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Ind. Eng. Chem. Res. 2000, 39, 4106-4113
Development and Application of Mathematical Models of Pilot-Scale Catalytic Combustors Fueled by Gasified Biomasses Gianpiero Groppi,*,† Enrico Tronconi,† Magnus Berg,‡ and Pio Forzatti† Dipartimento di Chimica Industriale e Ingegneria Chimica “G. Natta”, Politecnico di Milano, Piazza L. Da Vinci 32, 20133 Milano, Italy, and TPS Termiska Processer AB, 611 82 Nyko¨ ping, Sweden
The mathematical modeling of the catalyst section of an atmospheric pilot-scale combustor fueled by gasified biomasses is addressed. The development of distributed three-dimensional (3D) and two-dimensional (2D) models of the single channel of the monolith catalyst is first described. The results of models derived under different assumptions are then compared in order to identify the simplest accurate mathematical description. According to this procedure, a 2D model for circular channel geometry, which includes axial conduction in the solid walls, can be regarded as the most suitable model for parametric investigations requiring a large number of simulations. Such a model is finally applied to the analysis of the results obtained in an experimental 30 kW pilot facility. A reasonable fitting of the experimental data is achieved, and the key role of hightemperature homogeneous and catalytic kinetics in determining the combustor performances is pointed out. In particular, evidence is provided in favor of temperature self-control of the palladium catalyst because of a drop of CH4 combustion activity associated with thermal decomposition of PdO. 1. Introduction
Table 1. Composition of Gasified Biomasses
Following the Kyoto protocol on the reduction of net CO2 emissions in the atmosphere, the use of renewable fuels, e.g., from gasification of biomasses, has been increasingly considered.1 Combustion of such low heating value fuels (LHV ) 5-6 MJ/Nm3) in conventional gas turbines (GT) requires serious modifications in design and operational parameters. The use of catalytic combustors may improve the operation stability and decrease the formation of both thermal and fuel NOx. Such potentialities were investigated in a European project, ULECAT, aimed at the development of a dual fuel catalytic combustor suitable for burning gasified biomasses and diesel fuel.2 Mathematical modeling was included as a main task in the project, being recognized as an important tool in the development and the design of the catalytic combustor. The modeling activity was devoted to the following two objectives: (i) scale-up of laboratory-scale data and preliminary design of the industrial combustor; (ii) analysis of pilot-scale data obtained in an atmospheric facility. In view of this, a wide range of operating conditions had to be covered. Indeed, under the pressurized conditions of the industrial combustors (10-20 atm), either transitional (laminar to turbulent) or turbulent flow regimes typically prevail in the channels of GT monolith combustors because of the extremely high specific flow rates. On the other hand, the pilot-scale facility in the ULECAT project was operated at atmospheric pressure with gas velocity and residence times similar to those of the industrial combustor, which corresponds to a laminar flow regime in the channels. * Corresponding author. Phone: ++39-02-23993258. Fax: ++39-02-70638173. E-mail:
[email protected]. † Politecnico di Milano. ‡ TPS Termiska Processer AB.
species % (v/v)
H2
CO
CH4
C2H4
H2O
CO2
N2
13.0
14.5
3.0
0.5
10
13.5
45.5
In Table 1 typical gas composition from an air-blown, atmospheric, fluidized-bed gasifier is reported. Massive amounts of CO, H2, and CH4 are present as the major fuel components along with gasification byproducts, CO2 and H2O, and N2 coming from gasification air. Besides minor amounts of tars, N- and S-containing compounds (mostly NH3 and H2S) are present which can markedly affect NOx formation and catalyst performances. According to the literature,3 the simulation of combustion of mixtures containing fuel components with widely different diffusion rates and homogeneous/ heterogeneous reactivity in monolith catalysts with laminar flow conditions in the channel should be preferably performed with distributed models, i.e., accounting for variable distributions over both the cross section and the peripheral and axial coordinates. Indeed, the use of lumped models, based on the concentration of the cross-sectional and peripheral distribution of variables, may result in misleading predictions of heterogeneous and homogeneous ignitions and, consequently, of fuel conversion and catalyst wall temperatures.3 On the other hand, the computational duty associated with numerical solution of highly nonlinear balances for several species in a multidimensional domain is so severe to make any adequate approximation attractive. In this work specific aspects associated with mathematical modeling of the catalyst section of an atmospheric pilot combustor fueled by gasified biomasses are addressed. In particular, the effects of axial and peripheral heat transfer associated with solid wall conduction are investigated, and simulation results obtained with three-dimensional (3D) and two-dimensional (2D) models of a single monolith channel with square and circular
10.1021/ie990872d CCC: $19.00 © 2000 American Chemical Society Published on Web 10/12/2000
Ind. Eng. Chem. Res., Vol. 39, No. 11, 2000 4107
Governing Equations.
