorjai GA. Kinetics of the wateregas shift reaction over several alkane activation and wateregas shift catalysts. Appl Catal A Gen 1993;101(2): 317e38. Ryi S-K, Park J-S, Kim S-H, Cho S-H, Kim D-W, Um K-Y. Characterization of PdeCueNi ternary alloy membrane prepared by magnetron sputtering and Cu-reflow on porous nickel support for hydrogen separation. Sep Purif Technol 2006;50(1):82e91. Guo Y, Lu G, Wang Y, Wang R. Preparation and characterization of PdeAg/ceramic composite membrane and application to enhancement of catalytic dehydrogenation of isobutane. Sep Purif Technol 2003; 32(1e3):271e9. Froment GF, Bischoff KB. Chemical reactor analysis and design. John Wiley and Sons; 1979. Davis ME, Davis RJ. Fundamentals of chemical reaction engineering. McGraw-Hill; 2003. Lim S, Bae J, Kim K. Study of activity and effectiveness factor of noble metal catalysts for wateregas shift reaction. Int J Hydrogen Energy 2009;34(2):870e6. Hla SS, Park D, Duffy GJ, Edwards JH, Roberts DG, Ilyushechkin A, et al. Kinetics of high-temperature wateregas shift reaction over two iron-based commercial catalysts using simulated coal-derived syngases. Chem Eng J; 2009. Rui ZB, Zhang K, Li YD, Lin YS. Simulation of methane conversion to syngas in a membrane reactor: part I A model including product oxidation. Int J Hydrogen Energy 2008; 33(9):2246e53. Oyama ST, Hacarlioglu P. The boundary between simple and complex descriptions of membrane reactors: the transition between 1-D and 2-D analysis. J Membr Sci 2009;337(1e2): 188e99. Israni SH, Harold MP. Methanol steam reforming in singlefiber packed bed PdeAg membrane reactor: experiments and modeling. J Membr Sci 2011;369(1e2):375e87.