Modeling heterogeneous and homogeneous reactions in the high-temperature catalytic combustion of methane

Transcription

1 Chemical Engineering Science 54 (1999) 5791}5807 Modeling heterogeneous and homogeneous reactions in the high-temperature catalytic combustion of methane C. T. Goralski Jr., L. D. Schmidt* Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, MN 55455, USA Received 9 September 1998; accepted 31 December 1998 Abstract A high-temperature, short-contact-time catalytic methane combustor is modeled as a plug-#ow tubular reactor including both homogeneous and heterogeneous chemistry. The gas-phase chemistry is modeled with GRI-mech 2.11 and the heterogeneous chemistry is modeled using an elementary 19-step mechanism for combustion of methane on platinum. Calculations are made at a variety of pressures, temperatures, compositions, and catalyst pore sizes to determine their e!ects on the reactor exhaust compositions. Comparisons are made between results for cases where only homogeneous chemistry is allowed, only heterogeneous chemistry is allowed, and where both mechanisms are allowed. It is found that the homogeneous chemistry in all cases is signi"cantly inhibited by the heterogeneous chemistry, although alone each of these mechanisms takes place on similar time scales. This inhibition is a result of the adsorption of radical species from the gas phase to the surface of the catalyst, which prevents initiation of the gas-phase free-radical chain reactions Elsevier Science Ltd. All rights reserved. Keywords: Methane catalysis; Natural-gas conversion; Catalytic combustion; Short-contact-time reactor; Reactor modeling 1. Introduction High-temperature, short-contact-time catalytic reactors show great promise in many applications ranging from the production of syngas and ole"ns to catalytic combustion and incineration. Using this type of reactor, it has been shown that it is possible to completely combust fuel-lean mixtures of alkanes and volatile organic compounds (VOCs) in air at residence times as short as several milliseconds. A short-contact-time catalytic combustor can safely operate both leaner than the lower #ammability limits as well as within the lower homogeneous #ammability limits for alkane fuels ranging from methane to butane. While it is not surprising that the presence of a catalyst will improve performance outside the #ammability limits (where homogeneous reactions are not self-sustaining), it is less clear what e!ect the catalyst will have in the regime where both homogeneous and heterogeneous chemistry can take place. Experimental results have shown that the presence of a catalyst drastically improves exhaust emissions of carbon monox- * Corresponding author. Tel.: # ; fax: # ide, unburnt hydrocarbons, and nitrogen oxides, even when operating within the #ammability limits. It is therefore of great interest to model the chemistry that takes place under these conditions to better understand the roles of heterogeneous and homogeneous chemistry in a high-temperature catalytic combustion reactor. There have been numerous e!orts to model catalytic monolith reactors. Many of these models are two-dimensional models that include detailed heat and mass transfer in an attempt to accurately model the reactor operation (Deutschmann & Schmidt, 1998,1999; Hayes, Kolaczkowski & Thomas, 1992). Unfortunately, because of the numerical complexity involved in solving the resulting partial di!erential equations, simpli"ed or lumped-parameter reaction mechanisms are often used to describe the homogeneous reactions (Deutschmann & Schmidt, 1998). Many of the models (Deutschmann & Schmidt, 1999; Hayes et al., 1992) assume that gasphase chemistry is negligible in the system being modeled. Other models (Hayes et al., 1992; Spence et al., 1993) have used simpli"ed heterogeneous mechanisms to avoid solving the highly non-linear surface-species balances along the length of the catalyst. Simpli"ed kinetic mechanisms can give reasonable understanding of the rates of reaction and evolution of heat in a monolith /99/$ - see front matter 1999 Elsevier Science Ltd. All rights reserved. PII: S ( 9 9 )

2 5792 C. T. Goralski Jr., L. D. Schmidt / Chemical Engineering Science 54 (1999) 5791}5807 reactor, but because the mechanisms themselves contain assumptions regarding the product distributions, they provide little insight into the chemistry taking place in the reactor. The high temperatures observed in short-contact-time catalytic reactors, in conjunction with operation well into the #ammability limits, renders it important to model simultaneously both the heterogeneous and homogeneous chemistry using detailed mechanisms to better understand the role of each mechanism in determining the product distributions and reaction rates in the reactor. A plug-#ow reactor geometry can be assumed to reduce the governing partial di!erential equations to easily integrable ordinary di!erential equations coupled with algebraic expressions to describe the surface chemistry. We have used existing mechanisms as published to simulate both the heterogeneous and homogeneous chemistry in a plug-#ow tubular reactor to attempt to gain insight into the interaction between these two mechanisms in a high-temperature catalytic combustion reactor. 2. Short-contact-time catalytic reactors The short-contact-time catalytic reactor consists of a monolith catalyst in a tubular reactor, as shown in Fig. 1a. Premixed gas streams containing either fuel and air or fuel and oxygen are passed over the catalyst at #ow rates of &5 standard liters per minute (slpm) at catalyst temperatures in excess of 10003C, resulting in residence times on the order of several milliseconds. These reactors operate at very high conversion ('99.5%) of the limiting reactant (fuel for combustion and oxygen for partial oxidation) and have been shown to give high selectivities to desired products. For the scope of this paper, the catalysts consist of Pt-coated ceramic foam monoliths approximately 17 mm in diameter and 10 mm deep with a void volume of &0.8. The monolith substrates discussed here have nominal pore sizes between 10 and 80 pores per linear inch (ppi). An important feature of these catalysts is that the noble metal is deposited directly on the substrate without the addition of any washcoat, resulting in a very-low-surface-area catalyst that has approximately the same surface-area-to-volume ratio as the support. This procedure results in a catalyst that has very little low-temperature activity but has enhanced high-temperature stability because there is no high-area washcoat to sinter and deactivate the catalyst. The short-contact-time reactor is insulated by placing bare monoliths ahead and downstream of the catalyst to prevent heat loss via radiation in the axial direction, and it is insulated externally with high-temperature insulation to prevent conductive and radiative losses in the radial direction. The reactor is ignited by providing an Fig. 1. (a) Short-contact-time reactor setup. (b) Catalyst is modeled as a single pore. external heating source, such as a bunsen burner, to the catalyst. When the catalyst is visibly ignited, the heat is removed, external insulation added, and the reactor operates autothermally. 3. Model The chemistry that takes place during the steady-state operation of the short-contact-time catalytic reactor is modeled using a plug-#ow tubular reactor (PFTR) geometry to model a single pore of the catalyst as a tubular reactor as shown in Fig. 1b. A PFTR geometry is assumed to simplify the governing partial di!erential equations for the #ow in three dimensions to ordinary di!erential equations along the length of the catalytic monolith. The temperature is considered constant down the length of the pore. The assumption that the monolith is isothermal agrees well with experimental results which indicate su$cient back#ow of heat to the front of the monolith to maintain the front-face temperature within &503C of the temperature of the downstream face. The species balance down the length of the reactor for a given species i can be written as dc dz "1 υ r, (1) where C is the concentration of the ith species, z is the distance from the entrance to the catalyst, υ (z) is the super"cial velocity of the gas mixture in the catalyst at axial position z, and r is the net volumetric production rate of a given species. Eq. (1) can be rewritten as dy dτ "M ρ r (2)

