Modeling Temperature Profiles of a Catalytic Autothermal Methane

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Modeling Temperature Profiles of a Catalytic Autothermal Methane Reformer with Nickel Catalyst Diego Scognamiglio,† Lucia Russo,*,‡ Pier Luca Maffettone,† Lucia Salemme,† Marino Simeone,† and Silvestro Crescitelli† Dipartimento di Ingegneria Chimica, UniVersita` degli Studi di Napoli Federico II, P.le V. Tecchio, 80-80125, Napoli, Italy, Istituto di Ricerche Sulla CombustionesConsiglio Nazionale delle Ricerche-CNR, P.le V. Tecchio 80-80125, Napoli, Italy

In this work, a one-dimensional heterogeneous model for the autothermal reforming of methane in a catalytic (Ni/Al2O3 catalyst) fixed-bed reactor is proposed. The kinetic model implements an indirect reaction scheme and includes a reduction factor that is dependent on the oxygen concentration. Such a factor delays the reforming and water-gas shift reactions, with respect to the oxidation reactions. Experiments at different steam-tomethane ratios and feed flow rates were conducted in a small-scale reactor to identify and validate the proposed mathematical model. To this end, temperature profiles in the solid phase were measured with an infrared camera. The agreement between experimental data and model predictions is very good for all the investigated operating conditions. In particular, the model predicts the strong separation between the oxidation and the experimentally observed reforming zones well. 1. Introduction The ever-growing importance of an efficient and clean use of fossil fuels motivates the development of new technologies for energy production. In this regard, the design of small-scale, inexpensive, and efficient hydrogen production processes has gained a large amount of interest recently. Indeed, hydrogen is a pollution-free energy carrier for fuel-cell applications, which currently represent the most-promising clean, flexible, and efficient energy production systems for both stationary and mobile applications.1,2 However, the development of large-scale hydrogen production is limited by problems connected with storage, transport, and safety.1,2 One way to solve these problems is to decentralize the hydrogen production by developing smallscale processes for on-site applications.1,2 On a large scale, the most-efficient technology for hydrogen production from fossil fuels is steam reforming (SR),3-5 which is characterized by very high energy efficiency close to the thermodynamic one (70%). Such a process is conducted by feeding fuel and steam into a catalytic reformer. As the reforming is a highly endothermic process, an efficient external energy supply is required. This aspect prevents the possibility to operate in this way at a small scale. Indeed, the most promising technologies for small-scale hydrogen production are catalytic partial oxidation (CPO) 6-11 and autothermal reforming (ATR).12-18 Both these processes are potentially autothermal and, thus, do not, in principle, require external energy supplies. CPO is generally characterized by very high reaction rates and, thus, represents a viable technique for microscale to small-scale applications. On the other hand, ATR is characterized by slower reaction rates and, thus, is most favorable for small-scale applications. The CPO process is conducted in a catalytic reactor by feeding fuel and air with a substochiometric ratio, with respect * To whom correspondence should be addressed. Tel.: +39 0817682262. Fax: +39 0815639639. E-mail addresses: [email protected]; [email protected]. † Dipartimento di Ingegneria Chimica, Universita` degli Studi di Napoli Federico II. ‡ Istituto di Ricerche Sulla CombustionesConsiglio Nazionale delle Ricerche-CNR.

to the total oxidation. The energy and steam produced by the exothermic oxidation reactions sustain the endothermic reforming reactions, so that the process can be easily performed autothermally. Drawbacks of this technology are the high temperatures attained and, especially, the possible hot spots, both of which severely stress the catalyst and reduce its lifetime. The ATR process may be considered as a CPO process with steam added to the feed: hydrogen yield is thus increased and the catalyst average temperature is reduced. However, because exothermic and endothermic reactions poorly overlap, hot spots may still be present, as has been reported in several works.8,19-23 It is then apparent that the prediction of the effective temperature profiles and of the exothermic and endothermic reaction overlapping in the ATR reactors is very important for the design and the operation of ATR processes. In this regard, numerical simulation of the reactor temperature profiles would be of primary importance for the estimation of the exothermic and endothermic reaction overlapping. However, only a few papers exist that examine the modeling and simulations of ATR processes.14,15,24-26 Moreover, mainly integral experimental data at the reactor exit were used for model identification and validation. Hoang et al.15 considered a two-dimensional (2-D) heterogeneous model that was validated based on the temperature profiles obtained with thermocouple measurements. However, they did not address the problem of the separation of the exothermic and endothermic reactions, because their temperature measures along the bed were too few to give an accurate estimation of the peak temperature. From the other hand, Biesheuvel and Kramer26 analyzed the ATR process by considering a complete separation in the space of the oxidation and reforming reactions to estimate the maximum temperature, but they did not compare their calculation with experimental measured temperatures. In this paper, a mathematical model of a fixed-bed ATR reactor with a nickel catalyst is identified and validated using experimentally measured temperature profiles, together with data taken at the reactor exit. The kinetic model implements an indirect reaction scheme and includes a reduction factor that is dependent on the oxygen concentration, as suggested by De Groote and Froment8 for the CPO process. Such a factor delays

