Numerical Modeling of Catalytic Ignition - CiteSeerX

Twenty-Sixth Symposium (International) on Combustion/The Combustion Institute, 1996/pp. 1747–1754

NUMERICAL MODELING OF CATALYTIC IGNITION O. DEUTSCHMANN, R. SCHMIDT, F. BEHRENDT and J. WARNATZ Universita¨t Heidelberg Interdisziplina¨res Zentrum fu¨r Wissenschaftliches Rechnen (IWR) Im Neuenheimer Feld 368, D-69120 Heidelberg, Germany

Catalytic ignition of CH4, CO, and H2 oxidation on platinum and palladium at atmospheric pressure is studied numerically. Two simple configurations are simulated: the stagnation flow field over a catalytically active foil and a chemical reactor with a catalytically active wire inside. The simulation includes detailed reaction mechanisms for the gas phase and for the surface. The gas-phase transport and its coupling to the surface is described using a simplified multicomponent model. The catalyst is characterized by its temperature and its coverage by adsorbed species. The dependence of the ignition temperature on the fuel/oxygen ratio is calculated and compared with experimental results. The ignition temperature of CH4 oxidation decreases with increasing CH4/O2 ratio, whereas the ignition temperature for the oxidation of H2 and CO increases with increasing fuel/oxygen ratio. The kinetic data for adsorption and desorption are found to be critical for the ignition process. They determine the dependence of the ignition temperature on the fuel/oxygen ratio. A sensitivity analysis leads to the rate-determining steps of the surface reaction mechanism. The bistable ignition behavior observed experimentally for lean H2/O2 mixtures on palladium is reproduced numerically. The abrupt transition from a kinetically controlled system before ignition to one controlled by mass transport after ignition is described by the time-dependent codes applied.

Introduction Extensive experimental and theoretical attention has been given to catalytic combustion in the past decade. The potential of heterogeneous processes in reducing emission of pollutants, improving ignition, and enhancing stability of flames has been recognized. Two simple configurations are often used to investigate catalytic combustion experimentally: the stagnation flow field over a catalytically active foil [1– 5] and a chemical reactor with a catalytically active wire inside [6,7]. In these setups, the temperature of the catalyst is controlled by resistive heating of the catalytic foil or wire. The modeling and simulation of such heterogeneous systems require the coupling of reactive flows with gas-surface interactions. Therefore, computational tools for both systems have been developed recently providing the capability to analyze the elementary chemical and transport processes at the gas-surface interface and to couple them with a description of the surrounding gas phase. The aim is to achieve a quantitative understanding of catalytic combustion. Catalytic ignition is an abrupt transition from a kinetically controlled system to one controlled by mass transport. Therefore, the complex interactions of chemical and transport processes in the gas phase as well as at the surface have to be included. Thus, the numerical simulation of catalytic ignition and the comparison of calculated and experimental results

represents a suitable tool to validate the models and the reaction mechanisms proposed. In the present paper, the numerical codes developed are applied to the heterogeneous ignition of mixtures of oxygen with methane on a platinum foil, with CO at a platinum wire, and with H2 on a palladium foil at atmospheric pressure. The catalysts are heated resistively. Ignition temperatures are calculated as function of fuel concentration and are compared to experimental results. The ignition behavior is explained by elementary processes at the gas–surface interface. The dependence of ignition temperature on the fuel/ oxygen ratio is explained. A sensitivity analysis is applied to the surface reaction mechanism to find the controlling reaction steps. The ignition of hydrogen/ oxygen mixtures on palladium is found to exhibit bistability for lean mixtures. Numerical Model The mathematical models are based on the numerical solution of the governing equations in their one-dimensional form, considering the geometry of the problems. The independent variables are the time and distance normal to the catalytic surface. In the stagnation-flow configuration, a flow with uniform velocity distribution is imposed at a certain distance from a flat foil. By confining the attention to the center of this foil, edge effects can be

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CATALYTIC COMBUSTION

TABLE 1 Surface reaction mechanism on platinum (units: A [mol, cm, s], Ea [kJ/mol], S0 [1]). Pt(s) denotes bare surface sites. The order of H2 adsorption is unity concerning Pt(s), and the order of CO adsorption is 2 with regard to Pt(s). The O2 sticking coefficient is temperature dependent: S0O2 4 0.07 T0/T with T0 4 300 K. A H2 2 H(s) H O2 2 O(s) O H2O H2O(s) OH OH(s) H(s) H(s) OH(s) CO CO(s) CO2(s) CO(s) CH4 CH3(s) CH2(s) CH(s) C(s) CO(s)

