Design of a PlateType Catalytic Microreactor with

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In these reactors, a gas permeation membrane is placed beside the reaction channels. Theoretical- ly, 100% conversion of the limiting reactant can be achieved.
Membrane reactor

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Takashi Fukuda Taisuke Maki

Research Article

Kazuhiro Mae

Design of a Plate-Type Catalytic Microreactor with CO2 Permeation Membrane for Water-Gas Shift Reaction

Kyoto University, Department of Chemical Engineering, Kyoto, Japan.

A method for designing membrane reactors with microchannels is discussed. The design equations were simplified under various assumptions, and a simple model that only incorporates the material balance equations was developed. The activity of the catalyst and the membrane capacity are important properties of a membrane reactor. In the proposed design method, these two parameters are combined into the nondimensional number j. The simple model was applied to the water-gas shift reaction and the results were compared with those obtained from the detailed model by computational fluid dynamics calculations. Moreover, a reactor was designed that could achieve a CO concentration of 10 ppm or less. In this plate-type reactor, the temperature distribution in the channel can be controlled by adjusting the wall temperatures. Keywords: Catalysts, Computational fluid dynamics, Membrane reactor, Microreactor, Water-gas shift reaction Received: November 14, 2011; revised: February 10, 2012; accepted: February 10, 2012 DOI: 10.1002/ceat.201100599

1

Introduction

In any reaction, a thermodynamic equilibrium state exists. The temperature and pressure of the reaction determine the final composition of the system. Each reactant has an equilibrium conversion value, and the reaction is terminated once it has reached an equilibrium state. However, if the reaction products are separated and removed, the reaction will continue to reach a new equilibrium state. Membrane reactors have been devised to realize this concept. In these reactors, a gas permeation membrane is placed beside the reaction channels. Theoretically, 100 % conversion of the limiting reactant can be achieved in a membrane reactor. Furthermore, the combination of membrane and catalysis, a so-called catalytic membrane reactor, has the advantage to obtain a high product yield in an equilibrium reaction system by simultaneous separation of by-products. Here, the water-gas shift (WGS) reaction is chosen as model reaction for the assumed membrane reactor. The study of membrane reactors using the WGS reaction was reviewed by Babita et al. [1]. This reaction is used to purify H2 by reducing CO or to adjust the H2/CO ratio for syngas production, and so on. Particularly, we focused on reducing CO

– Correspondence: Prof. K. Mae ([email protected]), Kyoto University, Department of Chemical Engineering, Kyoto-daigaku Katsura, Nishikyo-ku, Kyoto 615-8510 Japan.

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in the outlet gas. Reducing the CO concentration produces a highly purified hydrogen product which can be used as a feed gas for polymer electrolyte membrane fuel cells (PEMFCs) and will downsize the overall process equipment. Usually, this process requires a large-sized reactor to reach WGS equilibrium, but it can be avoided by shifting the balance of components with the help of a membrane. Downsizing, one of the main goals in this study, leads to the development of portable systems. However, there are a few problems to operate the packedtype reactor as follows: (i) The temperature control within the catalyst (including micropore) is difficult under endothermic or exothermic reactions; (ii) the operation temperature is limited by the membrane strength, so the reaction is not performed at optimum reaction temperature; (iii) since the ratio of membrane area to reaction zone volume is high, the rates of reaction and separation are not matched. To enhance sufficiently the potential of a catalytic membrane reactor, the above drawbacks should be qualified by the reactor design. In microchannels, rapid mass transfer and heat transfer are easily achieved in a laminar flow. These characteristics are expected to help in the design of an efficient catalytic membrane microreactor in which the catalyst is placed as a thin layer at the opposite side of the membrane. Such a microreactor is characterized by two main features: (i) The reaction and separation temperatures are individually controlled by catalyst setting and temperature gradient in laminar flow, and (ii) the reaction rate can be matched to the separation rate by the cata-

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lyst layer thickness (the amount of catalyst) and the microchannel width between catalyst and membrane. In addition, the above reactor system allows to easily control the heat transfer between catalyst and bulk flow. In general, temperature gradients in the pores of a catalyst can arise from unwanted side reactions. Microchannels can solve this problem by maintaining a constant temperature and a uniform temperature distribution within the catalyst layer. In addition, they can provide products with high quality and at high yields with minute flow and rapid mass transfer to control the mixing of the components in a complex reaction system. In this study, a method for designing reactors with both microchannels and gas permeation membranes are proposed, and the microreactor performance for reaction control is demonstrated by computational fluid dynamics (CFD) simulations.