10.1021/ie800518e CCC: $40.75  2009 American Chemical Society Published on Web 01/26/2009

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Figure 1. Scheme of the experimental apparatus.

the reforming and water-gas shift (WGS) reactions, with respect to the oxidation reactions, and thus empirically account for the spatial separation of the exothermic and endothermic reactions. We estimated, for the ATR process, the entity of such separation through a comparison of experimental and numerical solid temperature profiles. Here, measurememt of the temperature profiles in the reactor is performed using infrared (IR) thermography. Although this technique is generally limited to solid surface measurements, it provides measurements that are more reliable than those obtained using thermocouples, which provide an average of the solid- and gas-phase temperatures.27 It was surmised that a sound model could be constructed only if accurate profiles are available, as shown for CPO processes by Bizzi et al.28 For the ATR process, a model that has been validated based on IR measurements is not yet available in the literature. 2. Experimental Setup In this section, a description of experimental apparatus and procedure is given. More details are available in ref 27. 2.1. Experimental Apparatus. The experimental apparatus consists of an instrumented catalytic fixed-bed reactor, as illustrated in Figure 1. The control and measurement signals are sent to a National Instrument PCI-E card (Model NI-PCI-6229), and they are continuously monitored using ad hoc Labview software. The reactor is essentially a quartz tube (the internal diameter is 21 mm) covered by thermal insulation that is composed of ceramic material. In the reactor, there are 5 g of catalyst in pellets 1-1.18 mm in diameter to ensure a turbulent and mixing flow. This catalyst bed, whose length is 14 mm, is placed between two inert beds that are 12 cm long. The inert pellets have the same diameter as that of the catalyst pellets. The first inert bed improves reactant mixing and feed preheating.

Table 1. Catalyst Properties property

value

NiO content CaO content Si content Al2O3 content bulk density crush strength size of the spheres

16.5 wt % 6.0 wt % 0.1 wt % balance 0.95 kg/L 400 N/cm 1-1.18 mm

Temperature profile in the catalyst bed was measured with IR thermography equipment (Phoenix, Flir Systems) that was capable of collecting the radiation emitted in the wavelength range of 2-5 µm, with a resolution of 320 × 256 pixels. 2.2. Catalyst. The catalyst is a nickel-based commercial catalyst (Engelhard) that is usually applied in industrial steam reforming processes. The main catalyst characteristics are reported in Table 1. 2.3. Experimental Protocol. The experimental procedure can be divided in four stages: reactor loading, catalyst pretreatment, reactor startup, and composition and solid-phase temperature profile measurements. 2.3.1. Reactor Loading. The reactor, loaded with the catalyst and the inert pellets, is placed in the oven, which allows the catalyst pretreatment, the reactor startup, and the reactant preheating. 2.3.2. Catalyst Pretreatment. After the loading, the catalyst is reduced for 1 h with a gas stream that contained 30% H2. The pretreatment temperature was 873 K, which was attained starting from 673 K with an heating velocity of 5 K/min. 2.3.3. Reactor Startup. Oven temperature is set to the desired value, and then, to limit coke formation, the catalyst bed is preheated up to 973 K by burning a gas stream of hydrogen and air. Finally, the reactor is fed with a feed

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Figure 2. Schematic picture of the fixed-bed reactor.

