Influence of the Methane Combustion Kinetic Model on the Operating

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Ind. Eng. Chem. Res. 2001, 40, 5199-5205

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Influence of the Methane Combustion Kinetic Model on the Operating Conditions of an Autothermal Catalytic Reactor Eduardo Lo´ pez, Noemı´ S. Schbib, Carlos E. Gı´gola, and Vero´ nica Bucala´ * PLAPIQUI (UNS-CONICET), Camino La Carrindanga, Km 7, 8000 Bahı´a Blanca, Argentina

This work focuses on the study of the influence of the methane combustion kinetics on the operation of an autothermal catalytic reactor for heat generation (domestic scale). The feed (methane and air) is preheated by means of a direct heat exchange by recycling a fraction of the hot gases leaving the catalytic combustor (recycle monolithic reactor). Two kinetic models are proposed to represent the reaction. The kinetic parameters were adjusted using experimental data obtained from methane combustion over a laboratory catalyst (Pd on γ-Al2O3 wash-coated cordierite monolith). Experiments were carried out for different feed temperatures (310-500 °C), total flow rates [250-750 cm3/min (STP)], and inlet methane concentrations (0.8-1.6%). A heterogeneous unidimensional steady-state model was employed to analyze the autothermal reactor performance. Using the best-fitted reaction rate expressions, conservative operating conditions are estimated to guarantee reactor stability, almost complete methane conversion (i.e., minimal unburned hydrocarbon emissions), and a high heat generation rate. Introduction Catalytic combustion processes have been seriously investigated since the late 1950s, focusing on its capacity to remove volatile organic compounds (VOCs) via total oxidation. A decade later, researchers started to study the catalytic combustion applied to heat generation. The principal motivation of this new application was to minimize the great amounts of NOx generated by conventional homogeneous combustion units.1 Nitrogen oxides generation is highly favored by temperatures above 1500 °C. This thermal level or even higher values are reached in homogeneous combustion processes. Conversely, catalytic combustion can be achieved at temperatures considerably below, and consequently the nitrogen oxides generation can be dramatically reduced. Monolithic structures are used in a great variety of catalytic processes, the catalytic combustion probably being the outstanding one. The monoliths present interesting characteristics; among others, they offer higher external surface/reactor volume ratios, higher mechanical strength, lower pressure drop, and lower gas channeling than conventional fixed-bed units.1,2 Different kinetic expressions for the catalytic combustion of methane are presented elsewhere. There are several studies reporting kinetic parameters obtained using Pt or Pd catalysts, supported on Al2O3 powders;3-7 however, few kinetic expressions for methane combustion using pellets or monolithic catalysts can be found.8-10 A power-law-type expression is usually chosen to represent the reaction rate behavior for methane catalytic combustion. Reaction orders equal to or below the unity for methane and zero for the other species involved in the reaction are often used. Few works propose orders different from zero for oxygen or for the reaction products. Yao (1980)4 found an oxygen reaction order slightly above zero for some experiments. Ribeiro et al. * To whom correspondence should be addressed. Tel: 54291-4861700, ext. 265. Fax: 54-291-4861600. E-mail: vbucala@ plapiqui.edu.ar.

(1994)8 present a power-law-type expression with reaction orders for water and carbon dioxide of -1 and 0 or -2, respectively. Li (1997)10 reports a LangmuirHinshelwood-Hougen-Watson (LHHW)-type expression for methane catalytic combustion, taking into account the inhibition effect produced by the reaction products (H2O and CO2). Although the catalytic combustion can be carried out at lower temperatures than the homogeneous one, the operating temperature is still far from room temperature. Therefore, a device to preheat the reactor feed stream from room temperature up to the reaction temperature becomes necessary. Usually homogeneous combustion is selected to preheat the reactant stream; however, this alternative involves the generation of contaminants. Therefore, an autothermal system, where the feed is preheated using the heat generated in the catalytic reaction, is an attractive option. In fact, it is more convenient to avoid the release of contaminants rather than include a system to eliminate them.1,11 A performance comparison of two different autothermal systems for domestic-scale heat generation (based on natural gas combustion) was presented by Lo´pez et al. (2000).12 The systems studied by the authors included a catalytic reactor with an external heat exchanger and a recycle catalytic reactor. The second one, where the preheating problem was solved by mixing the cold feed with a recycle of hot exhaust gases generated in the catalytic unit (simultaneous mass and heat feedback), appeared as the best choice. To properly design an autothermal catalytic heater and define appropriate operating conditions leading to high methane conversion, a laboratory catalyst was prepared and tested. Experimental data were obtained for different inlet methane molar fractions and temperatures. In fact, these are inlet operating conditions expected to be subjected to disturbances during the catalytic heater operation. In addition, the flowrate was modified within a range of high values to obtain kinetic information at conditions close to those of a domesticscale heater. Two kinetic expressions were fitted from the experimental data. Both rate equations, which