2

3

Basic Concept of a Catalytic Membrane Microreactor

Fig. 1 presents a scheme of the catalyst membrane microreactor. Reforming gas is supplied to the reaction-side channel, and sweep gas, which is used to remove the gas of interest, is supplied to the penetration-side channel in a countercurrent flow. Gas penetrates the membrane according to the permeation coefficient Pi and the concentration gradient (or the partial pressure gradient), which is the driving force. The transmitted gas is transported by the carrier gas and is discharged. The reactant gas comes into contact with the catalyst through diffusion or convective flow. After reaction, the generated gases move into the bulk phase.

Model Reaction and Target of Reactor Performance

The design equations are complex and difficult to solve by hand. Therefore, conditions are considered that promote the reaction, such as the concentration distribution or the flow, and the equations are simplified by imposing constraints on these conditions. The design equation is then simplified by omitting the concentration distribution and the flow. The reaction can then be solved analytically, and the results can be used to generate charts that are useful in the design process. Here, it is focused on modeling the WGS reaction in the membrane reactor. This reaction is used to improve the purity of H2 by reducing the amount of CO, which causes catalyst poisoning. Usually, the WGS reaction is followed by the pressure swing adsorption (PSA) process, but if the reaction is highly efficient, it can be avoided. A low CO concentration in the output gas is required if the gas is to be used as a feed for PEMFCs. As mentioned above, CO is a catalytic poison and competes with H2 for adsorption sites on the catalyst. The presence of CO significantly decreases the reactivity [2]. The PEMFC catalyst is no exception, and the CO concentration in the fuel must be 10 ppm or less. This is equivalent to a 99.99 % CO conversion for the reactant composition (H2/CO/CO2/H2O = 0.55/0.10/ 0.05/0.30, S/C = 3) that was applied in this study. Because the WGS reaction is exoergic, it is favored at low temperatures. However, in industrial applications, the rate is not high enough when the reaction is carried out at low temperatures with a Cu catalyst. This low rate is caused by the CO2 inhibition reaction. Many studies have been performed on the activities and reaction mechanisms of catalysts that were used in industrial applications in the low-temperature regime (LT) [3–7] or in the high-temperature regime (HT) [4, 8–12]. The inhibition of the Cu catalyst by CO2 in the LT-WGS reaction was discussed. All of these issues can be addressed with a membrane reactor. Here, a method is proposed for designing a microchannel membrane reactor that uses a CO2-selective permeation membrane and an LT activity catalyst. The performance of this reactor was excellent. To evaluate the quality of the proposed reactor, the target CO concentration of the WGS reaction was 10 ppm or less [2].

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Figure 1. Schematic representation of the membrane reactor.

3.1

Simple Model for Simple Reversible Reaction

A ! B :

 rA ˆ kc qC CA

CB Keq

 (1)

First, a simple reaction system consisting of components A and B is discussed. To simplify the model, the following assumptions are set: (i) the diffusion in the X-direction can be disregarded, (ii) there is no concentration gradient in the Y-direction, and (iii) the concentration of B on the carrier gas side is negligible. These assumptions were found to be valid when the parameters were set to (i) Pe >100; (ii) Pe* CO2 ‡ H2

3.2.1 Simple Model

(10)

hB ˆ CB0 =CA0

3.2

The applicability of the simple and the detailed model is compared and CFD is used to evaluate the performance of the reactor design for the WGS reaction.