` → ` ` → ` ` → ` → ` ` ` ` → → ` ` ` ` ` ` `

2 Pt(s) H2 Pt(s) 2Pt(s) O2 Pt(s) Pt(s) H2O Pt(s) OH O(s) OH(s) OH(s) Pt(s) CO CO2 O(s) 2Pt(s) Pt(s) Pt(s) Pt(s) O(s) Pt(s)

→ ` → → ` → → ` → ` s s s → ` ` → → → → → → →

2 H(s) 2 Pt(s) H(s) 2 O(s) 2 Pt(s) O(s) H2O(s) Pt(s) OH(s) Pt(s) OH(s) H2O(s) H2O(s) CO(s) Pt(s) Pt(s) CO2(s) CH3(s) CH2(s) CH(s) C(s) CO(s) C(s)

S0

Ea

0.046 3.7 • 1021

67.4–6.0 • HH(s) 1.00 0.07

3.7 • 1021

213.2–60 • HO(s) 1.00 0.75

1.0 • 1013

40.3

1.0 • 1013 3.7 • 1021 3.7 • 1021 3.7 • 1021

192.8 11.5 17.4 48.2

1.0 • 1013 1.0 • 1013 3.7 • 1021

125.5 20.5 105.0

3.7 • 1021 3.7 • 1021 3.7 • 1021 3.7 • 1021 1.0 • 1018

20.0 20.0 20.0 62.8 184.0

1.00 ` ` `

Pt(s) Pt(s) O(s)

0.84

` ` ` ` ` ` `

neglected, permitting use of the one-dimensional analysis of the Navier–Stokes equations describing this system [8]. The dependent variables (density, momentum, temperature, and mass fraction of each gas-phase species) are independent of the radius and depend only on the distance from the foil. This system is closed by the ideal gas law. The boundaryvalue problem that has to be solved has been stated by Evans and Greif [9] and by Kee et al. [10]. For the wire configuration, a cylindrical computational domain around the wire (placed along the cylinder axis) is used. The formulation of the governing equations in cylindrical coordinates and the application of a modified Lagrange transformation leads to one-dimensional governing equations in which the convective terms are eliminated [11,12]. Detailed models for the chemical reactions and for the molecular transport are included in the governing equations. The state of the catalytic surface is described by its temperature and the coverage with adsorbed species. The reactive flow has to be coupled with the heterogeneous chemical reactions and the transport at the gas–surface interface. Therefore, conservation equations for species masses and energy are established at the interface, considering a small control

Pt(s) H(s) H(s) H(s) H(s) Pt(s) O(s)

0.01

volume dV adjacent to the surface. Then, the mass fraction of a gas-phase species i at the surface is determined by the diffusive and convective processes and the production or depletion rate s˙i of that species by surface reactions ]Yi

# q ]t dV 4 1# (Wj ` qY uW ) nW dA ` # s˙ M dA (i 4 1, . . . , N ) i

i

(1) where q is the density, Yi the mass fraction of species i in this control volume, Wj i the diffusive flux (including thermal diffusion), Mi the molecular mass of species i, Ng the number of gas-phase species, and dA the surface area. nW is the outward-pointing unit vector normal to the surface. If chemical surface reactions occur, the velocity can be nonzero at the catalytic surface. This so-called Stefan velocity uW is given by i

nW uW 4

i

g

1 Ng s˙ M q i41 i i

o

(2)

The temperature of the catalyst is derived from various contributions to the energy balance at the catalyst. The conductive, convective, and diffusive energy transport from the gas phase adjacent to the

NUMERICAL MODELING OF CATALYTIC IGNITION

surface, as well as the chemical heat release at the surface, the thermal radiation, and the resistive heating of the catalyst are included. This results in

# (qc

p

1

` qcatccat)

]T dV 4 ]t

]T

# k ]Wr dA

Ng

o # hi (Wj i ` qYiuW ) nW dA i 1 4

# re (T 1 T ) dA 1 o # s˙ M h dA ` I R 1

4

4 ref

Ng`Ns

i4Ng`1

i

i i

2

(3)