3 C. T. Goralski Jr., L. D. Schmidt / Chemical Engineering Science 54 (1999) 5791} by de"ning the residence time τ as τ, z (3) υ and using the de"nition of mass fraction of the ith species y " C M ρ, (4) where ρ is the bulk mass density of the mixture and M is the molecular weight of the ith species. In the case of lean combustion, υ is approximately constant since there is no mole-number change for reaction of methane and oxygen to carbon dioxide and water and the catalyst is assumed to be isothermal. The reaction rate r of each species contains two portions: r "r! σ A #ux, (5) where r is the net rate of homogeneous production of the ith species, σ is the wetted perimeter of the pore, A is the cross-sectional area of the pore, and #ux is the net #ux of the ith species to the surface of the catalyst. The net #ux of each gas-phase species to the surface is calculated by solving for the steady-state fractional surface coverage of each species at each time step and then solving for the net #ux by calculating the net rate of adsorption and desorption of each species. For example, for the adsorption/desorption of hydrogen, the net #ux of hydrogen to the surface is calculated as #ux "k P Θ!k Θ, (6) where the fractional coverages of hydrogen atoms (Θ ) and vacant surface sites (Θ ) are calculated by solving the steady-state versions of the di!erential balances for the fractional coverages of the surface species. The ordinary di!erential equation solver DVODE is used to solve the system of ordinary di!erential equations that represent the species balances and energy balance for the catalytic reactor. DVODE is a software package of subroutines to solve sti! or nonsti!"rst-order ordinary di!erential equations. DVODE has been shown (Byrne & Dean, 1993) to provide accurate results when used to integrate sti! problems with detailed chemical kinetics. A solution method for sti! problems using a numerically generated Jacobian matrix is speci"ed for the model presented here. DVODE uses the variable-order, "xed-leading-coe$cient backward di!erentiation formula method for integrating sti! systems of equations (Brown, Byrne & Hindmarsh, 1989). 4. Gas-phase mechanism The gas-phase chemistry is modeled with GRI mech 2.11 (Bowman et al., 1998; Frenklach et al., 1995). GRI-mech 2.11 is an elementary-step mechanism for methane oxidation, including reactions with nitrogen. The inclusion of nitrogen chemistry is important for operation in the fuel-lean regime where production of NO is observed. The mechanism contains 49 gas-phase species and 277 reversible reactions. The Chemkin-II package for the analysis of gas-phase chemical kinetics is used to calculate the homogeneous reaction rates of the gas-phase species as well as handle thermodynamic data for the system (Kee, Rupley & Miller, 1991). 5. Heterogeneous mechanism The surface mechanism in the fuel-lean regime, where complete combustion products are formed, is a mechanism proposed by Deutschmann et al. (1996), hereafter called the `Deutschmann mechanisma. This mechanism was developed to predict ignition and steady-state operation for the catalytic combustion of methane on Pt surfaces. The mechanism includes 10 surface species and 25 reactions including the adsorption and desorption of reactants and products, as well as surface reaction steps. The reaction steps and the values of the rate parameters in the Deutschmann mechanism are shown in Table 1. Note that the Deutschmann model assumes hydrogen adsorption is "rst order in surface sites even though hydrogen adsorbs dissociatively. In the model, hydrogen adsorbs as a diatomic species and then dissociates, with the rate-limiting step as the H adsorption. The Deutschmann mechanism also assumes that methane is irreversibly adsorbed and that carbon monoxide adsorption is second order in Pt sites. It is important to point out that this mechanism allows interaction with the gas-phase mechanism via the molecules H,O,CH, CO, CO, and H O, as well as the radical species H ),O), and OH ). The fractional coverage of each species is determined by writing di!erential balances on all surface species and assuming that the surface is in equilibrium with the gas phase. The di!erential equations then become a set of coupled algebraic equations. These equations for the Deutschmann model are dθ dt "0"2k P Θ!2k Θ #k P Θ #k P Θ!k Θ Θ #k Θ Θ!k Θ Θ #k Θ Θ #k Θ Θ #k Θ Θ #k Θ Θ, (7)