(8)

AS ˆ 4=…dc ‡ df ††

CB 1 ˆ ……1 1 j CA0

1207

(19)

AS RCO2 RCO2 ˆ kc CH2 O0 qC0 dc kc′ qC

(20)

The design equations can then be solved analytically, and the solutions are as follows:   kc qC CH2 O CCO ˆ exp X CCO0 uX CCO2 1 ˆ ……1 xCO †j CCO0 1 j ˆ …1

xCO † hCO2

(21)

…1 xCO ††‡ hCO2 …1 xCO †j

ln…1

xCO †

(22)

…j ≠ 1†



… j ˆ 1†

(23)

In this simple model, the heat transfer equation is not included because it is assumed that the catalyst layer has a uniform temperature. According to this model, the temperature of the catalyst layer is roughly uniform, therefore, the heat transfer equations are not needed.

3.2.2 Detailed Model The mass transport can be described which includes the diffusion, the convection flow in the reactor, and the energy transport by the following equations: ∇

 DPi ∇Ci P ˆ ri P



 kP ∇T P ˆ

(16)

uP ∇Ci P

r P DH P

(24)

qmix Cp;mix uP ∇T P

© 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

(25)

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Subscript i denotes each component and superscript P denotes each phase (c: catalyst phase, f: feed phase, m: membrane phase, p: permeation phase) in the reactor. The boundary conditions are as follows:

Table 1. Calculation parameters.

kc [m6mol–1s–1kgcat–1]

8.041 · 105exp(–79849/RT)

Continuity at Y ˆ dc ; dc ‡ df ; dc ‡ df ‡ dm

Keq [–]

9.266 · 10–3exp(–40056/RT)

(25)

Properties of catalyst (without inhibition reaction by CO2)

qC0 [kg m–3] c;p

dC Di c;p i ‡ Ci c;p uY c;p ˆ 0 at dY Y ˆ 0; dc ‡ df ‡ dm ‡ df Ci f ˆ Ci0 f ; Di p

dC c;m Di c;m i ‡ Ci c;m uX c;m ˆ 0; dX

dCi p ˆ 0 at X ˆ 0 dX

Ci p ˆ Ci0 p ; Di f

Di c;m

DH [J mol ]

(27)

(28)

–41166

Initial composition [–] y0, CO

y0, H2O

y0, CO2

y0, H2

0.5563

0.0986

0.0493

0.2958

2 –1

Diffusion coefficients [m s ] DH2O

DCO

dCi c;m ‡ Ci c;m uX c;m ˆ 0; dX

f

dCi ˆ 0 at X ˆ L dX

–4

(29)

at Y ˆ 0

(30)

T c ˆ Tsweep ;

at Y ˆ dc ‡ df ‡ dm ‡ df

(31)

T f ˆ 160 o C;

kc;m;f

dT c;m;p ˆ 0 at X ˆ 0 dX

(32)

T p ˆ 120 o C ;

kc;m;f

dT c;m;f ˆ 0 at X ˆ L dX

(33)

By solving the momentum transport equation, the energy transport equation and the mass transport equation simultaneously, one can obtain the penetration, velocity distribution, concentration distribution, temperature distribution, and reaction rate through the membrane of the membrane reactor. The calculations were performed using COMSOL®3.5. The operational conditions for WGS reaction are listed in Tab. 1. The physical properties of the catalyst, which does not prevent the formation of CO2, are based on our laboratory data. j is found to be 2 at the inlet region. The physical properties of the catalyst with inhibition by CO2 are summarized in Tab. 2 for Eqs. (34)–(37). H2-selective membranes are usually Pd-based [14, 20]. A CO2-selective membrane was also studied [16]. From the viewpoint of carbon capture and storage (CCS), one advantage of using CO2selective membranes is that they can recover CO2 in a more energy-efficient manner than chemical adsorption techniques because CO2 is easily to separate from the sweep gas. In this study, a CO2-selective membrane is applied. The CO2 permeation membrane has a penetration speed on the order of 10–4 mol m–2 s–1 kPa–1, and 5 · 10–4 mol m–2 s–1 kPa–1 was chosen as the CO2 penetration speed for this calculation. j is dependent on RCO2, and xCO is dependent on GHSV. Here, the channel form is used that is described in Tab. 3 (df, dm, dp, dc etc.). With respect to assumption (iii), there are reports that address the separation of H2 from the GHSVsweep [17, 21].