Here, k is the thermal conductivity and hi the specific enthalpy of species i, either in the gas phase or at the surface. In the radiation term, r is the Stefan– Boltzmann constant, e is the temperature-dependent surface emissivity, and Tref is the reference temperature to which the surface radiates. The term I2R represents an energy source corresponding to resistive heating of the catalyst, where I is the current and R the electrical resistance depending on temperature. Ns is the number of surface species and cp the specific heat capacity of the gas at the wall; ccat denotes the specific heat capacity of the catalyst, while qcat is the density of the catalyst. dV includes the catalyst volume and a small control volume in the gas phase adjacent to the surface. The variation of the surface coverage Hi (i.e., the fraction of surface sites covered by species i) is given by ]Hi s˙ 4 i ]t C

(4)

where C is the surface site density of the catalyst. The numerical solution is performed by the method of lines. Spatial discretization of the partial differential–equation system using finite differences on statically adapted grids leads to large systems of ordinary differential and algebraic equations. These systems of coupled equations are solved by an implicit extrapolation method using the software package LIMEX [13]. The codes compute species mass fractions, temperature, and velocity (in the stagnation flow case) profiles in the gas phase, fluxes at the gas–surface interface, and surface temperature and coverage as a function of time. Since the codes are fully time dependent, transient phenomena such as ignition, oscillation, extinction, or catalyst poisoning can be described in detail. Physical Chemistry The chemistry is modeled by elementary reactions on a molecular level in the gas phase and on the surface. The temperature dependence of the reaction rate is described by a modified Arrhenius equa-

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tion. Special care is taken for an additional coverage dependence of the rate of some surface reactions [14]. For reversible reactions, the rate coefficients are related to the forward rate coefficients through the equilibrium constant. The reaction scheme for the gas phase is adopted from modeling work on flame chemistry without further modification [15,16]. The mechanisms used here involve the H2, CO, C1, and C2 systems. The reactions of hydrogen, oxygen, and methane on polycrystalline platinum with their rate expressions are shown in Table 1. The symbol Pt(s) denotes a bare surface site, and species with a label (s) are adsorbed at the surface. All preexponential factors A are chosen to be independent of temperature. Details on reaction steps and rate data are discussed elsewhere [8,17]. The thermochemical data needed to calculate the equilibrium constants for reversible reactions are taken from Warnatz et al. [8]. Based on thermochemical and kinetic data for the interaction of hydrogen and oxygen with palladium, as given in literature, a surface reaction scheme has been established (Table 2). Palladium leads to the same reaction scheme as platinum; however, different rate coefficients have to be used. The initial sticking coefficient for the dissociative hydrogen adsorption is chosen to be 0.7, which presents an average value of the literature data [18–20]. For the associative hydrogen desorption, A 4 4.8 2 1021 cm2 (mol s)11 [18] and Emax 4 84 kJ mol11 [19] are a used. Here, an additional decrease of the activation energy with increasing hydrogen coverage because of adsorbate–adsorbate interactions is taken into account: Ea 4 Emax 1 HH(s) 2 15 kJ mol11. For the a interaction of oxygen with palladium, S0 4 0.4 and 11 Edes are used [21,22]. The preexa 4 230 kJ mol ponential factor is derived from the vibrational frequency of a Pd–O bond of 1.1 2 1013 s11 [23]. The desorption energies for OH and H2O desorption are also taken from Ref. 23. Due to lack of kinetic data for the remaining reactions, the kinetic data derived for a platinum surface are used. The preexponential factors for these reactions include the differences between the surface site densities of platinum and palladium. In the present work, the palladium mechanism is validated by the study of ignition temperatures of hydrogen oxidation on a palladium foil.

Results and Discussion To determine the catalytic ignition temperature, the reactive mixture (diluted by nitrogen) flows slowly at atmospheric pressure around a catalytic wire or in a stagnation flow toward a catalytic foil. The mixtures are initially at room temperature. The temperature of the catalyst is increased by a stepwise increase of the current applied to the catalyst. After each increase, the system is allowed to reach its

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TABLE 2 Surface reaction mechanism on palladium (units: A [mol, cm, s], Ea [kJ/mol], S0 [1]). Pd(s) denotes bare surface sites. A H2 H 2 H(s) O2 O 2 O(s) H2O H2O(s) OH OH(s) H(s) H(s) OH(s)

