Monolithic three-way catalysts are applied to reducethe emission of combustion engines. The design of sucha catalytic converter is a complex process involving theoptimization of different physical and chemical parame-ters. Simple properties such as length, cell densities ormetal coverage of the catalysts influence the catalyticperformance of the converter.
Numerical simulation is used as an effective tool forthe investigation of the catalytic properties of a catalyticconverter and for the prediction of the performance ofthe catalyst. To attain this goal, a two-dimensional flowfield description is coupled with a detailed chemicalreaction model.
In this paper, results of the simulation of a monolithicsingle channel are shown. In a first step, the steady stateflow distribution was calculated by a two dimensionalsimulation model. Subsequently, the reaction mecha-nism of the chemical species in the exhaust gas wasadded to the simulation process. The performance of thecatalyst was simulated under lean, nearly stoichiometricand rich conditions. For these characteristic conditions,the oxidation of propen and CO and the reduction of NOon a typical Pt/Rh coated three-way catalyst were simu-lated as a function of temperature. The numerically pre-dicted conversion data are compared with experimen-tally measured data. The simulation further reveals thecoupling between chemical reactions and transport pro-cesses within the monolithic channel.
INTRODUCTION
Today three-way catalysts are used extensively toreduce the emissions of combustion engines. Themajority of automotive catalytic converters have a mono-lithic structure, which is coated with an alumina wash-
coat that supports the noble metal such as platinum,palladium and rhodium. These monoliths can be made ofeither ceramic or of metal. To achieve a large catalyticsurface area, the substrates consist of numerous parallelchannels with a diameter of approximately 1 mm. For thedesign of a catalytic converter, several chemical andphysical properties of both the catalyst and the exhaustgas must be considered:
• cell geometry (length and diameter of the channel,wall thickness),
• species of noble metal and noble metal loading,• species of promotors,• temperature, velocity and chemical composition of
the exhaust gas.
The experimental characterization of the catalyticperformance of the converter is time-consuming andrequires a large experimental setup. Moreover, multipleexperimental measurements should be made to ensurereproducibility. Numerical simulation offers an interestingalternate method for the investigation of the catalyticactivity of a converter. This method is also efficient inanalyzing the transient flow and thermal phenomena inthe catalytic converter and may help to understand thecomplex interactions between the flow field and thecatalytic surface chemistry.
In recent years, several proposals were made for thenumerical simulation of catalytic converters /1-6/. In mostof these studies, a global model for the chemistry wasused. This global model however neglects the varioussingle reactions which occur on the surface. An alternateapproach is the description of the chemical reactions bya set of elementary reaction steps. The reaction equa-tions of the elementary steps describe the reactions on a
molecular level, so the approach is much more accuratethan a globally fitted kinetic. The main advantage ofthese detailed reaction mechanisms is their potential topredict the behavior of the chemical system at differentexternal conditions. The disadvantage of using elemen-tary chemical reactions is the large number of reactionequations which demands a large computational capac-ity. Furthermore, the rate coefficients of all the singlesteps have to be known.
In this study, we do not only use a more accuratechemical reaction model but also a detailed descriptionof the flow field. One single channel of the monolith ismodelled by the two-dimensional Navier-Stokes equa-tions. The flow field simulation is based on the commer-cially available CFD-code FLUENT /7/. FLUENT wascoupled with the chemistry module DETCHEM /8/ in aformer study /9/. DETCHEM models chemical reactionsin the gas phase and on the surface using elementarystep reaction mechanisms. This computational tool wasalready successfully used to model catalytic partial oxi-dation processes in monolithic reactors /9/. In the pres-ent work, we use this code to study the emission reduc-tion in a single channel of an automotive three-waycatalytic converter.
The channel of the monolith is assumed to be a tubereactor. The flow inside this reactor is laminar and thetransport coefficients depend on composition and tem-perature. A detailed multi-step reaction mechanism isused to model the catalytic reactions and to calculate thesurface mass fluxes. The surface coverage of the spe-cies on the catalytic material is also calculated as afunction of the position in the channel. The mechanismincludes only surface chemistry, gas phase chemistrycan be neglected because of the low pressure and theshort residence time of the species inside the catalyst.The conversion calculated for a variety of conditions willbe compared with experimental data, measured in labo-ratory-scale experiments using commercially used three-way catalysts.