mixture consisting of air, methane, and steam. Measurements start after stationary conditions are attained. 2.3.4. Composition and Solid-Phase Temperature Profile Measurements. The experiments are performed by varying the space velocity between 1.5 and 6 NL/min and the feed ratio H2O/CH4 between 0 and 2. Product composition was measured by means of a ABB gas analyzer that was equipped with a thermal conductivity sensor (model Caldos 17) for H2; an infrared sensor (model Uras 14) for CO, CO2, and CH4; and paramagnetic sensor (model Magnos 106) for O2. A condenser and a CaCl2 trap were placed before the ABB gas analyzer, to reduce water content below the limits that are mandatory for the instrument. The solid-phase temperature profile in the catalyst bed was measured with IR thermography equipment (Phoenix, Flir Systems) that was capable of collecting the radiation emitted in the wavelength range of 2-5 µm, with a resolution of 320 × 256 pixels. The spatial resolution, depending on the distance between the IR thermography equipment and the reactor, in this work, was 3 pixels/mm. IR image acquisition was performed by rapidly opening the oven and sliding the ceramic insulating material upward to visualize the catalyst bed. To minimize the decrease in reactor temperature, the entire procedure lasted less than 5 s. Upon exposure to the environment, the reactor temperature decreased at a rate of ∼2 °C/s, as measured by continuous IR acquisition for a time interval of 10 s from oven opening.29 During the experiments, the outlet composition is continuously monitored and the solid-phase temperature profiles along the bed are measured instantaneously (opening the oven and shifting the insulation within just a few seconds), according to the procedure described in ref 27. 3. Mathematical Model The process was modeled with a one-dimensional (1D) heterogeneous description of a fully insulated packed-bed reactor. The model includes the mass balance equations for each species (CH4, O2, CO, CO2, H2, H2O, N2) and enthalpy balance equations for both the gas phase and the solid phase. The gasphase balance equations are dispersive, whereas an effective conduction, which also accounts for radiation effects, is considered for the solid phase. The momentum balance equation was neglected, because the pressure drop is negligible (see below). The gas phase is assumed to be ideal. All these assumptions are considered for both catalyst and inert beds. The boundary conditions of the catalyst bed (at z1 and z2 in Figure 2) impose the continuity of the mass and enthalpy flows, of the compositions, and of the temperatures. Fixed compositions and gas-phase temperature are specified at the domain inlet (z ) 0 in Figure 2), and flat

profiles for these variables are prescribed at the outlet (z ) L in Figure 2). For the solid-phase temperature, a radiation boundary condition has been imposed at both the inlet and the outlet of the computational domain (0,L) (see refs 9 and 28). The model equations with the appropriate boundary conditions are reported in Table 2. The model, overall, consists of 9 differential equations and 7 algebraic equations. The differential equations are discretized with a finite difference method with 200 nodes, and the resulting system of equations is numerically solved with Mathematica software.30 The number of nodes required for model convergence was assessed by repeating the simulation with an increasing number of nodes. The results proved to be independent of spatial discretization above 150 nodes. 3.1. Model Discussion. In this section, the main model assumptions will be discussed and justified. 3.1.1. Pressure Losses. The mathematical model is written by neglecting the momentum balance equation, because we assume that the pressure decrease in the catalytic bed is negligible. We checked such an assumption by estimating the pressure decrease with the Ergun equation:31 f)

( )]

[

1-ε 1-ε 1.75 + 150 Rep ε3

where f)

∆PFggdp LG2

A conservative estimate considers temperatures of ∼1000 K, a flow rate of 8.33 NL/min, a porosity of 0.42, and a pellet diameter of 1 mm, thus giving a friction factor on the order of 100, which corresponds to a pressure decrease per unit length on the order of 0.01 bar/cm. 3.1.2. Homogeneous Kinetics. As reported in previous papers,32,33 under our experimental conditions (i.e., at atmospheric pressure), the homogeneous gas-phase reaction rates can be assumed to be negligible. 3.1.3. Model Heterogeneity. To choose correctly between a pseudo-homogeneous and heterogeneous description of the reactor, it is necessary to estimate the heat-transfer limitations between the solid and gas phases. To this end, we used the Mears criterion34 for a preliminary evaluation of the interphase heat-transfer limitation. The criterion states that, if the actual reaction rate deviates 50, then mixing transport phenomena can be neglected. In our case, the pellet diameter is 1 mm and the bed length is 1 cm, thus leading to an L/dp ratio of 10, which does not allow us to neglect mixing effects. A more precise evaluation of the mixing relevance on the mass-transport phenomena can be done through the calculation

