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Ind. Eng. Chem. Res. 2010, 49, 1063–1070

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Modeling of Autocyclic Reactor for the Removal of Unburned Methane from Emissions of Natural Gas Engines Massimiliano Zanoletti, Danilo Klvana,* Jitka Kirchnerova, and Michel Perrier Department of Chemical Engineering, Ecole Polytechnique, P.O. Box 6079, Station Centre-Ville, Montreal, QC, H3C 3A7

Natural gas represents an environmentally attractive alternative to diesel and gasoline fuels to reduce all automotive emissions. However, a relatively high content of unburned methane in the exhaust gases outweighs these benefits. To treat such emissions, a counter-current type fixed bed autocyclic reactor (ACR) was designed and built for laboratory testing. The efficiency of the ACR, loaded with palladium based catalysts (pellets and monoliths) was evaluated experimentally under a wide range of conditions. As a first step in modeling the ACR performance, a HT1-D model was developed to suit the actual reactor configuration. This model reproduced adequately the axial temperature profiles and methane conversion, but tuning parameters had to be used to account for heat transfer. To permit investigation of radial heat transfer and thus better understanding of the ACR behavior, a two-dimensional model was developed, and successfully validated against experimental data. The new HT2-Dt model allowed a full range of the ACR performance simulations. 1. Introduction Natural gas (NG), composed mostly of methane, represents the cleanest alternative of the available fossil fuels.1 Operating under lean conditions, NG-fuelled engines typically emit not only less carbon dioxide but also considerably less CO, nonmethane organic gases, and NOx, in comparison with liquid fuel engines. However, these benefits are in part offset by relatively high emissions of unburned methane.2 Even though methane is nontoxic and photochemically inert, its removal is required, because its green house effect is very high. Because of the methane refractory character for oxidation and relatively low temperatures of exhaust gases, traditional automotive converters are inefficient to reduce methane concentration to acceptable levels as discussed by many authors.3-5 To alleviate the problem of low temperatures, use of reversed flow (cyclicfeed) type of reactor has been evaluated.6-8 Even though the reversed flow reactor showed a good potential for application as a converter for emission control after automotive engines, it suffers from several technical inconveniencies such as valve operation and control, making it not well suitable for transportation. An alternative solution could potentially be found by adopting a counter-current-type reactor consisting of a nonadiabatic fixed-bed reactor featuring two concentric compartments, thermally coupled by fins (Figure 1). The innovative design of this reactor takes advantage of the heat release of exothermic reactions in a way to ensure a selfregulating, that is, autocyclic operation.9 This and the simplicity of its operation offset to some extent the disadvantages of recuperative heat exchange characterizing counter-current reactors, or circulation loop reactor and the internal recirculation reactor).10-12 The feed mixture entering the reactor flows first across the outer annular catalytic bed to the extremity of the reactor where it enters the inner bed and flows in the countercurrent direction toward exit. The outlet part of the inner reactor tube is equipped with longitudinal straight fins to improve heat transfer.13 This physical coupling of the outlet with the entrance part of the annulus provides a continuous heat recovery to improve the autothermicity, and if the front moves up to the * To whom correspondence should be addressed. E-mail: [email protected].

exit of the inner reactor compartment its heat may reignite the incoming combustion mixture. This so-called autocyclic reactor (ACR) was successfully tested to treat low methane concentration not only in air but especially in synthetic exhaust gas containing 7 vol % carbon dioxide and 14 vol % water.14 The ACR, loaded with highly active laboratory prepared palladiumbased catalysts (monoliths and pellets), showed a good potential for removing low methane concentrations from exhaust gases of natural gas engines. To examine the operational limits of the autocyclic reactor, a 1-D heterogeneous mathematical model was developed as a first step. In this model the heat transfer between inlet and outlet compartments and the heat loss were taken into account by tuning parameters determined on the basis of experimental data.14 Although the simulations by HT1-D model described adequately the experimental data, the HT1-D model could not illustrate properly the radial heat transfer. Thus, to investigate the complete behavior of the ACR, a more advanced 2-D model was developed as presented in this work. The relatively complex physical characteristic of the studied ACR is represented in Figure 2. For the purpose of modeling, the reactor bed was divided into several zones.

Figure 1. The autocyclic reactor.

10.1021/ie900701h  2010 American Chemical Society Published on Web 09/15/2009

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Figure 2. The internal configuration of autocyclic reactor: schema of the catalytic bed zones and position of thermocouples.