4 5794 C. T. Goralski Jr., L. D. Schmidt / Chemical Engineering Science 54 (1999) 5791}5807 Table 1 Reactions and rate constants for the Deutschmann mechanism. A, E, and S are the preexponential factor, activation energy, and sticking coe$cient, respectively A (mol cm s) E (kj/mol) S H # 2 Pt(s) P 2 H(s) H(s) P H # 2 Pt(s) H # Pt(s) P H(s) 1.00 O # 2 Pt(s) P 2 O(s) O(s) P O # 2 Pt(s) O # Pt(s) P O(s) 1.00 H O # Pt(s) P H O(s) 0.75 H O(s) P H O # Pt(s) OH # Pt(s) P OH(s) 1.00 OH(s) P OH # Pt(s) H(s) # O(s) P OH(s) # Pt(s) OH(s) # Pt(s) P O(s) # H(s) H(s) # OH(s) P H O(s) # Pt(s) H O(s) # Pt(s) P H(s) # OH(s) OH(s) # OH(s) P H O(s) # O(s) H O(s) # O(s) P OH(s) # OH(s) CO # Pt(s) P CO(s) 0.84 CO(s) P CO # Pt(s) CO (s) P CO # Pt(s) CO(s) # O(s) P CO (s) # Pt(s) CH # 2 Pt(s) P CH (s) # H(s) 0.01 CH (s) # Pt(s) P CH (s) # H(s) CH (s) # Pt(s) P CH(s) # H(s) CH(s) # Pt(s) P C(s) # H(s) C(s) # O(s) P CO(s) # Pt(s) CO(s) # Pt(s) P C(s) # O(s) dθ dt "0"2k P Θ!2k Θ #k P Θ!k Θ Θ #k Θ Θ #k Θ!k Θ Θ!k Θ Θ!k Θ Θ #k Θ Θ, dθ "0"k P Θ!k Θ Θ, (13) dt dθ "0"k Θ Θ!k Θ Θ, (14) dt dθ "0"k P dt Θ!k Θ #k Θ Θ!k Θ Θ #k Θ!k Θ Θ dθ "0"k P Θ!k Θ #k Θ Θ dt (8) (9) dθ "0"k Θ Θ!k Θ Θ, (15) dt dθ dt "0"k Θ Θ!k Θ Θ #k Θ Θ, (16) Θ "1!Θ!Θ!Θ!Θ!Θ!Θ!Θ!Θ!Θ!Θ. (17)!k Θ Θ!k Θ Θ #k Θ Θ!2k Θ #2k Θ Θ (10) dθ "0"k P Θ!k Θ!k Θ Θ dt #k Θ Θ!k Θ Θ, (11) dθ "0"k Θ Θ!k Θ, (12) dt 6. Results Calculations are performed using the model developed above at a variety of compositions and temperatures to approach an understanding of the chemistry that is actually taking place in a high-temperature catalytic combustor. To this end, three di!erent types of calculations are executed. The "rst calculations are for the case where only homogeneous chemistry is assumed. This case

5 C. T. Goralski Jr., L. D. Schmidt / Chemical Engineering Science 54 (1999) 5791} would model a typical thermal or homogeneous combustion process with the walls only acting to stabilize the temperature. The reactor was then modeled taking only heterogeneous reactions into account. While it is impossible `to turn o! a homogeneous chemistry in a real reactor, these calculations can give insight into the rate at which the heterogeneous processes take place and the surface-chemistry products. The "nal modeling case allows both heterogeneous and homogeneous chemistry. Parameter studies are then performed to examine the e!ects of pressure, temperature, pore size, and composition using both heterogeneous and homogeneous chemistry to determine the relative importance of each of these reaction pathways at conditions similar to those seen in a high-temperature catalytic combustor Homogeneous reactions only The results of the calculations where only homogeneous chemistry is allowed are shown in Fig. 2. These calculations were performed at a composition of 7% methane in air at 12003C and a pressure of 1 atm. These conditions were chosen because they represent a common temperature and composition for a high-temperature catalytic combustor. Panel a of Fig. 2 shows the conversion of methane as a function of position in the Fig. 2. Results for homogeneous reaction only. 7% methane in air, 12003C, 1 atm. (a) Conversion vs. position, (b) ppm CO vs. position, (c) ppm NO vs. position, (d) mole fraction CH ) vs. position, (e) mole fraction CH ) vs. position, (f ) mole fraction CH ) vs. position.

6 5796 C. T. Goralski Jr., L. D. Schmidt / Chemical Engineering Science 54 (1999) 5791}5807 catalyst. It can be seen that little conversion takes place in the "rst few millimeters of the reactor, at which point the rate of reaction increases rapidly, and conversion is nearly complete in the next two millimeters of the reactor. This ignition delay occurs because gas-phase radical species (H ),O), and OH ) ) must accumulate in the gas phase prior to ignition. These radical species go on to react with methane and initiate the chain-branching combustion reactions which then proceed at a very fast rate (Steinfeld, Francisco & Hase, 1989). This ignition delay followed by a steep increase in conversion is typical of homogeneous combustion chemistry. Panel b of Fig. 2 shows the variation of the concentration of carbon monoxide down the length of the reactor. The plot shows that CO is produced almost immediately as the gases enter the reactor and continues to be produced until the methane conversion is complete, just over 4 mm into the reactor. Once the methane is completely consumed, the CO reacts with the excess oxygen in the reactor to form CO. The homogeneous model shows that the amount of carbon monoxide in the reactor exhaust for these conditions is &100 ppm. The concentration (ppm) of NO as a function of position in the reactor is shown in panel c of Fig. 2. Virtually no NO is formed in the reactor until the conversion of methane is complete. Once the methane is completely converted, there is a large jump in the amount of NO in the exhaust. The NO production continues for only a short distance and levels out at a concentration of &5 ppm where it remains until the reactor exit. Panel d shows that the mole fraction of CH radicals reaches a peak just after the methane is completely reacted. Panels e and f show that the CH ) and CH ) mole fractions peak just after the CH ) peak in the reactor Heterogeneous reactions only For purely heterogeneous chemistry, the reactor is simulated at a temperature of 12003C, methane composition of 7% in air, and a 45 pore-per-linear-inch (ppi) Pt catalyst (pore size &0.5 mm). The results of these simulations are shown in Fig. 3. Panel a shows the conversion of methane as a function of axial position in the catalyst. Methane begins to react immediately upon entering the catalyst and continues to react at a nearly constant rate until it is completely consumed &4 mm into the catalyst. The plot of conversion versus position looks similar to that of a "rst-order chemical reaction in a PFTR, because the rate of reaction of methane in the purely heterogeneous case is simply the net #ux of methane to the surface of the catalyst which is "rst order in the partial pressure of methane since methane is assumed to adsorb irreversibly. Panel b of Fig. 3 shows the concentration in ppm of the partial-oxidation products carbon monoxide and hydrogen as a function of axial position in the catalyst. This Fig. 3. Results for heterogeneous reaction only. 7% methane in air, 12003C, 1 atm, 45 ppi catalyst, 5 l/min #ow rate. (a) Conversion vs. position, (b) ppm CO and H vs. position, (c) mole fraction H O and CO vs. position. plot shows that CO is made initially at the entrance to the reactor and then is gradually burned out to form CO along the length of the catalyst. The concentration of CO at the catalyst exit is &110 ppm. The hydrogen concentration starts initially very low and then increases slightly along the length of the catalyst until it reaches a steady value of &8 ppm at the exit from the catalyst. The mole fractions of the complete oxidation products CO and H O are shown in the third panel of Fig. 3. This plot shows that the increase in mole fractions of these species follows much the same trend as the conversion of