2D model gas phase ∂mi
Fu
)
geometry are compared in order to identify the simplest accurate model. The selected model is then applied to the analysis of the results obtained in an experimental facility in order to assess quantitatively the roles of the different physicochemical phenomena in determining the combustor performances, so as to gain insight into the catalyst behavior under severe conditions. 2. Description of Mathematical Models
Fucp
∂T
1 ∂
)
r ∂r
∂z
∂r
(
)
∂T
ktgr
∂r
+ Mi
∑j vijVjhom
mass balance of i species (1) -
∑j ∆Hr,jVjhom enthalpy balance (2)
solid phase 4
FDi
|
∂mi
deq
∂r
r)R
) Mi
∑j ξvijηjVjhet mass balance of i species (3)
∂2Tw
(ktsλ + ktwξ)
∂z Assumptions. Honeycomb catalysts consist of bundles of parallel channels with identical geometry (Figure 1). Based on the assumptions of negligible heat dispersion and uniform distribution of variables at the inlet section, which are well matched in GT combustors, a singlechannel description has been adopted for the monolith catalyst. Ceramic honeycombs are typically extruded with square cells, but washcoat deposition results in corner rounding due to accumulation of material. Accordingly, the actual geometry of the cross section of a monolith cell is intermediate between square and circular. In view of this, two distributed models, accounting for a 3D and a 2D description of square and circular channels, respectively, have been developed under the following assumptions: (i) steady-state conditions; (ii) boundary layer approximation with fully developed laminar flow; (iii) negligible axial mass and heat diffusion in the gas phase; (iv) negligible radiation effects but for heat dispersion at the catalyst inlet; (v) negligible pressure drops along the monolith channels in the isothermal catalysts layer; (vi) intraporous mass diffusion in the washcoat accounted for by analytical calculation of the effectiveness factor; (vii) T-dependent gas properties according to the following power laws: Dk ∝ Tg1.75; ktg ∝ Tg0.75; cp ∝ Tg0.2. Kinetics of the heterogeneous reactions have been derived from laboratory tests on powder catalysts assuming a first-order dependence on fuel concentration. Homogeneous reactions have been included using simple molecular kinetics.4,5 The presence of small amounts of tars and N- and S-containing compounds has been neglected, the attention being focused on the prediction of the ignition behavior and of the gas heating rate, which are both dominated by the main fuel components. The governing equations consist of the enthalpy balance of the i species (CO, H2, CH4, C2H4, CO2, H2O, and O2) mass balances for the solid and gas phases and of a global mass balance for the gas phase.
)
∂mi
FDir
r ∂r
∂z
Figure 1. Schematic of the monolith honeycomb catalyst.