` ` → ` ` → ` → ` → ` ` `

2 Pd(s) Pd(s) H2 2 Pd(s) Pd(s) O2 Pd(s) H2O Pd(s) OH O(s) OH(s) OH(s)

→ → ` → → ` → ` → ` s s s

2 H(s) H(s) 2 Pd(s) 2 O(s) O(s) 2 Pd(s) H2O(s) Pd(s) OH(s) Pd(s) OH(s) H2O(s) H2O(s)

S0

Ea

0.70 1.00 4.8 • 1021

84 1 15 • HH(s) 0.40 1.00

7.1 • 1021

230.0

1.3 • 1013

44.0

1.3 • 1013 6.5 • 1021 6.5 • 1021 6.5 • 1021

213.0 11.5 17.4 48.2

0.75 1.00 ` ` `

Fig. 1. Ignition temperature of CH4/O2 mixtures on a platinum foil as a function of fuel concentration. Comparison of experimental (circles [24]) and numerical results (line).

steady-state temperature. When reaching the ignition temperature, Ti, the temperature of the catalyst rises rapidly because of heat release by the exothermic surface reactions. A few seconds later, a new steady state is established, now controlled by mass transport of reactants toward and products away from the catalyst. Ignition temperatures are determined as a function of fuel concentration, given by a 4 pfuel/(pfuel ` pO2). Figure 1 shows the catalytic ignition temperatures for a stagnation point flow of a CH4/O2 (6% in N2 dilution) on a platinum foil. The ignition temperature decreases with increasing CH4/O2 ratio. A quantitative agreement with experimental results [24] is achieved (error bars for the experimental ignition temperature are `/115 K) and validates the surface reaction mechanism proposed.

Pd(s) Pd(s) O(s)

Fig. 2. Ignition temperature of CO/air mixtures at a platinum wire as a function of fuel concentration. Comparison of experimental (circles [6]) and numerical results (line).

In contrast to the decrease of Ti with increasing fuel/oxygen ratio for the CH4/O2 system, investigations of the catalytic ignition of H2/O2 and CO/O2 show an increase of Ti with increasing fuel/oxygen ratio. For illustration, catalytic ignition temperatures for the CO oxidation on a platinum wire and for the H2 oxidation on a palladium foil [24] are presented in Figs. 2 and 3. Beside that, the H2/O2 system shows a bistable behavior for low hydrogen concentration (curves a and b in Fig. 3, see discussion later). The different ignition behavior can be explained considering the elementary steps at the gas–surface interface. To illustrate the state of the catalyst surface, the species surface coverages and the surface temperatures as a function of time are shown in Figs. 4–6. In the CH4/O2 system (Fig. 4) before ignition, the surface is covered primarily by oxygen because of a


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Fig. 3. Ignition temperature of H2/O2 mixtures on a palladium foil as a function of fuel concentration. Comparison of experimental (circles [24]) and numerical results (line).

Fig. 5. Calculated time-dependent surface coverage and surface temperature during heterogeneous ignition of a CO2/air mixture for a 4 0.2. The time is set to be zero at the final increase of electrical current.

Fig. 4. Calculated time-dependent surface coverage and surface temperature during heterogeneous ignition of a CH4/O2 mixture for a 4 0.5. The time is set to be zero at the final increase of electrical current.

Fig. 6. Calculated time-dependent surface coverage and surface temperature during heterogeneous ignition of a H2/ O2 system for a 4 0.5. The time is set to be zero at the final increase of electrical current.

higher sticking probability of O2 in comparison to that of CH4. An increase of the surface temperature by power supplied to the catalyst leads to a point at which the adsorption/desorption equilibrium of oxygen shifts to desorption, resulting in bare surface sites where CH4 can adsorb. H abstraction leads to adsorbed C(s) and H(s) atoms reacting immediately with the surrounding O atoms to form CO(s) and OH(s). This leads to a relatively fast formation of H2O and CO2, which desorb. So, more and more surface sites become available for CH4 adsorption and for further O2 adsorption, leading to an increased oxidation rate. The chemical heat release by this exothermic reaction causes an increase of surface temperature accelerating the reaction rate, that is, ignition occurs. Since the adsorption rate depends on gas-phase

concentration, higher O2 concentrations in the gas phase lead to fewer bare surface sites and are responsible for the increase of ignition temperature at decreasing CH4/O2 ratios. In the H2/O2 and CO/O2 systems, the catalytic ignition is also connected with the adsorption/desorption kinetics (see Figs. 5 and 6). However, in these cases, before ignition, the main species at the surface is the fuel causing an inverse dependence of the ignition temperature on fuel/oxygen ratio. A prerequisite for catalytic ignition is the availability of a sufficient number of uncovered surface sites. Therefore, the influence of rate coefficients of surface reactions on this is studied by a sensitivity analysis. In Fig. 7, the sensitivity coefficients are given for the CH4 oxidation on a platinum foil immediately before ignition takes place. The