2. Description of the 2-D Mathematical Model As mentioned and indicated in Figure 2, both parts of the catalytic bed of the ACR (concentric and the annular) consisted of a pellet layer (zone II and VI) and a monolith layer (zone III and V). Each of these layers (zones) required a different approach in modeling. While the pellet sections could have been simply treated as a packed bed, modeling the monolith layers was more difficult. Most of the existing mathematical models (1-D, 2-D, or 3-D) for monolithic catalysts refer to reactors operating under adiabatic conditions. Consequently, modeling on channel scale is currently still the most affordable choice. However, the experimental autocyclic reactor is not adiabatic and in this case all of the channels, which thermally interact with each other, have to be taken into account. To consider the differences in flow and temperature in different channels, a number of representative channels, or even all of the channels, rather than a single one, have to be chosen in order to achieve good accuracy. Full scale models provide more details and give highest accuracy, but demand expensive computing facilities.15 Very few articles in the literature have investigated nonadiabatic monolithic reactors.16-19 Usually the monolithic geometry is reconfigured by arranging the channels in N coaxial rings to ensure circular symmetry.16,19 This discrete approach has the advantage that the performance of individual channels can be predicted. However, even if it represents the most accurate interpretation of the monolith behavior, it cannot be applied to the whole monolithic reactor, without some difficulties. In contrast to a discrete approach, continuous models provide an interesting alternative.20 Mathematical models based on a continuum approach are similar in concept to the two phase heterogeneous model for a packed-bed reactor. In effect, the honeycomb structure is replaced with a homogeneous structure containing both a gas phase and a solid phase. This approximation is acceptable if the diameter of the whole monolith differs by orders of magnitude from the dimensions of a single channel.21 In this work, we developed an axi-symmetric 2-D (r, z) heterogeneous model for the whole ACR unit, based on a heterogeneous packed-bed model for the pellet sections and on continuous approach for the monolithic reactor section. The evident similarities between these two modeling approaches contributed to give a unique mathematical representation of the mixed catalytic bed (pellets and monoliths). Moreover, to investigate the response of the reactor to the variation of inlet conditions (in terms of temperature and methane concentration) the transient term was also included in the mass and energy balance equations. The general assumptions of this axi-symmetric 2-D (r, z) heterogeneous model are: (i) the gas phase moves through the reactor in plug flow; (ii) the properties of the fluid phase are calculated as a function of temperature; (iii) the fluid is assumed as incompressible and nonconservative equations for mass and

energy balances are used; (iv) the gas mixture is assumed ideal since pressure is low and species are small, mostly nonpolar molecules; the maximum deviation was shown by steam at the inlet conditions considered here: ZH2O (723 K, 1 bar) ) 0.9994; (v) the solid phase heat transfer equation is modeled using effective values for thermal conductivities. The monolith channel cross-sectional area is considered to be constant and the flow distribution at the inlet of the reactor is uniform; (vi) the gas and the solid phases are coupled through the use of appropriate heat and mass transfer coefficients; (vii) homogeneous chemical reaction is neglected, since at the considered moderately high temperature gas-phase reactions do not occur; (viii) the catalyst distribution is homogeneous; (ix) no temperature gradient was considered in the catalyst pellets (Prater number β < 10-3), because the treated methane concentrations and consequently the corresponding combustion heat are very low. Even if nonuniformities in the inlet flow distribution (or velocity field) in monolith reactors can cause changes in performance due to localized high/low space velocities, we assumed that the first part of catalytic bed (composed only by pellets) may prevent efficiently nonuniform gas phase distribution. The main equations are presented here for completeness. In the packed bed (Figure 2, zones II and VI) mass transfer occurs by diffusion in both axial and radial direction and by convection in the axial direction. In the monolith sections (Figure 2, zones III and V) separated channels prevent radial diffusion of mass. The generic mole balance for the gas phase in the reactor is ∂c c eff∇c) ) -kmav(c - cs) - u¯ · ∇c + ∇ · (-D ∂t

(1)

The generic mole balance for the solid phase in the reactor is km(c - cs) ) η(-rCH4)

(2)

where the first-order reaction rate rCH4 is evaluated at the temperature of the surface. The average reaction rate in the catalyst, that is the actual rate, can be related to the rate evaluated at the concentration and temperature at the external surface of the catalyst through the use of an effectiveness factor η. Depending on the reactor zone considered (pellets or monoliths), appropriate correlations of η were used.22,23 For the inert pellets section (Figure 2, zone I), the rate of methane disappearance was not considered. The energy balance for the fluid takes into account axial and radial diffusion and axial convection. The generic equation for the gas phase is FCp