MATHEMATICAL AND NUMERICAL MODEL
The numerical simulation is based on the CFD codeFLUENT /7/. The code is well established and can easilybe used to set up fluid flow problems and to solve them.However, modeling of detailed chemistry in current ver-sions is limited because of a maximum number of reac-tions and because of the difficulties with handling com-plex chemistry which yield a stiff differential equation set.Furthermore, FLUENT’s surface reaction model does nottake the surface coverage into account. Therefore, theFLUENT code was coupled to external subroutines thatmodel surface chemistry using FLUENT’s interface ofuser-defined subroutines. The reader is referred to /9/ fora more detailed description of the coupling procedure.
CONSERVATION EQUATIONS
The basic conservation equations for laminar flowfields, as used in FLUENT /7/, are summarized in thissection. Due to the axial symmetry of the problem, cylin-drical coordinates are used, resulting in the followingequations:
continuity equation:
(1)
axial momentum:
(2)
radial momentum:
(3)
species conservation equation:
(4)
with diffusion mass flux:
(5)
thermal energy:
(6)
Here are ρ = density, t = time, r = radial spatial coor-dinate, z = axial spatial coordinate, u = axial velocity, v =radial velocity, p = static pressure, Yi = mass fraction ofspecies i, Ri = net rate of production of species i due tochemical reactions, Di, m = diffusion coefficient of speciesi in the mixture, T = temperature, hi = enthalpy of speciesi, Ng = number of gas phase species.
The density is computed via the ideal gas law. Theviscosity µ and the thermal conductivity Λ of the mixtureas well as the diffusion coefficient of species i in themixture Di,m depend on the local composition and on thetemperature and they are calculated via kinetic theory.The specific heat cp,i at constant pressure of species i ismodeled as a polynomial function of temperature.
FLUENT solves the conservations equations using acontrol volume based finite difference method. A non-staggered system is applied for storage of discretevelocities and pressure. The resulting equations aresolved using SIMPLE-like algorithms with an iterativeline-by-line matrix solver and multigrid acceleration.
SURFACE CHEMISTRY MODEL
Chemical reactions on the catalytic reactor wall leadto the following boundary conditions:
(7)
where is�
is the creation or depletion rate of species i by
adsorption and desorption processes, ij�
the diffusive
flux and Yi the mass fraction of species i in the gasphase adjacent to the surface, vst the Stefan velocity andF the ratio between catalytic active surface area andgeometric surface. The active catalytic surface wasexperimentally determined. η is the effectiveness factorto account for pore diffusion within the washcoat. In thiswork, the effectiveness factor is related to the diffusion ofthe species CO (lean and stoichiometric mixtures) or O2
(rich mixtures) within the pores of the washcoat,because CO and O2, respectively, are the most crucialspecies in the surface kinetics. The effectiveness factordepends on the porosity, the gas-phase species con-centration at the wash coat, the surface reaction ratesand diffusion coefficients using the Thiele moduleapproach /10/.
The state of the catalytic surface is described by itstemperature and the coverages of adsorbed specieswhich vary in the flow direction. External subroutinescalculate the surface coverages Θi (the fraction of sur-face sites covered by species i) at each computationalcell at the tube wall. The same apply for the calculationsurface mass fluxes (left term of Eq. 7). The surfacechemistry is modeled by elementary reactions. Thechemical source terms is
�
of gas phase species due to
adsorption/desorption and surface species (i.e. adsorbedspecies) are given by:
(8)
where Ks is the number of elementary surface reactions(including adsorption and desorption), νik (right sideminus left side of reaction equation) and νik’ (left side ofreaction equation) are the stoichiometric coefficients and
Ns is the number of species adsorbed. The concentration[Xj] of an adsorbed species is given in mol/ m2 andequals the surface coverage (Θi) multiplied by the sur-face site density (Γ).
The temperature dependence of the rate coefficientsis described by a modified Arrhenius expression:
(9)
This expression takes an additional coveragedependence into account using the parameters µik andεik.
The rate coefficient for adsorption processes is cal-culated from the initial sticking coefficient S0, that is thesticking probability at vanishing coverage:
(10)
where τ is the number of occupied adsorption sites ofspecies i.