(
1 ∂
4
+
deq
2
ktg
∂T
∑j ξ∆Hr,jηjVjhet
)-
∂r
enthalpy balance (4) global mass balance
∫AFu dA ) ∫AF°u° dA
(5)
with
[ (Rr ) ] 2
u ) 2u j 1-
(6)
boundary conditions T ) T°, mi ) mi°, (ktsλ + ktwξ) σe(Tw4 - T-∞4)
∂Tw ) ∂z
at the catalyst inlet (z ) 0) (7)
∂Tw )0 ∂z
outlet condition (z ) L)
(8)
∂T ∂mi ) )0 ∂r ∂r symmetry conditions at the channel axis (r ) 0) (9) Tw, T, mi,w ) mi
at the catalytic walls (r ) R) (10)
3D model gas phase Fu
∂mi
∂
)
∂z
∂x
(
FDi
) (
∂mi ∂x
+
∂
∂y
FDi
)
∂mi ∂y
+ Mi
∑j vijVjhom
mass balance of i species (11)
Fucp
∂T ∂z
)
∂ ∂x
( ) ( ) ktg
∂T ∂x
+
∂
∂y
ktg
∂T ∂y
-
∑j ∆Hr,jVjhom
enthalpy balance (12)
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solid phase 4
FDi
deq
|
∂mi ∂n
n)1/2
∑j ξvijηjVjhet mass balance of i species (13)
(ktsλ + ktwξ)
∂2Tw ∂z
-
) Mi
2
+ (1 - )kts
∂2 T ∂p
∑j ξ∆Hr,jηjVjhet
2
+
4 deq
ktg
|
∂T
)
∂n n)1/2
enthalpy balance (14)
global mass balance
∫AFu dA ) ∫AF°u° dA
(15)
u)u j ψ(x,y)
(16)
with
coupled PDEs (partial differential equation system). They have been solved in dimensionless form. Orthogonal collocation techniques based on symmetric Jacobi polynomials6 were implemented for the discretization of the dimensionless variable profiles either along the radial coordinate (2D model) or over the cross section (3D model) of the monolith. In the case of the 3D model for square channels, only one-eighth of the whole cross section has been considered by taking properly into account the geometrical symmetry. To account for steep temperature gradients associated with the ignition front, orthogonal collocations on finite elements6 were adopted for discretization of the variable profiles along the axial coordinate, with a third-order polynomial approximation over each element. An adaptive mesh algorithm7 based on a weighted distribution of a fixed number of nodes was developed for automatic location of the axial grid points. It implements the following node density function in order to locate most of the elements in the proximity of the ignition front:
dT/w
where
ψ(x,y) ) ∞ (-1)(i-1)/2 cosh[κiy/(deq/2)] κix 1cos (17) t deq/2 cosh(κi) i)1,3,... i3
∑
[
] ( )
with
t)
6/κ3 1 - 3/κ5( tanh(iκ)/i5)
∑
κ ) π/2 boundary conditions T ) T°, mi ) mi°, (ktsλ + ktwξ) ∂Tw )0 ∂z
∂Tw ) σe(Tw4 - T-∞4) ∂z at the catalyst inlet (18)
outlet condition (z ) L)
(19)
∂T ∂T ∂mi ∂mi ) ) ) )0 ∂x ∂y ∂x ∂y symmetry conditions at the channel axis (x ) y ) 0) (20) ∂Tw )0 ∂p symmetry conditions at the wall side axes (p ) 0, n ) l/2) (21) ∂Tw ∂Tw ) )0 ∂n ∂p no heat exchange with adjacent channels (p ) l/2, n ) l/2) (22) Tw ) T, mi,w ) mi continuity conditions at the catalytic walls (n ) l/2) (23) Numerical Methods. The governing equations above constitute a boundary value problem involving a set of
Ψ(z) ) (1 - c) + c max
dz/ dT/w
( ) dz/
z∈0-1
with c ) 0.8 (24)
The resulting system of nonlinear algebraic equations was solved by means of a continuation method.8 Convergence of cross-sectional and axial discretization was checked by increasing the number of collocation points and the number of nodes, respectively, until the model predictions would not significantly change by further increments. In the most demanding case of square channels, convergence was achieved using four crosssectional collocation points and six axial elements. The resulting algebraic system consisted of almost 1000 equations. In the case of a multisegment catalyst configuration, the equations have been solved numerically for each segment according to an in-series procedure. The cupmix average value of the gas-phase outlet temperature and concentrations from one segment has been taken as the inlet condition for the following one, assuming that ideal mixing occurs in the intersegment space. 3. Results Model Discrimination. Despite the use of efficient discretization algorithms, a multicomponent 3D description of square monolith channels requires a considerable numerical effort, i.e., the solution of a strongly nonlinear system consisting of about 1000 equations. Such a complexity calls for adequate approximations. Accordingly, the results of mathematical models derived under different assumptions have been compared in order to discriminate the simplest accurate model. All of the calculations have been performed by setting the model parameters to the values reported in Table 2, which are representative of the operation of the atmospheric pilot plant. a. Effect of Solid Wall Conductivity. The numerical duty is significantly reduced if boundary conditions at the catalyst outlet associated with axial heat transfer by solid wall conduction can be eliminated. Accordingly, the role of such a backward heat-transfer contribution has been investigated. For this purpose, simulations