DCO2 –4

1.454 · 10

T c ˆ Tcat ;

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1200

–1

1.111 · 10

D H2 –5

8.939 · 10

1.412 · 10–4

Thermal conductivity [Wm–1K–1] kcat

kgas

kmem

2.0

0.1118

0.271

etc. Cp, mix [J mol–1K–1]

lmix [Pa s]

31.55

1.811 · 10–5

Table 2. Parameters for calculation of rate equations (34)–(37) [3, 26]. Parameter values

(valid for T = 180–200 °C)

k0 [mol h–1Pa–2gcat–1]

1.188

a

–1

E [kJ mol ]

36.658

Ka0CO

–1

2.283 · 10–24

[Pa ]

Ka0H2O [Pa–1]

1.957 · 10–28

Ka0CO2 [Pa–1]

5.419 · 10–4

Ka0H2 [Pa–1]

2.349 · 10–4

DHaCO [kJ mol–1]

–45.996

DHaH2O

–1

–79.963

–1

–16.474

DHaCO2 DHaH2

[kJ mol ] [kJ mol ] –1

[kJ mol ]

–13.379

Table 3. Geometry parameters.

© 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

L [m]

0.2

dc [m]

0.0002

df [m]

0.0004

dm [m]

0.0002

dp [m]

0.0005 –1

GHSVsweep [h ]

50000

Tcat [°C]

180

Tsweep [°C]

120

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According to these reports [15–17, 21], H2 should be separated by applying a pressure difference across the membrane (e.g., by vacuuming rather than using a sweep gas). In the detailed model, the sweep gas flows in the opposite direction as the reaction gas, which creates higher separation efficiency than when it flows in the same direction [13, 22].   Ea k503 ˆ k0 exp (34) RT503   Ea 1 kc ˆ k503 exp R T  Ki; 503 ˆ K 0 i exp

DH a i RT503

1

(35)

T503 

  DH a i 1 Ki ˆ Ki; 503 exp R T

3.3



(36) 1

 (37)

T503

Figure 2. Relationship between xA and MB (Keq = 8, solid line: h = 0, dotted line: h = 3).

 Mi ˆ 

Quality Assessment

The relationship between GHSV value and concentration was investigated under the channel conditions that are described in Tab. 3. Three values of j (j = 0, 0.2, and 2 at a reactor entrance) were investigated. j = 0 represents a packed-bed reactor without a separation membrane, because it means that the permeability rate is zero (or that the reaction rate is too much faster than the CO2 permeation rate). Here, the use of catalysts with and without CO2 inhibition is studied. When j = 0.2, the value of RCO2 was 1/10 of its original value. The concepts from Section 3.2 describing a system without inhibition by CO2 cannot be applied to a system with inhibition by CO2 because the rate equations of the reaction are different. However, the definition of j (Eq. (20)) was applied to make a rough approximation.

3.4 Temperature Control in a Channel by Adjusting the Wall Temperature

p Fi;out



p Fi;out



  f ‡ Fi;out

(38)

When j < 0.1, the permeation of component B through the membrane was low. Therefore, there was no advantage to operating either the reaction or the separation at j < 0.1, i.e., the separation membrane cannot perform effectively when the reaction is inhibited. In contrast, when j > 10, component B is sufficiently separated, even at low values of xA (e.g., MB > 0.9 when xA > 0.5). These tendencies increase markedly when h > 0. The amount of B in the reactor channels was noticeably reduced when j > 2. Next, the effect of the membrane was examined for the case in which the equilibrium constant is small. The relationship between the equilibrium constant and the amount of the catalyst that was required to achieve xA = 0.9999 is indicated in Fig. 3. For example, when j < 0.1 and Keq = 10, the reaction required ten times more catalyst to reach xA = 0.9999. How-

It is demonstrated that the performance of a reactor does not deteriorate significantly when there is a gap between the catalyst layer and the membrane (i.e., when df > 0). When there is a gap, the catalyst layer and the membrane can be at different temperatures, and both temperatures can be optimized. The temperature of the catalyst sidewall was raised so that the membrane temperature reached the heatproof limit, and the reactivity as a function of df was studied using CFD calculations. The conditions are described in Tabs. 1 and 3 (however, df and Tcat are variable).