The steady state solution is the point of interest.Hence, the time variation of the surface coverage (Θi) iszero:
(11)
In DETCHEM, this equation system is solved toobtain surface coverages and surface mass fluxes.Here, FLUENT provides the concentration of the gasphase species and the temperature at each computa-tional cell with a catalytic wall as boundary. In theDETCHEM module, coverages and surface mass fluxesare calculated for each “global” iteration, keeping thelocal species concentrations and temperature constant.The algebraic equation system (Eq. 11) is solved by atime integration of the corresponding ODE system until asteady state is reached. An implicit method based onLIMEX /11/ is used for the time integration. DETCHEMprovides an analytical Jacobian, which is automaticallygenerated from the surface reaction mechanism. Thecoverage data of the former iteration are used as initialconditions for the next step. Under-relaxation of thevariation of the surface mass fluxes may be necessary,e. g. if a species which is largely produced on the sur-face has a high sticking coefficient such as CO in ourexamples.
GEOMETRY AND BOUNDARY CONDITIONS
A tube reactor serves as a model for a single channelof the monolithic catalyst. The tube has cylindricalgeometry with the axial direction z and the radial direc-tion r. The equations are solved in radial directionbetween r = 0 and r = d/2 with d as channel (tube)
diameter. At the tube centerline (r = 0), a symmetryboundary condition is applied.
The flow enters the computational domain with aknown velocity, gas composition and temperature. A flatprofile of the axial velocity u and a vanishing radialvelocity v are used in the simulation at the inlet bound-ary. At the reactor exit, an outlet boundary is applied atwhich values for all variables are extrapolated from theinterior cells adjacent to the outlet.
A structured grid is used for the simulation. The gridhas to be very fine around the catalyst entrance and thecatalytic wall to resolve the flow field and also to deter-mine the variations in the species concentration due tothe chemical reactions at the catalytic wall. The totalnumber of computational cells used for the single chan-nel were 20 cells in radial direction and 72 cells in axialdirection.
EXPERIMENTAL
The catalyst used in this study is a commerciallyavailable tree-way catalyst. The catalyst contains 50 g/ft3
of metal (Pt/Rh = 5:1) impregnated on a ceria stabilizedγ-alumina washcoat. The washcoat was supported by acordierit monolith with a cell density of 62 cells per cm2
(400 cpsi) and a wall thickness of 0.165 mm (6.5 mil).
The experimental determination of the conversionrate and therefore the performance of the three-waycatalyst was done in a laboratory-scale tube reactor. Forthis application, a sample of 22 mm in diameter and29 mm in length was taken from the catalyst. Before theinvestigation the sample was treated for one hour at atemperature of 650°C for conditioning. Table 1 showsthe composition and the concentration of the species inthe exhaust gas used for the conditioning process.
TABLE 1
Composition and concentration of the species used for the conditioningprocess (1h at 650°C).
Species Concentration [Vol.%]C3H6 0.0450C3H8 0.0450CO 1.4200NO 0.1000O2 1.0875H2O 13.1000N2 balance
After conditioning the sample was treated with differ-ent gas mixtures in a temperature range of 150-600°C.Table 2 summarizes the composition and the speciesconcentrations of the simulated exhaust gas. The oxy-gen concentration was varied in order to simulate a stoi-chiometric, a rich and a lean exhaust gas mixture. Theλox-values are defined as the inverse of the redox ratio/1, 5/:
(12)
With this definition λox = 1 represents a stoichiometric,λox > 1 a lean and λox < 1 a rich mixture. The volume flowof the simulated exhaust gas into the sample was15 l/min at standard conditions (25°C). A uniform axialinlet velocity of 1.35 m/s corresponds to this volumeflow. The reactor was heated with a tubular oven with aheat rate of 100°C/h. The oven leads to an isothermalsample temperature. The concentration of the differentspecies and therefore the conversion rate was measuredin 20°C-steps, the steady state of the system wasgranted.
TABLE 2
Composition of the simulated exhaust gas and concentration of the gasspecies used for the simulation studies.
Species Concentration [Vol.%]nearlystoichiometricmixture(λox=0.9)
The CO2 concentration in the inlet exhaust gas mix-ture was zero due to experimental reasons. Tests haveshown that there was no difference in the conversionrate of CO, HC and NO between measurements withand without CO2 in the inlet gas.
