TWO-DIMENSIONAL MODELING OF PARTIAL OXIDATION OF METHANE ON RHODIUM IN A SHORT CONTACT TIME REACTOR

Transcription

1 Twenty-Seventh Symposium (International) on Combustion/The Combustion Institute, 1998/pp TWO-DIMENSIONAL MODELING OF PARTIAL OXIDATION OF METHANE ON RHODIUM IN A SHORT CONTACT TIME REACTOR OLAF DEUTSCHMANN and LANNY D. SCHMIDT Dept. of Chemical Engineering and Materials Science University of Minnesota 151 Amundson Hall 421 Washington Ave. SE Minneapolis, MN 55455, USA Partial oxidation of methane in monolithic catalysts at very short contact times has recently been shown to offer a promising route to convert natural gas into syngas (CO, H 2 ), which can subsequently be converted to higher alkanes or methanol. Detailed models are needed to understand the complex interaction of transport and kinetics occurring in these reactors. In this work, the partial oxidation of methane on rhodium is studied numerically as an example of short contact time reactor modeling. A tube wall catalytic reactor, which serves to model a single pore or channel of the monolithic catalyst, is simulated. The simulation is carried out using a fully two-dimensional flowfield description, which is coupled with a detailed surface reaction model. The catalyst is characterized by its temperature and coverages of adsorbed species, which vary in the flow direction. The simulation offers a detailed description of the complex interaction between mass and heat transfer as well as chemistry. At the catalyst entrance, an extremely rapid variation of temperature, velocity, and transport coefficients is found. The competition between complete and partial methane oxidation is explained using the calculated surface coverages whereby CO 2 and H 2 O are formed in the entrance region of the catalytic reactor. Methane conversion as well as H 2 and CO selectivity are found to increase with increasing temperature. Increasing reactor pressure reduces methane conversion, although the syngas selectivity decreases only slightly. Introduction Catalytic combustion and conversion of methane, the main component of natural gas, have recently received extensive experimental and theoretical attention because of their potential to reduce pollutant emissions and synthesize useful chemicals. The catalytic reactors used for these processes, such as foam or extruded monoliths, wire gauzes, or sintered spheres, have a complex interaction between the reactive flow and reactions on the catalytic surface. Therefore, the description of these heterogeneous reactors requires a detailed description of the coupling of the flowfield and the catalyst. The direct partial oxidation of light alkanes in a monolithic catalyst at very short contact times has recently been shown to offer a promising route to convert light alkanes to syngas, higher hydrocarbons, and oxygenates [1 3]. Syngas formation from methane/oxygen mixtures on noble metal catalysts is characterized by the competition between a complete oxidation channel globally written as CH4 2O2 CO2 2HO 2 DHR 890 kj/mol and a partial oxidation channel written as CH 1/2 O CO 2H DH R 36 kj/mol Appropriate catalytic material and residence time must be chosen to achieve high syngas (CO, H 2 ) selectivity. Rhodium-coated foam or extruded catalysts with a residence time of approximately 1 ms were found to be capable of producing this high syngas selectivity ( 90%) with a high methane conversion ( 90%) [1]. These processes, which can be run nearly autothermally and adiabatically, exhibit an extremely fast variation of temperature, velocity, and transport coefficients of the reactive mixture near the catalyst entrance. This variation causes strong disturbance of the parabolic flowfield and two-dimensional effects in heat and mass transfer. Furthermore, a significant amount of the chemistry in this system takes place in the entrance region of the catalyst. In this paper, we study the partial oxidation of methane in a tubular reactor with a rhodium catalytic surface. The complex behavior at the catalyst entrance region, the competition between complete and partial oxidation, and the role of surface kinetics are discussed. The dependence of conversion and 2283

