Kinetics and Reactor Modeling of a High Temperature Water− Gas

4086

Ind. Eng. Chem. Res. 2008, 47, 4086–4097

Kinetics and Reactor Modeling of a High Temperature Water-Gas Shift Reaction (WGSR) for Hydrogen Production in a Packed Bed Tubular Reactor (PBTR) Prashant Kumar,†,‡ Enefiok Akpan,† Hussam Ibrahim,† Ahmed Aboudheir,‡ and Raphael Idem*,† Hydrogen Production Research Group, Process Systems Engineering, Faculty of Engineering, UniVersity of Regina, 3737 Wascana Parkway, Regina, SK, Canada S4S 0A2, and HTC Purenergy, 001, 2305 Victoria AVenue, Regina, SK, Canada S4P 0S7

Kinetic, experimental, modeling, and simulation studies of a catalytic high temperature (673-873 K) water-gas shift reaction (WGSR) were performed in a packed bed tubular reactor (PBTR) at several values of W/FA0 (ratio of the mass of the catalyst to the mass flow rate of CO, g(cat) · h/mol of CO) over a new Ni-Cu/ CeO2-ZrO2 (UFR-C) catalyst. Out of the kinetic models evaluated, the one that best predicted the experimental rates was based on the Langmuir-Hinshelwood (LH) formulation, assuming that the rate determining step (RDS) was the surface reaction between molecularly adsorbed carbon monoxide and water to give a formate intermediate and atomically adsorbed hydrogen. Reactor modeling was performed using a comprehensive numerical model consisting of two-dimensional coupled material and energy balance equations. The best mechanistic kinetic model developed was incorporated in the reactor model, which also contained the axial dispersion term, and was solved using the finite elements method. The validity of the reactor model was tested against the experimental data and a satisfactory agreement between the model prediction and measured results were obtained. In addition, the predicted concentration and temperature profiles for our process in both axial and radial direction indicate that the assumption of plug flow isothermal behavior is justified within certain kinetic operating conditions. Moreover, the well-known criteria for neglecting the axial dispersion term have been met in this case and it can conclusively be recommended to be eliminated from the model. 1. Introduction One of the possibilities to overcome the lack of the existence of large scale hydrogen production, storage, and distribution infrastructure is to produce hydrogen from logistic fuels for which these types of infrastructure already exists, either by onboard or onsite reforming.1–4 This may lead us to realizing the potential of using fuel cell technology for future energy generation for stationary, distributed, and mobile applications. In the short to medium term, processing of fossil fuels (natural gas) and other renewable sources (such as crude-ethanol, glycerol, and biodiesel) will play a significant role in hydrogen generation for the fuel cell.4,5 However, the hydrogen rich gas produced from these reformation processes typically contains about 5-20% carbon monoxide (CO) by volume, and therefore, additional processing of the reformate is required. The water-gas shift reaction (WGSR, eq 1) can be used in many fuel processing schemes to reduce the concentration of CO to desirable levels. CO + H2O S CO2 + H2 [A]

[B]

[C]

(∆H° ) -41.1

kJ/mol)

(1)

[D]

The reaction is moderately exothermic (∆H° ) -41.1 kJ/mol) and equilibrium limited, and therefore, low CO levels can be achieved only at low temperatures, even though the kinetics is more favorable at higher temperatures. As a result, two WGS reactors are typically used in industry. However, both the commercial high-temperature shift (HT) and low-temperature shift (LT) reactors have certain drawbacks that make them unsuitable for fuel processors being developed for use in onboard vehicle or for distributed power or hydrogen production.6–8 It * To whom correspondence should be addressed. Fax: 1-306-5854855. E-mail:[email protected]. † University of Regina. ‡ HTC Purenergy.

is therefore essential to develop a novel water-gas shift (WGS) catalyst in order to meet the necessary criteria for use in modern fuel processors. The research in our laboratory2,3,6,8–10 for the past few years has focused in this area of high purity hydrogen production using different fuel processors and hydrogenpermeable membrane coupled with WGSR when used with novel and advanced WGS catalysts.3 The role of WGSR in the reforming systems for the fuel cell is growing and a lot of research activities are currently in progress dealing with the new catalyst formulation, as well as kinetic and reactor modeling.11–14 Also, in most of the hydrocarbon processors, the WGSR is the biggest and heaviest component because the reaction is relatively slow at low temperatures compared to other reactions and is inhibited at high temperatures by thermodynamics.15 Therefore, reducing the size of the WGS reactor is an important issue to be addressed by using an advanced catalyst. The key to the development of an advanced catalyst lies in understanding the reaction mechanisms at high temperatures, the nature of the active sites, and the origin of deactivation during long-term intermittent use. The kinetics of WGSR is required in order to design an efficient fuel reformer and to optimize its operating conditions.16–19 A number of rate expressions have been reported in the literature and tested to evaluate the WGSR rate for various catalysts, particularly the commercially available LT (Cu-Zn-Al) and HT (Fe-Cr) systems.20–26 However, there are discrepancies in the kinetic data and reaction mechanism on various catalysts for both LT and HT water-gas shift, which could be due to different catalysts composition, surface properties and the reaction conditions (pressure and feed mixture compositions) adopted in the individual studies. Thus, the idea of using other catalyst combinations for high temperature WGSR should not be ruled out.3,27,28

10.1021/ie071547q CCC: $40.75  2008 American Chemical Society Published on Web 05/17/2008

Ind. Eng. Chem. Res., Vol. 47, No. 12, 2008 4087

In this contribution, we have focused on kinetic and reactor modeling of the high temperature WGSR in a packed bed tubular reactor (PBTR) on a new WGSR catalyst (UFR-C) developed in our laboratory.3 By using the experimental data from the PBTR, a set of WGS kinetic models are evaluated and discriminated over the catalyst (UFR-C) as a function of temperature and feed flow rate. Also, a detailed comprehensive modeling and simulation of WGSR using a two-dimensional, nonisothermal, pseudohomogeneous dispersion model is reported. We have also demonstrated whether or not the exclusion of the axial dispersion term in the partial differential equations used in representing packed bed reactors will affect the accuracy of the results. These results are presented and discussed in this paper.

consideration. The mechanism can be described by the following elementary steps: k2,k-2

CO + S T CO(s) H2O + S T H2O(s)

(3)

k4,k-4

H2O(s) + S T OH(s) + H(s)

(4)

k5,k-5

2OH + S T H2O(s) + O(s)