Ci,g ) Cfeed i,g

∂Ci,g )0 ∂z

- keff,s

- keff,s

∂Ts ) σes(Tg4 - Ts4) ∂z

∂Ts ) σes(Ts4 - Tg4) ∂z

of the mass Peclet number (Pem), representing the ratio between the rate of transport by convection and that by mass dispersion: Pem )

VintL Deff

Correlations for the calculation of the axial mass dispersion coefficients in fixed beds are reported in the literature.37 Considering that the flow rate is equals to 3 NL/h, the real gasphase velocity increases to values of ∼0.7 m/s if we include the presence of the solid (e.g., with a fixed-bed porosity of 0.42), the effect of high temperature in the reactor (e.g., 800 K), and a diffusion coefficient of ∼3 × 10-4 m2/s, the mass Peclet number is given as Pem ≈ 30. By comparison with data reported in the literature,38 at these Pem values (2.8, whereas the maximum hydrogen yield is obtained at an air/CH4 ratio of ∼3. Such results agree with previous thermodynamic calculations.57,58 Thus, the experimental campaign was conducted at an air/CH4 ratio of 3.125. The ratio between water and methane (H2O/CH4) was varied in the range of 0-2, and the flow rate (Q) was varied in the range of 1.5-6 NL/min. The other operating parameters are reported in Table 8. 4.2. Estimation of the Reduction Factor. As previously mentioned, the kinetic expressions described in reactions 2-4 are multiplied by a reduction factor, which delays the reforming and WGS reactions, with respect to the oxidation reaction. Such a delay factor is dependent on oxygen conversion and introduces the only adjustable parameter of the model (the parameter n). Figure 3 shows the solid temperature profile that is experimentally measured at Q ) 4 NL/min, Tph ) 623 K, air/CH4 ) 3.125, and H2O/CH4 ) 1.2. The experimental profile is

Figure 4. Numerical computation of oxygen conversion and delay factor along the fixed bed. Conditions: Q ) 4 NL/min, Tph ) 623 K, air/CH4 ) 3.125, and H2O/CH4 ) 1.2.

compared with those obtained via numerical simulations for three different values of the parameter n. As it appears from the numerical results reported in Figure 3, an increase in the parameter n determines an increase of the maximum temperature attained in the reactor and, correspondingly, a reduction of the exit temperature. This latter behavior is due to the fact that, as n increases, the oxidation and reforming reactions progressively separate in space (i.e., the oxidation reactions occur in the first part of the reactor, while the reforming reactions occur toward the final part of the bed, where the oxygen conversion has become unity). Consequently, the reaction overlapping decreases as n increases. Comparison of the experimental data with the numerical predictions shows good agreement when n ) 12. This value is the same found in ref 8 for a partial oxidation process, and, therefore, one might be tempted to infer that water addition does not affect the overlapping between the oxidation and reforming reactions. From now on, all the simulations are performed with n ) 12 (i.e., the only adjustable parameter appearing in the model is fixed once and for all). For the sake of clarity, the oxygen conversion and delay factor along the fixed bed obtained by numerical computation are reported in Figure 4 for n ) 12. Not unexpectedly, the delay factor is negligibly small in the first part of the fixed bed, where the reforming reactions rates are very low, whereas much larger values are observed in the final part of the bed, in correspondence with the 90% conversion of oxygen, where the reforming reactions are dominant. Thus, a very scarce overlapping of the oxidation and reforming reactions is found. This fact is in agreement with other experimental results found in the literature with nickel-based catalysts for the ATR process.21-23 4.3. Model Validation: Effect of the Flow Rate. Figure 5 shows the experimental and theoretical temperature profiles of the solid phase as the flow rate is changed. A peak in the temperature profile is visible close to the reactor entrance for all the investigated flow rates, and its axial position is only slightly affected by the flow rate. Figure 5 seems to suggest that an increase of the flow rate implies an increase of the temperature inside the catalytic bed, because of improved heat generation. On the other hand, the increase in flow rate determines a reduction of the temperature in the inert bed preceding the reactor for the more-efficient cooling, because of a more-efficient convection transport mechanism, with respect to heat dispersion (i.e., radiation and conduction). It is worth

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Figure 5. Comparison between the experimental and numerical temperature solid profiles at flow rates of Q ) 1.5, 3, and 6 NL/min. Conditions: Tph ) 623 K, air/CH4 ) 3.125, H2O/CH4 ) 1.2.