2 2284 CATALYTIC COMBUSTION Fig. 1. Sketch of the tubular reactor model representing a single pore of a monolithic catalyst (top), axial velocity (middle), and temperature (bottom) profiles around catalyst entrance. The axial position (z)is zero at the catalyst entrance, axial and radial (r) axes have the same scale. selectivity on temperature and pressure is calculated, and the data are compared with experimental results. Numerical Model The tube wall catalytic reactor, as shown in Fig. 1, serves as a model of a single pore or channel in monolithic catalysts. Typical pore diameter varies between 0.25 and 1 mm, and its length is typically 1 cm. In these small diameter channels the flowfield is always laminar with a Reynolds number of approximately 20, which has the same order of magnitude at the inlet and under reactor conditions. Experimental measurements indicate only small temperature gradients over the catalyst for cases simulated in this work, so the catalytic wall is assumed to be isothermal. An adiabatic inert wall, 1 cm in length, is used in the model to simulate the heat shields in front of and behind the catalytic section. Simulations of catalytic reactors often use a simplified model of either the flowfield or chemistry. This approach can be risky if there is a strong interaction between flow and chemistry as occurs in short contact time reactors. Most previous studies have assumed a plug flow tubular reactor model where radial mass and heat transfer are included only through effective mass or heat transfer coefficients, which are often assumed to be constant over the length of the reactor. The resulting initial value problem is easy to solve even for a system involving many equations. This method was applied to study the high-temperature surface chemistry of CH 4 oxidation on Pt and Rh [1]. However, the plug flow tubular reactor model is not able to consider two-dimensional effects of the complex interaction between mass and heat transport as well as chemistry. A more-sophisticated boundary layer model was successfully applied to simulate catalytic oxidation [4] over flat plates, although diffusion in flow direction is still neglected (for a detailed discussion see Ref. [5]) and this model is not capable of simulating a more complex reactor geometry such as a wire gauze reactor [3,6]. Because one motivation of this work is to develop numerical tools that can be easily applied to various reactor configurations, a fully two-dimensional elliptic model is used based on the commercial CFD code Fluent [7]. Only the use of a detailed surface reaction mechanism allows the explanation of characteristic features of a catalytic reactor such as ignition or poisoning [8]. Therefore, we coupled Fluent to external subroutines that model detailed surface chemistry. Here, the state of the catalytic surface is described by its temperature and its coverage with adsorbed species, which vary in the flow direction. We have developed subroutines to calculate the surface coverages ( i ) and the surface mass fluxes (ṡ i M i )atthe catalytic wall. On the catalytic wall, the boundary condition for gas-phase species i becomes r r r ṡ M ( j qy u) n (i 1,..., N ) i i i i g where ṡ i is the creation or depletion rate by surface r reactions, M i the molar mass, j i the diffusive flux, q r the density, Y i the mass fraction, u the Stefan veloc- r ity, n the unit vector normal to the surface, and N g the number of gas-phase species.

3 PARTIAL OXIDATION OF METHANE 2285 The chemistry is modeled by elementary reactions on a molecular level. The chemical source term ṡ i of gas phase and surface species is given by K s Ng Ns ṡ m k [X ] m ik i ik fk i k 1 i 1 where K s is the number of elementary surface reactions (including adsorption and desorption), m ik (right side minus left side of reaction equation) and m ik (left side of reaction equation) are stoichiometric coefficients, k fk is the forward rate coefficients, N s is the number of species adsorbed, and [X i ] the concentration of species i. For adsorbed species, the concentrations are given in mol/m 2 and equal the surface coverage i multiplied by the surface site density C. The temperature dependence of the rate coefficients is described by a modified Arrhenius expression: N s bk E ak l e ik i fk k i k k AT exp exp RT i 1 RT This expression takes an additional coverage dependence into account. Here, the factor l has to be considered in connection to the factor [X] m in the equation for ṡ i. We are interested in the steady-state solution, hence the variation of the surface coverage i is zero: i ṡi 0 (i Ng 1,..., Ng N s) t C In the external subroutines, this equation system is solved to obtain surface coverages and surface mass fluxes. Here, Fluent provides the concentration of the gas-phase species and the temperature at each computational cell with a catalytic wall as the boundary. In the