7 C. T. Goralski Jr., L. D. Schmidt / Chemical Engineering Science 54 (1999) 5791} methane, as would be expected since they are the main products when methane reacts in fuel-lean compositions. There are no nitrogen-containing products shown in Fig. 3 because in the model these products can only be formed via the homogeneous mechanism Heterogeneous and homogeneous reactions Fig. 4 shows the model results for the case when both heterogeneous and homogeneous chemistry are allowed to take place in the reactor at a temperature of 12003C and a methane concentration of 7% in air. The model simulates the operation of a 45- ppi Pt catalyst (pore size &0.5 mm). Panel a shows that the conversion is complete slightly faster than for purely heterogeneous reaction, at &3.5 mm into the catalyst. The composition of carbon monoxide as a function of position in the catalyst, shown in panel b, is close to the purely heterogeneous case, starting out at almost 200 ppm and decreasing to well below 1 ppm at the reactor exit. The concentration in parts per million of NO is plotted as a function of axial position in the catalyst in panel c of Fig. 4. This plot shows that NO is produced in very small quantities as the methane is being converted (up to Fig. 4. Results of calculations using homogeneous and heterogeneous chemistry. 7% methane in air, 12003C, 1 atm, 45 ppi catalyst, 5 l/min #ow rate. (a) Conversion vs. position, (b) ppm CO vs. position, (c) ppm NO vs. position, (d) mole fraction CH ) vs. position, (e) mole fraction CH ) vs. position, (f ) mole fraction CH ) vs. position.

8 5798 C. T. Goralski Jr., L. D. Schmidt / Chemical Engineering Science 54 (1999) 5791} mm into the catalyst) and then the production rate slows as NO is formed continuously until the end of the reactor. Although NO is produced continuously in the reactor when both heterogeneous and homogeneous chemistry are allowed, the concentration at the reactor exhaust is less than 110 ppm at the reactor exhaust, compared to just over 5 ppm produced in the homogeneous calculations. Panels d, e, and f of Fig. 4 show the mole fractions of the radicals CH ),CH ), and CH ) as a function of axial position in the reactor, respectively. For these species, the peak concentrations occur between 0.5 and 2 mm, just prior to the completion of methane conversion. These peaks occur much sooner than in the homogeneous case where the concentrations peak at &4 mm, just after the conversion of methane is complete. It is also important to note that the peak mole fractions are much lower when both heterogeneous and homogeneous chemistries are allowed (&610 for CH ) than when only homogeneous chemistry is allowed (&1.210 for CH ). Fig. 5 shows plots of the fractional coverages of each surface species as a function of axial position in the reactor. Fig. 5a shows the fractional coverages of oxygen (O) and vacant surface sites (Pt) as a function of axial position and Fig. 5b shows the fractional coverages of the remaining surface species as a function of axial position. It is clear from Fig. 5 that the surface is primarily covered with oxygen with the remainder of the surface sites vacant. The only other species with an appreciable coverage is OH ), but its coverage is (1%. The surface contains &60% oxygen at the reactor entrance. The coverage of oxygen then falls steadily to &40% at a position 4 mm into the catalyst where the conversion of methane is complete. The coverage of all hydrogen-containing species remains constant once the methane conversion is complete, but the coverages of carbon monoxide and carbon dioxide continue to decrease as the CO that is formed early in the catalyst is gradually burnt out Pressure dependence Combustion chambers for gas-turbine applications are typically operated at pressures in excess of 10 atm. For this reason, there is interest in determining the e!ect of the addition of a catalyst to a turbine combustion chamber on emissions of CO and NO. Homogeneous reactions are primarily second-order chemical reactions, and hence homogeneous rates will tend to increase by a factor of the pressure squared (Dietz III & Schmidt, 1995), whereas heterogeneous reactions are typically limited by the #ux of material to the surface of the catalyst which varies linearly with pressure. Thus, as pressure is increased, the in#uence of homogeneous chemistry in a high-temperature combustor should increase. Fig. 6 shows how the methane conversion depends on the axial position in the catalyst for a 45-ppi monolith Fig. 5. Results of calculations using homogeneous and heterogeneous chemistry. 7% methane in air, 12003C, 1 atm, 45 ppi catalyst, 5 l/min #ow rate. Fractional surface coverages vs. position for: (a) vacant sites (Pt) and oxygen and (b) OH ),H),H O, CO, C, CO, and CH ) species. operating at 7% methane in air and 12003C for pressures ranging from 1 to 25 atm. As the pressure is increased to 3 atm in panel b, initially the conversion curve is slightly concave up, but then essentially "rst-order reaction behavior in a PFTR is observed. This phenomenon is clear in panels c and d where the pressure increases to 5 and 10 atm, respectively. This feature resembles the ignition delay seen in the purely homogeneous case, indicating that the importance of homogeneous chemistry is increasing. The overall rate of reaction also increases with pressure, as can be seen in panels e and f where the methane conversion is complete less than 2 mm into the catalyst at 15 and 25 atm, respectively. Fig. 7 shows the concentrations of NO, NO and CO at the end of a 10-mm-thick 45-ppi Pt catalyst operating at 7% methane in air at temperatures of 1200, 1300, and 14003C. Panel a shows that at 12003C, the amount of NO in the exhaust increases from &110 ppm at 1 atm to 110 ppm at 25 atm. This increase, while two orders of magnitude, still shows signi"cantly less NO than the 5 ppm produced by the homogeneous chemistry alone. As the temperature is increased to 14003C, the amount of NO in the exhaust increases from &310 to &910 ppm, showing that higher temperatures