Ind. Eng. Chem. Res., Vol. 39, No. 11, 2000 4109
Figure 2. Effect of axial conduction. Table 2. Simulation Parameters for Model Discrimination Catalyst Geometry channel equivalent diameter ) 1.2 mm channel length ) 4 cm void fraction ) 0.60 washcoat thickness ) 30 µm washcoat porous fraction ) 0.5 pore radius ) 10 nm Operating Conditions gas inlet temperature ) 505 K pressure ) 1.05 atm adiabatic reaction temperature ) 1305 K inlet gas velocity ) 7.3 m/s Catalytic Kinetics species
k° at 653 K (s-1)
Eact (cal/mol)
H2 CO CH4
2372 1200 60
10 500 11 000 24 000
have been performed by varying the conductivity of the solid wall over a wide parametric range. The predicted axial T profiles plotted in Figure 2 show that axial backward heat transfer results in a progressive upstream shift of the light-off on increasing the solid wall conductivity. At high solid wall conductivities characteristic of metallic monoliths [ks ) 15 W/(m/K)], the light-off is pushed backward to the catalyst inlet. However, the upstream shift of the light-off position is also significant for the low values of thermal conductivity characteristic of ceramic supports [ks ) 1-2 W/(m/ K)]. These results point out that axial heat transfer cannot be neglected in atmospheric pilot-scale combustors. This is apparently at variance with previous results reported by some of the authors9 on the negligible effect
of solid wall conductivity in ceramic monolith combustors. Such a difference is due to the low specific mass flow rates considered herein, which are over 1 order of magnitude lower than those in industrial combustors. b. Effect of Peripheral Conduction. In view of the comparison of the simulated performances of circular and square channels, one of the major sources of discrepancies is related, according to the literature,9,10 to the presence of corner effects associated with the lower gas-solid heat- and mass-transfer rates in the square angles. The peripheral heat transfer associated with solid wall conduction can have a serious impact on such effects and has been, therefore, addressed. Figure 3 compares the calculated temperature profiles along the square channel side obtained by either neglecting or including the contribution associated with peripheral conduction in eq 14. It is evident that, because of the small cell size, peripheral conduction completely smooths the temperature gradients along the square sides also for the low values of thermal conductivity characteristic of ceramic monoliths. This homogenization of peripheral temperature profiles markedly suppresses corner effects. Indeed, in square channels ignition occurs first in the corners because of the less efficient gas-solid heat transfer that results in a faster buildup of the reaction enthalpy. When peripheral conduction is not included, such a local buildup results in an anticipated light-off with respect to circular channels associated with marked temperature gradients along the square perimeter. On the other hand, heat transfer by peripheral conduction causes ignition to immediately propagate over the whole perimeter but simultaneously results in a quenching effect on the square corners. Such an effect has a marked impact on the overall simulated performances of the monolith catalyst, as shown in Figure 4, where the axial profiles of the average catalyst and gas temperatures calculated with and without peripheral conduction are compared. It is evident that the quenching of the square corners results in a marked downstream shift of the light-off position. Notably, as shown in Figure 5, quite accurate results are obtained by assuming infinite peripheral conduction (i.e., uniform peripheral temperature), indicating that lumping of the peripheral distribution of the variables (of the solid temperature at least) can provide a reasonable approximation. A similar indication was reported in the literature11 for simulation of CO combustion in
Figure 3. Effect of solid conduction on the calculated peripheral profile of the catalyst temperature: (a) with peripheral conduction neglected; (b) with actual peripheral conduction. (ks ) 1.4 W/(m/K)).
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Figure 4. Effect of peripheral conduction on the calculated axial profiles of (a) the average catalyst temperature and (b) the cupmix average gas temperature.