surface chemistry subroutines, coverages and surface mass fluxes are calculated by an implicit method, where gas-phase concentrations and temperature are kept constant. The tube wall catalytic reactor itself is described by the two-dimensional conservation equations using cylindrical geometry. Detailed description of the molecular transport are included in the equations, and the transport coefficients depend on both composition and temperature. However, thermal diffusion effects are ignored in these calculations. For the simulation, a structured grid is used that must be very fine around the catalyst entrance to resolve the flowfield. The total number of grid points varies between 10 3 and 10 4 depending on the reactor diameter and external conditions such as temperature. The number of computational cells with surface reaction boundaries varies between 30 and 100. The numerical calculations were performed on a Cray C916/ Typically, a CPU time of about 20 minutes is required to obtain a converged solution. Chemical Reaction System In our simulations we use the surface reaction scheme proposed by Hickman and Schmidt for the high-temperature methane oxidation in a short contact time reactor with a Rh-coated foam monolith [1]. Table 1 shows the reaction mechanism with associated rate expressions. This scheme assumes dissociative methane and oxygen adsorption, formation of CO, CO 2,H 2, and H 2 O via OH, and desorption of products. All reaction steps are reversible except methane adsorption and CO 2 desorption. It is assumed that oxygen is adsorbed noncompetitively with other species, whereas all other species are adsorbed competitively. The site density (C) is assumed to be mol/m 2, which is atoms/cm 2. For more details such as reaction order, please refer to the original work [1]. Only the conservation equations for stable species CH 4,O 2, CO, H 2,CO 2,H 2 O, and N 2 are considered in the gas phase. Gas-phase reactions are assumed to be negligible under given conditions of about 1 ms contact time and approximately 1200 K temperature. The simulation of a homogeneous chemical reactor using a detailed gas-phase reaction mechanism that includes C 1 C 4 species [9] shows that only for the high-pressure calculation ( 10 bar, see discussion below), gas-phase chemistry might have some influence. Results and Discussion As an example of the catalytic oxidation of methane on rhodium in short contact time reactors, the simulation of the following case is discussed: a methane/oxygen mixture (ratio: 1.8, 30% nitrogen dilution) flows at a uniform inlet velocity of 1 m/s and at 298 K with a total pressure of 1.4 bar into a cylindrical tube 3 cm in length having a diameter of 0.5 mm (Fig. 1). The 1-cm-long inner catalytic wall in the center of the tube has a constant temperature of 1123 K. The wall is adiabatic and inert in front of and behind the catalytic section. The catalyst entrance is characterized by an extremely fast variation of velocity, temperature, and transport coefficients of the reactive mixture. In Fig. 1, the axial velocity and the temperature field around the catalyst entrance are shown. The temperature increases inward 1 mm, which corresponds to a length of two tube diameters, to 1000 K. Simulations using different tube diameters show an even smaller entrance region of one tube diameter length for a 0.25-mm diameter, which corresponds to the frequently used 80 ppi (pores per inch) monolith. The entrance length was found to decrease approximately as D 2 with tube diameter D. Furthermore, the incoming gas is preheated immediately in front of the catalyst by upstream thermal conductivity. We note that radiation is not explicitly taken into account

4 2286 CATALYTIC COMBUSTION TABLE 1 Surface reaction mechanism on rhodium (units: A [mol, cm, c], E a [kj/mol], s [ ]) taken from Hickman and Schmidt [1], to which the reader is referred for further details Reaction A E a s CH 4 (g) C 4H O 2 (g) 2O 0.01 H 2 (g) 2H 0.16 CO(g) CO 0.50 H 2 O(g) H 2 O O O 2 (g) H H 2 (g) CO CO(g) co H 2 O H 2 O(g) H O OH OH O H H OH H 2 O H 2 O H OH OH OH H 2 O O C O CO CO C O CO O CO 2 (g) (g) gas-phase species Fig. 2. Mass fraction of methane (top) and oxygen (bottom) as a function of position in the reactor. The axial position (z) is zero at the catalyst entrance, the catalytic wall is at the radial position (r) of 0.25 mm. because the large thermal conductivity of the monolith results in an isothermal wall. The rapid increase of the velocity from 1 m/s to greater than 10 m/s at the catalyst entrance is