10.1021/ie001063t CCC: $20.00 © 2001 American Chemical Society Published on Web 07/25/2001

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Table 1. Reaction Rate Expressions model I rIA

)

I k∞,A

exp(-EIA/RTs)(CAs)nAI

model II rII A

properly represent the small-scale results, were considered to evaluate their influence on the autothermal catalytic combustor performance. Laboratory Reactor Experimental Section. The monolithic catalyst was wash-coated following the guidelines given by Skoglundh et al. (1996)13 and To¨rncrona et al. (1997).14 The samples consist of cylindrical pieces of cordierite with a length of 0.075 m and a diameter of 0.008 m. The monolith cell density is 620 000 cells/m2. The channels are square-shaped, with a hydraulic diameter of 0.001 m. Additional catalyst and preparation details can be found in Lo´pez et al. (2001).15 The laboratory monolith catalyst was inserted in a quartz tube 0.6 m length, which was placed inside an electrical furnace. The first 0.25 m of the quartz tube was used to preheat the reactive stream up to the desired inlet temperature. This temperature was maintained at the desired value by means of an electronic controller. To prevent flows from bypassing the reactor, a high-temperature cement seal was placed between the reactor outside wall and the quartz tube. Two mass flow controllers were used to prepare the reactive stream (chromatographic quality air and 99.3% methane chemically pure). The feed and reactor exit streams were analyzed by gas chromatography (GC) using a Chromosorb 102 80/100 packed column. Two to three GC analyses were performed for a given set of operating parameters. Methane and CO2 were measured using flame ionization (FID) and thermal conductivity (TCD) detectors, respectively. In all of the experiments the mass balance was closed with high accuracy. To measure the feed temperature, a type K thermocouple was placed at the reactor entrance. Because the laboratory reactor was found to be nonisothermal nonadiabatic, solid axial temperatures were measured every 0.5 cm by a moveable type K thermocouple inserted in one channel (closed at its entrance to prevent flow through it). The measured axial profiles indicated that the differences between the maximum and minimum temperatures were lower than 12 °C. Experiments were carried out at feed temperatures ranging from 310 to 500 °C, for different total flow rates [250, 500, and 750 cm3/min (STP)] and different inlet methane concentrations (0.8, 1.2, and 1.6%). All of the experiments were performed using excess oxygen. The flowrates, which are relatively high, were selected to operate the laboratory reactor at conditions of very low space times (τ). The experimental τ values are very similar to those expected for a domestic-scale heater [i.e., high flowrates, τ = 0.2 s (STP)].12 Mathematical Modeling. A steady-state one-dimensional heterogeneous plug-flow model has been used to represent the behavior of the laboratory reactor. Internal and external mass-transfer resistances have been taken into account. On the basis of a dimensionless Peclet-type analysis and the rigorous solution of a dispersion model,2 the axial dispersion term was neglected. For different operating conditions, very small Prater numbers were calculated (below 0.0009); from these results, the temperature gradients inside the

)

II k∞,A

nAII/[1 exp(-EII A /RTs)(CAs)