Figure 5. Comparison of the calculated average wall and cupmix gas temperature profile with actual peripheral conduction (solid lines) and upon lumping of peripheral wall temperature profiles (dotted lines).
catalytic mufflers. According to the results reported herein, such a simplification can be safely extended to the modeling of multicomponent fuels consisting of species with wide ranges of diffusivities. c. Comparison of 2D and 3D Models. Parts a and b of Figure 6 present simulation results of 2D and 3D models of circular and square monolith channels, respectively. To isolate the effect of the channel shape, the comparison has been performed by assuming the same equivalent diameter and the same void fraction for the two geometries. The profile of maximum catalyst temperature calculated as a function of the gas inlet temperature (Figure 6a) indicates that the 3D model predicts light-off at a gas inlet temperature 10 °C lower than the ignition temperature calculated by the 2D model. On the other hand, once light-off has occurred for both geometries, the 2D model calculates slightly
Figure 6. Comparison of 3D and 2D model predictions.
higher gas outlet temperatures (Figure 6b). Both the anticipated ignition and the lower heating of the gas phase predicted by the 3D model are associated with the lower heat- and mass-transfer rates in square channels than those in circular ones. However, also because of the smoothing effect of peripheral conduction, discrepancies between 2D and 3D model predictions are limited in comparison with the uncertainties affecting other parameters (including kinetics and inlet conditions). On the other hand, the 2D model can afford important numerical savings (solution of 2D model equations typically requires a CPU time lower by 1 order of magnitude than solution of 3D model equations). Thus, considering also the uncertain definition of the actual geometry of the channels upon washcoat deposition, the 2D model has been chosen for simulation of the atmospheric pilot test facility. Simulation of the Pilot-Scale Facility. The 2D model has been applied to the simulation of experiments performed in an atmospheric pilot-scale facility, which has been described in detail elsewere.12 Briefly, the experimental setup consists of a 30 kW, airblown, fluidized bed connected to a combustor rig with an inner diameter of 78 mm equipped with a multisegment catalyst section. The average composition of the fuel gas, after cleaning from particles in a cyclone and hightemperature particulate filters, is reported in Table 3. During the experiments the temperature was continuously monitored by means of thermocouples placed upstream of the catalyst section and in the channels of the last catalyst segments. The concentrations of CO and total hydrocarbon (mainly CH4) were monitored as
Ind. Eng. Chem. Res., Vol. 39, No. 11, 2000 4111 Table 3. Composition and Heating Value of Fuel from the Gasifier species
% vol
CO
CO2
H2
H2O
N2
CH4
C2H4
LHV (MJ/Nm3)
15.4
11.8
12.6
10.0
47.1
2.6
0.4
4.5
Table 4. Model Parameters in the Simulation of the Pilot-Scale Combustor Catalyst Geometry diameter length segment no. 1 2 3
77 mm 2.3 × 3 cm
catalyst type
CPSI
void fraction
washcoated Pd catalysts commercial HA commercial HA
200/12
0.589
62
250/17 250/17
0.513 0.513
bulk bulk
pressure flow rate Wair Wfuel
washcoat thickness (µm)
Operating Conditions 1 atm 43.68 Nm3/h 12.32 Nm3/h
Catalytic Kinetics ri ) KiCi [mol/(cm3/s)] species
K° (s-1) at 653 K
Eact (cal/mol)
H2 CO CH4 C2H4
Pd Catalyst 791 400 20 200
10 500 11 000 21 000 17 000
H2 CO CH4 C2H4
HA Catalyst 13 75 0.14 0.28
13 000 15 300 23 900 19 000
well immediately downstream of the catalyst section by means of IR and flame ionization detectors, respectively. Several catalyst configurations have been investigated, but the analysis is herein focused just on the one that provided promising light-off and emission performances. This configuration consists of one segment of a washcoated Pd-based catalyst with high activity followed by two Mn-substituted hexaaluminate (HA) segments with high thermal stability of 2.3 cm length each. The geometric and kinetic parameters of this catalyst configuration are reported in Table 4 along with the set of model parameters adopted in the simulation of the pilot-scale combustor. A parametric investigation performed with the mathematical model described herein13 singled out the hightemperature kinetics of both the homogeneous and the catalytic reactions as the most critical parameters in determining the model fit of the experimental emission trends. To better assess the contribution of the homogeneous reactions under the investigated conditions, a study was performed by means of a detailed kinetic model of gasphase combustion.14 Such an investigation evidenced the presence of strong promoting effects on CH4 combustion
