The implementation of a noble-metal catalytic combustor in a natural-gas fired turbine for NOx (nitrogen oxides) reduction has drawn great attention in recent years (Dalla Betta et al. 1994). Currently NOx emissions from stationary gas turbine systems are controlled either by lowering the combustion temperature with water injection or by removing NOx through exhaust gas treatment such as selective catalytic reduction. In a catalytic combustor, a major portion of fuel conversion takes place on the catalyst surface; consequently, the gas phase NOx production route via the prompt (or Fenimore) pathway is avoided (Schlegel et al. 1994). In addition, the peak gas phase combustion temperature is substantially reduced leading to low thermal (or Zeldovich) NOx formation rate.
Catalytic combustion includes several essential processes: (1) diffusion of the reactants from the gas phase to the catalytic surface, (2) adsorption of the reactants onto the catalytic surface, (3) movement of adsorbed species, (4) reaction on the surface of the catalyst, (5) desorption of the products from the surface, and (6) diffusion of the products from the catalytic surface to the gas phase. Depending on the conditions, each of these processes can be rate limiting. Since measuring chemical activities near or on a catalyst surface is difficult, experimental data of surface kinetics, temperature, or concentrations of gas phase species near the catalyst surface are scarce. As a result, catalytic combustors have conventionally been modeled as a “black box” that produces a desired amount of fuel conversion. While this approach has been useful for proof-of-concept studies, we expect practical applications to emerge from a greater understanding of the details of the catalytic combustion process.
In the present study, a numerical model simulating a honeycomb catalytic combustor is developed. Modeling of the chemical interaction between the gas phase and the surface is accomplished by an improved multistep surface reaction mechanism for methane oxidation on platinum. The performance of the chemical model is assessed by comparing the numerical predictions with available experimental measurements. First, a series of calculations of a perfectly-stirred reactor with catalytically active surface are performed to determine the apparent activation energy at several methane-air equivalence ratios. The results are compared with the measurements by Trimm and Lam (1980) and by Griffin and Pfefferle (1990). Second, the surface ignition temperatures of various methane-air compositions are computed by using the proposed surface chemistry model. The predicted surface ignition temperatures are assessed with the measured data by Griffin and Pfefferle (1990). Third, following the satisfactory predictions of the essential features of the methane catalytic combustion, the monolith honeycomb catalytic reactor experiment by Bond et al. (1996) is simulated by a two-dimensional flow code with active catalyst surfaces. The computational domain contains two regions - a gas phase reactor channel and a solid phase substrate wall. The energy conservation equation is solved for the solid wall so that the conductive heat transfer within the substrate can be properly determined. The predicted gas phase temperatures, methane percentage conversions, and carbon monoxide (CO) mole fractions are compared with the measurements by Bond et al. (1996). Fourth and finally, the pressure effects on methane conversion in a catalytic flow reactor are explored by a parametric study using the proposed surface chemistry and the two-dimensional numerical model.
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Due to limited knowledge of the elementary surface reaction kinetics, numerical studies of methane catalytic combustion were often performed with a single step global surface reaction. Song et al. (1991) used a single step surface reaction for predictions of methane catalytic combustion in a stagnation flow. With this simple chemical kinetic model, their calculations showed success in predicting surface ignition/extinction temperatures of lean methane-air mixtures. Since surface ignition temperatures of methane-air catalytic combustion are low, ca. 600C (Williams et al. 1991), the heterogeneous ignition process is dominated by the surface reaction due to its much lower activation energy compared to those of gas phase reactions. As calculations with a single-step reaction do not involve radicals, the well predicted ignition temperatures of lean methane-air mixture by Song et al. suggest that, under fuel- lean conditions, the interaction between catalytic and gas phase reactions is not important because the heterogeneous ignition is driven by the heat release of surface reaction. However, for high temperature conditions (> 1200 K), the interaction between catalytic and homogeneous reactions via radicals such as hydroxyl (OH) and O atom may potentially affect the ignition process (Pfefferle et al. 1989, Griffin et al. 1989). In order to include the radical interaction between surface and gas phase at high temperatures, Markatou et al. (1993) modified the single step surface reaction model by introducing a coefficient to regulate the amount of OH desorbing from surface. The value of this coefficient was determined from experimental data. Their results show that the OH desorbed from the surface enhances the gas phase reactions and, hence, the generation of radicals in the boundary layer for surface temperatures above 1300 K. Markatou et al. (1993) suggested the need of detailed surface kinetics and gas-surface energy balance to properly couple phase and surface processes in catalytic combustion calculations.Multi-Step Surface Mechanisms