II nwII] + k∞,w exp(-EII w /RTs)(Cws)

washcoat layer have been neglected.2,16 Third- or fourthorder polynomials have been used to fit the measured solid axial temperatures, with the R-squared values being higher than 0.98 for all cases. Because the energy balance is not solved, these polynomials were used to simulate the laboratory reactor. Using the fitted axial temperature profiles, only the following mass balances for the gas and solid phases are needed to model the monolith:

Mass balances dFA 4km )(CA - CSAs) dz d Deff

d2CAs dξ

2

) rI,II A (CAs,Ts)

(1)

(2)

Boundary conditions z)0

CA ) CA0

(3)

ξ)0

dCAs )0 dξ

(4)

ξ ) Lwc

Deff

( ) dCAs dξ

ξ)Lwc

) km(CA - CSAs)

(5)

The effectiveness factor was calculated as follows:

∫0L

wc

η)

rI,II A (CAs,Ts) dξ/Lwc S rI,II A (CAs,Ts)

(6)

To solve the reactor model (eqs 1-5), the mass balance inside the washcoat (eq 2) was discretized using second-order central finite differences. The resulting differential-algebraic equation system was solved using a backward-difference formula (BDF algorithm). The mass-transfer coefficient between the gas and the channel walls was evaluated using an expression reported by Groppi et al. (1995).17 The pressure drop in the monolith reactor was neglected for modeling purposes. The physical properties of the gas mixture were assumed to be dependent on temperature and composition. The effective diffusivity was calculated based on the parallel pore model (Hayes and Kolaczkowski, 1997).2 An overall washcoat porosity of 0.40 was obtained by mercury porosimetry, following the guidelines provided by Hayes et al. (2000)18 and Li (1997).10 The tortuosity factor was assumed to be equal to 4, with this being a recommended value.19 Kinetic Models and Parameter Fitting. Two different kinetic expressions have been used to model the reaction rate behavior and are shown in Table 1. Model I corresponds to a power-law-type rate expression dependent on the methane concentration. This model has been extensively used to represent the methane catalytic combustion over powders,3-7 pellets,8 and monolithic structures9,10,15 probably because of its simplicity. For model II, the reaction rate is represented by a LHHW formulation where the only inhibition effect

Ind. Eng. Chem. Res., Vol. 40, No. 23, 2001 5201 Table 2. Kinetic Parameters Model I I k∞,A ) 750 gmol1-nA/(m2-3nA s) EIA ) 8.6 × 104 J/gmol nIA ) 0.3 σI ) 2.58 Model II II k∞,A ) 1.07 × 105 gmol1-nA/(m2-3nA s) 5 EII A ) 1.09 × 10 J/gmol ) 0.37 nII A σII ) 1.46

II k∞,w ) 1.5 m3nw/gmolnw 3 EII w ) -9.8 × 10 J/gmol nII ) 0.97 w

the standard error of the estimate (σ), which is defined as follows: Nexp

σ)[ Figure 1. Methane conversion for different inlet methane molar fractions as affected by the inlet temperature [Q ) 250 cm3/min (STP)].

Figure 2. Methane conversion for different inlet flow rates as a function of inlet temperature (yA0 ) 0.008).

considered is that caused by the water. Li, in his Ph.D. thesis (1997),10 studied the effect of the CO2 concentration on the methane combustion reaction rate over a Pd/γ-Al2O3 catalyst. In this study, for a fixed inlet molar fraction of methane of 1% and an inlet molar fraction of water of 0.0%, the inlet CO2 molar fraction was varied from 0.0 to 2.9%. For these conditions, the methane combustion reaction rate was evaluated for a wide range of solid temperatures (600-1000 K). On the basis of experimental results, the author concluded that the reaction rate can be said to be independent of the value of the CO2 concentration. Because for our experimental studies the CO2 molar fraction (inside the reactor) varied from 0 to 1.6%, we neglected the CO2 inhibition effect based on the results obtained by Li (1997).10 Experimental methane conversions as affected by the inlet temperature for different yA0 and total flowrates are shown in Figures 1 and 2, respectively. To minimize the influence of the internal mass-transfer resistances, laboratory data obtained for inlet temperatures between 310 and 420 °C were used to obtain the intrinsic kinetic parameters. On the other hand, for the temperature range 420-500 °C, the experimental methane conversions were used to evaluate the model predictions. A Marquardt routine20 was used to estimate the kinetic parameters. The objective function to be minimized is