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Fig. 7. Sensitivity of the uncovered surface area HPt(s) on rate coefficients of surface reactions immediately before catalytic ignition of CH4 oxidation on a platinum foil; a 4 0.5. The unimportant reactions are not shown.

Fig. 8. Calculated methane mole fraction as a function of time and distance from the catalytic surface during heterogeneous ignition of a CH4/O2 mixture on a platinum foil for a 4 0.5. The time is set to be zero at the final increase of electrical current. The figure corresponds to Fig. 4.

adsorption/desorption kinetics of the reactants is shown to determine the ignition process, for example, the adsorption of CH4 supports the creation of bare surface sites because of the subsequent oxidation. The rate coefficients of these rate-limiting steps need to be well-known. For the H2/O2/Pd system, bistable solutions are identified under fuel-lean conditions (Fig. 3). Calculations starting with different initial coverage (hydrogen or oxygen covered surface or a bare palladium surface, respectively) but otherwise identical conditions end up at different solutions. For calculations starting with the surface covered by hydrogen atoms (case a), an ignition-like temperature curve is observed and an ignition temperature can be determined (i.e., a certain electrical heating is required for ignition). Otherwise, starting with a surface ei-

Fig. 9. Calculated oxygen mole fraction as a function of time and distance from the catalytic surface during heterogeneous ignition of a CH4/O2 mixture on a platinum foil for a 4 0.5. The time is set to be zero at the final increase of electrical current. The figure corresponds to Fig. 4.

ther bare or covered with oxygen (case b), oxidation of hydrogen begins immediately (i.e., without electrical heating). This bistability reproduces experimental observations for lean mixtures in which the measurements have to be started with a hydrogen covered surface (i.e., starting with a pure hydrogen flow) to prevent immediate ignition. A few seconds after ignition, a new steady state is established. Now, the global process is controlled by diffusion of reactants to the catalyst and of products away from the catalyst. The total surface coverage is lower than before ignition. A sufficient number of free surface sites is available for adsorption of oxygen and hydrogen. Figures 8 and 9 clearly show the effect of mass transport from and to the catalyst before and after ignition for the catalytic ignition of methane/oxygen mixtures on platinum (corresponding to Fig. 4). Strong gradients for gas-phase mole fractions of methane and oxygen develop during ignition. For the fuel-rich mixture considered, the oxygen concentration at the catalyst approaches zero, and, hence, the oxygen transport to the catalyst becomes the rate-limiting step after ignition. Conclusions Catalytic combustion is modeled by detailed models for chemistry and transport and is numerically simulated for two simple configurations. Elementary reaction mechanisms are applied in the gas and at the surface; the coupling of the catalytic surface to the surrounding reactive flow is accounted for by a detailed transport model. Numerical results for the catalytic ignition of the CH4, CO, and H2 oxidation on Pt and Pd catalysts are presented and discussed.


A quantitative agreement between measured and calculated ignition temperatures is achieved. The time-dependent simulation offers a detailed description of the transition from a kinetically controlled to a transport-limited regime during ignition. The onset of ignition is shown to depend on the adsorption/desorption reaction steps. Hence, further investigations are recommended to improve the kinetic data for these key reaction steps. Special attention should be given to possible coverage dependences of these rate coefficients. In the present paper, the surface properties are described by values averaged over the total surface, that is, the mean-field approximation has been applied. However, for future work, it is necessary to include lateral processes on the surface (e.g., species diffusion on the surface, island formation) in the model. One possible approach is the coupling of averaged results of Monte Carlo calculations for the surface reactions to the Navier–Stokes equations describing the gas phase. Acknowledgment This work was supported by the Deutsche Forschungsgemeinschaft (DFG) within the Sonderforschungsbereich 359 “Reaktive Stro¨mung, Diffusion und Transport.”