Previous numerical studies of catalytic methane oxidation
by using multiple-step surface reactions have been reported by
Hickman and Schmidt (1993), by Deutschmann et al.(1994), and
by Behredt et al. (1995). These multi-step surface reaction
mechanisms were developed with available kinetic and thermal
data along with several assumptions, such as Langmuir-
Hinshelwood type surface reaction mechanism, dissociative
adsorption of O2 and CH4, perfect catalyst surface,
no substrate diffusion, and monolayer surface coverage. Following
the framework of these existing surface reaction mechanisms, an improved surface mechanism is developed
in this study by optimizing pre-exponential factors/activation
energies and by adding one new reaction. The resulting
mechanism consists of several basic reactions: adsorption of reactants (O2 and CH4) and
intermediate species (CO, H2, and OH), surface reactions of
adsorbed species, and desorption of products (CO2 and H2O) and
intermediate species. Details of these surface reactions are
tabulated in Table 1. The surface reaction rates are described
by an Arrhenius expression or by an initial sticking
coefficient for adsorption processes. The new reaction
included in the present mechanism is
CH4 + O(*) + PT(*) => CH3(*) + OH(*), (A3)where PT(*) denotes a free surface site and species with a label, (*), are those adsorbed at the surface. Since there is no kinetic data available for reaction (A3), the sticking coefficient and activation energy used in this study are chosen such that at low surface temperatures, the surface mechanism predicts an apparent activation energy of 188 kJ/mole as measured by Griffin and Pfefferle (1990). With the assumption of Langmuir-Hinshelwood surface reaction mechanism, the onset of surface ignition is determined by the competition between O2 and CH4 for surface sites. Based on their experimental observation, Trimm and Lam (1980) concluded that the dominant limiting process changes from oxygen desorption to methane adsorption as the surface temperature increases. When the surface temperature is low, the O2 adsorption process, reaction (A1), dominates and the catalyst surface is entirely covered by adsorbed O atom, O(*). The newly-added reaction (A3) is important for methane conversion at low surface temperatures (or high oxygen atom surface coverage O(*)) because it allows the direct reaction between the gas phase methane and adsorbed O atom. Moreover, it provides a thermal mechanism for initiating surface ignition via the self-heating process. Bond et al. (1996) observed surface ignition (i.e., light-off) in their experiments without external heat addition to the catalyst. Through reaction (A3), conversion of methane may proceed on surfaces with high coverage of O(*). The heat generated by this reaction raises the surface temperature. As the surface temperature increases, the surface O(*) coverage drops and the methane adsorption process via reaction (A2) starts to increase. When the surface temperature reaches a certain point, the methane adsorption rate exceeds the oxygen adsorption rate such that reaction (A2) becomes dominant. Consequently, more heat is generated and ignition soon takes place on the catalyst surface. Similar surface ignition processes have been postulated by Behrendt et al. (1995). In the following sections, we will use the proposed multi-step surface mechanism to model various catalytic combustion systems. Results of these numerical simulations will be compared with available experimental measurements.
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Using the present surface mechanism, calculations with the SPSR model are repeated to determine the apparent activation energies of various mixture equivalence ratios. The predicted Arrhenius plot for stoichiometric CH4-air mixture is presented in Figure 1. As seen in the figure, the numerical model exhibits two regimes of different kinetic behaviors as observed by Trimm and Lam (1980). An activation energy of 172 kJ/mole is predicted when the surface temperatures are below ca. 800 K and a value of 102 kJ/mole is obtained for higher surface temperatures. These activation energies and the transition temperature agree reasonably well with the experimental observation. In addition, surface species information predicted by the model shows that the surface is mainly covered by oxygen for surface temperatures below 800 K. When the surface temperature is around 800 K, the surface oxygen coverage decreases rapidly and CO becomes the major species formed at the surface thereafter. These features obtained by the present model are consistent with the postulation offered by Trimm and Lam (1980).