not only a result of the density change due to the temperature increase but also caused by the change of the composition, which leads to almost two moles of products for each reactant under given conditions; methane oxidation starts immediately at the catalyst entrance. In the first noncatalytic section of the tubular reactor a parabolic flowfield is quickly established. This parabolic flowfield is strongly disturbed at the catalyst entrance, and two maxima occur that can be seen from the contour line at 4 m/s in Fig. 1. A few tube diameters downstream the parabolic velocity field is again established. The rapid variation of the transport coefficients at the catalyst entrance is caused by the temperature increase and the composition change. The rise in thermal conductivity, a factor of 10 between inlet and reactor conditions, once again leads to an acceleration of the gas temperature increase. Also, the diffusion coefficients and the kinematic viscosity vary approximately by a factor of 10 at the catalyst entrance. The variation of the transport coefficients due to chemical reactions is caused mainly by the formation of hydrogen. The hydrogen mole fraction increases to 0.5 during the reaction. Figures 2 4 show the mass fraction of the gas phase species as a function of position in the reactor. The catalytic part of the tubular reactor is between

5 PARTIAL OXIDATION OF METHANE 2287 Fig. 3. Mass fraction of the complete combustion products, CO 2 (top) and H 2 O (bottom), as a function of position in the reactor. The axial position (z) is zero at the catalyst entrance, the catalytic wall is at the radial position (r) of 0.25 mm. a 0- and 10-mm axial position and the radial position is set to zero at the tube axis so that the catalytic wall is at 0.25 mm. Methane oxidation starts directly at the catalyst entrance where large radial and axial gradients are formed. Oxygen is completely consumed by catalytic reactions. However, there is still some methane left at the catalyst exit, the methane conversion being 95%. The catalytic formation of hydrogen and carbon monoxide as the desirable products and water and carbon dioxide as the complete oxidation products starts at the catalyst entrance. Here a competition between the partial and the complete oxidation paths occurs. In the beginning, the oxygen concentration is large enough to quickly produce a significant amount of CO 2 and H 2 O, which leads to steep radial concentration gradients of these species (Fig. 3). The desorbed water can again be readsorbed. In contrast to H 2 O, the adsorption of CO 2 molecules is negligible due to the very low heat of adsorption for CO 2 on Rh. These kinetic differences and the larger diffusion coefficient for water are responsible for the higher peak of CO 2 at the catalytic wall. After a 1- mm catalyst length, the complete oxidation channels practically extinguish, although there is still a considerable amount of oxygen in the gas phase. Now Fig. 4. Mass fraction of the partial oxidation products, CO (top) and H 2 (bottom), as a function of position in the reactor. The axial position (z) is zero at the catalyst entrance, the catalytic wall is at the radial position (r) of 0.25 mm. oxygen is completely used for CO formation. The activation energy for OH formation on rhodium is higher than for CO formation, in contrast to platinum surfaces [1,8]. Therefore platinum can be used for complete catalytic oxidation of methane, whereas rhodium is preferred for partial oxidation, for syngas formation. Furthermore, in the downstream direction an increasing number of carbon atoms on the rhodium surface is available to consume oxygen. This is illustrated in Fig. 5 where the surface coverages are shown as a function of the axial position. Here, it can be clearly seen that the oxygen coverage decreases in the first part of the catalyst, so farther downstream any adsorbed oxygen is consumed immediately. In the first part of the catalyst, CO is the major adsorbed species, which explains the formation of CO 2 in this range. Here, the rate-limiting step for water production is the OH formation. OH immediately leads to water due to the high hydrogen coverage. Therefore, the OH coverage is lower than At the catalyst entrance, the C coverage is still low. The activation energy for CO 2 formation is similar to that of OH formation. Both these factors lead to water formation in the first part of the catalyst. The increasing carbon coverage agrees with the experimentally indicated carbon surface coverage at the catalyst exit.