Figure 6. Exit composition as the flow rate is varied. Conditions: Tph ) 623 K, air/CH4 ) 3.125, H2O/CH4 ) 1.2.

remarking that the good agreement between numerical and experimental data reveals that the flow rate does not affect the oxidation/reforming reaction overlapping, at least in the investigated range, because a value of n ) 12 gives satisfactory predictions for Q ) 1.5-6 NL/min. Some comments on the temperature profiles are needed here. The observation that the peak position is not dependent on the flow rate is in agreement with the experimental data given in refs 9 and 10 for the CPO process over rhodium catalysts, whereas it varies with the predictions presented in refs 8 and 59 for the CPO process. Under great pressure, model simulations8,59 predict a significant shift of peak position as the flow rate Q increases. The appearance of the peak is flow-rate-dependent, as experimentally shown by Simeone et al.27 with the same reactor, and this is confirmed by our simulations (not shown in Figure 5) because the peak disappears for Q < 1 NL/min. In this regard, Halabi et al.25 have predicted a strong dependence of the peak on the pressure. Actually, at a slightly larger H2O/ CH4 ratio, their model does not predict the peak formation. The presence of water could certainly depress temperature levels (see below); however, we believe that the absence of the temperature peak is due to their kinetic model, which does not introduce any shift between oxidation and reforming reactions. A comparison between the predicted and experimental exit composition as the flow rate is varied is reported in Figure 6.

Figure 7. Exit methane conversion as the flow rate is increased. Comparison between thermodynamics (dotted line), model predictions (continuous line), and experimental data (square dots). Conditions: Tph ) 623 K, air/CH4 ) 3.125, H2O/CH4 ) 1.2.

Again, the model predictions are quantitatively similar to the experimental data in the investigated flow rate range. We now show that, as the imposed flow rate increases from 1.5 NL/min to 6 NL/min, the reactor passes from transport control to kinetic control. Figure 7 shows the dependence of CH4 conversion on the flow rate. Experimental data are plotted as symbols and are measured at the reactor exit; the solid line represents model predictions, and the dashed line represents thermodynamic calculations (performed with Aspen Plus software). The thermodynamic predictions are made at the temperature measured at the reactor exit and at the reactor pressure. It is worth mentioning that, although the pressure decrease through the catalyst bed always remains negligible, the pressure decrease through the entire plant (i.e., from gas feed to gas analysis) increases significantly as the feed flow rate increases. As a result, the reactor pressure increases from 1.25 bar to 1.81 bar when the feed flow rate increases from 1 NL/min to 5 NL/ min. Experimental data show a rapid increase in the methane conversion at low flow rates, in agreement with previous experimental results that have been reported in the literature for partial oxidation and autothermal reforming processes.10,15 As the flow rates increase further, a slight maximum in conversion is achieved, followed by a mild reduction. It is apparent that the thermodynamic predictions are in good agreement with the experimental data, up to Q ) 4 NL/min, whereas at higher flow rates, a significant deviation is observed with an appreciable overestimation of the experimental methane conversion. On the other hand, model predictions (the solid line in Figure 7) slightly overestimate the CH4 conversion at low flow rates, whereas at high flow rates, the predictions correctly follow the experimental data. Consequently, one can infer that, at low flow rates, the process is limited by transport phenomena while at high flow rates, the process is limited by the kinetics. Within this description, the increase in conversion at low flow rates is due to the increase in mass transfer between the gas and solid phases. Indeed, as more reactant reaches the catalytic surface, more heat is generated by the oxidation reaction, and this favors endothermic reactions, thus increasing the overall methane conversion.10,28,54 In contrast, as the flow rates increase further, the process becomes limited by the kinetics, and the methaneconversiondecreasesastheresidencetimedecreases.10,25,28 However, note that as the flow rate increases, the pressure slightly increases, and this fact slightly contributes to the overall decrease in methane conversion.