Griffin and Pfefferle (1990) studied gas phase and catalytic ignition of methane and ethane over platinum. They measured ignition temperatures of various mixture equivalence ratios and deduced the apparent activation energies at the surface ignition temperatures for both fuels. Their results show that the activation energy varies with the equivalence ratio, f. The activation energy is about 188 kJ/mole for f > 0.4 and 88 kJ/mole for 0.2 < f < 0.4. Since the surface ignition temperature varies with the equivalence ratio, the dependence of activation energy on equivalence ratio can be used to provide a relationship between activation energy and surface temperature. The activation energy plot for methane obtained by Griffin and Pfefferle (1990) also shows two kinetic regimes with a transition temperature ca. 870 K corresponding to the surface ignition temperature for a mixture with f = 0.4. Because this mixture is lean, it is unlikely that CO would be the major species formed on the catalyst surface even at high temperatures. This change in activation energy might not be caused by the change in oxygen adsorption as seen in Trimm and Lam's experiments. Griffin and Pfefferle (1990) suggested that the higher activation energy at high surface temperatures may be the result of the greater reactivity of surface oxygen when its surface coverage is low.
Figure 2 shows the Arrhenius plots of the overall reaction rate predicted by the SPSR model for equivalence ratios of 0.3, 0.4, and 0.5. The Arrhenius curves in Figure 2 show a smooth transition in the predicted activation energy from low values of 66-88 kJ/mole to high values of 166-212 kJ/mole. These apparent activation energies agree well with those determined by Griffin and Pfefferle (1990). The numerical model also predicts the transition of activation energy occurring at surface temperatures between 900 and 1000 K. Griffin and Pfefferle (1990), however, observed the transition in activation energy taking place at slightly lower surface temperatures between 800 and 873 K. Curve-fittings of the Arrhenius relationship for CH4-air mixture of equivalence ratio 0.4 are shown in Figure 3. The predicted apparent activation energy is seen to decrease from 186 kJ/mole to 77 kJ/mole when the surface temperature increases from 750 K to 1100 K. Note that the predicted overall activation energy by fitting the calculations over the entire temperature range is 136 kJ/mole which is close to the value used by the one-step surface reaction numerical models (Song et al. 1991, Markatou et al. 1993).
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Surface ignition temperature is another important feature which should be properly predicted by the surface reaction mechanism. Griffin and Pfefferle (1990) measured methane surface ignition temperatures on a platinum wire. Their experimental results show the surface ignition temperature decreases with mixture equivalence ratio. By using the present surface mechanism and a two- dimensional tube flow model to be described in the next section, the surface ignition temperatures of lean methane-air mixtures are determined numerically. The predicted surface ignition temperatures along with the measurements by Griffin and Pfefferle (1990) are plotted in Figure 4 for 0.3 < f < 0.8. The predicted surface ignition temperatures are seen to agree reasonably well with the experimental results.
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Bond et al. (1996) measured gas phase temperatures, CH4 conversion, and CO concentrations in their honeycomb catalytic combustor. In the reactor, the catalyst honeycomb is segmented into wafers with gaps between each wafer permitting sampling access. A schematic of Bond's reactor is shown in Figure 5a. The objective here is to investigate the catalytic combustion by using the newly-developed surface mechanism. In the present study, the CURRENT code developed by Winters et al. (1996) is modified to include an energy balance equation for the gas-catalyst interface. Similar to the flamelet approach described in the previous chapter, the CURRENT code solves the two- dimensional, low Mach number, variable-property Navier-Stokes equations along with energy and species conservation equations in general non-orthogonal curvilinear coordinates. The flow code is coupled with the CHEMKIN software libraries (Kee et al. 1996), providing generality for treating chemically reacting mixtures of gases including multicomponent diffusion and thermal diffusion. Surface chemistry is incorporated into the code using SURFACE CHEMKIN (Coltrin et al. 1996).
In the present study, a single channel in the honeycomb reactor is modeled by assuming that conditions in all channels are identical. Since the catalyst is deposited on a washcoat of aluminum that was applied to the inner surface of the honeycomb channel, corners of the square channel are rounded off by the thick washcoat deposit. Great simplification is achieved when, instead of modeling the actual round-cornered square channel in the honeycomb reactor, a circular tube with an equivalent hydraulic diameter is used. Detailed dimensions are shown in the sketch presented in Figure 5b. The computational domain contains both the gas phase (area enclosed by B-A-F-E-B) and the wall surrounding it (shaded area C-B-E-D-C). In order to describe the heat conduction in the solid wall, the following equation is solved for the wall. (1)
In the gas phase region, a non-uniform mesh with grid points clustered near the catalyst surface and the channel entrance is used. The mesh system consists of 201 grid points in the streamwise direction and 31 grid points in the cross-stream direction and will provide sufficient resolution for the computational domain (see Fig. 5b). The inlet profiles of velocity, gas temperature, and species mass fractions are assumed to be uniform (i.e., "plug flow" inlet conditions). The boundary conditions of species and energy conservation equations at the gas-solid interface are described next.