6 2288 CATALYTIC COMBUSTION Fig. 5. Surface coverage as a function of the axial position in the reactor. The axial position is zero at the catalyst entrance. Fig. 6.H 2 and CO selectivity as well as CH 4 conversion as a function of temperature. The symbols refer to an experiment with a 65 ppi foam monolith [10]. Figure 4 shows the final high syngas selectivity, where in this case the hydrogen selectivity is 93% and the CO selectivity is 97%. The higher diffusion coefficient of hydrogen compared with that of carbon monoxide leads to the larger radial gradients of CO. At the catalyst entrance some backward diffusion of the products occurs as indicated by the profiles in Figs. 3 and 4. Because the processes at the catalyst entrance are decisive for global selectivity and conversion, a detailed description of these phenomena is necessary, which can only be done using an elliptic model. The program was used to carry out parameter studies such as the dependence of selectivity and conversion on temperature, pressure, catalytic material, pore diameter, and the methane/oxygen ratio. The dependence on temperature and pressure is discussed here in more detail. Fig.7.H 2 (squares) and CO (triangles) selectivity as well as CH 4 conversion as a function of pressure. The symbols refer to an experiment with a 80 ppi foam monolith [11]. The short contact time reactor allows the running of the syngas formation on rhodium nearly autothermally and adiabatically if reactor insulation is used. Only a small temperature gradient over the axial reactor position has been recorded [10]. Consequently, the reactor temperature is determined by conversion, selectivity, and heat loss. A higher reactor temperature could be achieved by preheating the inlet gases. We studied the influence of temperature variation on selectivity and conversion numerically by varying the isothermal catalytic wall temperature. Fig. 6 shows the increase of methane conversion and syngas selectivity with increasing temperature. This tendency agrees with the experimental observation for preheated gases [1]. Furthermore, a comparison with an experimental measurement on a 65 ppi Rh/ -Al 2 O 3 foam monolith is shown [10]. In this experiment, the autothermal operating reactor temperature was 1073 K, which was determined experimentally by a thermocouple. In spite of the fact that the tubular reactor model is a simplification of a foam monolith, the calculation and experimental data agree quite well. The industrial application of short contact time reactors depends on the possibility of running these processes at higher pressures. In laboratory experiments, measurements of the pressure dependence are very limited due to safety and costs. In contrast, the numerical simulation of higher pressure is relatively straightforward. Therefore, a former experimental study has been extended to higher pressures by using the numerical code. In Fig. 7, the calculated conversion and selectivity are shown and compared with experimental data for the low pressure region. In the experiment, a methane/oxygen ratio of 2 with 20% nitrogen diluent, a gas inlet velocity of 3.7 m/s, and a Rh-coated 80 ppi foam monolith were used [11]. These data are also used in a simulation whereby a single pore of the 80 ppi catalyst is modeled by a tube 0.25 mm in diameter. The adiabatic

7 PARTIAL OXIDATION OF METHANE 2289 reactor temperature, which is calculated from total selectivity and conversion, is used as catalyst temperature. Both the experimental and the calculated data show the same qualitative behavior: decreasing methane conversion and only slightly decreasing syngas selectivity with increasing pressure. The simulation shows that for higher pressures, the catalyst is not long enough for complete conversion, although the selectivities remain nearly constant. The quantitative differences between experiment and simulation can be caused by an oversimplified model of the porous foam monolith, the uncertainty in the experimental measurement, or the application of a surface reaction mechanism that was established using a one-dimensional model. Furthermore, homogeneous reactions might become significant at higher pressures ( 10 bar), which would result in more CO 2 and H 2 O. Conclusions A two-dimensional elliptic model based on the CFD code Fluent has been coupled with external subroutines that describe detailed surface chemistry. We have applied this newly developed numerical