4

Results and Discussion

4.1

Simple Model for Simple Reversible Reaction

Fig. 2 illustrates the relationship between the reaction rate xA and the separation rate MB when h = 0 and 3.

Chem. Eng. Technol. 2012, 35, No. 7, 1205–1213

Figure 3. Relationship between Keq and the amount of the catalyst.

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ever, the amount of catalyst required decreased as j and Keq increased. When Keq > 102 and j > 1, the effect of the backward reaction could be ignored. When Keq = 0.1, xA = 0.9999 could be achieved with only twice the amount of catalyst. From these results, one can conclude that at large Keq and low temperatures, the rate of the WGS reaction only improves when j = 1. However, when there was inhibition by CO2, j > 10 was required to achieve a high permeation rate.

4.2

Simple and Detailed Models in WGS Reaction

The validity of applying the simple model to the WGS reaction was evaluated. Fig. 4 presents the solution of the detailed model simulated by CFD and the analytical solution of the simple model extended to the WGS reaction. Both models exhibited a gap at low or high reaction rates, which indicates that the simple model cannot reproduce the concentration distribution in the X-direction. For example, at low GHSV values, the temperature changed significantly because the reactions progressed rapidly near the reactor inlet, however, in the simple model, the temperature of the catalyst layer was assumed to be uniform. The simple model and the detailed model coincided well at j > 10. Therefore, a membrane reactor could be easily designed by using the information in Fig. 4, which was obtained from j and Eqs. (22) and (23).

Figure 4. Relationship between xCO and MCO2 in a plate-type membrane reactor.

Next, the effect of j on a reactor was discussed that had a realistic geometry. Using a catalyst with a density of qC0 = 1200 kg m–3, a maximum gap of dc = 40 lm was required if the reaction was operated at j > 10 and df = 0 (i.e., a packed-bed reactor). Even if a hollow fiber was used to increase the specific surface area, a maximum gap of dc = 160 lm was required (the inner diameter of the Al2O3 hollow fiber was 1 mm, and it was an H2-selective membrane [21, 23]). Because the low-temperature WGS reaction had a Keq > 102, a 99.99 % CO conversion could be achieved when j = 1 and there was no inhibition by CO2. In this case, dc could not exceed 400 lm, so it was also difficult to use a pellet-type catalyst, unless the permeation rate of the membrane increased.

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The pellet-type catalyst consists of large to uniformly filled microchannels with a particle diameter usually exceeding 100 lm. It is likely that the limits proposed on Pe, Pe*, and Da in Sect. 3.1 may not be satisfied as the dc is increased and its apparent density gets reduced for a given Wcat. Conversely, as dc is minimized through particle size reduction in the case of coated microchannels, its apparent density increases and the limits on Pe, Pe*, and Da are satisfied. In a plate-type microreactor, the catalyst is, therefore, advantageously coated on the walls and by maintaining df > 0, the contact between membrane and catalyst layer is avoided. This prevents the membrane from being overheated in a CO2 permeation-based WGS reaction. In this membrane reactor, the diffusion rate must be greater than the reaction rate (i.e., j must be large). Conversely, at high diffusion rates, the performance of the reactor would be maintained, even if df > 0. The effect of the gap between catalyst layer and membrane, df, on the CO conversion is illustrated in Fig. 5. When df < 1.5 mm, there is no change in the CO conversion which is independent of the GHSV value. Therefore, the WGS reaction proceeded according to the rate-limiting reaction. This knowledge is important for avoiding the membrane heatproof temperature restriction. Here, the GHSV in the figures is the void tower velocity of the catalyst layer volume. If the GHSV of the whole reaction is required, the original GHSV should be multiplied by dc/(dc+df ). In the next section, the relationship between df and the temperature of the catalyst is described.

Figure 5. Effect of df (noncatalyst layer) on xCO.