Since the surface is chemically active, boundary conditions on the catalyst are more complicated than those on a non-reactive surface. Boundary conditions of species and energy at the catalyst surface (along the line B-E in Fig. 5b) are derived by balancing the flux and source/sink of an interface control volume with infinitesimal thickness. The mass flux of a gas phase species k at the interface is determined by molecular diffusion and convection due to Stefan velocity :, (k = 1,...,kg) (2)
where is the unit vector normal to the solid wall pointing toward the gas phase (see Fig. 5b), kg is the total number of the gas phase species, is the diffusive mass flux, Yk is the gas phase species mass fraction, Wk is the molecular mass, and is the net production (desorption) rate (moles/cm2-sec) of gas phase species k by surface reactions. The mass-weighted Stefan velocity is determined by summing Eq.(2) over all gas phase species. (3)
The temperature boundary condition is derived by balancing the thermal energy of an interface control element:, (4)
where l is the thermal conductivity, hk is the enthalpy of species k, and kg and ks are the total number of gas phase and the surface species respectively. Subscripts g and s denote gas phase and solid phase respectively. The boundary conditions, Eqs. (2) and (4), are solved by a damped Newton’s scheme (Winters et al. 1996) before each flow field iteration to provide the values and fluxes of species and enthalpy (temperature) at the catalytic active surface. Typically, 4000 iterations are carried out before reaching a convergent solution.
Boundary conditions of axial and radial velocities, temperature, and species mass fractions are required for gas phase channel flow calculations. The plug flow condition is specified at the channel inlet (line A-B in Fig. 5b) for all variables. For the first catalyst section, the inlet conditions are obtained from the experiment by Bond et al. (1996). For the second and the third catalyst sections, the averaged values at the exit of the previous section are used. An extrapolation scheme (Winters et al. 1996) is used for outflow boundary (line E-F) and a zero flux (symmetric) condition is imposed at the centerline of the channel (line A-F). Since the gas-surface energy balance equation (4) requires information on the amount of heat flux from the substrate, an energy conservation equation describing the heat conduction in the solid phase is used to resolve the temperature field in the substrate, Eq. (1). The substrate used in the experiment is a 200-cpi honeycomb cordierite monolith and the wall thickness is 0.3 mm. Since the conditions and geometry of all channels are assumed identical, only one-half of the wall thickness is included in the computational domain and an adiabatic thermal boundary condition is used at the imaginary interface dividing the solid wall (line C-D in Fig. 5b). Because the inlet gas temperature is assumed uniform, a constant temperature boundary condition is imposed at the front end of the substrate (line B-C) and is set as the inlet gas temperature. At the exit end of the substrate (line D-E), a zero gradient boundary condition is specified. Because surface ignition occurs near the entrance of the channel, the axial temperature gradient is expected to be small near the exit end of the substrate. In addition, the thermal conductivity of cordierite is only 3.2 W-m-1-K-1 at 1000 K which is only 10% of the thermal conductivity of metals (e.g., stainless steel = 25.4 W-m-1-K-1 at 1000 K). Consequently, the resulting heat loss to the surroundings through the exit is very small and the assumption of adiabatic boundary should have a negligible effect on the temperature field prediction.