(5)

k6,k-6

OH + S T O(s) + H(s)

(6)

k7,k-7

CO(s) + H2O(s) T CO2(s) + H2(s)

(7)

k8,k-8

H2(s) T H2 + S

2. Kinetic Modeling Essentially, there are currently two reaction mechanisms for LT and high temperature WGSR.20,21,29 One of them is a regenerative (oxidation-reduction cycle) mechanism, which is based on the dissociation of water on the catalyst surface to produce hydrogen and an oxidized surface, which in turn, is reduced by carbon monoxide to complete the cycle.17,30–32 This mechanism is thought to be the dominant pathway for high temperature WGSR. The other mechanism is the associative mechanism which is based on the interaction of adsorbed carbon monoxide and water to form an intermediate33,34 which breaks down to form products. From these two mechanisms, a variety of rate expressions (based on LH for a Langmuir-Hinselwood mechanism, R for a redox type mechanism, and ER for an Eley-Rideal mechanism) can be derived. On the basis of these studies, it can be said that there is evidence to support both mechanisms at low temperatures for Cu-Zn-based or preciousmetal/oxides catalysts. On the other hand, most authors favor the regenerative mechanism for Fe-Cr high temperature catalysts. It is also suggested that the kinetics of the high temperature WGSR can best be described by LH and the powerlaw (PL) models as they could accurately accommodate all of the experimental results, thereby making them suitable for reactor design.15,23,35 Ceria or ceria-zirconia support systems are known to be able to store and release oxygen and hydrogen from the surface and bulk vacancies.36 However, a detailed understanding of the influence of ceria or ceria-zirconia on the catalytic process is still a matter of considerable debate.27,37 The role of formates as potential reaction intermediates has also been discussed as an alternative route to a redox mechanism.22,26,34,38 In this connection, a very recent finding by Meunier et al.,26 by using isotopic transient kinetic analyses, suggests the minority role of formates as a reaction intermediate in a ceria-based catalyst, though not involved in the primary pathway. Also, cerium oxide stabilized copper has been reported as an active water-gas shift catalyst at high temperatures.25,39 2.1. Proposed Mechanisms and Kinetics Models. The use of CexZr1-xO2 as support materials for WGSR at high temperature is now well-established.3,22,24 This fact is based on the higher mobility of the lattice oxygen facilitated by the distortion of the O2 sublattice in the mixed oxide. This in turn not only improves the oxygen storage capacity, redox property, and thermal stability but also enables the reaction to proceed at a relatively higher temperature, up to 773 K.36,40,41 The proposed mechanism is therefore based on the experimental data and relevant literature data put together in such a way that all the reaction steps involved during the WGSR are readily taken into

(2)

k3,k-3

(8)

k9,k-9

CO2(s) T CO2 + S

(9)

k10,k-10

CO(s) + H2O(s) T COOH(s) + H(s)

(10)

k11,k-11

COOH(s) T CO2 + H(s)

(11)

k12,k-12

2H(s) T H2 + 2S

(12)

k13,k-13

CO + Os T Rs + CO2

(13)

k14,k-14

H2O + Rs T Os + H2

(14)

where S, Os, and Rs represent unoccupied, oxidized, and reduced sites, respectively. In the adsorptive or associative mechanism, CO and H2O adsorb on the catalyst surface (reaction steps 2 and 3) and are in equilibrium. Similarly reaction steps 4–6, 8, 9, and 11–14 are assumed to be in equilibrium.20 Reaction steps 7 and 10, which indicate the formation of intermediate species, are not in equilibrium and could be taken as the rate determining steps (RDS). Many research groups have tried to prove the existence and form of the intermediates such as the formate species through chemical trapping experiments, isotopic labeling, or Fourier transform infrared (FTIR) spectroscopy.5,21,26 The role of formate species as an intermediate species also stems from the fact that the use of (Ce-Zr)O2 generally promote the formation of these species on the ceria-zirconia surface.22 From this adsorptive mechanism, Langmuir-Hinshelwood (LH) type rate expressions can be derived. The following rate expression is derived from two elementary steps depicted in eqs 2 and 3 with a surface reaction of molecularly adsorbed reactants (eq 7) as the RDS. Model 1:

- rA )

(

koe-Ea/RT NCONH2O -

NCO2NH2

)

KP (1 + KCONCO + KH2ONH2O + KCO2NCO2 + KH2NH2)2

(15)

This rate equation has been tested in several studies,7,12,42 and it has been suggested that the LH model could accommodate all of the experimental data. Similarly, another model was derived from the LH mechanism assuming that the RDS was the surface reaction between molecularly adsorbed carbon monoxide and water to give a formate intermediate and atomically adsorbed hydrogen (eq 10). This rate expression also assumes that the presence of high excess of water inhibits the reverse water-gas shift reaction, and thus, the concentration

4088 Ind. Eng. Chem. Res., Vol. 47, No. 12, 2008

of CO2 in the intermediate step (eq 11) can be considered negligible. Model 2:

- rA )

(

koe-Ea⁄RT NCONH2O -

NCO2NH2 KP

)

(1 + KCONCO + KH ONH O + KCO NH 0.5NCO 0.5 + KH 0.5NH 0.5)2 2

2

2

2

2

2

2

(16) The regenerative or surface redox mechanism, on the other hand, is the cycling of the two steps. In the first step (eq 13), water adsorbs and dissociate on reduced site of (Ce-Zr)O2 surface to produce hydrogen while oxidizing a site in the following step (eq 14) where, CO is oxidized to CO2 on this oxidized site. Many groups have found evidence of oxygen migration from the (Ce-Zr)O2 onto the deposited metal particles at relatively lower temperature.35,43 The rate equation derived for this model can be represented as follows:

Model 3:

- rA )

(

koe-Ea⁄RT NH2O 1+

NCO2NH2 NCOKP

KCONCO2

)

(17)

NCO

Figure 1. Schematic diagram of a packed bed tubular reactor (PBTR).