9 C. T. Goralski Jr., L. D. Schmidt / Chemical Engineering Science 54 (1999) 5791} Fig. 6. E!ect of pressure on conversion vs. position for 45 ppi catalyst, 7% methane in air, 12003C, 5 l/min #ow at (a) 1 atm, (b) 3 atm, (c) 5 atm, (d) 10 atm, (e) 15 atm, and (f ) 25 atm. favor the production of nitrogen oxides. This trend continues in panel b which shows the concentration of NO as a function of pressure and temperature. The exhaust concentrations of CO are shown in panel c which reveals that except at high temperatures ('14003C), higher pressures tend to repress CO formation Temperature dependence The operating temperature of a catalytic combustor could be controlled in many ways: adding preheat will increase the operating temperature, while allowing heat losses will decrease the temperature. It is therefore of interest to investigate the temperature dependence of the exhaust composition of a catalytic combustor to determine if it is possible to improve emissions by `tuninga the reactor temperature. Fig. 8 shows the results of modeling a high-temperature catalytic combustor at a methane concentration of 7% methane in air and 5-atm pressure using a 45-ppi Pt-coated catalyst for temperatures between 1000 and 18003C. The adiabatic reaction temperature for this composition would be &14003C. Panel a of Fig. 8 shows how methane conversion varies with catalyst temperature, and panel b shows the dependence of methane conversion on axial position in the catalyst at various temperatures. Fig. 8a shows that at 10003C, the

10 5800 C. T. Goralski Jr., L. D. Schmidt / Chemical Engineering Science 54 (1999) 5791}5807 methane conversion is only &50% for a 10-mm-long catalyst. The conversion increases to 99.5% as the temperature is increased to 11003C and quickly increases to 100% thereafter. Fig. 8b shows that as the reactor temperature is increased, the rate of conversion increases and that the curve maintains the general shape of a "rst-order reaction. Fig. 8c and d show semi-log plots of the NO and NO exhaust compositions as a function of catalyst temperature. Fig. 8c shows that the amount of NO produced always increases with temperature, including the temperatures when methane conversion is incomplete. Once the temperature reaches 12003C and methane conversion is complete, the amount of NO in the reactor exhaust increases with temperature at a higher rate than when methane conversion is incomplete. At 18003C, the NO in the exhaust has increased to 6 ppm, the amount that was produced homogeneously at a temperature of 12003C. Fig. 8d shows that the amount of NO in the exhaust increases initially from &10 ppm to 610 ppm as the temperature is increased from 1000 to 11003C, and then decreases to &10 ppm at 12003C. As the reactor temperature is then raised from 1200 to 18003C the amount of NO in the exhaust increases to &510 ppm. The amount of CO in the reactor exhaust is shown as a function of reactor temperature in Fig. 8e. The CO in the exhaust falls rather rapidly from 1000 to 11003C as the conversion of methane goes to 100%. The rate of decrease then falls from 1100 to &13003C where the amount of CO in the exhaust reaches a minimum at &410 ppm. The exhaust CO then increases steadily as the temperature is increased from 1300 to 18003C, where it reaches 20 ppm. Fig. 8f shows a plot of the CO concentration as a function of axial position in the catalyst at temperatures of 1300}18003C. This "gure shows that the initial and "nal amounts of CO produced in the reactor are higher at higher temperatures and that the rate at which the CO is burnt out also increases with temperature Pore size dependence Fig. 7. Calculation results for varying pressure. ppm NO, NO, and CO vs. pressure at temperatures of 1200, 1300, and 14003C. 7% methane in air, 45 ppi catalyst, 5 ms residence time. The pore size of a catalyst in a high-temperature combustion reactor could potentially have an important effect of the relative rates of homogeneous and heterogeneous chemistry. Smaller pore sizes will result in higher platinum surface-area-to-volume ratios and will increase the relative rate of heterogeneous chemistry, whereas larger pores will tend to allow more homogeneous chemistry. The pore size is expressed as the number of pores per linear inch (ppi); note larger ppi means smaller pores. Fig. 9 shows the results of model calculations at a composition of 7% methane in air, 12003C, and 5-atm pressure. The pore sizes were varied from &2.5 to &0.25 mm (i.e., 10}80 ppi) in the calculations shown in Fig. 9. Fig. 9a is a plot of conversion as a function of axial position in the reactor for the two limiting porosities of 10 and 80 ppi. Comparison of this "gure to Figs. 2 and 3a shows that the 10-ppi results look qualitatively more similar to the homogeneous results shown in Fig. 2a while the 80-ppi results more closely resemble the heterogeneous results shown in Fig. 3a. Fig. 9b shows the exhaust concentration of CO as a function of the ppi of the catalyst. The plot shows a maximum in CO