∂T + ∇ · (-kc∇T) ) hav(T - Ts) - FCpu¯ · ∇T ∂t

(3)

For the monolithic bed, the radial conduction term was eliminated. The energy balance in the solid phase was modeled considering the effects of accumulation, axial and radial conduction, and energy generation by the reaction, as necessary. The form

Ind. Eng. Chem. Res., Vol. 49, No. 3, 2010 Table 1. Dimensions of the Laboratory Scale Auto Cyclic Reactor reactor section inside diameter, inner pipe (2 in. sch. 40) inside diameter, outer tube length, inner pipe length, outer tube number of fins fin dimensions axial displacement (zone IV) annular inert section length (zone I) annular pellet catalytic section length (zone II) annular monolith section total length (zone III) diameters annular monolith inner monolith section total length (zone V) diameter inner monolith inner pellet catalytic section length (zone VI)

102 mm × 1.5 mm 470 mm 500 mm 14 9.5 mm × 176.4 mm × 3.2 mm 20 mm 10 mm 177 mm 280 mm 92 mm × 62 mm 280 mm 41 mm 187 mm

of the equation is the same for both packed bed and monolith sections: FCp

Table 2. Kinetic Parameters for the Catalysts

dimension 52 mm × 3.9 mm

∂Ts + ∇ · (-kc∇Ts) ) -hav(T - Ts) - ∆Hrη(-rCH4) ∂t (4)

Appropriate physical properties for both solid and gas phases were used in the balance equations. Heat and mass transfer coefficients (h and km) were calculated for both pellets and monolith catalysts and they were expressed in dimensionless Sherwood number (Sh) and Nusselt (Nu) number. To calculate the local Sh and Nu values for square channels, correlations developed by Groppi et al.24 were applied, while Wakao and Kaguei correlations25 were used in the model to evaluate Sh and Nu for spherical catalytic pellets. Fins were considered in the boundary conditions by multiplying the surface exposed to the heat transfer by a coefficient F representing the surface increased by the fins. This coefficient (F ) 2.40) takes into account the real geometry of the reactor and was calculated as the ratio of the finned surface exposed to the gas fluid in the annular section divided by the surface of the tube without fins. Main dimensions of the reactor (can be found) are summarized in Table 1. For the solution of eqs 1-4, the spatial velocity at STP was calculated by dividing the total volume flow rate (140 L/min) by the open frontal area of the different zones in the reactor (u ) 0.8-1.8 m/s). Even if a full momentum balance was not considered necessary, since pressure drop is small across the reactor, the effect of the temperature on velocity was taken into account. Finally, in order to consider the heat losses between reactor and its surroundings, reactor walls were treated as nonadiabatic. Overall thermal resistance was calculated by thermal-electrical analogy, considering a uniform layer of insulating material (i.e., mineral wool) around the reactor. The system of partial differential equations was first discretized and then solved by finite element method, using COMSOL Multiphysics commercial software. Values of all necessary physical can be found in the previous article,14 but the kinetic parameters determined experimentally,14 are for convenience to the reader reproduced in Table 2. 3. Results and Discussion Even though the objective (focus) of the overall project was to assess the capacity of the ACR to remove unburned methane

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catalyst

Eapp [kJ/mol]

ln A [ln(mol/kg s bar)]

enriched 0.90 wt % Pd/Al2O3 pellets enriched 0.90 wt % Pd/Al2O3 pellets (presence of CO2 and water) washcoated monolith 0.80 wt % Pd washcoated monolith 0.80 wt % Pd (presence of CO2 and water)