2.2. Power Law (PL) Model: In contrast to these rate expressions from detailed reaction, mechanisms, and rate determining steps, there are simple empirical rate expressions, which do not consider any mechanism. This model is also used as a reference for assessing the accuracy of empirical kinetic data. This can be represented as follows: Model 4:

- rA ) koe-Ea⁄RTNCOaNH2ObNCO2cNH2d(1 - β) (18)

where, rA (mol(CO)/g(cat) · h) is the reaction rate and is calculated based on the fractional conversion of CO (XCO) and weight of the catalyst (W) and flow rate of CO (mol/h) as follows. -rA )

dXCO d(W/FA0CO)

(19)

Ni is the corresponding molar flow rate (mol/h) of component i whereas, a, b, c, and d are the apparent reaction orders of the component CO, H2O, CO2, and H2, respectively; ko is the preexponential factor, Ea is the apparent activation energy (J/mol), R is the universal gas constant (8.314 J/mol · K), and T is the reaction temperature (K). β is the term for backward reaction or approach to equilibrium and is defined as β)

NCO2NH2 KPNCONH2O

where, KP is an equilibrium constant for the WGS reaction. The power law model seems to work in many cases and has been extensively used by several groups for high temperature WGSR for kinetic studies.19,23,35 2.3. Numerical Modeling: A theoretical numerical model was used for modeling and simulating the performance of the packed bed tubular reactor (PBTR). This model consists of mass and energy balance equations, which were developed by carrying out steady state mass and energy balances around the reactor in the presence of a pseudohomogenous chemical reaction as documented in the literature.2,6,14,44,45 The momentum conservation equation was neglected based on the fact that the particle

size of the catalyst was not too small so as to create a substantial pressure drop across the bed and the fact that the bed height was small. On the basis of the reactor geometry illustrated in Figure 1, the model conservation equations for each of the component species i can be expressed in the radial, r, and axial, z, directions in cylindrical coordinates system as given below in eqs 20 and 21 for mass and energy balance equations, respectively, with r and z as the independent variables. Deff

[

∂2Ci ∂r2

+

]

∂2Ci ∂Ci 1 ∂Ci + Deff 2 + FBνirj ) uz r ∂r ∂z ∂z

[

(20)

]

∂2T(r, z) 1 ∂T(r, z) ∂2T(r, z) + + λeff ) 2 r ∂r ∂r ∂z2 ∂T(r, z) (21) FgCpuz ∂z The terms of the equations are defined in Table 1. Considering the geometry of the PBTR used for the experimental work shown in Figure 1, appropriate boundary conditions, which are shown below (eqs 22–24) were coupled with the conservation equations (the material and energy balance equations, eqs 20 and 21). In the radial direction, the equations are solved between r ) 0 and r ) r1 with r1 as the tube diameter.

(∆Hj)FBνirj(r, z) + λeff

Ci(r, 0) ) C0i ,

T(r, 0) ) T0 at z ) 0 and 0 e r e r1 (22)

∂Ci (0, z) ) 0, ∂r

∂T ( ) 0, z ) 0 at r ) 0 and 0 e z e L ∂r (23)

∂Ci (r , z) ) 0, ∂r 1

λeff

∂T (r , z) ) -Utw(T - T0) at r ) ∂r 1 r1 and 0 e z e L (24)

The flow enters the computational domain (z ) 0 cm, r) at the known velocity, composition, and temperature. A flat profile of the axial velocity, u, and a zero radial velocity, V ) 0, is

Ind. Eng. Chem. Res., Vol. 47, No. 12, 2008 4089

used in all simulations at this inlet boundary. Equally, the radial velocity was assumed to be zero (plug flow) throughout the entire bed. At the tube wall (z, r ) r1), the axial velocity is constrained to zero. At the tube centerline (z, r ) 0), a symmetry boundary condition is applied at which the values for all variables have a zero normal gradient (eq 23). At the reactor exit (z ) L, r), it can be assumed that the convective part of the mass and heat transport is dominating.2,7 The material balance equation can be transformed into a molar flow rate format as given in eq 25. The derived form in terms of molar flow rate is given below. ∂2Fi Deff ∂Fi ∂2Fi ∂Fi ) Deff 2 + + Deff 2 + FBuzArj (25) ∂z r ∂r ∂r ∂z The resulting partial differential equations were solved simultaneously using the finite elements technique subject to the initial and boundary conditions without any simplifying assumptions as reported by Aboudheir et al.6 u

3. Experimental Procedure 3.1. Catalyst. The UFR-C catalyst used for this study is a cost-effective and homemade formulation based on nonprecious metals, which has shown its improved durability under stringent conditions (high temperature). The (UFR-C) catalyst developed was synthesized by utilizing the interaction of hydrous oxide of CexZr1-xO2 with the cationic surfactant under basic condition followed by nickel and copper impregnation, the details of which are reported elsewhere.3,9,10 The chemical composition (weight percent) as measured by inductively coupled plasma (ICP) can be described as follows: 58Ce, 30Zr, 4Ni, and 8Cu. The key finding of these studies on Ce-Zr catalytic systems was that the WGS activity increased dramatically as the crystallite size of the oxides in the composites is reduced in the nanoscale regime.

3.2. Experimental Setup and Analyses. The reaction was carried out using a conventional catalytic fixed-bed tubular reactor operated isothermally at atmospheric pressure (Figure 2). It was made of Inconel 625 metal alloy tube of 12.7 mm internal diameter (D) placed vertically in a furnace with a single heating zone. The gas flows were metered and regulated by an Aalborg digital flow controller (GFC171S). Water was pumped through a HPLC pump (Alltech) at the desired flow rate. The reaction temperature was measured through a sliding thermocouple placed inside the catalyst bed. The error in temperature measurement was within (1 K. Prior to each experimental run for catalyst evaluation, the catalyst was activated by in situ reduction at 973 K with 5% H2 in N2 (Praxair). The feed and product gases were analyzed with an online gas chromatograph (HP-6890, Agilent Technologies) equipped with a thermal conductivity detector (TCD) using Haysep Q and Molsieve 13X columns (Alltech Associates) for complete separation of the gaseous components. 3.3. Kinetic Studies. Experimental kinetic data were collected at atmospheric pressure; temperatures of 673, 773, and 873 K; and having a contact time measured in terms of W/FA0CO in the range of 0.2 to 1.6 g(cat) · h/mol(CO). In order to approach plug flow conditions and minimize back mixing and channelling, a bed height of 70 mm (L) was used. This ensures that certain operating criteria as prescribed by Froment and Bischoff were fulfilled.46 Accordingly, the ratio of catalyst bed length to catalyst particle size (L/Dp) was 87 and the ratio of the inside diameter of the reactor to particle size (D/Dp) was 16. The kinetic experimental data were collected over a 3 h time-onstream (TOS) to ensure stable performance of the catalyst under the prevailing set of operating conditions. The CO conversion and H2 selectivity were calculated using the formulas as follows: conversion of CO (XCO % ) ) (moles of COin moles of COout) ⁄ moles of COin × 100