by C2H4 and H2 associated with the enrichment of the radical pool during the activation of these more reactive species. To account for such a promoting effect, the kinetic expression for CH4 combustion, originally derived from the literature,4 was accordingly modified by reducing the apparent activation energy as reported in Table 5. The high-temperature kinetics of the catalytic reactions significantly affects the predicted emission performances of the combustor, too. In particular, the rate of CH4 combustion over Pd-based catalysts at high temperature must be carefully considered. Indeed, it is widely reported in the literature that CH4 combustion activity markedly drops upon thermal reduction of PdO to Pd metal because of an increase of the catalyst temperature above the PdO thermodynamic decomposition threshold. For natural gas combustion, it is well documented15,16 that such an activity drop results in a temperature self-control capability of the palladium catalyst (chemical thermostat). This effect could be relevant also to combustion of gasified biomasses. In fact, the adiabatic temperature rise associated with combustion of the CO-H2 fraction of such fuels is sufficient to exceed the thermodynamic threshold of PdO decomposition. To clarify this point, simulations have been performed under the following alternative assumptions: (i) the first Pd-based segment is active in CH4 combustion in the whole temperature range according to kinetics derived from the data collected at low temperature in laboratory reactors; (ii) the Pd-based segment is inactive in CH4 combustion following the temperature rise associated with CO and H2 ignition. In Figure 7a,b, the THC and CO emissions calculated as a function of the outlet gas temperature under the two assumptions above are compared with those obtained in the pilot-scale tests. The experimental outlet concentrations of THC and CO show the following typical trends: THC, whose inlet concentration is about 7000 ppm, gradually decrease above 800 °C and are completely consumed above 950 °C; CO, whose inlet concentration is about 3%, shows a very smooth decrease from 7000 to 4500 ppm in the temperature range 800-930 °C and only upon complete THC consumption exhibits a marked decrease down to about 1000 ppm at 1000 °C, thus originating a characteristic “two-slope” trend. Figure 7a,b shows that the model provides a reasonable fit of such trends when assuming the first Pd-based segment to be inactive in CH4 combustion. A progressive reduction of THC emissions is predicted above 800 °C up to complete THC consumption at 950 °C. Calculated CO emissions are lower than the experimental ones but exhibit the same qualitative trend with a smooth decrease up to the temperature at which THC combustion is completed (=950 °C) followed by a marked drop. This reasonable fit has been achieved by properly considering the role of homogeneous combustion. In fact, CH4 consumption via a gas-phase reaction is associated with the formation of CO as the intermediate oxidation product.14 This additional production sustains the outlet
Table 5. Kinetics of Homogeneous Reactions reaction
rate expression [mol/(cm3/s)]
preexponential factor
Eact (cal/mol)
H2 + 0.5O2 f H2O CO + 0.5O2 f CO2 CH4 + 1.5O2 f CO + 2H2O C2H4 + 2.5O2 f 2CO + 2H2O
r ) KCH2CO2 r ) KCCOCO20.25CH2O0.5 r ) KCCH40.7CO20.8 r ) KCC2H40.7CO20.8
2.196 × 1012 3.98 × 1014 1.58 × 1013 1.58 × 1014
26 100 40 000 39 700 39 700
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Figure 7. Comparison of predicted and experimental emissions as a function of the outlet temperature: (a) THC outlet concentration; (b) CO outlet concentration.