88 113

16.3 17.4

100 154

15.4 20.9

from exhaust emissions of natural gas fuelled engines, it was instructive to evaluate its performance not only for combustion of methane in synthetic exhaust gas, but also for combustion of methane in air. Since the methane combustion in the presence of excess water vapor and carbon dioxide is considerably inhibited and therefore slower, especially at lower temperatures,14 comparing the two systems allows illustrating the effect of different kinetics on the ACR behavior. Furthermore, the data for methane combustion in air might be relevant for some other potential applications, for example for methane removal from fugitive methane gases. Thus, the developed HT2-Dt mathematical model was first validated by reproducing the previously obtained experimental data.14 Furthermore, the model was run to assess by simulation a wide range of ACR behavior under different operational conditions. 3.1. Validation of the HT2-Dt Model. To validate the new HT2-Dt model, its numerical solutions were compared to representative experimental data14 as shown in Figure 3 for the case of methane combustion in air and in Figure 4 for the case of methane combustion in synthetic exhaust gas. The solutions by the previous HT1-D model are included in the figures for comparison. In both figures points represent the experimental temperatures registered by thermocouples Ti (Figure) along the ACR, T1-T11 at r ) 0.048 m of the annulus, while the dotted and continuous lines correspond to the HT1-D and HT2-Dt model, respectively. It should also be noted that the points at z > 0.7 correspond to thermocouples T12, T13, and Tout (Figure 2) inserted in the center of the internal tube, that is, r ) 0, to different depth. At the first sight, it could be argued that both models reproduce the data similarly well. However, on closer examina-

Figure 3. Axial temperature profiles along the ACR reactor for the steadystate catalytic combustion of methane in air (140 L/min). Points are experimental; the dotted and continuous lines are simulations by the HT1-D and the HT2-Dt model, respectively. Inlet conditions: (]) CCH4,in ) 3000 ppm, Tin ) 400 °C; (∆) CCH4,in ) 3000 ppm, Tin ) 320 °C.

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Figure 4. Axial temperature profiles along the ACR reactor for the steadystate catalytic combustion of methane in synthetic gas (140 L/min). Points are experimental; the dotted and continuous lines are simulations by the HT1-D and the HT2-Dt model, respectively. Inlet conditions: (*) CCH4,in ) 1500 ppm, Tin ) 450 °C; (]) CCH4,in ) 3000 ppm, Tin ) 400 °C.

tion, the fit of the HT2-Dt model appears superior, especially for situations of lower temperatures in the reactor. Certainly, the HT2-Dt predicts correctly the position of the reaction front (highest temperature), while the predictions by the HT1-D model tend to be slightly off, the degree of the shift depending on the situation. The weakness of the HT1-D model stems from the need of using system specific tuning parameters to account for the heat transferred between the external and the internal compartments of the reactor and the heat loss from the annular compartment to its surroundings. Estimation of these parameters, different for pellet and monolith sections of the bed is not necessarily straightforward and typically requires adjustment by trial and error. On the other hand, the HT2-Dt model can be used for multiple inlet conditions and geometries, and can thus be employed for predictive and scaling purposes. The HT2-Dt model (continuous line) can describe well the change of temperature not only in the catalyst bed, but also the outlet methane conversion. Indeed, total conversion of methane was predicted for the cases represented in Figure 3 (CCH4,in ) 3000 ppm, Tin ) 400 °C; CCH4,in ) 3000 ppm, Tin ) 320 °C); for those in Figure 4, complete conversion was predicted for CCH4,in ) 1500 ppm with Tin ) 450 °C, whereas it was only 80% for CCH4,in ) 3000 ppm, with Tin ) 400 °C, all in agreement with the experimental data. 3.2. Simulations. Using the developed HT2-Dt model, a series of simulations was run to illustrate the effect of various conditions on the ACR behavior under the combustion of methane in air, or in synthetic exhaust gas (containing 7 vol % carbon dioxide and 14 vol % water) and to assess the overall ACR performance. 3.2.a. Methane in Air. Figures 5-8 represent a series of simulations run to illustrate the ACR temperature profiles developing under different inlet temperatures and methane concentrations. For example, in Figure 5 two steady state temperature profiles are compared. When for 3000 ppm methane the inlet temperature is 400 °C, the reaction front is positioned at the level of thermocouple T2. Decreasing the inlet temperature for the same methane concentration induces a movement of the front to

Figure 5. Temperature profiles along the ACR reactor for the steady-state catalytic combustion of methane in air (140 L/min). CCH4,in ) 3000 ppm, with Tin ) 400 °C, reaction front corresponding to T2 position; CCH4,in ) 3000 ppm, Tin ) 320 °C, reaction front corresponding to T5 position.

Figure 6. Effect of decreasing Tin on the reaction front movement under steady state combustion of methane in air for 140 L/min: (a) CCH4,in ) 2000 ppm and Tin ) 400 °C; reaction occurring at position T2 (Figure 2); (b) CCH4,in ) 2000 ppm and Tin ) 350 °C; (c) CCH4,in ) 2000 ppm and Tin ) 300 °C; reaction occurring at position T5.

position of T5. Note that the temperature scales in this and successive figures are not uniform, each showing the minimum and the maximum.