Table 1. Operating Conditions and Parameters Used in the Numerical Modeling of the Laboratory Packed Bed Tubular Reactor (PBTR)

selectivity to H2 (SH2 % ) ) moles of H2 out ⁄ (XCO × moles of COin) × 100

parameter

4. Results and Discussion

T0 VZ W/FA0 Dp Dt R L Fg FB λz and λr Cp Dz and Dr ∆H UTW k0 E KA KB KC KD Ptot KP FA0 FB0 yA0 yB0 Mave

definition and units feed inlet temperature superficial velocity space time catalyst particle diameter internal diameter of the tube of the reactor radius of packed bed tubular reactor catalyst bed length gas density bulk density of catalyst in the reactor effective thermal conductivity heat capacity, effective diffusivity heat of reaction overall heat transfer coefficient collision coefficient activation energy adsorption constant adsorption constant adsorption constant adsorption constant total pressure equilibrium constant at T0 inlet molar flow rate of CO inlet molar flow rate of H2O inlet mole fraction of CO inlet mole fraction of H2O average molecular weight of feed mixture

values 773 K 0.24 km/h 1.3 g(cat) · h/g(CO) 0.8 mm 12.7 mm 6.35 mm 70 mm 0.37 kg/m3 21.6 kg/m3 38.2 J/m · h · K 1.0 kJ/kg · K 1.15 × 10-3 m2/h -4.1 × 104 J/kmol 1.8 × 102 J/m2 · h · K 2.01 × 108 4.27 × 104 J/mol 69.6 17.4 82.3 198.3 101.3 kPa 4.9 0.199 mol/h 0.53 mol/h 0.27 0.72 19.5

4.1. Thermodynamics and Equilibrium Conversion. A thermodynamic equilibrium analysis was performed to determine the limit for CO conversion at various temperatures. The main reactions that take place during the WGSR process are as follows CO + H2O T H2 + CO2

(26)

CO2 + 4H2 T CH4 + H2O

(27)

CO + 3H2 T CH4 + H2O

(28)

CH4 + H2O T CO + 3H2

(29)

CH4 T C + 2H2

(30)

C + H2O T CO + H2

(31)

Since the amount of methane formation is very small, the species taken into consideration for the thermodynamic equilibrium calculations were H2O, CO2, CO, and H2, and accordingly, the equilibrium constant for the water gas shift reaction can be derived in a conventional way as shown in the following equation lnKP )

- 4.33 ( 4577.8 T )

(32)

4090 Ind. Eng. Chem. Res., Vol. 47, No. 12, 2008

Figure 2. Schematic diagram of the experimental setup for the water-gas shift reaction, WGSR, using a packed bed tubular reactor, PBTR.

Figure 4. Effect of total volumetric feed flow rate on the methane conversion for WGSR (H2O/CO ) 2.7) at 673 K with a constant residence time of 1 s. Figure 3. Equilibrium conversion of CO for WGSR as a function of temperature (total pressure, Ptot ) 1 atm and H2O/CO ) 2.7).

According to the above equation, the equilibrium constant of WGS reaction is 11.7, 4.9, and 2.87 at 673, 773, and 873 K, respectively. At a given temperature and at a given equilibrium constant with a given feed (e.g., H2O/CO ) 2.7), composition and equilibrium conversion (Xeq) for the WGSR as presented in Figure 3 can be calculated using the following equation: KP )

Xeq2 (1 - Xeq)(2.7 - Xeq)

(33)

It can be seen that the equilibrium conversion of CO decreases as the temperature increases. The equilibrium conversion of 95.7, 91.7, and 87.9 were calculated at the reaction temperatures of 673, 773, and 873 K, respectively. On the basis of this and to further minimize the influence of methanation in this kinetic investigation, the feed rates were varied to keep the CO conversion far from the thermodynamic equilibrium. Also, the high water to CO ratio was used deliberately in order to compensate for the CO2 influence on equilibrium due to reverse water gas shift reaction. The use of higher water concentration in the feed could minimize this effect as reported elsewhere.20,21 4.2. Preliminary Tests. Further preliminary experiments and some theoretical calculations were carried out in order to determine suitable conditions for which external mass transfer and internal pore mass transfer are not predominant. Considering

the effect of external mass transfer, the total gas flow rate (CO + N2 and steam) was varied between 230 and 515 mL/min under a constant residence time of 1 s at 673 K. As shown in Figure 4, the conversion of CO was found to be independent of the total gas velocity when the gas flow rate was equal to or higher than 285 mL/min, indicating the absence of external mass transfer effects at this flow rate. The impact of intraparticle diffusion on the catalyst particle size was also considered before selecting the correct particle size. Therefore, the reaction on different average particles sizes of the catalyst (0.15-0.8 mm) were carried out in order to confirm that the experiments were performed within the region of intrinsic kinetics. It was observed that the catalyst with the particle size less than 0.8 mm showed no intraparticle diffusion limitation in the range of conditions studied. 4.2.1. Heat Transport Effects. The internal pore heat transfer resistance was estimated using the Prater analysis given by ∆Tmax,particle )

Deff(CAs - CAc)(∆Hr) λeff

(34)

where ∆T max, particle is the upper limit to temperature variation between pellet center and its surface, ∆Hr is the heat of reaction, CAs and CAc are, respectively, the concentrations at the pellet surface and center (assumed, respectively, to be the same as bulk concentration and zero, as suggested by Levenspiel),47 Deff

Ind. Eng. Chem. Res., Vol. 47, No. 12, 2008 4091 Table 2. Experimental Kinetic Data run

T (K)

NA (mol/h)

NB (mol/h)

NC (mol/h)

ND (mol/h)

rate mol(CO)/g(cat) · h

KP

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34

673 673 673 673 673 673 773 773 773 773 773 773 773 773 773 773 773 873 873 873 873 873 773 773 773 773 773 773 773 773 773 773 773 773

0.125 0.169 0.110 0.200 0.195 0.122 0.068 0.126 0.089 0.083 0.108 0.167 0.183 0.119 0.144 0.192 0.110 0.069 0.069 0.090 0.121 0.106 0.132 0.141 0.161 0.108 0.170 0.113 0.146 0.183 0.113 0.156 0.187 0.116