11 C. T. Goralski Jr., L. D. Schmidt / Chemical Engineering Science 54 (1999) 5791} Fig. 8. Calculation results for varying temperature. 7% methane in air, 1 atm pressure, 45 ppi catalyst, 5 l/min #ow rate. (a) Conversion vs. temperature, (b) Conversion vs. position, (c) ppm NO vs. temperature, (d) ppm NO vs. temperature, (e) ppm CO vs. temperature, (f ) ppm CO vs. position. concentration of 0.5 ppm at 25 ppi; the CO decreases to 0.25 ppm as the pore density is increased to 80 ppi. Fig. 9c shows the mole fraction of CH radicals as a function of axial position in the catalyst for the 10- and 80-ppi cases. It is important to note that the peak radical concentration in the 10-ppi case comes later in the catalyst and shows a higher peak value than in the 80-ppi case. Fig. 9d shows the concentrations of NO and NO as a function of catalyst ppi. This "gure shows that as the pore size is increased (ppi decreased), the amounts of both NO and NO in the reactor exhaust increase Composition dependence Catalytic combustors can be operated over a broad range of compositions. The stoichiometric concentration for the formation of carbon dioxide and water for methane combustion is &9.5%. Fig. 10 shows the methane conversion and exhaust concentrations of CO, NO and NO at inlet concentrations varying from 1 to 9.5% methane in air over a 45-ppi Pt catalyst operating at 12003C and 5-atm pressure. Fig. 10a is a plot of methane conversion as a function of methane inlet concentration for a 10-mm-thick catalyst. The conversion is nearly

12 5802 C. T. Goralski Jr., L. D. Schmidt / Chemical Engineering Science 54 (1999) 5791}5807 Fig. 9. Calculation results for varying pore size C, 7% methane in air, 5 atm pressure, 5 l/min #ow rate. (a) Conversion vs. position, (b) ppm CO vs. catalyst ppi, (c) mole fraction CH ) vs. position, (d) ppm NO and NO vs. catalyst ppi, (e) mole fraction CH ) vs. position, (f ) mole fraction CH ) vs. position. complete for all compositions but falls o! slightly for compositions leaner than 2.5% and richer than 6.5%. Panel b of Fig. 10 shows that the amount of CO present in the reactor exhaust increases with composition, especially as the amount of methane in the feed exceeds &5%. From panels c and d of Fig. 10, the NO concentration increases steadily as the concentration of methane is increased until the conversion begins to fall o! at &6.5% methane in air. At this point, the NO in the exhaust begins to decrease slightly. The amount of NO in the reactor exhaust decreases initially as composition is increased and then increases until there is &8% methane in air. The amount of NO then drops sharply from 8 to 9.5% as the amount of excess oxygen in the inlet mixture is decreased. Fig. 11 is a plot of methane conversion as a function of axial position at various inlet methane concentrations for the reactor conditions described above. From this plot it is clear that higher concentrations lead to slower overall conversion. First-order kinetics would predict conversion to be independent of initial concentration, whereas homogeneous kinetics would predict longer conversion times for higher inlet concentrations. Fig. 11 strongly suggests that homogeneous

13 C. T. Goralski Jr., L. D. Schmidt / Chemical Engineering Science 54 (1999) 5791} Fig. 10. Calculation results for varying methane concentration C, 5 atm pressure, 45 ppi catalyst, 5 ms residence time. (a) Conversion vs. %CH in air, (b) ppm CO vs. % CH in air, (c) ppm NO vs. % CH in air, (d) ppm NO vs. % CH in air. Fig. 11. Calculation results for varying methane concentration. Conversion vs. position for various methane inlet concentrations C, 45 ppi catalyst, 5 atm pressure, 5 l/min #ow rate. chemistry is important in this temperature}pressure} composition regime. 7. Discussion 7.1. Homogeneous vs. heterogeneous chemistry The results presented here show that there is a strong coupling between the heterogeneous and homogeneous reaction mechanisms in high-temperature catalytic combustion reactors. The results in Figs. 2 and 3 for the purely homogeneous and heterogeneous calculations show that each mechanism has characteristic features, which can be helpful in analyzing results where both reaction pathways are important. The most noticeable feature is the di!erence in the shape of the conversionversus-position curves. The homogeneous case clearly shows an induction period followed by very fast reaction to completion, whereas the heterogeneous case very closely resembles conversion in a "rst-order reaction in a PFTR. The di!erence in the shapes of these curves can be used as an indicator of the type of chemistry that is taking place in the reactor. Also, examining the gas-phase concentrations of species that are only produced in the homogeneous mechanism } such as fuel-radical species and nitrogen oxides } can determine the in#uence of homogeneous chemistry. The calculations for the base case (12003C, 7% methane in air, 1 atm pressure, 45 ppi Pt catalyst) where both heterogeneous and homogeneous pathways are allowed (Fig. 4) seem to be nearly identical to the heterogeneous results (Fig. 3). When the conversion and carbon monoxide curves are compared, they look nearly identical in shape and the position in the catalyst, indicating that heterogeneous chemistry is dominating. This observation