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Figure 7. Gas phase temperature profiles in the reactor for 140 L/min, methane in air (°C): (inlet conditions) (a) CCH4,in ) 0 ppm and Tin ) 350 °C; (b) CCH4,in ) 1000 ppm and Tin ) 350 °C, steady state; (c) CCH4,in ) 1000 ppm and Tin ) 240 °C, after 10 min, final methane conversion < 60%; (d) CCH4,in ) 1000 ppm and Tin ) 240 °C, after 30 min, reaction extinguished.

Figure 8. Temperature evolution with time in the reactor under methane combustion in air for 140 L/min: (a) CCH4,in ) 0 ppm and Tin ) 400 °C; (b) CCH4,in ) 2000 ppm and Tin ) 400 °C, steady state. Response to the change of inlet temperature Tin from 400 to 300 °C, 2000 ppm methane: (b) t ) 0; (c) after 10 min; (d) after 30 min; (e) after 1 h.

Similar, but gradual movement of the reaction front is illustrated in Figure 6 for lower methane concentration. Here, three steady state temperature profiles for combustion of 2000 ppm methane at three inlet temperatures can be compared. The model predicts a fairly quick response to changes in inlet conditions. Rapid variations in the gas feed temperature induce the reaction front displacement, as shown in Figure 6. Temperature profiles a, b, and c represent steady-state methane combustion. If the inlet temperature decreases from 400 to 300 °C, by steps of 50 °C, the hottest gas phase (reaction front) temperature, initially at the inlet of the reactor, moves toward the catalytic bed, because of the colder incoming combustion mixture. If the heat generated by the reaction is sufficiently high to allow the reaction to occur, new steady state combustion is reached. The reaction front then advances along the reactor from position T2 to position T5. Similar behavior was observed experimentally in the ACR pilot unit for comparable inlet conditions of temperature and methane concentration.14 Figure 7 illustrates well the effect of steady state combustion of 1000 ppm methane in air on the temperature profile in the reactor and its response to decreasing the inlet temperature from 350 to 240 °C during combustion, in this case leading to extinction. As the methane mixture is introduced, the hottest (reaction) zone moves along the reactor axis, increasing at the same time the temperature at the outlet. When the inlet temperature is decreased (during combustion), the reactor responds quickly to the change;14 in the illustrated case, conversion dropped to less than 60% in about 10 min, the highest temperature zone moved toward the exit and shortly after the combustion extinguished, the whole reactor cooled down.

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Figure 9. Simulated temperature profiles along the reactor. The ACR unit fed by methane in synthetic exhaust gas (140 L/min) with CCH4,in ) 3000 ppm at different inlet temperatures Tin. Arrow indicates the maximal temperature (i.e., reaction front position in the reactor).