0.360 0.493 0.306 0.560 0.513 0.320 0.272 0.454 0.292 0.242 0.313 0.373 0.505 0.323 0.232 0.181 0.181 0.272 0.232 0.293 0.363 0.313 0.466 0.475 0.539 0.319 0.549 0.323 0.480 0.561 0.324 0.490 0.566 0.327

0.031 0.034 0.015 0.026 0.008 0.003 0.057 0.076 0.036 0.019 0.018 0.019 0.022 0.005 0.059 0.034 0.015 0.057 0.032 0.035 0.035 0.020 0.132 0.119 0.146 0.136 0.166 0.172 0.053 0.039 0.009 0.043 0.034 0.007

0.028 0.030 0.013 0.023 0.009 0.003 0.053 0.072 0.033 0.016 0.016 0.017 0.019 0.006 0.055 0.030 0.013 0.052 0.029 0.032 0.031 0.017 0.068 0.059 0.061 0.015 0.051 0.010 0.136 0.115 0.117 0.196 0.178 0.202

8.116 9.206 10.760 11.319 13.385 13.882 14.362 19.895 24.570 28.915 30.514 31.922 33.376 35.177 21.351 21.919 22.207 27.286 39.987 45.832 51.619 67.766 16.829 25.158 31.440 18.600 23.418 26.380 18.913 21.293 22.580 14.461 17.242 18.847

11.7 11.7 11.7 11.7 11.7 11.7 4.9 4.9 4.9 4.9 4.9 4.9 4.9 4.9 4.9 4.9 4.9 2.8 2.8 2.8 2.8 2.8 4.9 4.9 4.9 4.9 4.9 4.9 4.9 4.9 4.9 4.9 4.9 4.9

is the effective mass diffusivity obtained from Deff ) (DABε/ τ)48 where DAB is the bulk diffusivity of component A in B (i.e., CO in water), which, in turn, is estimated using Brokaw equation.49 The value for DAB was found at the maximum temperature of 873 K to be 1.8 × 10-4 m2/s. The effective diffusivity Deff was estimated to be 1.1 × 10-5 m2/s. Here, ε is the void fraction (estimated as the ratio of the volume occupied by voids to the total bed volume ) 0.5), τ is the tortuosity factor taken as 8,48 λeff is the effective thermal conductivity obtained using the correlation, λeff/λ ) 5.5 + 0.05NRe (in ref 45) for packed bed tubular reactors. The term λ is the molecular thermal conductivity calculated using Wassiljewa correlation to be 7.4 × 10-5 kJ/m · s · K.49 The effective thermal conductivity λeff was found to be 1.7 × 10-3 kJ/m · s · K. Substituting these values in eq 34, a value of 1.1 K was obtained for ∆Tmax,particle which shows that a pellet more or less had a uniform temperature. Further, the external heat transfer limitation across the gas film was determined using L(-rA,obs)(∆Hi) (35) ∆Tmax,film ) h where, ∆Tmax,film is the upper limit of temperature difference between the gas bulk and the pellet surface, L is the characteristic length, rA,obs is the observed rate of reaction, h is the heat transfer coefficient (estimated from the correlation JH ) JD ) (h/CpνF)N2/3 where JH is the heat transfer J factor, Npr ) Cpµλ, where λ is the molecular thermal conductivity). JD factors are given by the following correlations JD ) (0.4548/ε)NRe-0.4069 and JD ) (kc/V)NSc2/3;50 NSc ) (µ/FDAB), NRe ) Fνdp/µ(1 - ε). Also, kc is the mass transfer coefficient which is 7.9 × 10-2 m/s. The heat transfer coefficient h was determined to be 9.8 × 10-2 kJ/m2 · K · s. A value of 22.5 K was obtained for ∆Tmax,film. It is worth mentioning that these calculations were performed

considering the worst-case scenario where there is a complete mass transfer resistance at the entrance of the reformer. This maximum temperature gradient rapidly drop to almost zero at the exit of the catalyst bed as was evident in the study of Pacheco et al.51 Pacheco, in a similar study, concluded that it is likely that the actual mass transfer resistance will be shared between the external boundary layer and the intraparticle mass transfer; therefore, the external temperature gradient will be lower than the estimated one. On the basis of these results, the absence of any heat transfer limitations externally and internally can be assumed. This also led us to believe that isothermal conditions were prevailing during the course of the reaction. Additionally, a more rigorous criterion for determining the onset of heat transport limitation during reaction which was developed by Mears52 was also used to further ascertain the insignificance of heat transfer resistance in the rate of reaction robsFbRcE(∆H)

< 0.15 (36) hT2R On substituting the numerical values for the terms on the lefthand side (LHS) of eq 36 to a typical condition (run number 19 in Table 2) at 873 K, a value of 0.11 is obtained which is less than 0.15. On the basis of this result, the interparticle heat transfer limitation is considered to be absent in this case. 4.2.2. Mass Transport Effects. The internal pore mass transfer resistance was calculated using the Weisz-Prater criterion as given by Cwp,ipd )

-rA,obsFcRc2 DeffCAs

(37)

where Cwp,ipd is the Weisz-Prater criterion for internal pore diffusion, Fc is the pellet density, and Rc is the catalyst radius.

4092 Ind. Eng. Chem. Res., Vol. 47, No. 12, 2008

The estimated value for Cwp,ipd was 67.5, which is higher than the criterion value of 1 indicating the existence of mass transfer limitation within the catalyst pores. However, to further ascertain that the external mass transfer resistance has no effect on the rate of reaction, the ratio of observed rate to the rate if external resistance controls was examined. Equation 38 illustrates this criterion. -rA,obs dp observed rate ) rate if external resistance controls CAbkc 6

(38)

The estimated value for the ratio in eq 38 was 3.2 × 10-7. This result indicates that the observed rate is very much lower than the limiting external mass transfer rate. Thus, the resistance to external mass transfer should not influence the rate of reaction.47 Since the Mears’ criterion48 is often considered a more rigorous criterion for determining the onset of external mass transport limitation, we therefore decided to apply this criterion to determine if there was any mass transfer limitation during the collection of the kinetic data. This correlation is given in eq 39. robsFbRcn < 0.15 kcCA

(39)