14 5804 C. T. Goralski Jr., L. D. Schmidt / Chemical Engineering Science 54 (1999) 5791}5807 can be veri"ed by the small amount of NO that is formed (&710 ppm) compared to the amount formed in the homogeneous case (5 ppm). Closer examination of the methane conversion as a function of position shows that the rate of methane conversion is actually fastest when both mechanisms are allowed, as is shown in Fig. 12 where methane conversion as a function of axial position in the reactor is shown for the homogeneous, heterogeneous, and combined mechanisms. This plot is an indication that, although surface chemistry is the dominant reaction pathway, gas-phase chemistry still makes some contribution to the conversion of methane. Increasing the pressure should increase the rate of homogeneous reactions. Plots of conversion as a function of position at various pressures (Fig. 6) show that as the pressure is increased the curves begin to show an induction or ignition-delay feature at the beginning of the curve, but overall the curves still appear to more closely resemble a heterogeneous or "rst-order process. In each case, the overall rate of methane conversion increases with pressure. However, the conversion is complete at just over 1 mm into the catalyst at 25 atm, whereas at 1 atm conversion is complete at 4 mm } clearly inconsistent with a rate increase that is dependent upon pressure squared. In fact, the increase in reaction rate is less than what would be expected for a "rst-order process. Fig. 7 also shows that the amount of nitrogen oxides in the exhaust, which are only formed homogeneously, increases with increasing pressure. Therefore, more homogeneous chemistry is taking place at higher pressures, although the heterogeneous pathway is still apparently dominant. The dependence of the reaction rate of methane on pressure can be explained by examining the mechanism of homogeneous reaction. While it is true that most homogeneous reactions are bimolecular and hence second order in pressure, combustion reactions take place via a chain-branching mechanism where radical species build up to form a radical pool and initiate the chainbranching reactions. This build-up of radicals causes the ignition delay shown in Fig. 2, followed by the very fast chain-branching reactions. The limiting step in ignition is the "rst-order dissociation of fuel molecules to form a hydrogen radical and fuel radical which then initiate the chain-branching mechanism. Since these dissociation reactions are only "rst order, the rate of the homogeneous pathway relative to the heterogeneous pathway should increase at roughly the same rate with increasing pressure, resulting in the pressure dependence shown in Figs. 6 and 7. In these cases, the heterogeneous reactions take place faster than the homogeneous initiation steps, e!ectively preventing the onset of signi"cant homogeneous reaction. It is clear that increasing pressure does increase the rate of homogeneous reaction in these systems, but the crucial homogeneous initiation steps are signi"cantly hindered by the presence of the catalyst that Fig. 12. Conversion vs. position for homogeneous chemistry, heterogeneous chemistry, and coupled homogeneous}heterogeneous chemistry C, 7% methane in air, 45 ppi catalyst, 5 l/min #ow rate, 1 atm pressure. the homogeneous reactions never propagate to a signi"- cant degree. The dependence of the reaction pathway on temperature is subtler than the pressure dependence. Temperature can have a signi"cant e!ect on the rates of reaction in the homogeneous or heterogeneous pathways, depending upon the activation energies of the steps of each mechanism. It is clear from Fig. 8 that at temperatures below 11003C there is not complete methane conversion in a 10-mm-long catalyst. As the temperature is increased the overall reaction rate increases but the plot of conversion versus position (Fig. 8b) still resembles a "rst-order or heterogeneous process. The plot of NO concentration as a function of temperature shows that the amount of NO in the exhaust drastically increases with temperature, particularly at temperatures above 14003C. NO can only be produced in the gas phase, but it is likely that at these elevated temperatures at least a portion of this NO is formed via the thermal mechanism. In general, high temperatures favor more homogeneous chemistry, but the magnitude of the contributions is unclear. One of the main di!erences between the calculation results where both heterogeneous and homogeneous pathways are allowed versus the purely homogeneous calculations is the magnitude and location of the fuelradical peaks. Fig. 2 shows that the peak mole fractions of both CH ) and CH ) come just after all of the methane has been converted. (It is these species that are precursors to the formation of prompt NO.) By comparison, for combined surface and gas-phase chemistry (see Fig. 4), the CH ) and CH ) peaks come much earlier in the catalyst and are two orders of magnitude less than the peaks in the purely homogeneous case. Note the overall methane conversion occurs at approximately the same position in the reactor for each calculation. The shift in position and magnitude of the fuel-radical peaks can be most easily seen by examining Fig. 9 where the pore size of the catalyst has been varied. As the