Finally, Figure 8 depicts the reignition-cycling mechanism, the special feature of the ACR, represented by the temperature evolution with time when for CCH4,in ) 2000 ppm the inlet temperature is changed from Tin ) 400 to 300 °C. If a drastic reduction of inlet temperature (from 400 to 300 °C) occurs, the reaction front moves rapidly from position of T2 to the position of T13 close to the exit of the inner reactor compartment. Here the generated heat is transferred by the fins toward the annulus inlet, where it reignites the incoming combustion mixture and a new cycle begins (after 1 h). 3.2b Methane in Synthetic Gas. Engine operation typically follows a complex pattern between different operating modes, especially under conditions of urban driving. Consequently, the catalytic converter often operates in an unsteady regime induced by changes in temperature and composition of exhaust gas. For better understanding of the potential use of autocyclic reactor we explore the effects of changing operational parameters individually (i.e., inlet methane concentration and inlet gas temperature). Typically, depending on the mode of operation, values for inlet gas temperature may range between 250 and 540 °C, while the inlet methane concentration may vary from 500 ppm at high temperatures, to as high as 5000 ppm at low temperatures.3,8 The effect of varying inlet gas temperature on temperature profiles during combustion of 3000 ppm methane in synthetic gas is shown in Figure 9. Note that Figure 9 can be considered as an extension of Figure 4. As illustrated, at 540 °C a very narrow reaction front positioned close to the inlet and accompanied by the highest temperature increase develops. As the inlet temperature decreases, the reaction front moves along the reactor and broadens while the temperature peak diminishes. Below a given temperature (500 °C), methane combustion is complete, independently from the methane inlet concentration. Specifically, for Tin ) 540 °C methane is completely removed from the gas stream in 50 s. As the inlet temperature decreases, so does the conversion (see Figure 10). Nevertheless, for temperatures >400 °C as the combustion ignites, conversion rises rapidly for the few first seconds, before it starts to plateau. For instance, at 450 °C in about 30 min the predicted conversion is around 80%, while to reach the steady state conversion of >95% takes 3 h. An interesting feature, apparently related to the heat balance in the reactor and confirmed by experimental data,14 is the difference in conversions for the two methane concentrations when the inlet temperature is 400 °C. When the inlet gas temperature was 350 °C, conversion barely attained 15% after 2000 s, regardless the initial methane concentration, approaching 20% at the steady state, as determined by steady state simulations. In fact, this low sustained conversion was also observed experimentally. Since the lower limit for the inlet stream temperature to achieve adequate methane combustion seems to be approximately 400 °C, this temperature was selected to evaluate by HT2-Dt model simulations the methane conversions as a function of inlet methane concentration. Figure 11 shows methane conversion profiles as a function of time for different inlet methane concentrations at Tin ) 400 °C. As one can see, the lower limit of methane inlet concentration is 1500 ppm to achieve a satisfactory conversion (>50%). However, the reaction occurs also if the concentration is lower (1000 ppm), reaching 30% conversion after 2000 s and 38% conversion at steady state. Nevertheless, at 400 °C, 500 ppm methane is clearly insufficient to sustain the reaction. Even though some conversion takes place initially, in less than 15 min, the conversion starts to decrease, thus the reaction seems to be extinguished. Overall, the developed HT2-Dt model provided description of the ACR performance within a mean relative error of less than 2%, which is satisfactory.

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∆Hr ) heat of reaction, J/mol k ) thermal conductivity, W/(m · K) km ) mass transfer coefficient, m/s r ) radial dimension, m -rCH4 ) reaction rate, mol/(m3 · s) or mol/(m2 · s) T ) temperature, °C Tin ) inlet temperature, K TS ) surface temperature, °C u ) spatial velocity, m/s z ) axial dimension, m Greek Letters 4Hr ) heat of reaction, J/mol η ) effectiveness factor, dimensionless F ) mass density, kg/m3 Subscripts

Figure 11. Simulated cumulative methane conversion (fractional) profiles calculated at the exit of the reactor for different inlet methane concentrations. ACR unit is fed by methane in synthetic exhaust gas (140 L/min). Inlet synthetic exhaust gas temperature: 400 °C.

app ) apparent CH4 ) relating to methane in ) inlet S ) surface

Literature Cited 4. Summary and Conclusions We have developed a heterogeneous 2-Dt model for the counter-current type autocyclic reactor loaded with a combination of pellet and monolithic catalysts. The model was based on a heterogeneous packed-bed for the pellet sections and continuous approach for the monolithic catalyst section. Validated against previously published experimental data, the HT2Dt provided better representation of temperature profiles and methane conversions, in comparison with the previous HT1-D model. In contrast to the HT1-D model, the new developed model allowed a wide range of simulations including the heat transfer, contributing thereby to better analysis and understanding of the ACR behavior. The HT2-Dt model predicted correctly the position of reaction front. When run for a number of simulated inlet conditions, the HT2-Dt model predicted a fairly quick response to changes in inlet conditions and could also predict correctly the reaction front displacement. Moreover, analysis of the transient behavior conducted by simulations showed that if the reaction front moves toward the exit of the reactor, its heat may reignite the incoming combustion mixture. The HT2-Dt model responded correctly also to the different kinetics for the mixtures of methane in synthetic exhaust gas and allowed the mapping of the ACR capacity for a potential use to remove unburned methane from emissions of natural gas engines. Acknowledgment This work was supported by grants from Natural Sciences and Engineering Research Council of Canada and from Natural Gas Technology Center, Montreal. Notations av ) ratio of particle surface area to volume, m2/m3 A ) pre-exponential factor in Arrhenius equation, mol/(kg · s · bar) c, C ) concentration, mol/m3 Cp ) constant pressure heat capacity, J/(kmol · K) or J/(kg · K) Deff ) effective diffusion coefficient, m2/s Eapp ) apparent activation energy, kJ/mol h ) heat transfer coefficient, W/(m2 · K)

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ReceiVed for reView April 30, 2009 ReVised manuscript receiVed August 26, 2009 Accepted August 28, 2009 IE900701H