(xj,calc - xj,exp)2/(Nexp - Npar)]1/2 ∑ j)1

The number of parameters (Npar) to be fitted varied from 3 (model I) to 6 (model II), while a number of experiments (Nexp) equal to 99 were used for both kinetic models. For a given set of kinetic parameters (provided by the Marquardt routine) and for each experimental point, the calculated methane conversion is obtained by solving the mathematical model (eqs 1-5) and using the measured axial temperature profile. The best-fitted kinetic parameters along with the σ values are shown in Table 2. For model I the estimated activation energy is in reasonable agreement with the values reported for methane combustion over Pd/γ-Al2O3.3-6,8,15 The observed conversion decrease as yA0 increases (Figure 1) is in agreement with a reaction order lower than unity. Model II becomes similar to model I for low methane conversion (i.e., low water concentrations); in fact, both kinetic expressions have similar methane reaction orders and allow accurate fitting of the experimental data. The water adsorption energy value obtained in the present work is in a good accordance with that reported by Hayes and Kolaczkowski (1997).2 Figures 1 and 2 also present the calculated methane conversions obtained using the fitted parameters for both kinetic models. For yA0 or flowrate changes, the calculated conversions using either model I or II follow the general trend exhibited by the experimental data. For operations with different inlet methane concentrations (Figure 1), the experimental methane conversions are accurately adjusted by both kinetics. Moreover, the use of either model I or II allows proper prediction of the conversion values for the temperature range 420500 °C (experimental points not used in the fitting procedure). However, as the flowrate is increased (Figure 2), better predictions can be achieved by using model II. This observation agrees with the lower σ values found for this kinetic model. Particularly, model II follows the experimental conversions with high accuracy for all of the studied inlet temperatures and flowrates of 250 and 500 cm3/min (STP). For 750 cm3/min (STP), model II adequately predicts the experimental data for inlet temperatures between 310 and 420 °C. The use of both kinetic expressions leads to lower conversions than the experimental values for high temperatures and high flowrates. Using model I, internal mass-transfer limitations were not detected for the inlet temperature range used in the fitting procedure. For model II and temperatures between 380 and 420 °C, the internal mass-transfer

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Figure 3. Schematic of the autothermal recycle reactor. Table 3. Dimensions and Operating Variables for the Monolith Reactor dimensions Dm ) 0.2 m d ) 0.001 m channel shape: square cell density: 620 000 cells/m2

operating variable yAf ) 0.008-0.016 (IPR and experiments) yAf ) 0.025-0.027 (autothermal reactor) Qf ) 0.22-4.60 m3/min (STP) Tf ) 0-40 °C

resistance becomes slightly noticeable. Therefore, the adjusted intrinsic kinetic parameters should not be influenced by the effective diffusivity estimation. Regarding external mass-transfer limitations, the mass-transfer coefficient was set to one order of magnitude higher and lower than the value predicted by Groppi’s correlation.17 For all of the cases, insignificant changes for the calculated outlet conversion were observed. This fact ensures that for the experimental conditions the external mass-transfer resistances are negligible. Although model II shows a σ value lower than that of model I, it is not overwhelmingly superior. Experiments should have been conducted under conditions that would give maximum divergence between these two models, that is, at high total flowrates. However, the flowrates could not be further increased because of limitations in the laboratory equipment. For this reason and considering that both kinetic models have been used by other authors to represent the catalytic methane combustion, models I and II have been taken into account for the design and selection of the operating conditions of the autothermal catalytic heater. Domestic-Scale Reactor Lo´pez et al. (2000)12 presented an autothermal catalytic combustor which was found to be very efficient for heat generation applications. A simplified scheme of this reactor is shown in Figure 3. The reactor is a single adiabatic monolith that solves the preheating problem by mixing the cold feed (at Tf) with a recycle of hot exhaust gases generated in the catalytic unit. The converter has been designed to satisfy the following constraints: high outlet methane conversion, maximum allowable temperature (gas and solid phases) lower than 700 °C to prevent the deactivation of the catalyst, and low heat flux (domestic scale). Table 3 shows the dimensions and operating variables of the studied unit. The autothermal recycle reactor offers interesting features: it provides an exit stream at the highest feasible thermal level (for a given maximum allowable temperature), and the recycle dilutes the feed stream, allowing one to operate with higher fresh methane molar fractions without surpassing the maximum allowable temperature. Moreover, dynamic studies demonstrated that the reactor can operate in a stable way after an appropriate start-up procedure that involves a short transient period.12