CO concentration up to complete CH4 conversion, thus originating the observed “two-slope trend”. This effect is present only to a minor extent when assuming that the first Pd-based catalyst is highly active in CH4 combustion. In fact, depletion of CH4 in the first segment, where the gas temperature is too low for homogeneous ignition, would markedly decrease in this case the contribution of the gas-phase reaction in the following HA catalysts. Accordingly, as shown in Figure 7a,b, the calculated values of THC and CO emissions are much lower than the experimental ones. On the other hand, the CH4 combustion activity of the first segment has only a minor effect on the ignition behavior: a light-off temperature of about 270 °C is estimated under both the assumptions on the behavior of the Pd catalyst in CH4 combustion, which compares well with the experimental value. Indeed, ignition is governed by the most reactive components (CO and H2),17 whose activities have been taken as identical in both cases. Finally, the results in Figure 8a,b demonstrate that the drop of CH4 combustion activity due to PdO decomposition can be used as an effective control method of the catalyst temperature in combustion of gasified biomasses. Comparison of calculated axial profiles of catalyst and cupmix gas temperatures shows that assuming the first catalyst to be inactive in CH4 combustion results in a lower calculated temperature of the Pd catalyst that, once ignition has completely occurred, remains well below the adiabatic reaction temperature because of the unreacted CH4 fraction of the fuel. Nevertheless, it is still higher than the
Figure 8. Calculated axial profiles of the catalyst temperature (solid lines) and cupmix gas temperature (dotted lines): (a) with the first segment active in CH4 combustion; (b) with the first segment inactive in CH4 combustion.
decomposition temperature of PdO, confirming that the combustion of the H2-CO fraction of the fuel (and to a minor extent of C2H4) can be sufficient to increase the catalyst temperature above the PdO decomposition temperature. 4. Conclusions The comparison of multidimensional models of the single channel of a combustor monolith fueled by gasified biomasses at atmospheric pressure has allowed one to identify the simplest accurate model to be used for simulation purposes. In particular, the following indications have been obtained: (i) Axial backward heat transfer through conduction in the solid walls must be taken into account also in ceramic monoliths because of the relatively low specific mass flow rate associated with pilot runs at atmospheric pressure. (ii) Peripheral heat transfer through solid wall conduction markedly smooths corner effects in square channels. In view of this, predictions of ignition and conversion performances of the combustor monolith provided by 3D models of square channels and by 2D models of circular channels compare reasonably well. Accordingly, also in view of the uncertain definition of the actual channel geometry, the 2D model, which guarantees significant savings of computational time with respect to the 3D one, can be effectively used for simulation purposes. Application of the 2D model to the simulation of the experimental results obtained in an atmospheric pilot-
Ind. Eng. Chem. Res., Vol. 39, No. 11, 2000 4113
scale combustor has pointed out the key role of hightemperature homogeneous and catalytic kinetics in determining the combustor performances. In particular, evidence has been collected in favor of temperature selfcontrol of palladium catalyst due to the CH4 combustion activity drop associated with thermal decomposition of PdO. Acknowledgment This work has been performed under UE Contract JOR3-CT96-0071. Notation A ) area of the channel cross section [m2] cp ) mass specific heat [J/(kg/K)] Di ) mass diffusivity of the i species [m2/s] deq ) equivalent diameter of the monolith channel [m] ∆Hr,j ) heat of the j reaction [J/mol] e ) emissivity factor kt ) thermal conductivity [W/(m/K)] mi ) mass fraction of the i species in the gas phase Mi ) molar weight of the i species [kg/kmol] L ) monolith length [m] l ) square side length [m] n ) perpendicular coordinate to the square perimeter [m] p ) parallel coordinate to the square perimeter [m] r ) radial coordinate [m] R ) deq/2 [m] Re ) vdeq/v ) Reynolds number T ) gas temperature [K] Tw ) catalyst temperature [K] T*) T/T° dimensionless temperature u ) gas velocity [m/s] Vj ) rate of the j reaction [mol/(m3/s)] x, y ) cross-sectional coordinates [m] z ) axial coordinate [m] z/) z/L dimensionless axial coordinate Greek Letters ) void fraction φj ) Thiele modulus of the j reaction ηj ) Th(φj)/φj effectiveness factor of the j reaction λ ) fraction of inert support ν ) kinematic viscosity [m2/s] νi,j ) stoichiometric coefficients of the i species in the j reaction F ) density [kg/m3] σ ) Stefan-Boltzmann constant [5.67 × 10-8 W/(m2/K4)] ξ ) active washcoat fraction Subscripts and Superscripts b ) bulk average value g ) gas phase
het ) heterogeneous reaction hom ) homogeneous reaction ° ) inlet conditions s ) inert support w ) active washcoat
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Received for review December 2, 1999 Revised manuscript received May 5, 2000 Accepted August 16, 2000 IE990872D