Four sets of calculations were performed to assess the sensitivity of current numerical model results to surface chemistry models and gas-catalyst interface conditions. The predicted gas phase temperature, methane conversion, and carbon monoxide (CO) mole fraction distributions along the catalytic reactor for the condition with equivalence ratio f = 0.39 (Bond et al. 1996 run No. 4) are presented in Figures 6 to 8. Numerical results of case 1 obtained by the present surface mechanism and the gas- catalyst interface conditions, Eqs. (2) and (4), are denoted by solid lines in these figures. Case 2 was performed to assess the effect of energy balance treatments for the gas-catalyst interface by calculations with a prescribed surface temperature distribution and the results are denoted by the dashed lines. The surface temperature in each catalyst section is assumed constant and its value is adjusted so that the gas temperature at the exit of each section matches the experimental value of Bond et al. (1996). In prescribed surface temperature cases, the computational domain contains only the gas phase region (area B-A-F-E-B in Fig. 5b) and hence the self-heating effect of catalytic combustion are excluded. In cases 3 and 4, we evaluate the importance of the newly-added surface reaction (A3). Calculations using the surface reaction mechanism given by Bond et al. (1996) with the gas-catalyst interface conditions (case 3) and with the prescribed surface temperature distribution (case 4) were performed. The major difference between Bond's surface reaction mechanism (Bond et al. 1996) and the present one is the absence of reaction (A3) in Bond's mechanism. mechanism is The results of case 3 and case 4 are shown in dash-dot- dot lines and in dash-dot lines, respectively. The experimental data obtained by Bond et al. (1996) are denoted by the filled squares in Figures 6 to 8. Measurements were taken at three locations, between catalyst wafers, as sketched in Figure 5a.
Since the measurements were made at the center of gaps between catalyst wafers, the predicted gas temperature and species mole fractions are averaged over the cross section of the channel for comparison purpose. Figure 6 presents the averaged gas temperature distributions along the axial direction. In case 2 and case 4, the surface temperatures are adjusted so that the predicted gas phase temperatures at the catalyst exit of each section agree perfectly with the experimental data. Consequently, case 2 and case 4 have identical gas phase temperatures because of the same prescribed surface temperature distribution. In case 1 and case 3, the numerical model includes the energy balance, Eq. (4), between the gas phase and the solid substrate including heat generated on the surface and conduction inside the substrate. The predicted results of case 1 (solid line) are seen in good agreement with the data at the exit of first section. Compared to the data, higher gas temperatures at the second and the third catalyst exits are predicted. The overprediction of the gas phase temperature can be caused by several possible reasons. One is the present surface chemistry and others are the model’s neglect of radiation heat loss and the uncertainties in substrate thermal model. These factors will be explored in the following sections. On the other hand, case 3 (dash-dot-dot line) underpredicts gas phase temperatures at the second and the third catalyst exits. The gradually increasing gas temperature profile predicted by case 3 indicates the surface mechanism without reaction (A3) yields slower surface reaction rates and a less noticeable surface ignition than the present surface mechanism (case 1) as well as the actual catalytic process observed by the experiment.TEMPERATURE CONTOUR PLOT OF THE SECOND CATALYST SECTION.
Figure 7 compares the predicted and measured overall methane conversion. The agreement among the numerical results and the data is seen poor. The predicted conversion shows a strong sensitivity to the surface mechanism and a weak dependence on the treatment of surface temperature. For case 1 and case 2, the predicted amounts of methane conversion in the second and the third sections are 30% or so higher than the experimental data. With the prescribed surface temperature (case 2), the present surface mechanism yields a high surface reaction rate at elevated temperatures. As the self- heating effect is included in case 1, the model yields even higher fuel conversions. Because higher fuel consumption is predicted by the present surface chemistry model, the gas temperature predicted by the model is also higher than the experimental data as seen in Figure 6.
In case 3 and case 4, calculations were performed without reaction (A3) and the results are presented by the dash-dot-dot line and the dash-dot line respectively in Figure 3.10. Without reaction (A3), the surface mechanism yields fuel conversions 30% lower than the experimental data. Furthermore, the fuel conversion profiles predicted by the surface mechanism without (A3) do not exhibit any indication of surface ignition while case 1 and case 2 as well as the measurement show surface ignition taking place in the second section. This comparison suggests that the newly-added reaction (A3) is a key reaction to initiate the surface ignition process.CH4 CONTOUR PLOT OF THE SECOND CATALYST SECTION.