Figure 4. Methane conversion of a domestic-scale adiabatic reactor for different inlet flowrates as a function of the inlet temperature (yA0 ) 0.016 and L ) 0.25 m).

Prior to analysis of the influence of the kinetic model on the performance of an autothermal catalytic reactor, the effect on a reactor without recycle (independently preheated reactor, IPR) will be studied. IPR. a. Mathematical Model. As for the laboratory reactor, a steady-state one-dimensional heterogeneous plug-flow model has been used to represent the behavior of the domestic-scale reactor. Equations 1-6 and the energy balances for both solid and gas phases that follow were used to represent the adiabatic reactor.

Energy balances dTg 4h (T - Tg) ) dz dGcp,g s

(7)

h(Ts - Tg) ) (-∆H)ηLwcrI,II A

(8)

Additional boundary condition z)0

Tg ) T0

(9)

A BDF algorithm was used to solve the differentialalgebraic equations system. The physical properties and the transport parameters were evaluated, as has been detailed in the laboratory reactor section. The heat- and mass-transfer coefficients between the gas and the channel walls were evaluated using an expression reported by Groppi et al. (1995).17 b. Results and Discussion. Figure 4 shows the outlet conversion of the reactor (L ) 0.25 m) versus the inlet temperature (T0) found for different total flowrates and using models I and II. Lower flowrates permit one to reach total conversion at lower temperatures because of the residence time increase. For a flowrate of 0.22 m3/min (STP), calculated conversions using the kinetic model I are higher than those estimated with model II. However, as the flowrate is increased, the conversions given by model I start to be similar and then lower than those calculated from model II. This behavior change can be attributed to the capacity of model II to provide higher conversion values for higher flowrates (Figure 2). When the flowrate is changed from 0.22 to 4.60 m3/ min (STP), the light-off temperatures (defined as the inlet temperature for which the methane outlet conversion reaches 50%) vary from 316 and 325 °C to 475 and 453 °C using models I and II, respectively. The autothermal units for heat generation will operate at elevated flowrates; therefore, the simulations using kinetic model II would indicate lower light-off temperatures.

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Figure 5. Methane conversion of a domestic-scale adiabatic reactor for different inlet molar fractions as a function of the inlet temperature [Q0 ) 1.40 m3/min (STP) and L ) 0.25 m).

Calculated conversions for different methane inlet molar fractions versus inlet temperatures are presented in Figure 5. A flowrate of 1.40 m3/min (STP) was selected to adequately represent the operation of an adiabatic domestic-scale catalytic heater. For both kinetic models, the light-off temperatures are not strongly influenced by the yA0 values. The crossing of the curves for each kinetic expression can be explained by analyzing the reactor operation at low and high inlet temperature levels. As is well-known, higher yA0 lead to higher adiabatic temperature rises. However, for low T0 values the energy generated by the reaction cannot produce significant differences in the gas and solid temperatures along the reactor for different yA0. Therefore, for similar temperature profiles, the reachable conversion values are mainly influenced by the inlet methane concentrations. This observation agrees with the fact that, for reaction orders below unity and isothermal operations, lower conversions are achieved with higher methane molar fractions. On the other hand, for high inlet temperatures, the axial average gas and solid temperatures are higher when higher yA0 are selected; for these situations, the outlet conversions are significantly improved. For the studied yA0, the simulation using model II predicts also lower light-off temperatures than those using model I. To analyze the internal mass-transfer limitations for the domestic-scale adiabatic reactor, the methane concentration and reaction rates inside the washcoat have been studied. Calculated methane concentration profiles inside the washcoat using models I and II are presented in Figure 6. The abscissa value of 9 × 10-5 m represents the pore mouth. This Lwc value has been measured by scanning electron microscopy for the laboratory catalyst.15 Dimensionless methane concentrations at the catalyst surface become lower than unity as the conversion (or, in other words, the temperature) increases. This behavior is due to the increasing influence of the external mass-transfer resistances. At the reactor entrance (x ) 0, Ts ) 402.3 °C), negligible internal masstransfer limitations are observed. For reactor conversion levels of 50% (Ts ) 558.7 °C), a considerable concentration gradient along the washcoat is observed, ending in a value 1 order of magnitude lower than that of the pore entrance. Steeper descents are calculated for conversion levels of 90% (Ts ) 677.4 °C), leaving unused around 75% of the washcoat length. Internal and external masstransfer limitations become more important as the