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Figure 8. Oxidation and reforming reactions along the bed for different values of the flow rate. Conditions: Tph ) 623 K, air/CH4 ) 3.125, H2O/ CH4 ) 1.2.

Figure 9. Comparison between experimental and numerical temperature solid profiles at three different H2O/CH4 ratios: 0, 0.5, and 2. Conditions: Q ) 4 NL/min, Tph ) 623 K, air/CH4 ) 3.125.

The passage from thermodynamic control to kinetic control is even more clear if one considers the predicted reaction rates along the reactor. Figure 8 shows the oxidation and reforming reaction rate for three different flow rates. An increment in the flow rate determines an increment in the oxidation rates at any reactor axial position. Regarding the reforming reaction rate, the maximum increases and shifts toward the reactor exit. The inset shows an enlarged view of the reactor exit zone, where it is apparent that, at large flow rates (Q ) 6 NL/min), the reforming rates are still nonzero and, thus, equilibrium conditions are not yet attained. 4.4. Model Validation: Effect of Feed Composition. An analogous good agreement between the model predictions and experimental data is found when the feed composition is varied. Figure 9 reports a comparison between the numerical and experimental temperature profiles of the solid phase for different values of the steam-to-carbon ratio (H2O/CH4), keeping the rate of feed flow constant. The agreement between the data and the predictions guarantees that the model is robust to variations of feed composition. From Figure 9, it clearly appears that the addition of water to the feed reduces the temperature along the inert and the catalytic bed, shifting the entire temperature profile downward. Note that the temperature peak position is not influenced by the water content, and this is an indication that

Figure 10. Numerical and experimental exit composition, relative to varying H2O/CH4 ratios. Conditions: Q ) 4 NL/min, Tph ) 623 K, air/CH4 ) 3.125.

Figure 11. Oxidation and reforming reactions rates along the bed for different H2O/CH4 ratios. Conditions: Tph ) 623 K, air/CH4 ) 3.125, Q ) 4 Nl/min, P ) 1.7 bar.

the addition of water does not affect the overlapping between the oxidation and reforming reactions. The theoretical and the experimental exit composition are reported in Figure 10. Again, the model predictions are in good agreement with the experimental results. The addition of water causes both an increase in the partial pressure of water and a decrease in the reactor thermal level; in the range investigated, the two effects act in such a way that the methane conversion and hydrogen yield at the catalyst bed exit increase with water content. The effect of water addition on the interaction between oxidation and reforming reactions can be analyzed in Figure 11, which shows the reaction rates of the oxidation and reforming reactions as the feed content of steam is increased. The overall effect of the increase of water in the feed is to reduce both the oxidation and reforming reaction rates. Indeed, a higher concentration of steam reduces the partial pressures of methane and oxygen in the first part of the bed and, thus, the oxidation reactions are decreased. As a consequence, less heat is generated, and the corresponding temperature reduction also determines a decrease of the rate of the reforming reactions. The reduction in the oxidation and reforming reaction rates does not reflect reductions in the methane conversion and hydrogen yield (see

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Figure 13. Composition profiles at P ) 1.7 bar, Q ) 4 NL/min, air/CH4 ) 3.125, H2O/CH4 ) 1.2, Tph ) 623 K.

Figure 12. (a) Numerical gas and solid temperature profiles at flow rates of Q ) 6 and 1.5 NL/min. (Conditions: Tph ) 623 K, air/CH4 ) 3.125, H2O/CH4 ) 1.2.) (b) Difference between the gas and solid temperature profiles at flow rates as the flow rate is changed. (Conditions: Tph ) 623 K, air/CH4 ) 3.125, H2O/CH4 ) 1.2.)

Figure 10), because of the different methane entrance concentrations, which decrease with the addition of water to the feed. 4.5. Gas Temperature Profiles. The necessity of using heterogeneous models for ATR reactors clearly appears from the simulated solid and gas temperature profiles reported in Figure 12. Figure 12a shows the temperatures of the gas (TG) and solid (TS) along the axial length at two different values of the flow rate, whereas Figure 12b displays the corresponding difference between them (TS - TG) along the catalytic bed. It can be observed that, in the flow rate range investigated here, the difference between the gas and solid temperatures is never negligible, and, therefore, a heterogeneous model is needed. Figure 12b indicates that the solid temperature in the inert part is higher than that of the gas phase. This is due to the fact that, in the catalytic zone, the reactions occur on the solid, which results in higher solid temperatures than the gas-phase temperatures. Because of the large amount of heat transfer, which is due to the radiation and the conduction in the solid phase, such an effect also is visible in the inert zone. The difference between the gas and solid temperatures increases along the part of the catalytic bed where oxidation reactions occur. It then decreases where the reforming reactions are dominant, eventually increasing again when reforming reactions slow for the dispersion in the solid phase. Such difference is predicted to be higher at larger flow rates.