Figure 8 compares the predicted and the measured gas phase CO mole fractions. All the four cases under-predict the gas phase CO levels. Since only the CO mole fractions between the catalyst wafers are measured in the experiment, the CO distribution inside the catalyst is not available. The experimental data indicate that CO level first increases slightly after the first section; then it shows a sharp increase across the second section and decreases thereafter. Among the four cases, only case 1 which uses the present surface mechanism and the surface energy balancing scheme qualitatively captures the measured CO trend along the catalytic combustor. In case 1, the numerical model predicts a small amount of CO leaving the first catalyst section (~0.1 ppm). When the methane adsorption rate is accelerated in the second section due to surface ignition, a large amount of CO is generated on the surface and the gas phase CO (due to desorption) increases sharply right after the channel entrance. When the surface reaction rate slows down due to the limitation of gas-to-surface diffusion process, much of the gas phase CO is re-adsorbed and consumed on the surface. Hence, the CO level decreases monotonically thereafter. A similar CO distribution is predicted in the third section. Since the gas mixture entering the third section contains about 1% of methane, the surface reactions are limited in comparison with the second section. Therefore, the CO distribution shows a smaller and wider peak than the one observed in the second section. As seen in Figure 8, the two numerical models without reaction (A3) (case 3 and case 4) predict a monotonically increasing trend in CO distribution along the axial direction. Again, this is indicative of the importance of reaction (A3). Also being revealed in Figure 8, numerical models with a prescribed surface temperature profile (case 2 and case 4) predict less CO than the ones using the energy balance scheme, Eqs. (2) and (4) at the gas-catalyst interface (case 1 and case 3).CO CONTOUR PLOT OF THE SECOND CATALYST SECTION.
In the prescribed surface temperature cases (case 2 and case 4), a constant surface temperature is assumed in each section. Although the exit gas temperatures of case 2 and 4 match the measurement precisely, the prescribed surface temperature likely is not the actual surface temperature profile on the catalyst surface. In case 1, the surface temperature distributions for the three catalyst sections are predicted and the results are shown in Figure 9. Unlike the prescribed surface temperature cases (case 2 and case 4), the surface temperature profiles in Figure 9 are part of the solution which satisfies the surface boundary conditions, Eqs. (2) and (4). As seen in Figure 9, the computed surface temperatures are fairly uniform inside each honeycomb section except in the region near the entrance. In the second section, a peak in the surface temperature distribution is predicted. This peak denotes the location where the catalytic combustion is shifting from surface kinetic controlling to mass transport controlling (i.e., diffusion limited). Because the species concentration profiles are assumed uniform at the entrance of each catalyst wafer channel, sufficient fuel is available to the surface at the entrance and the catalytic combustion is limited by the surface kinetics at the entrance. This is consistent with the results obtained by Markatou et al. (1993) who found that the surface reaction is not limited by mass transfer near the leading-edge of a catalyst plate. Beyond the entrance, species concentration boundary layers start to develop due to the creation/consumption of the gas species at the catalytic surface. When the surface reactions accelerate due to the heat generated on the surface, the deficient reactant (CH4 under fuel-lean conditions) near the surface will be completely exhausted. Hence, the catalytic combustion is limited by the availability of deficient reactant to the surface. That is, the mass transport rate of the reactant from the bulk gas to the surface is controlling the rate of the combustion process; often called "diffusion limited".
The relation between the two rate-limiting factors and the deficient reactant CH4 can be shown by the CH4 radial profile. The predicted CH4 radial profiles at eight axial locations inside the second catalyst wafer are plotted in Figure 10. For locations near the entrance, the predicted CH4 radial profiles are quite flat in the center portion of the channel and there is sufficient CH4 available to the catalyst surface. Therefore, the surface reaction is kinetically-controlled near the entrance. Further downstream of the entrance (x > 0.5 cm), the normalized CH4 radial profiles collapse onto one curve and become self- similar as seen in Figure 10. At these locations, gas phase CH4 near the catalyst surface are almost completely consumed and the CH4 boundary layer is fully-developed. The exhaustion of CH4 near the catalyst surface is indicative of diffusion-limited surface reaction. The ignition point on the catalyst surface can be located by examining these CH4 radial profiles. From Figure 10, the axial location at which the CH4 concentration near the surface becomes zero is around x = 0.3 cm.
Since the operating pressure of catalytic combustors ranges from the ambient pressure (residential heater) to more than 20 atm (stationary gas turbine; Dalla Betta 1997), it is of great practical interest to understand the dependence of the catalytic reactors on pressure. Although the present surface mechanism is optimized from experimental data at the ambient pressure, its usage may be extended to pressures up to 20 atm if the fundamental characteristics of surface reaction remain unchanged. In the present study, the pressure effects are explored by simulations carried out for pressures from 1 atm to 20 atm. The inlet velocity and gas temperature are kept constant at 1 m/sec and 800 K, respectively. The equivalence ratio of the fuel mixture is 0.4 and the geometry is the same as depicted in Figure 5b. As a result, the overall residence time is fixed for all runs.