Figure 6. Dimensionless methane concentration along the washcoat coordinate for different bulk conversions [yA0 ) 0.012, T0 ) 400 °C, and Q0 ) 1.40 m3/min (STP)].

Figure 7. Methane conversion as affected by the recycle ratio for fixed values of Tf, yAf, and Qf.

conversion increases. This effect is a consequence of the simultaneous increase of both the catalyst temperatures and reaction rates. The effectiveness factors were calculated for the concentration profiles shown in Figure 6. For the same conversion level (equal catalyst temperature), lower effectiveness factors are found for model II. In spite of the lower effectiveness factors, model II leads to higher conversions (because it predicts higher reaction rates) than model I for those operations that represent the domestic-scale catalytic heater conditions (i.e., high flowrates and methane inlet molar fractions in the range of 0.008-0.016). Autothermal Catalytic Reactor. a. Mathematical Model. Equations 1-9 were used to simulate the autothermal reactor. The reactor inlet temperature (T0) and methane molar fraction (yA0) were estimated by solving the mass and energy balances in the mixing point of the fresh feed (yAf and Tf) and the recycled stream. The equations were solved by means of a shooting method. The recycle ratio (λ) is an important parameter; in fact, for given feed conditions it defines, in addition to the T0 and yA0 values, the total flowrate circulating through the reactor. b. Results and Discussion. The heat feedback toward the reactor inlet is a source of instability. In fact, up to three different steady states can be found for the same inlet conditions.12 Figure 7 shows, in a schematic way, the outlet conversion of methane as a function of the recycle ratio. If the system operates at λ1 < λmin, only one steady state corresponding to the extinguished reactor operation can be achieved. For this case, the T0

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Figure 8. Methane conversion as affected by the recycle ratio for different values of the feed temperature [yAf ) 0.026, Qf ) 1.40 m3/min (STP), L ) 0.8 m].

those given by model II. As cooler fresh feeds are used, higher recycle ratios are needed to maintain the reactor operating at stable conditions. Figure 9 shows the methane conversion as a function of λ for different feed methane molar fractions. As yAf is increased, the autothermal operation with lower values of λ is feasible. The maximum yAf selected (yAf ) 0.027) leads to an outlet temperature of around 700 °C (equal to the maximum allowable temperature); therefore, higher values of yAf cannot be used. The λmin values estimated using models I and II differ, as in the previous case, by about 4%. Again, the use of model II indicates the possibility of using slightly lower λ values to achieve steady states of complete conversion. For the feed conditions yAf ) 0.026, Tf ) 20 °C, and Qf ) 1.40 m3/min (STP), an operation of complete conversion provides a reactor outlet temperature of 673 °C (lower than the maximum allowable value). For this set of operating conditions, a recycle ratio of around 0.7 appears as appropriate for a safe operation of the studied autothermal reactor. In fact, this λ is far enough from the λmin values calculated from different kinetic expressions and for different inlet conditions representative of feed disturbances during the heater operation. Conclusions