15 C. T. Goralski Jr., L. D. Schmidt / Chemical Engineering Science 54 (1999) 5791} pore size of the catalyst is increased (ppi decreased) more homogeneous chemistry is expected because the available catalyst surface area is decreased, thus decreasing the overall catalytic-reaction rates. Fig. 9a shows that as the pore density is decreased from 80 to 10 ppi, a plot of conversion versus axial position begins to change from resembling a purely heterogeneous process to a shape that shows some ignition-delay characteristics of a homogeneous process. Fig. 9d shows that the amount of NO produced as the ppi is decreased increases rather dramatically. Panels c, e, and f from Fig. 9 show that the increasing NO corresponds to a shift downstream of the CH ),CH ) and CH ) peaks as well as an increase in the magnitude of each of these peaks. This trend indicates both that more homogeneous chemistry is taking place as well as that NO production correlates with the position of these peaks CO production Experimental results have shown that catalytic combustion systems produce less carbon monoxide than homogeneous systems operating at the same conditions. The calculations presented here agree with this experimental result. The homogeneous calculations in Fig. 2 show that CO is produced continuously until methane conversion in complete, at which time the CO is gradually burned out by the excess oxygen in the reactor. The heterogeneous calculations in Fig. 3 show that a signi"cant amount of CO is formed at the very front of the catalyst but immediately begins reacting to form CO. After complete methane conversion, the CO in the gas phase remains essentially constant throughout the reactor. This result is important: in a catalytic system, as long as methane conversion is nearly complete, the CO emissions should remain low, whereas in a homogeneous reactor, CO emissions are at their peak value just when methane conversion is complete. The CO emissions for calculations where both reaction pathways are allowed are nearly identical to the heterogeneous results, suggesting a primarily heterogeneous mechanism. The calculations show that CO emissions tend to decrease with increasing pressure even though the contribution of homogeneous chemistry, which tends to produce more CO than does heterogeneous chemistry, increases with increasing pressure. Fig. 7c even shows that at a temperature of 12003C the amount of CO produced initially increases as the pressure is increased from 1 to 3 atm and then falls o! quickly as the pressure is raised to 25 atm. Any CO that is formed will tend to react with the excess oxygen via either a homogeneous or heterogeneous pathway to form CO. As pressure is increased, this reaction will be forced towards CO because there is an overall mole number decrease in the reaction, leading to less CO in exhaust even though there is more homogeneous chemistry taking place in the reactor NO production The results presented here indicate that the presence of a catalyst can signi"cantly reduce NO emissions from high-temperature combustion processes. At temperatures below 15003C, the primary mechanism by which NO is formed is the prompt-no mechanism, whereas above 15003C formation of NO via the thermal mechanism can become signi"cant. The species responsible for the initiation of the prompt-no mechanism are CH and CH radicals. Fig. 4 shows that the presence of a catalyst both reduces the magnitude of CH ) and CH ) in the gas phase as well as shifts the peaks upstream in the catalyst when compared to the homogeneous results in Fig. 2. These species can then either react to form combustion products or can go to react with N to form HCN and then NCO. Both of these species then react to form NO. Fig. 13 shows a plot of NCO and HCN concentration as a function of position in the catalyst for calculations where both pathways were modeled as well as calculations where only homogeneous chemistry was used. The conditions for these calculations were 7% methane in air at a reactor temperature of 12003C and atmospheric pressure. Both HCN and NCO show a peak at the same axial position in the reactor as the CH ) and CH ) peaks for the homogeneous calculations. In the calculation where heterogeneous chemistry was included, there is no peak for HCN and NCO. This is strong evidence that prompt NO is responsible for the formation of NO under these conditions Model limitations The heterogeneous mechanism used to model the surface reactions in these calculations includes the adsorption and desorption of O ),H), and OH ) but not the adsorption or desorption of carbon-containing radicals. However, the results show that even though the mechanism does not allow CH and CH radicals to be adsorbed on the catalyst surface from the gas phase, the catalyst can inhibit the formation of these species by preventing the accumulation of O, H, and OH radicals in the gas phase. It is the H ) and O ) species that are primary chain-branching agents in homogeneous combustion mechanisms (Park & Vlachos, 1998) and their removal by the catalyst surface inhibits homogeneous chemistry from taking place to any signi"cant degree } even at high temperatures and pressures. However, to completely understand the complex interaction of homogeneous and heterogeneous chemistries in these systems, future mechanism-development e!orts should seek to include the adsorption and desorption of fuel-radical species because the homogeneous chemistry could be

16 5806 C. T. Goralski Jr., L. D. Schmidt / Chemical Engineering Science 54 (1999) 5791}5807 Fig. 13. Prompt-NO precursors as a function of position for the homogeneous calculation and for the coupled mechanisms C, 7% methane in air, 45 ppi catalyst, 5 l/min #ow rate, 1 atm pressure. High-temperature short-contact-time catalytic combustion reactors can operate well within the homogeneous #ammability limits and still provide signi"cantly lower emissions of carbon monoxide and nitrogen oxides than homogeneous combustion processes. These reactors have been simulated using a plug-#ow model including both homogeneous and heterogeneous chemistry to understand the role of each of these reaction pathways in determining the product distribution. The calculations have shown that the presence of a catalyst signi- "cantly inhibits the homogeneous chemistry even well into the #ammability regime at high temperatures and pressures. According to the model, the adsorption of the radical species O ), H) and OH ) inhibits the homogeneous chemistry enough that negligible amounts of NO and CO are formed, while homogeneous chemistry alone predicts signi"cant amounts of each of these species. The plug-#ow reactor model with detailed homogeneous and heterogeneous mechanisms provides a semiquantitative description of the coupling between gas-phase and surface chemistry. A full two-dimensional calculation with rigorous #uid mechanics and transport coe$cients would be necessary for a quantitative simulation, but this is not yet possible with detailed chemistry, and, even with such simulations, computation time would be too long for such comprehensive parameter variation as shown here. Thus, these results give a "rst approximation to coupling and pressure e!ects, to which future calculations can be compared. sensitive to small changes in concentrations of these species. A plug-#ow reactor model was chosen for these calculations because the numerical simplicity involved in solving the resulting mass-balance equations allows for the examination of many variables that in#uence the reactor. While these results o!er signi"cant insight into how heterogeneous and homogeneous chemistry couple in high-temperature reacting environments, it would be dif- "cult to draw more than qualitative conclusions from the results presented here. By neglecting mass-transfer limitations to and from the catalyst surface, we have overestimated the heterogeneous reactions rates. In reality, as mass transfer limits the supply of species to the surface of the catalyst, the overall rate of heterogeneous chemistry will be decreased, allowing more homogeneous chemistry to take place. More complicated models including radial mass transfer will provide more quantitative results (Deutschmann & Schmidt, 1999), but only at the cost of numerical complexity and increased computational time. Notation A cross-sectional area of catalyst pore, cm C gas-phase concentration of ith species, mol/cm #ux net #ux of ith species to the catalyst surface, mol/cm s k forward rate constant of ith reaction, mol, cm, s k reverse rate constant of ith reaction, mol, cm, s M molecular weight of ith species, g/mol P partial pressure of ith species, Pa r net pseudohomogeneous reaction rate of ith species, mol/cm s r net homogeneous reaction rate of ith species, mol/cm s y mass fraction of ith species z axial distance from catalyst entrance, cm Greek letters 8. Conclusions Θ ρ σ τ υ fractional coverage of ith species bulk density of gas mixture, g/cm wetted perimeter of catalyst pore, cm residence time, s super"cial velocity of gases in catalyst, cm/sec