REFERENCES 1. Ljungstro¨m, S., Kasemo, B., Rose´n, A., Wahnstro¨m, T., and Fridell, E., Surf. Sci. 216:63–92 (1989). 2. Song, X., Williams, W. R., Schmidt, L. D., and Aris, R., Twenty-Third Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1990, pp. 1129–1137. 3. Williams, W. R., Stenzel, M. T., Song, X., and Schmidt, L. D., Combust. Flame 84:277–291 (1991). 4. Ikeda, H., Sato, J., and Williams, F. A., Surf. Sci. 326:11–26 (1995). 5. Deutschmann, O., Schmidt, R., and Behrendt, F., Proc. 8th International Symposium on Transport Phenomena in Combustion, San Francisco, 1995.

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6. Cho, P. and Law, C. K., Combust. Flame 66:159–170 (1986). 7. Rinnemo, M., Fassihi, M., and Kasemo, B., Chem. Phys. Lett. 211:60–64 (1993). 8. Warnatz, J., Allendorf, M. D., Kee, R. J., and Coltrin, M. E., Combust. Flame 96:393–406 (1994). 9. Evans, G. and Greif, R., ASME J. Heat Transfer 109:928–935 (1987). 10. Kee, R. J., Miller, J. A., Evans, G. H., and DixonLewis, G., Twenty-Second Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1988, pp. 1479–1494. 11. Maas, U. and Warnatz, J., Combust. Flame 74:53–69 (1988). 12. Goyal, G., Maas, U., and Warnatz, J., Combust. Sci. Technol., in press (1996). 13. Deuflhard, P., Hairer, E., and Zugk, J., Num. Math. 51:501–516 (1987). 14. Coltrin, M. E., Kee, R. J., and Rupley, F. M., “SURFACE CHEMKIN (Version 4.0): A Fortran Package for Analyzing Heterogeneous Chemical Kinetic at a Solid-Surface–Gas-Phase Interface,” Sandia National Laboratories Report No. SAND90-8003B, 1990. 15. Warnatz, J., in Combustion Chemistry (Gardiner, W. C., Ed.), Springer, New York, 1984, pp. 197–360. 16. Baulch, D. L., Cobos, C. J., Cox, R. A., Esser, C., Frank, P., Just, T., Kerr, J. A., Pilling, M. J., Troe, J., Walker, R. W., and Warnatz, J., J. Phys. Chem. Ref. Data 21:411–734 (1992). 17. Deutschmann, O., Behrendt, F., and Warnatz, J., Catal. Today 21:461–470 (1994). 18. Behm, R. J., Christmann, K., and Ertl, G., Surf. Sci. 99:320–340 (1980). 19. Christmann, K., Mol. Phys. 66:1–50 (1989). 20. Rendulic, K. D., Anger, G., and Winkler, A., Surf. Sci. 208:404–424 (1989). 21. Engel, T., J. Chem. Phys. 69:373–385 (1978). 22. Matolin, V., Channakhone, S., and Gillet, E., Surf. Sci. 164:209–219 (1985). 23. Stuve, E. M., Jorgensen, S. W., and Madix, R. J., Surf. Sci. 146:179–198 (1984). 24. Behrendt, F., Deutschmann, O., Schmidt, R., and Warnatz, J., in Heterogeneous Hydrocarbon Oxidation, ACS Symposium Series, 1996.

COMMENTS Robert Kee, Colorado School of Mines, USA. Quantitatively understanding time response should be important in the control of catalytic combustion. Your results show time constants of 10–20 sec for lightoff. Can you comment on temporal accuracy of the models? Author’s Reply. The time constant for lightoff of a catalytic reaction on foils and wires are experimentally found to have the same orders of magnitude as the numerical results presented in the given paper. e.g., the lightoff of

hydrogen oxidation on a platinum foil took about 20 seconds from rapid temperature rise to establishment of a new steady state (reaching a constant catalyst temperature), and a good agreement between experiment and simulation was achieved for this system[1]. It is essential to take all possible heat losses of the catalyst into account if an energy balance at the catalyst is considered to compute the catalyst temperature. In case of the one-dimensional stagnation flow field model difficulties arise due to heat conductivity on the backside and at the

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holder of the catalytic foil. Inert gas experiments are used to estimate these heat losses depending on catalyst temperature. Then, these additional heat losses are taken into account by an additional term in the energy balance. With this procedure a good agreement of temporal evolution of lightoff between experiment and computation is achieved. Neglecting these heat losses the catalyst temperature will be overestimated and the time constant is to short[2].