Figure 9. Methane conversion as affected by the recycle ratio for different values of the fresh methane molar fraction [Tf ) 20 °C, Qf ) 1.40 m3/min (STP), and L ) 0.8 m].

value is not enough to produce the reaction ignition. Conversely, for λ2 > λmin, two stable steady states [one of high conversion (point 1) and one of negligible conversion (point 3)] and an unstable intermediate steady state (point 2) can be found. As the recycle ratio is increased, the reactor inlet temperatures (T0) become higher, and it is enough to achieve almost complete conversion. However, as λ is increased, more mass is recycled and consequently the higher flowrates (Q0) entering the reactor originate higher pressure drops. To reduce the operative costs, the recycle ratio cannot be increased indefinitely. Therefore, the reactor operation is greatly influenced by the λ value, and its selection becomes relevant. For a given reactor geometry, the λmin value is affected by the uncertainties associated with the kinetic parameters. The kinetic models I and II were used to evaluate the λmin shift. The autothermal reactor geometry (Table 3) was defined in order to have a space time of around 0.2 s (similar to the values used for the experiments) to process the required Qf of 1.4 m3/min for a recycle ratio of 70%. Figures 8 and 9 show the methane conversion as affected by the recycle ratio for different values of Tf and yAf. These parameters have been selected because their values can suffer disturbances during the autothermal reactor operation. For usual fresh temperatures, intermediate and upper steady states are shown in Figure 8. The selected yAf value of 0.026 leads to a yA0 value of 0.011 for λ ) 0.7; for other λ values, the methane molar fractions at the reactor entrance approximately lie on the yA0 range used for the experiments. The reactor outlet temperature for the steady states of high conversion are for all of the recycle ratios lower than the defined maximum allowable temperature (700 °C). For Tf values of practical interest, the use of model I leads to λmin values around 4% higher than

The two candidate kinetic models (power-law and LHHW types) studied in the present work did not show significant differences to predict the experimental methane conversion values. Because one model is not clearly superior to the other, a kinetic model discrimination was not possible. The use of the best-fitted LHHW kinetics leads to higher reaction rates and consequently lower light-off temperatures than those given by the powerlaw-type expression. Therefore, the design of the autothermal unit based on the kinetics provided by model I is the more conservative one. In fact, for a given set of yAf, Tf, and Qf, the representation of the reaction rate by model I indicates the need of higher recycle ratios than model II to obtain stable steady states at high conversion. A recycle ratio close to 0.7 appears as an appropriate value to adequately operate the autothermal reactor, even at the most unfavorable operating conditions (low fresh feed temperatures and methane molar fractions). This λ value allows one to disregard the prediction differences given by both kinetic expressions. Nomenclature C ) concentration, gmol/m3 cp ) heat capacity, J/(kg K) d ) channel hydraulic diameter, m Deff ) effective diffusivity, m2/s Dm ) monolith diameter, m E ) activation energy, J/gmol F ) specific molar flow rate, gmol/(m2 s) G ) specific mass flow rate, kg/(m2 s) h ) heat-transfer coefficient, J/(m2 s K) k∞ ) preexponential factor km ) mass-transfer coefficient, m/s L ) reactor length, m Lwc ) washcoat thickness, m n ) reaction order Nexp ) number of experimental data used Npar ) number of parameters fitted Q ) flowrate, cm3/min or m3/min (STP) r ) reaction rate, gmol/(m2 s)

Ind. Eng. Chem. Res., Vol. 40, No. 23, 2001 5205 R ) universal gas constant, J/(gmol K) T ) temperature, K x ) conversion y ) molar fraction z ) axial coordinate, m Greek Letters ∆H ) heat of reaction, J/gmol η ) effectiveness factor λ ) recycle ratio σ ) standard error of the estimate τ ) space time, s ξ ) washcoat coordinate, m Subscripts 0 ) at the reactor inlet (z ) 0) A ) methane calc ) model calculated exp ) experimental data f ) fresh feed g ) gas phase s ) solid phase w ) water wc ) washcoat Superscripts S ) surface conditions I ) kinetic model I II ) kinetic model II