The value of the LHS for run number 19 (Table 2) at 873 K of the equation is 0.075, which is half of the specified value. On the basis of these results, it would be appropriate to assume the complete absence of external mass transport limitation. 4.3. Catalyst Activity Evaluation and Experimental Rates. Prior to kinetic experiments, a long-term stability test was carried out on UFR-C in the temperature range of 673-873 K. A representative data on this stability test is presented in Figure 5. It can be seen from this figure that the methane conversion is very stable for about 10 h at temperature between 673-873 K. The conversion remained unchanged during the entire reaction time employed, indicating that the catalyst had a high stability. This stability test also ensures that kinetic experiments were carried out without any evidence of catalyst deactivation during the course of data collection. The kinetics of WGS over UFR-C was studied by using four different variables: (i) flow rates of CO, (ii) H2O/CO ratio, (iii) introducing CO2 in the feed, and (iv) introducing H2 in the feed at different operating temperatures (673-873 K). This was achieved by changing the flow rate of CO and N2 in the range of 161-290 mL/min and water in the range of 0.04-0.18 mL/min while the amount of catalyst was varied from 20-250 mg. Each experimental run used a fresh catalyst and was carried out for 3 h time-on-stream (TOS) for each flow rate and temperature. This also ensured that the CO conversions for all experiments varied between 1 and ∼ 55%, well below the equilibrium conversion limit. The results corresponding to each set of operating conditions are presented in Figure 6i-iv, respectively. Figure 6i shows the variation of CO conversion with several values of W/FA0 (ratio of the mass of the catalyst to the mass flow rate of CO, g(cat) · h/ mol of CO) at reaction temperatures of 673, 773, and 873 K. From the figure, it can be seen that the increase in W/FA0 results in a slowing down of the increase of CO conversion for the three reaction temperatures. It also indicates that CO conversion depends on the feed rate and approaches equilibrium conversion with an increase in W/FA0. Similar decrease in CO conversion can also be observed when H2O/CO ratios are changed (Figure 6ii) and when the products (CO2 and H2) are introduced into the feed (Figure 6iii and iv), respectively. The detailed kinetic experimental data for WGS are presented in Table 2 where the

Figure 5. Stability tests for UFR-C catalyst for 10 h at various temperatures.

experimental reaction rates were calculated by taking the slopes at various points of the x vs W/FA0CO curves within the range of the operating conditions using eq 19. 4.4. Estimation of Parameters and Kinetic Models Validation. Estimation of the values of the model parameters was based on the minimization algorithm. This algorithm is essentially a combination of Gauss-Newton and LevenbergMarquardt methods using nonlinear regression software, NLREG. The values obtained for the parameters of the kinetic models that converged as well as that of the power law are presented in Table 3. The validation of the developed rate models has been carried out via the measurement of the percentage of average absolute derivation (AAD%) between the predicted rate using proposed kinetic model and the experimentally observed rate for each model. They were further subjected to scrutiny by imposing the restriction that an acceptable model should have an AAD e 15% with the activation energy comparable to the power law model. Figure 7 represents a comparison of measured rates of CO consumption and the model predicted rates of CO consumption. From Figure 7, it can be seen that model 2 shows the best fit for the kinetic data (AAD ) 11.0%), followed by power law with an AAD of 12.0%, whereas models 3 did not yield satisfactory results with a greater than 20 AAD%. Further, the fitting of models 1 and 2 is supported by activation energy values. Model 3 was rejected on the grounds that both its activation energy and its AAD% were not comparable to those for the power law model. Very similar results were also reported for surface redox mechanism which was found to be unsuitable for the WGS at high temperature.15,20,21,25 On the basis of some of the activation energy values presented in Table 4, it can be seen that besides Fe2O3/Cr2O3 type catalysts, the kinetic studies on other high temperature WGS catalysts, such as copper-ceria catalyst, 10% Cu/(Ce-La)Ox,25 5% Ni/ ceria,21 1% Ni/ceria, and 1% Pd/ceria,17 report similar activation energy values indicating that the mechanism might involve the metal-ceria interface, utilizing the redox properties of the support oxide, and is essentially independent of the metal. However, ceria is found to be susceptible to significant crystallite-size growth at high temperatures38 and deactivation during WGS reaction.27 The addition of lanthanum to ceria is reported to have a significant improvement for high temperature WGSR up to 600 °C on both copper and nickel impregnated catalyst39 with very comparable activation energy values. Similar results were also obtained on zirconia doped ceria support system using platinum.24 The activation energy value obtained (using model 2) for our catalyst (42.7 kJ/mol) is in the same range obtained elsewhere as presented in Table 4 and also compares reasonably well with the value obtained using the power law model (48.2 kJ/mol). The better fitting of the kinetic

Ind. Eng. Chem. Res., Vol. 47, No. 12, 2008 4093

Figure 6. CO conversion in CDRM as a function of contact time (W/FA0) using (i) different feed flow rates between 673-873 K, (ii) H2O/CO ratio at 773 K, (iii) CO2 in the feed at 773 K, and (iv) H2 in the feed at 773 K. Table 3. Estimate of the Fitted Values of the Parameters of the Models parameter

power law

ko E (kJ/mol) KCO KH2O KCO2 KH2 nCO nH2O nCO2 nH2

3.9E+04 48.2

model 1

model 2

model 3

1.90E+07 40.6 23.865 6.6171 9.51854 25.4462

2.01E+08 42.7 69.633 17.38 82.30598 198.3075

4.2E+05 55.3 0.9125

0.34 0.39 -0.09 -0.25

data with the power law model also suggests that the kinetic data in this work is adequate to quantitatively describe the kinetic performance of WGS over UFR-C catalyst. In this connection, it is pertinent to mention a study by Podolski and Young23 in which experiments carried out in a recycle reactor and statistical techniques were used to discriminate between rival models. These authors also re-examined some of the previously published data and concluded that only LH and power law models could adequately accommodate all of the experimental results and thus were the ones most suitable for reactor design.15,35 4.5. Numerical Model Predictive Performance. The objective of the numerical modeling and simulation of any system is to obtain a mathematical model that perfectly or almost perfectly describes what happens in the system. For a model to be acceptable, it should be able to duplicate the real system with minimum or acceptable error. Therefore once a model has been

Figure 7. Parity chart showing a comparison between predicted and measured rates of CO conversion.

put together, its predictive efficiency against experimental or real plant result must be validated. The kinetic model incorporated in the reactor model equations is model 2 and validation was done after solving the coupled material and energy balance equations subject to initial and boundary conditions using the

4094 Ind. Eng. Chem. Res., Vol. 47, No. 12, 2008 Table 4. Comparison of Activation Energies for WGSR over Various Metal Catalysts catalyst