After the experimental studies of the temperature-dependent conversion rate the sample was investigatedwith H2 chemisoption in order to obtain the properties ofthe active metal phase. The active metal surface of thecatalyst was determined to 28 m2/g, the dispersion of theconditioned catalyst was 33%. Calculation of the ratio ofactive metal surface area and geometrical surface area(F in Eq. 7) of the catalyst leads to a value of 70. Theratio of the platinum to rhodium surface was taken fromthe literature as 3:1 for a catalyst with a noble metalcomposition of Pt/Rh with 5:1 which corresponds to thecatalyst we used for our investigations /12/.
CHEMICAL REACTION SYSTEM
The conversion reactions of the harmful exhaustgases into harmless components inside a monolithicthree-way catalyst can globally be written as
CO + 1/2 O2 • CO2
CnHm + (n + m/4) O2 • n CO2 + m/2 H2O
CO + NO • CO2 + 1/2 N2
This kind of global chemistry has been used in mostof the studies described in the literature. The surfacereaction mechanism however consists of numerous ele-mentary reaction steps. In this study, we apply a moredetailed approach to model the surface chemistry. Thesample mixture used here consists of C3H6, CO, NO andO2 (see Table 2). The reaction scheme consists of 56elementary reaction steps and 31 chemical species, e. g.dissociative oxygen adsorption, nondissociative adsorp-tion of C3H6, CO and NO, the formation steps of carbondioxide (CO2), water (H2O) and nitrogen (N2) anddesorption of all species. Some activation energies (e. g.oxygen desorption) are coverage-dependent due tointeractions between adsorbed species. It is assumedthat all species are adsorbed competitively. The modelalso considers the different adsorption places (platinumor rhodium) on the metallic catalyst surface. However,on rhodium only surface reactions between NO, CO, O2
are considered /14,15/. The kinetic data of the mecha-nism was taken either from the literature or from fits toexperiments. In a forthcoming paper, the mechanism willbe presented in detail.
Parts of the surface reaction mechanism werealready used for numerical modeling of catalytic ignition/13/, simulation of total and partial oxidation of lighthydrocarbons on platinum /14/ and modeling the CO-O2
and NO-CO reactions on rhodium /15,16/.
RESULTS AND DISCUSSION
In this section, the results of the simulations are dis-cussed. First, the predicted conversion rates of the pol-lutants C3H6, CO and NO as function of temperature forthree different gas mixtures (see Table 2) will be shownand compared with experimentally measured data.Then, the interaction of transport and chemistry within asingle channel is described as revealed by the two-dimensional simulation.
CONVERSION RATE VS TEMPERATURE
In the simulation, the conditions used experimentallyand described above are applied. Table 3 summarizesthe input data for the simulation, the concentrations ofthe incoming exhaust gas are already given in Table 2.The gas flows at a uniform inlet velocity into the cylindri-cal tube. Due to isothermal sample temperature, thechannel wall is assumed to be isothermal.
In Fig. 1, the conversion rates of CO, C3H6 and NOare shown as function of temperature. The compositionof the inlet gas mixture is lean. The conversion of CO,C3H6 and NO starts at 300°C and increases up to 100%for CO and C3H6 at 500°C and 400°C, respectively. TheNO conversion shows a maximum at 360°C anddecreases at higher temperatures. The predicted con-version rates of all three species agree well with theexperimentally measured data. Especially the tempera-ture behavior of the NO conversion and the slowincrease of the C3H6 conversion in the temperaturerange above 360°C. The simulation shows some CO
conversion at temperatures lower than 300°C probablydue to the fact that in the reaction mechanism reactionsfor hydrocarbons on rhodium are not included. ThereforeC3H6 is not able to block the CO oxidation on Rh in con-trast to the CO oxidation on Pt.
TABLE 3
Input data used for the simulation studies.
Noble metal composition Pt/Rh, 5:1Noble metal loading 50 g/ft3
Active metal surface 28 m2/gSurface ratio Pts/Rhs 3:1Metal dispersion 33%Ratio active metal surface/geometrical surface
70
Channel diameter 1.0 mmChannel length 29 mmTemperature range 100-600°CVelocitytemperature dependent 1.35 m/s at 25°C
The conversion rates as a function of the temperaturefor the nearly stoichiometric mixture are shown in Fig. 2.Again, the conversion of CO, C3H6 and NO starts at300°C, but increases more slowly with temperaturecompared to the lean mixture. Because of the insufficientamount of O2 in the mixture, CO conversion is not com-plete. The conversion of C3H6 is complete at 500°C,which indicates that C3H6 can compete with CO for O2.Also, for temperatures higher than 450°C, NO reductionis complete. Concerning the conversion rates of CO andNO and the competition between CO and C3H6 for O2,the simulation results agree well with the experimentaldata. Only the C3H6 conversion rate shows deviationsbetween 340°C and 460°C. Compared to the experi-mental data the predicted conversion rate is too high.