Literature Cited (1) Cybulski, A., Moulijn, J. A., Eds. Structured Catalysts and Reactors; Marcel Dekker Inc.: New York, 1998. (2) Hayes, R. E.; Kolaczkowski, S. T. Introduction to Catalytic Combustion; Gordon and Breach Sci. Pub.: Amsterdam, The Netherlands, 1997. (3) Anderson, R. B.; Stein, K. C.; Freenan, J. J.; Hofer, L. E. J. Ind. Eng. Chem. 1961, 53, 809. (4) Yao, Y. Y. Ind. Eng. Chem. Prod. Res. Dev. 1980, 19, 293. (5) Baldwin, T. R.; Burch, R. Appl. Catal. A 1990, 66, 337. (6) Briot, P.; Primet, M. Catalytic Oxidation of methane over palladium supported on alumina. Appl. Catal. A 1991, 68, 301. (7) Hoyos, L.; Praliaud, H.; Primet, M. Appl. Catal. A 1993, 98, 125.

(8) Ribeiro, F. H.; Chow, M.; Dalla Betta, R. A. Kinetics of the Complete Oxidation of methane over Supported Palladium Catalysts. J. Catal. 1993, 146, 537. (9) Kolaczkowski, S. T.; Thomas, W. J.; Titiloye, J.; Worth, D. J. Catalytic Combustion of Methane in a Monolith Reactor: Heat and Mass Transfer under Laminar Flow and Pseudo-Steady-State Reactions Conditions. Combust. Sci. Technol. 1996, 118, 79. (10) Li, P. K. C. Catalytic Combustion of Methane in Monoliths and the Influence of Diffusion Barriers. Ph.D. Thesis, University of Bath: Bath, U.K., 1997. (11) Heck, R. M.; Ferrauto, R. J. Catalytic Air Pollution Control; Wiley: New York, 1995. (12) Lo´pez, E.; Errazu, A. F.; Borio, D. O.; Bucala´, V. Alternative Designs for a Catalytic Converter Operating under Autothermal Conditions. Chem. Eng. Sci. 2000, 55, 2143. (13) Skoglundh, M.; Johansson, H.; Lo¨wendahl, L.; Jansson, K.; Dahl, L.; Hirschauer, B. Cobalt-promoted palladium as a threeway catalyst. Appl. Catal. B 1996, 7, 299. (14) To¨rncrona, A.; Skoglundh, M.; Thormahlen, P.; Fridell, E.; Jobson, E. Low-temperature catalytic activity of cobalt oxide and ceria promoted Pt and Pd: influence of pretreatment and gas composition. Appl. Catal. B 1997, 14, 131. (15) Lo´pez, E.; Gı´gola, C.; Borio, D. O.; Bucala´, V. Catalytic Combustion of Methane over Pd/γ-Al2O3 in a Monolithic Reactor: Kinetic Study. In Reaction Kinetics and the Development and Operation of Catalytic Processes; Froment, G. F., Waugh, K. C., Eds.; Elsevier: Amsterdam, The Netherlands, 2001. (16) Froment, G. F.; Bischoff, K. B. Chemical Reactor Analysis and Design; Wiley: New York, 1990. (17) Groppi, G.; Betolli, A.; Tronconi, E.; Forzatti, P. A Comparison of Lumped and Distributed Models of Monolith Reactors. Chem. Eng. Sci. 1995, 50, 2705. (18) Hayes, R. E.; Kolaczkowski, S. T.; Li, P. K. C.; Awdry, S. Evaluating the effective diffusivity of methane in the washcoat of a honeycomb monolith. Appl. Catal. B 2000, 25, 93. (19) Satterfield, C. N. Mass Transfer in Heterogeneous Catalysis; MIT Press: Cambridge, MA, 1970. (20) Marquardt, D. W. An Algorithm for Least-Squares Estimation of Nonlinear Parameters. J. Soc. Ind. Appl. Math. 1963, 11 (2), 431.

Received for review December 6, 2000 Revised manuscript received May 8, 2001 Accepted May 11, 2001 IE001063T