tool to simulate the partial oxidation of methane on rhodium in a short contact time reactor. A 17-step elementary surface reaction mechanism and a detailed transport model have been used. The simulation offers a detailed description of the complex interaction between mass and heat transfer as well as chemistry. At the catalyst entrance, an extremely rapid variation of temperature, velocity, and transport coefficients occurs. The competition between complete and partial methane oxidation is explained using the calculated surface coverages in which CO 2 and H 2 O are formed in the entrance region of the catalytic reactor. Methane conversion and syngas selectivity increase with rising temperature. Increasing reactor pressure reduces conversion, whereas the syngas selectivity decreases only slightly. In the cases studied in this paper, an isothermal catalytic wall can be assumed, and gas-phase reactions do not seem to influence the chemistry. However, the application of the computational tools to some further chemical systems needs to involve models of both heat balances in the solid and detailed chemistry in the gas phase. Future work will address these problems. Acknowledgment We would like to thank Professor J. Warnatz for his continuous support in modeling of catalytic combustion. This research is supported by using the computer facilities of the Supercomputer Institute at University of Minnesota. Financial support by the Department of Energy under grant no. DE-FG02-88ER13878-A02 is acknowledged. Olaf Deutschmann gratefully acknowledges a grant from the DFG (Deutsche Forschungsgemeinschaft) for a oneyear stay at the University of Minnesota, Department of Chemical Engineering and Materials Science. REFERENCES 1. Hickman, D. A. and Schmidt, L. D., AIChE J. 39: (1993). 2. Huff, M. and Schmidt, L. D., AIChE J. 42: (1996). 3. Goetsch, D. A. and Schmidt, L. D., Science 271: (1996). 4. Warnatz, J., Allendorf, M. D., Kee, R. J., and Coltrin, M. E., Combust. Flame 96: (1994). 5. Karim, H., Pfefferle, L. D., Smooke, M. D., Markatou, P., and Xu, Y., Combust. Sci. Technol. 119: (1996). 6. Iordanoglou, D. I. and Schmidt, L. D., J. Catalysis 176: (1998). 7. Fluent 4.4, copyright Fluent Inc., Lebanon, NH, Deutschmann, O., Schmidt, R., Behrendt, F., and Warnatz, J., in Twenty-Sixth Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1996, pp Baulch, D. L., Cobos, C. J., Cox, R. A., Esser, C., Frank, P., Just, Th., Kerr, J. A., Pilling, M. J., Troe, J., Walker, R. W., and Warnatz, J., J. Phys. Chem. Ref. Data 21: (1992). 10. Bodke, A. S. and Schmidt, L. D., J. Catalysis 179: (1998). 11. Dietz III, A. G. and Schmidt, L. D., Catal. Lett. 33:15 29 (1995).

8 2290 CATALYTIC COMBUSTION COMMENTS Laxminarayan L. Raja, Colorado School of Mines, USA. The wall temperatures in your simulations are sufficiently high that gas chemistry can play a role. Comment on the accuracy of your solutions when you neglect this effect. Author s Reply. Indeed, the high temperature of more that 1000 K may lead to significant gas-phase reactions, even though the residence time of the mixture is only a few milliseconds in the hot reactor. The comment also addresses an important point concerning a commercial application of short contact time reactors. Here, the reactor has to be operated at higher pressures of bar that will additionally increase the influence of gas-phase reactions. Therefore, we recently coupled the CFD code FLU- ENT with a detailed gas-phase chemistry model [1]. In this model, 164 gas-phase reactions among 22 chemical species are used aside from the surface reaction mechanism. First, results revealed that gas-phase chemistry is not significant at all at atmospheric pressure. Hence, the solutions obtained with only surface chemistry as in the present paper are accurate at atmospheric pressure. However, at higher pressure (over 10 bar), gas-phase reactions become more and more important leading to an increase in CO 2 and H 2 O formation [1]. Here, the effect of gas-phase chemistry cannot be neglected. Because of the interaction of gas phase and surface chemistry, in particular, recombination of radicals, the currently used surface reaction mechanism must be improved by taking adsorption and desorption of intermediates into account. REFERENCE 1. Deutschmann, O. and Schmidt, L. D., Partial Oxidation of Methane in a Short Contact Time Reactor: Two- Dimensional Modeling with Detailed Chemistry, AIChE J., in