A practical implication of the difference between the gas and solid temperatures is that thermocouples may often substantially underestimate the solid temperature around the peak position and they overestimate the exit temperature.27 4.6. Model Predictions. Figure 13 reports typical concentration profiles along the fixed bed. The concentration of methane and oxygen fall near the catalytic bed inlet (z ) 0 cm), as a consequence of the oxidation reactions, and, correspondingly, the water content and the CO2 concentration increase. At z ) 0.18 cm, the water concentration reaches its maximum value and then decreases for the reforming reactions. When the reforming reactions start to be significant, an increase of CO concentration is also observed. For axial length of ca. 1 cm, all components reach a plateau value (i.e., all reactions rates become zero), which corresponds to thermodynamic equilibrium. Note that the exit molar fraction of water is less than that at the inlet values, which indicates that some water is converted to hydrogen. Figures 14a-c show the effect of the pressure on solid-phase temperature profiles. We have considered two different flow rates: one in the thermodynamic control (1.5 NL/min), and the other well within the kinetic control range (6 NL/min). Figure 14a shows the temperature profiles for four different pressure values at Q ) 1.5 NL/min. As the pressure is increased, the temperature in the catalytic bed uniformly increases. This feature is due to the beneficial effect of higher pressure on the oxidation reactions. Although a temperature increase favors the reforming reactions, the overall effect is a decrease in the methane conversion, as predicted by the thermodynamics at higher pressures (see Figure 14c). At higher flow rates, the effect of the pressure is slightly less pronounced. The temperature increase is less pronounced specially around the peak position (see Figure 14b) and the conversion decreases with a slightly lower slope (see Figure 14c). In both cases, the temperature peak close to the reactor entrance is clearly visible at all investigated pressures. At lower flow rates, however, the pressure increase determines a less-steep maximum in the temperature profile. Finally, it is worth mentioning that the passage from thermodynamic control to kinetic control does not qualitatively affect the influence of pressure on methane conversion. The effects of the preheating temperature on the solid temperature profiles and on the exit conversion are reported in Figure 15. In particular, Figure 15a shows that larger preheating temperatures determine an increase of the temperature along

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Figure 15. (a) Numerical solid temperature profiles at different temperatures: 473, 623, and 773 K. (Conditions: P ) 1.7 bar, Q ) 4 NL/min, air/CH4 ) 3.125, H2O/CH4 ) 1.2.) (b) Methane conversion as is varied. (Conditions: P ) 1.7 bar, Q ) 4 NL/min, air/CH4 ) 3.125, H2O/CH4 ) 1.2.)

Figure 14. (a) Numerical solid temperature profiles at different pressure values: 1.7, 5, 7.5, and 15 bar. (Conditions: Q ) 6 NL/min, Tph ) 623 K, air/CH4 ) 3.125, H2O/CH4 ) 1.2.) (b) Numerical solid temperature profiles at different pressure values: 1.7, 5, 7.5, and 15 bar. (Conditions: Q ) 1.5 NL/min, Tph ) 623 K, air/CH4 ) 3.125, H2O/CH4 ) 1.2.) (c) Methane conversion as the pressure is varied for two different flow rates: 1.5 and 6 NL/min. (Conditions: Tph ) 623 K, air/CH4 ) 3.125, H2O/CH4 ) 1.2.)