The rich mixture, shown in Fig. 3. contains0.4 Vol.% O2, which leads to only a maximum of COconversion of aprox. 33%. The conversion of NOreaches 100% for temperatures higher than 570°C. Incomparison with the results of the two other mixtures,the increase of the conversions of CO, C3H6 and NOwith the temperature is more slowly, in particular theC3H6 conversion rate. Regarding the CO and NO con-version, the simulations agree with the experimental val-ues. However, large deviations exist between the pre-dicted C3H6 conversion and the experimental data. Thisdeviations can be explained by the fact that in the richregime a wider variety of surface species. e. g. partialoxidation products of C3H6, resides on the catalytic sur-face, which can reduce the oxygen coverage and lead todifferent reaction paths. In the reaction mechanism usedin this study only a limited number of possible surfacespecies are included. Therefore further reactions andsurface species have to be included in order to improvethe prediction of the C3H6 conversion at richer mixtures.
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Figure 1. Conversion of CO, C3H6 and NO at lean conditions withincreasing temperature; comparison of experimental and calculateddata.
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Figure 2. Conversion of CO, C3H6 and NO at nearly stoichometricconditions with increasing temperature; comparison of experimentaland calculated data.
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Figure 3. Conversion of CO, C3H6 and NO at rich conditions withincreasing temperature; comparison of experimental and calculateddata.
TRANSPORT AND CHEMISTRY WITHIN A SINGLECHANNEL
In Fig. 4, the mass fractions of C3H6, CO, CO2 andNO for the lean mixture (see Table 2 ) at 407°C withinthe channel are shown. The input data are the same asin Table 3. The mass fraction profiles show that most ofthe C3H6 is converted within the first centimeter. In thisaxial range CO is nearly completely converted. The NOconversion is limited to the first centimeter and vanishesbehind.
This behavior can be explained by means of the sur-face coverages. The calculated coverages of the mostrelevant surface species on platinum and rhodium areshown as a function of the axial position along the chan-nel in Fig. 5 and 6, respectively. The coverages aredefined in respect of the whole catalytic area, consistingof rhodium and platinum.
In Fig. 5 it is revealed that at the axial distance of1.1 cm the surface coverage state varies strongly,because of the decreasing CO concentration in the gasphase, from a mainly CO(s) covered state to an O(s)covered state. This variation is initiated from thedecreasing CO/O2 ratio in the gas phase. During thistransition the number of free platinum sites, Pt(s),increases, which allows more NO to be adsorbed anddissociated. When the surface reaches the O(s) coveredstate the number of free platinum sites is decreased andthe equilibrium of NO dissociation is shifted to NO(s),resulting in a vanishing NO conversion.
The rhodium surface goes from a N(s) covered stateto an O(s) covered state. This transition phenomenoncan be seen in Fig. 6. The O(s) covered surface state onrhodium prevents also NO conversion. Below 1 cm thesurface is mainly covered with N(s) and active for NOconversion.
With increasing reaction temperature the transitionpoint moves toward the channel entrance, whichreduces the area that is active for NO conversion. InFig. 3 the resulting decrease of NO conversion withincreasing temperature can be seen.
Figure 4. Flow fields of the mass fraction of the species C2H6, CO, CO2
and NO at 407°C. Different scales are used in axial and radial directionfor visual clarity; lean mixture.
Figure 5. Surface coverage at 407°C on Pt as a function of the axialposition; lean mixture, (s) denotes surface species.
Figure 6. Surface coverage at 407°C on Rh as a function of the axialposition; lean mixture, (s) denotes surface species.
λ-WINDOW
A typical feature of the three-way converter is the“λ-window” behavior, that means, C3H6, CO and NO aresimultaniously converted with high efficiency in a narrowrange arround the stochiometric air/fuel ratio. Fig. 7 pre-sents the predicted conversions for the catalytic con-verter at 500°C for different gas mixtures. This choosentemperature is a typical catalyst inlet temperature forpartial load /17/. The experimental data were aleadypresented in the Fig. 1, 2 and 3. Our simulation well pre-dicts the “λ-window” in the lean region. For the rich re-gime, as already shown in Fig. 3, the CO conversion isalso well predicted, while there are major deficiencies forC3H6 conversion, as discussed above.