Ea (kJ /mol)

T (°C)

ref

Fe2O3-Cr2O3 Ni/CeO2 Ni/CeO2 Ni/Al2O3 Cu/CeO2 Cu/CeO2 Pd/CeO2 Pt/CeO2 Ce/LaOx Au/(Ce-La)Ox Cu/(Ce-La)Ox Ni/(Ce-La)Ox Cu/(Ce-La)Ox Pt/CeO2-ZrO2 Cu-Ni/CeO2-ZrO2 CuO/ZnO/Al2O3

59.8 85 44 78.2 56 51 45 46.2 58.5 40.0 30.4 38.2 70.4 71 42.7 41.8

450 300-1000 300 250 240 400 300 300 475 220 300 300 450 240 400-600 267

20 21 17 16 19 11 37 30 39 26 39 39 25 24 this work 29

finite elements method. The parameters used in the numerical modeling of the PBTR for the WGS are shown in Table 1. The predictive efficiency of the model in terms of CO conversion when compared with the experimental results gave an average absolute deviation (AAD%) of 12.8%. The simulation and experimental results are given in the parity plot of Figure 8, which compares the experimental conversions of CO with those predicted by solving model eqs 21 and 25. 4.6. Simulation of the Concentration and Temperature Profiles. The simulation of the concentration profile of the species in the system was carried out at a temperature of 773 K, W/FA0 of 1.3 g(cat) · h/g mol of CO and catalyst bulk density of 21.6 kg/m3. The concentration profiles are shown in Figure 9. A comparison of the exit concentration of the species predicted by the model with those obtained from experiment by GC analysis is shown in Table 5. An AAD% of 4.6 obtained from the comparison indicates that the simulation model has a good predictive efficiency. The corresponding axial temperature of the fluid at the same condition used in obtaining the concentration profile is shown in Figure 10. This figure shows the occurrence of an almost isothermal temperature profile. However, because of the unique behavior of an exothermic reaction, a hot spot was not completely absent although it was unpronounced since this system is only mildly exothermic. The hot spot in this system occurred between the bed height of 20 and 30 mm after which the temperature dropped very slightly. The temperature drop can be attributed first to the efficient heat transfer of the catalyst bed which transferred the heat away as it is being generated by the reaction and second to slowing down of the exothermic reaction due to low concentration of reactant species after the bed height of 30 mm coupled with the efficient heat transfer of the catalyst bed which removes the heat just as it is formed.

Figure 8. Comparison of measured and predicted CO conversion (mol %) within the temperature range from 673 to 873 K and W/FA0 range from 0.2 to 1.6 g(cat) · h/mol.

Figure 9. Axial concentration profiles along the reactor at a feed temperature of 773 K, W/FA0 of 1.3 g(cat) · h/mol of CO and having a bulk density of 21.6 kg/m3. Table 5. Outlet Concentration Profile of the Reactor at a Feed Temperature of 773 K and Bulk Density of 21.6 kg/m3 a fluid

experimental mole fraction

predicted molar fraction

AD %

CO H 2O CO H2

0.173 0.624 0.104 0.099

0.186 0.603 0.112 0.099

7.154 3.365 7.692 0.0

a

AAD % ) 4.6.

Figure 10. Axial temperature profile of the fluid along the center of the tubular reactor at W/FA0 of 1.3 g(cat) · h/mol of CO and inlet feed temperature of 773 K.

4.7. Effect of Axial Mixing Term. We have earlier stated in our earlier publications2,6 that established correlations are not enough conclusive reasons to eliminate this term until simulation studies have proven so. The importance of dispersion term in reactor modeling is usually considered by determining the Peclet number, which is a representation of the ratio between the rate of transport by convection and that by diffusion: Pe ) VL/D The high values of the Peclet number suggest that convection predominates over diffusion and dispersion phenomena, whereas low values indicate that mixing occurs in the axial direction. Some other authors have stipulated other conditions that are required to be satisfied in order to exclude the axial mixing term when setting up material and energy balance equations for a packed bed catalytic tubular reactor. For example, Hill53 and Carberry and Wendel54 suggested that when the length of the catalyst bed exceeds the diameter of catalyst particle diameter by a factor of 100, then the contribution from the axial mixing term is negligible. Also, Froment and Bischoff46 and Rase55 suggested the irrelevance of the axial term when the L/Dp ratio g 50 and the Db/Dp ratio g 10. In order to evaluate the applicability of these criteria in the WGSR reaction, we have solved eqs 21 and 25 subject to the initial and boundary

Ind. Eng. Chem. Res., Vol. 47, No. 12, 2008 4095

Figure 13. Effect of W/FA0 on CO conversion in the axial direction at 773 K having a catalyst bulk density of 21.6 kg/m3. Figure 11. Effect of axial dispersion term on CO conversion at a depth of 35 mm from the top of the catalyst bed at a feed temperature of 773 K and W/FA0 of 1.3 g(cat) · h/mol of CO.

Figure 12. Effect of axial dispersion term on the temperature profile at a depth of 35 mm from the top of the catalyst bed at a feed temperature of 773 K and W/FA0 of 1.3 g(cat) · h/mol of CO.

conditions with and without the axial dispersion terms. The results which are plotted in Figures 11 and 12 clearly show that there are no differences in the conversion and fluid temperature predicted by the model with and without the axial mixing term which goes on to support the established criteria. However, this has not always been the case as we have reported cases of differences in conversion and temperature when the model is solved with and without axial dispersion term2,6 using similar model equations. It therefore confirms what we have earlier said that the omission of this term should be done only after carrying out conclusive investigation through simulation to prove its irrelevance. 4.8. Effect of Increase in W/FA0 on Conversion. Often, the objective in any process design is to obtain the optimum combination of process variables that will increase the conversion of a reaction system to the desired products. For a given catalyst, the product’s selectivity depend on reaction temperature and such other things as the amount and type of catalyst used as well as flow rate of the feed material. It is well-known that an increase in the reactants species residence time will lead to increase in conversion; however, the best way to assess residence time in packed bed is the use of the ratio W/FA0. At a certain stage in process design, after a valid model has been obtained, the corresponding conversion can be obtained via simulation. For this process, we have been able to develop a valid model, hence, we can determine how much benefit in conversion we can obtain by varying the W/FA0 ratio at a constant temperature. Our objective is to see by how much the conversion can increase before reaching a point that the conversion profile would level off. This was investigated by using the same bed length, ratio of feed materials, and weight of catalyst used in collecting kinetic data. The W/FA0 values used for the investigation were 1.3, 2.6, 5.2, 13.0, and 15.6 g(cat) · h/g mol CO and the