both the inert and catalytic bed and the reduction of the temperature gradient. A more-uniform heat distribution along the bed favors endothermic reactions. Indeed, by increasing the preheating temperature, the methane conversion increases and complete conversion is attained at 773 K (see Figure 15b). 5. Conclusions We have proposed a one-dimensional heterogeneous model for autothermal reforming (ATR) fixed-bed reactors. The kinetic

model takes into account the separation between the oxidation and the reforming reactions by multiplying the reforming and water-gas shift (WGS) reaction rates by a reduction factor, as a function of the fractional oxygen conversion. The reduction factor is the only adjustable parameter in the model, and its value was adjusted once and for all under typical operating conditions and was then kept constant throughout the paper. The model validation was performed by comparing the predictions with experimental data of reactor temperature profile and exit product compositions. Special care was devoted to measure the temperature profiles accurately with an infrared thermocamera. The model correctly predicts the solid temperature profiles, as well as the exit composition as the H2O/CH4 ratio and the flow rate Q are varied in the ranges of 0-2 and 1.5-6 NL/ min, respectively. Therefore, the model can be used to estimate the temperature profiles and the location of its maximum value in industrial ATR reactors. As already observed in previous works, as the flow rate is increased, the system passes from thermodynamic control to kinetic control. The model gives good predictions of the exit composition in both ranges, even at high flow rates when under kinetic control. In all the explored conditions, the analysis of spatial profiles reveals that the oxidation and reforming reactions are rather separate in the space. In this regard, the reduction factor between the oxidation and reforming reaction has a very important role.

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The effect of flow rate, water content, and pressure on temperature profiles and reaction rates was also investigated. In agreement with the experimental data, the model shows that, as the flow rate is increased, the temperature peak position does not change. This information, together with the analysis of the reaction rates, indicates that the overlapping of the oxidation and reforming reactions is not enhanced by increasing the flow rate. Also, the effect of water in the feed is well-described by the model. Again, the temperature peak position is not influenced by the water content in the feed, and its overall effect is to reduce the temperature along the bed. Analysis of the kinetic rates shows that the addition of water decreases both the oxidation and reforming reaction rates. Regarding the effect of the reactor pressure, in contrast with previously literature, we observe the presence of the temperature peak at all pressure values, from atmospheric pressure to a pressure of 15 bar. The increase in pressure determines the increase in temperature along the bed and, correspondingly, a decrease in the total conversion of methane. Such a trend is more-pronounced at low flow rates. Nomenclature Main Symbols av ) catalyst specific area per unit of volume [m-3] Ci ) molar concentration of species i [kmol/m3] Cp ) specific heat capacity [kJ/(kmol K)] Di,mix ) mass diffusivity of species i in the gas mixture [m2/s] Deff,i ) effective diffusion coefficient of species i [m2/h] dr ) reactor diameter [m] dp ) pellet diameter [m] E ) activation energy [J/mol] es ) emissivity of the solid phase f ) frictional factor g ) gravitational acceleration [m/s2] G ) superficial mass flow rate [kg/(s m2)] ∆Hj ) enthalpy of reaction j [kJ/kmol] hf ) gas-to-solid heat-transfer coefficient [kJ/(m2 h K)] hoven ) external heat-transfer coefficient [J/(s m2 K)] L ) reactor length [m] MM ) mixture molar weight [kg/kmol] Nr ) number of reactions kmix ) gas phase thermal conductivity [J/(m s K)] keff ) effective thermal conductivity [J/(m h K)] ki,g ) gas-to-solid mass-transfer coefficient of species i [m/h] Ki ) kinetic constant rate [kmol/(kgcat h)] Kieq ) equilibrium constant of reaction i Kc,j ) adsorption constant of species i in combustion reaction Kj ) adsorption constant of species j in reforming reactions P ) pressure [KPa] Q ) gas volumetric flow rate [NL/min] R ) universal gas constant [J K-1mol-1] RT ) heat generation per unit reactor volume [J/(m s)] rj ) reaction rate for reaction j [kmol/(kgcat h-1)] T ) temperature [K] Toven ) external temperature [K] Tph ) preheating temperature [K] Vint ) interstitial velocity of the gas phase [m/h] yj ) molar fraction of species j [mol/mol] Greek Letters σ ) Stefan-Boltzmann constant [W/(m2 K4)] F ) density [kg/m3] ε ) bed void fraction Ψ ) shape factor in the mass-transfer coefficient equation Subscripts

s ) solid phase g ) gas phase

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ReceiVed for reView April 2, 2008 ReVised manuscript receiVed June 27, 2008 Accepted July 15, 2008 IE800518E