Since gas diffusive velocity is slower at high pressures due to the decrease of gas diffusion coefficients, the fuel in the bulk gas mixture needs more time to reach the surface. Consequently, the fuel is consumed more evenly and the catalyst surface is heated more evenly along the axial direction on the catalyst surface at high pressures than at low pressures. To see the influences of reactor pressure on the methane conversion, the gas phase methane distributions under 4 different reactor pressures (1, 2, 5, and 10 atm) are shown in Figure 11. The interval between the methane mass fraction contour lines is 2 × 10-3. The contour plots illustrate the development of methane boundary layer along the catalyst surface under various reactor pressures. As seen in Figure 11, methane boundary layers of high reactor pressures develop at much slower rates than those of low pressures. In the 10-atm case, the methane molecules near the center of the channel never reach the catalyst surface due to the slow diffusive velocity at this pressure. In addition to the reduction of gas diffusive velocity, increasing the reactor pressure reduces the surface area at which the combustion process is controlled by the surface chemistry kinetics.
The above numerical results indicate two competing factors that affect the overall fuel conversion when the reactor pressure is changed. First, the gas diffusive velocity decreases with pressure. In the diffusion-limited regime, the amount of fuel conversion at the surface is limited by the diffusive transport. Consequently, the overall fuel conversion is expected to decrease with pressure. Second, the amount of heat released by catalytic combustion increases with pressure. In the kinetically-limited regime, the surface reaction rates increase with the surface temperature. Increasing heat release tends to promote fuel conversion. The predicted dependence of fuel conversion rate on pressure is an outcome from these two competing factors as shown in Figure 12. The fuel conversion is seen to increase slightly between 1 and 2 atm and it decreases monotonically with pressure above 2 atm. The initial increase of fuel conversion with pressure is attributed to the increase of heat release with pressure. When the pressure is above 2 atm, the combustion process on much of the surface area is controlled by the gas-to-surface diffusion rate of fuel and the fuel conversion decreases with pressure.
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An improved surface mechanism of methane oxidation on platinum surface is proposed in the present study. Based on the multistep surface mechanisms developed by Hickman and Schmidt (1993) and by Deutschmann et al. (1994), an additional methane adsorption step (reaction A3) is included in the present surface mechanism. The newly- developed mechanism is applied to determine the apparent activation energy of CH4-air catalytic combustion showing good agreement with the measurements. The numerical model indicates that the change in activation energy corresponds to the change in oxygen desorption for the stoichiometric mixture as suggested by Trimm and Lam (1980). In addition, the model qualitatively predicts the dependence of the activation energy on the equivalence ratio as observed by Griffin and Pfefferle (1990). The surface ignition temperatures of lean methane-air mixtures are also determined and found to agree well with the experimental data by Griffin and Pfefferle (1990).
Another objective of the current study is to develop a two-dimensional numerical model for simulation of a monolith honeycomb catalytic reactor. With detailed gas phase and surface chemistry models, a two-dimensional code, CURRENT, is modified to include the energy balance on the gas-catalyst interface. In order to properly model the thermal conduction inside the substrate, the numerical model is expanded to solve the two-dimensional heat conduction equation for the solid phase. The predicted gas temperature, CH4 conversion, and CO mole fraction compare favorably with the measurements by Bond et al. (1996). The numerical model qualitatively captures the characteristics of the catalytic combustor. The model shows the surface ignition occurring in the second honeycomb section of the catalytic combustor as the experimental data indicated. Although the model overpredicts the gas temperature and the methane conversion after surface chemistry is ignited, the predicted trends of gas temperature and CO emission agree well with the experimental observations. In addition to the gas phase properties, the numerical model provides critical information on the catalyst surface, such as surface temperature and O atom fractional coverage. Moreover, the surface temperature prediction provides useful engineering information, such as the maximum temperature and temperature gradients, for better honeycomb designs.
The numerical model is further applied to study the pressure effect on the catalytic combustion. The model predicts that the surface temperature becomes higher and more evenly distributed at higher pressures. However, despite the gas diffusivity decreases monotonically with pressure, the predicted fuel conversion does not show the same trend. The predicted methane conversion rate first increases slightly, then it starts decreasing monotonically after the pressure reaches 2 atm.
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