Figure 14. Effect of catalyst bed length on CO conversion at various feed temperatures, a catalyst bulk density of 21.6 kg/m3, and W/FA0 of 1.3 g(cat) · h/ mol of CO.

corresponding percentage conversions were 34.7, 55.2, 74.0, 86.2, and 86.8, respectively. We can see from the plot in Figure 13 that the leveling off of the conversion was attained at a W/FA0 of 15.6. The maximum conversion obtained at the set condition was 86.8%. This simulation shows that a 100% conversion is not possible at the stated condition, but this does not mean that it cannot be obtained at some other condition. It is essential to remember that this was a very dilute system because of the amount of catalyst used. Again, the W/FA0 that gave the 86.8% conversion was really high especially at the laboratory scale for which the simulation was carried out. In view of this fact, it would be a good engineering judgment to go for the lower W/FA0 because their profiles were monotonically increasing even though the exit conversions were lower than that at the W/FA0 of 15.6. The unconverted products could be separated using a membrane. In all cases, it can be seen that increasing the W/FA0 leads to improvement in CO conversion. 4.9. Effect of Increase in Catalyst Bed Length. An alternative way of improving on the conversion of CO is by increasing the catalyst bed length. The increase in bed length will give rise to more residence time leading to an increase in conversion of reactant species. In this simulation, a CO molar flow rate of 0.199 mol/h was used in collecting the kinetic data at our reference condition of 773 K while increasing the bed height to 150 mm. It can be seen in Figure 14 that an additional 15% conversion in CO is obtained by the 80 mm increase in the length of the catalyst bed at 673 K when compared to a 20% conversion at a bed length of 70 mm. This is a substantial increase in conversion brought about by an increase in residence time. Again, the conversion profile is almost linear meaning that there would have been additional conversion should the bed height have been increased further. Also, increase in temperature by a 100 °C to 763 K would give a 64% conversion in CO at the same bed height, flow rate of CO, and catalyst concentration. The profile of the conversion profile at 873 K

4096 Ind. Eng. Chem. Res., Vol. 47, No. 12, 2008

suggests that the maximum conversion is more or less achieved and any increase in bed height would not bring about any reasonable gain in conversion. 5. Conclusions A new kinetic model based on the Langmuir-Hinshelwood (LH) formulation has been developed for the water-gas shift reaction (WGSR) over a new stable catalyst (UFR-C). The surface reaction between molecularly adsorbed carbon monoxide and water that results in a formate intermediate, and atomically adsorbed hydrogen was found to be rate determining; the model derived best predicted the experimental rates with an AAD of 11%. The better fitting of the kinetic data with the power law model also indicates that the kinetic data in this work is adequate to quantitatively describe the kinetic performance of WGS over UFR-C catalyst. A two-dimensional pseudohomogeneous reactor model was developed to simulate the packed bed tubular reactor for the WGSR. The reactor model was tested against the measured data and satisfactory agreement was found between model predictions and experimental results. The numerical investigation reveals that the proposed model can allow us to gain a reasonable insight into the packed bed WGSR system. Even on the laboratory scale, the simulation results were able to demonstrate that plug flow behavior is attained for each kinetic experimental condition. Moreover, the well-known criteria for neglecting the axial dispersion term have been met in this case and it can conclusively be recommended for elimination from the model. Acknowledgment The authors are very grateful for the financial support provided by the Canada Foundation for Innovation (CFI) and HTC Purenergy, Regina, SK., Canada. Literature Cited (1) Rostrup-Nielsen, J. R. Fuels and energy for the future: The role of catalysis. Catal. ReV. Sci. Eng. 2004, 46, 247. (2) Akpan, E.; Sun, Y.; Kumar, P.; Ibrahim, H.; Aboudheir, A.; Idem, R. O. Kinetics, experimental and reactor modelling studies of the carbon dioxide refroming of methane (CDRM) over a new Ni/CeO2-ZrO2 catalyst in a packed bed tubular reactor. Chem. Eng. Sci. 2007, 62, 4012–4024. (3) Kumar, P.; Idem, R. O. A comparative study of copper promoted water-gas-shift (WGS) catalyst. Energy Fuels 2007, 21 (2), 522–529. (4) Song, C. Fuel processing for low-temperature and high-temperature fuel cells: challenges, and opportunities for sustainable development in the 21st century. Catal. Today 2002, 77, 17–49. (5) Choi, Y.; Stenger, H. G. Kinetics, simulation and insights for CO selective oxidation in fuel cell applications. J. Power Sources 2004, 129, 246–254. (6) Aboudheir, A.; Akande, A.; Idem, R. O.; Dalai, A. Experimental studies and comprehensive reactor modeling of hydrogen production by the catalytic reforming of crude ethanol in a packed bed tubular reactor over a Ni/Al2O3 catalyst. Int. J. Hydrogen Energy 2006, 31, 752–761. (7) Ayastyuy, J. L.; Gutierrez-Ortiz, M. A.; Gonzalez-Marcos, J. A.; Aranzabal, A.; Gonzalez-Velasco, J. R. Kinetics of the low temperature WGS reactions over a CuO/ZnO/Al2O3 catalyst. Ind. Eng. Chem. Res. 2005, 44, 41–50. (8) Ibrahim, H. H.; Idem, R. O. Kinetic studies of the partial oxidation of isooctane for hydrogen production over a nickel-alumina catalyst. Chem. Eng. Sci. 2006, 61, 5912–5918. (9) Idem, R.; Kumar, P.; Sun, Y. Catalysts for hydrogen production. US Patent Application 20060216227, September 28, 2006. (10) Kumar P.; Sun, Y.; Idem, R. O. Nickel based ceria, zirconia and ceria-zirconia catalytic systems for low temperature carbon dioxide reforming of methane (CDRM). Energy Fuels, 2007, 21, 3112-3123. (11) Kusar, H.; Hocevar, S.; Levec, J. Kinetics of water-gas shift reaction over nanostructured copper-ceria catalysts. Appl. Catal., B 2006, 63, 194– 200.

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ReceiVed for reView November 14, 2007 ReVised manuscript receiVed February 22, 2008 Accepted March 20, 2008 IE071547Q