The possible applicability of the simple model and the detailed model for WGS reaction to a realistic channel was verified. The results of Section 4.2 were used to design a platetype membrane reactor, whose parameters are listed in Tab. 3. In the detailed model, CFD was applied to solve the equations for values of the parameters in the following ranges: 200 h–1 < GHSV < 10 000 h–1, 10 < Pe < 37 000, 0.0004 < Pe* < 60, 0.006 < Da < 0.4, and GHSVsweep = 50 000 h–1. The result is displayed in Fig. 6. The good agreement between the simple model and the detailed model indicates that a plate-type membrane reactor can be designed by the simple model. Next, the possibility of the plate-type membrane microreactor for CO elimination for PEMFCs was investigated. Figs. 7

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Figure 6. Relationship between xCO and MCO2 in a plate-type membrane reactor. Figure 8. Relationship between GHSV value and component concentration (CO or CO2) in a plate-type membrane reactor (with inhibition by CO2).

Fig. 9 demonstrates the effect of Tcat on the temperature distribution in a plate-type membrane reactor at X, indicating maximum temperature when GHSV = 2000 h–1 under the conditions that are summarized in Tabs. 1 and 3. The temperature distribution is linear for each domain as indicated in Fig. 9. 220

Temperature [°C]

200

Figure 7. Relationship between GHSV value and component concentration (CO or CO2) in a plate-type membrane reactor (no inhibition reaction by CO2).

and 8 illustrate the effect of GHSV on CO conversion and output concentration of CO and CO2. In the case with or without inhibition reaction by CO2, the CO2 concentration was reduced by the CO2-selective permeation membrane. The performance of the membrane reactor was remarkable when a Cu catalyst was used with inhibition reaction by CO2. When GHSV < 800 h–1, a CO concentration of less than 10 ppm, which is required by PEMFCs, could be achieved.

4.3

Control of the Temperature Profile in the Channel by Adjusting the Wall Temperature

Finally, it was tried to improve CO conversion by increasing Tcat with keeping the membrane temperature (Tm) of 180 °C, which is the upper limit of the CO2 separation membrane.

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180 160 140 120 100 0.0

0.2

0.4

0.6

d [mm]

0.8

1.0

1.2

Figure 9. Temperature profile in the plate-type membrane reactor (Tcat = 180 °C, Tsweep = 120 °C).

The temperature gradient keeps constant in the range of df and the relation between df and Tcat is linear under keeping Tm = 180 °C. Fig. 10 displays the linear relationship between df and Tcat demonstrating the increase in reaction rate with temperature rise and nonlinear relationship between df and CO concentration at Tm = 180 °C. At df =1.5 mm, the CO concentration was at its lowest. Between 0.5 mm and 2.0 mm, it dropped below 1 ppm, which was 1/10 to our target value and was equivalent to a 99.999 % conversion. Therefore, for df-values between 0.5 mm and 2.0 mm, this was the rate-limiting reaction. For example, a decay in the performance of PEMFCs has been reported when fuel gas containing only 1 ppm CO

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Symbols used

Figure 10. Relationship between df and CO concentration and between df and Tcat (sweep gas side wall: Tsweep= 120 °C).

was used because of the CO poisoning [8, 24, 25]. Therefore, these results could contribute to more efficient operation of PEMFCs.

5

[m–2] [mol m–3]

Ci0

[mol m–3]

Cp,mix

[J mol–1K–1]

dc df

[m] [m]

dm dp

[m] [m]

Da Di

[–] [m2s–1]

Ea Fi

[J mol–1] [mol s–1]

GHSV

[h–1]

GHSVsweep [h–1]

Conclusions

The flow and the mass transfer in a channel are limited by restricted operation conditions: (i) The diffusion direction can be disregarded in the X-direction; (ii) there is no concentration gradient in the Y-direction; (iii) the concentration of B on the side of the carrier gas flow is negligible. Under these assumptions, the design equation could be simplified in a way that the simple model only consisted of mass balance equations. The results of the detailed model were calculated using CFD simulations. The results indicate that for the WGS reaction, the simple model can be used to design a reactor. Moreover, a reactor was designed that could attain a CO concentration of 10 ppm or less. In addition, it was found that in a plate-type reactor, the temperature distribution in the channel can be controlled by adjusting the temperature of the walls. Actually, we will prepare the designed reactor and conduct verification experiments in future work. The proposed concept of the simple model should be applicable to other reaction systems. Once it is succeeds in creating charts like Fig. 2, the load of CFD simulations will decrease sharply, then a reactor can be designed more swiftly.