press. I. A. B. Reid, British Petroleum, UK. In conventional partial oxidation, the reaction takes place at higher temperature and 30 bar. The mixture is kept at high temperature for several seconds to equilibrate the mixture. The selectivity is similar to the SCTR at 1 bar. How can you develop high-pressure SCTR to maintain high selectivity if the gas-phase chemistry begins to dominate but temperature and residence time are too low to allow product equilibration to CO and H 2? Author s Reply. The increasing influence of gas-phase chemistry on selectivity really seems to be one of the crucial steps in the development of a high-pressure short contact time reactor (SCTR). Recent simulations including gas-phase chemistry actually show decreasing syngas selectivity at increasing pressure [1 in comment]. However, the impact of the catalytic surface on gas-phase intermediates (recombination of radicals) has still to be revealed. If the surface acts as a sink for these intermediates, what we expect, then catalytic monoliths with more channels per unit (i.e., a smaller diameter of each channel) will help to suppress undesired gas-phase chemistry. However, the occurring pressure drop has to be considered if thinner channels are used. Generally, work still has to be done to solve the problem described in the comment. Paul Shardlow, University of Sydney, Australia. How long does it take to solve for the temperature and species profiles shown? Are there any problems in getting a solution? Author s Reply. The numerical calculations were performed on a Cray C916/ Typically, a CPU time of about 20 min is required to obtain a converged solution. If detailed gas-phase chemistry is also added to the model, a simulation takes several CPU hours. Most of the time of this project was needed to develop a numerical algorithm to achieved stable solutions. In particular, a pseudo-implicit method for the surface coverage calculations and an under-relaxation procedure are used to simulate the coupling of surface chemistry (very fast time scales) and flow field. Now a new simulation, for example, varying the chemical kinetics, is straightforward. However, problems still occur in getting a converged solution if gas-phase chemistry is also taken into account. Work on this problem is in progress. Dion Vlachos, University of Massachusetts, USA. Do you use a Stefan velocity in the simulations, as implied in your talk, as the mass average velocity should be zero to conserve mass? Also, what are the discretizations and computational times at different conditions? Author s Reply. The Stefan velocity is automatically calculated in the CFD code used for the simulations. However, when the net mass flux at the surface is zero, the Stefan velocity vanishes by definition, as you said. Because steady-state solutions were calculated and there is no growth or ablation on the surface in the presented simulations, the Stefan velocity is always zero. The discretization is based on a control volume finitedifference method. The total number of grid points varies between 101 and 104 depending on the reactor diameter and external conditions such as temperature. The grid has to be fine around the catalyst entrance where rapid variations of the variables occur. Reference should be made to a previous comment concerning computational times.

9 PARTIAL OXIDATION OF METHANE 2291 Bruce Gerhold, Phillips Petroleum, USA. The model imposes a fixed temperature for the catalyst wall. This temperature can be critical in that it can determine whether or not the flow ignites or blows through unreacted (both solutions will be noted depending on gas-velocity). In reality, the catalyst wall temperature results from local thermal equilibrium between (1) catalyst wall heat conduction, (2) radiation from downstream, (3) radiation to cooler areas upstream, and (4) catalytic reaction. Can you provide estimates of these heat-transfer rates that support the assumed catalyst wall temperatures? Author s Reply. We agree that there are important considerations. Experiments show that the catalyst temperature varies by less than 100 C until much higher flow rates than those assumed in their calculations. We have included wall temperature variations in more recent calculations, and they confirm these assumptions. Radiation, while more difficult to include, will make axial variations smaller. The high flow rate situation and blowout possibilities need to be examined in more detail.