REFERENCES 1. Behrendt, F., Deutschmann, O., Schmidt, R., and Warnatz, J., Heterogeneous Hydrocarbon Oxidation, ACS Symposium Series, 1996. 2. Deutschmann, O., Schmidt, R., and Behrendt, F., Proc. 8th International Symposium on Transport Phenomena in Combustion, San Francisco, 1995. ● Lisa D. Pfefferle, Yale University, USA. Comparing individual surface reactions and model parameters between the several published mechanisms for the oxidation of methane over polycrystalline Pt, there are large differences even when global parameters are well predicted. In addition, for many conditions near the point of surface ignition the surface is mostly covered by O (as also shown in your work), under these conditions the mean field assumption breaks down. This has important consequences for extrapolating predictions of system behavior over large parameter regimes. What do you believe are the least certain steps in your reaction mechanism and the next model/experimental steps to address the issue? In the talk it was mentioned that Pd was also being modeled. In that the Pd/O system is not experimentally well understood even to the point of having no available data for the coverage dependence of the heat of adsorption of O on Pd, how can detailed modeling be usefully employed? Author’s Reply. The sensitivity analysis of the ignition of methane oxidation on Pt shows the adsorption/desorption reactions of methane and oxygen to be the crucial steps in the mechanism. Further experiments are necessary to obtain improved kinetic data for these steps. Furthermore, the possibility of desorption of intermediates during decomposition of the adsorbed CH3 radical and the possible formation of CHxO should be studied. A next step in our work will address problems of the mean field approximation used. One approach to get rid of this simplification consists in the coupling of the averaged results of Monte-Carlo calculations for the surface reactions to the Navier–Stokes equations describing the gas phase. The hydrogen oxidation processes on Pt and Pd are found experimentally and numerically to show a very similar behavior. The kinetic data used for the adsorption/desorption reactions of H2 and O2 on Pd—most important for the ignition process—are averaged values from litera-

ture data. Due to the lack of rate coefficients for the remaining reactions—less important for the ignition process—the kinetic data derived for the platinum surface are used. Considering the Pt–system the coverage dependence of the heat of adsorption of oxygen is not decisive for the hydrogen oxidation in the lower temperature regime (ignition temperature below 400 K) in contrast to the case of methane oxidation in a higher temperature regime. Due to the similarity of hydrogen oxidation on Pd and Pt the heat of adsorption of oxygen on Pd seems also to be not a critical point. We found that for the investigation of the hydrogen oxidation on Pd the absorption of hydrogen by the solid Pd–catalyst is more important then the Pd/O behavior which is not well understood. However, a better understanding of the Pd/O–system is obviously a prerequisite for detailed modeling of methane oxidation on Pd. ● D. G. Vlachos, University of Massachussetts, USA. The agreement between simulations and experiments on CH4 catalytic ignition is very good. How many reaction rate constants and of which surface reactions are fitted to your experiments? Also, how do you numerically describe your mass and energy boundary conditions at the Pt surface? In particular, please comment on the domain of integration in the volume integral present in the time dependent term. Author’s Reply. In the literature, there is a lack of kinetic data for some of the surface reactions, for other reactions a wide range of values exist. Therefore, the comparison between computed and measured ignition temperatures is used to determine some of these rate coefficients. For CH4 oxidation on Pt, the sticking coefficient and the decomposition kinetic data for CH4 as well as the dependence of the activation energy of oxygen desorption on oxygen coverage are fitted. The decrease of activation energy of hydrogen desorption with increasing hydrogen coverage was determined in former studies of H2 oxidation on Pt[1]. The volume integral in equation (1) denotes a small control volume adjacent to the catalytic surface. The accumulation term in this equation is important if adsorption/ desorption processes and diffusion in the gas phase have different time scales. Furthermore, the accumulation term improved the stability of the numerical solution if the integration starts with inconsistent initial conditions (due to unknown initial surface coverage). The domain of integration in the volume integral of equation (3) consists of the gas phase cell described above and the catalyst volume. Considering the heat capacity of the metal catalyst the heat capacity of the small gas phase cell is negligible.

REFERENCE 1. Behrendt, F., Deutschmann, O., Schmidt, R., and Warnatz, J., Heterogeneous Hydrocarbon Oxidation, ACS Symposium Series, 1996.