Acknowledgment This research was partially supported by the Ministry of Education, Science, Sports, and Culture, Grant-in-Aid for Young Scientists (A), 19686047, 2006-2008. The authors have declared no conflict of interest.

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As Ci

DH

[J mol–1]

DHai

[kJ mol–1]

kc

[m3s–1 kgcat–1]

kc′ kcat

[m3s–1 kgcat–1] [W m–1K–1]

kgas

[W m–1K–1]

kmem

[W m–1K–1]

k503

[mol h–1Pa–2gcat–1]

k0

[mol h–1Pa–2gcat–1]

Keq

[–]

Kai,503

[m3mol–1]

Kai

[m3mol–1]

Ka0i

[m3mol–1]

L Mi

[m] [–]

Ni

[mol m–2s–1]

© 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

specific surface area concentration of the i-th component initial concentration of the i-th component heat capacity of the mixed gas depth of the catalyst layer width of the reactant gas channel membrane thickness width of the reactant gas channel Damköhler number diffusion coefficient of the i-th component activation energy molar flow rate of the i-th component gas hourly space velocity of the feed of the catalyst phase volume standard gas hourly space velocity of the sweep gas enthalpy of the WGS reaction enthalpy of adsorption to the Cu catalyst of the i-th component reaction rate constant (or in [m6mol–1s–1kg-cat–1] or [mol · h–1Pa–2g-cat–1]) reaction rate constant thermal conductivity of the catalyst thermal conductivity of the gas thermal conductivity of the membrane reaction rate constant of the Cu catalyst at 503 K frequency factor of the Cu catalyst equilibrium constant of the WGS reaction i-th component adsorption constant at 503 K i-th component adsorption constant equilibrium constant of the adsorption length of the flow channel permeation rate of the i-th component flux of the i-th component through the membrane

Chem. Eng. Technol. 2012, 35, No. 7, 1205–1213

Membrane reactor

Pi

[m2s–1]

pT Pe Pe* r ri

[Pa] [–] [–] [mol m–3s–1] [mol m–3s–1]

Ri

[m s–1]

S/C T Tcat

[–] [K] or [°C] [°C]

Tm

[°C]

Tsweep

[°C]

T503 u uX

[K] [m s–1] [m s–1]

uXsweep

[m s–1]

W

[kg]

Wcat

[kg m–2]

WKeq=∞

[kg]

X

[m]

xi

[–]

Y

[m]

y0,i

[–]

permeation coefficient of the i-th component total pressure Péclet number modified Péclet number reaction rate generation speed of the i-th component i-th permeability of the gasphase concentration standard initial ratio of steam to CO temperature catalyst sidewall temperature membrane temperature (especially maximum value) sweep gas sidewall temperature 503 K velocity vector linear velocity of the reactant gas linear velocity of the sweep gas necessary amount of catalyst catalyst weight of horizontal plane area standard necessary amount of catalyst when Keq = infinite length of the horizontal direction conversion of the i-th component length of the vertical direction initial composition of the i-th component

Greek letters ecat j qC

[–] [–] [kgcat m–3]

qC0

[kgcat m–3]

qmix hi

[kg m–3] [–]

lmix

[Pa s]

porosity of the catalyst simple model parameter catalytic density of the catalyst phase and feed phase standard catalytic density of the catalyst phase standard density of the mixed gas initial rate of i to the limiting reactant viscosity of the mixed gas

Indices a i in out

adsorption component (A, B, CO, H2, CO2, H2O) inlet outlet

Chem. Eng. Technol. 2012, 35, No. 7, 1205–1213

P X Y

1213

phase in the reactor (c: catalyst, f: feed, m: membrane, p: permeation) horizontal direction vertical direction

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