Figure 7. λ-window at 500°C; comparison of experimental andcalculated data.
CONCLUSION
A two dimensional flow field description, including adetailed reaction mechanism for the conversion of CO,C3H6, O2 and NO has been used to simulate the exhaustgas treatment in a platinum/rhodium coated single chan-nel of a typical three-way catalytic converter. The simu-lation is based on the CFD code FLUENT and thechemistry module DETCHEM, which were coupled forthe simulations performed.
The computational tool was used to predict conver-sion rates at lean, nearly stoichiometric and rich condi-tions as function of temperature. The calculated data arecompared with experimentally measured data and agood agreement could be achieved. Only for rich condi-tions the predicition of C3H6 conversion is too high. Fur-thermore, the interaction of transport and kinetics withina single channel were revealed by the simulation.
Numerical simulation of the emission reduction insidea monolithic three-way catalyst offers an efficient methodto investigate converter performance. As a first step onthe way to a complete model, a reliable multi-step reac-tion mechanism has to be developed. This mechanismwill finally allow simulations to predict emissions over abroad range of conditions. In this work, a surface reac-tion mechanism consisting of 56 reactions among 31species was used and validated by a comparison withexperimental data.
OUTLOOK
The simulation presented in this paper is carried outfor a single channel in a monolithic catalytic converter.In the ongoing research, several extensions will be madefor a more accurate model for the real catalytic con-verter. The next step in using numerical simulation is toexpand the model from a single channel model to thetotal monolith. A simulation of the total monolith usingFLUENT requires too much computer time and memory.Therefore, a boundary layer model will be used as analternate method to simulate the behaviour of the singlechannel. This future work will also take the thermal con-ductivity of the catalyst into account for the calculation ofthe heat distribution of the whole monolithic converter.The final goal is the simulation of the behaviour of anautomotive catalytic converter during a whole test cycleusing models that are based on the real physical andchemical processes. The test cycle simulation willinclude the light-off behaviour of the converter.
In order to improve the prediction quality for richmixtures, further reactions have to be included in thereaction mechanism.
ACKNOWLEDGMENTS
The authors like to thank Sven Kureti and OliverGörke, University of Karlsruhe, for their experimentalmeasurements of the converter performance.
/2/ T. Kirchner and G. Eigenberger, “On the dynamicbehavior of automotive catalysts”; Catal. Today, 28, 3(1997).
/3/ G.P. Ansell, P.S. Bennett, J.P. Cox, J.C. Frost,P.G. Gray, A.-M. Jones, R.R. Rajaram, A.P. Walker,M. Litorell and G. Smedler, "The development of amodel capable of prediciting diesel lean NOx catalystperformance under transient conditions"; Appl. Catal. B,10, 183 (1996).
/4/ A.L. Boehman, "Numerical Modeling of NO ReductionOver Cu-ZSM-5 Under Lean Conditions"; SAE 970752.
/5/ C.N. Montreuil, S.C. Williams and A.A. Adamczyk,"Modeling Current Generation Catalytic Converters:Laboratory, Experiments and Kinetic ParameterOptimization-Steady State Kinetics" SAE 920096.
/6/ S.-J. Jeong and W.-S. Kim, “A Numerical Approach toInvestigate Transient Thermal and ConversionCharacteristics of Automotive Catalytic Converter”;SAE 980881.
/7/ FLUENT 4.4, Fluent Inc., Lebanon, NH (1997).
/8/ DETCHEM, Version 1.2, O. Deutschmann, IWR,University of Heidelberg, Germany (1998).
/9/ O. Deutschmann and L.D. Schmidt; “Modeling thePartial Oxidation of Methane in a Short-Contact-TimeReaction“; AIChE Journal, 44 (11), 2465 (1998).
/10/ M Baerns, H. Hofmann and A. Renken, "ChemischeReaktionstechnik"; Georg Thieme Verlag Stuttgart,New York, Vol. 1 (1992).
/11/ P. Deuflhard, E. Hairer and J. Zugk, “One-Step andExtrapolation Methods for Differential-AlgebraicSystems”; Num. Math., 51, 501 (1987).
/12/ E. Rogermond, N. Essayem, R. Frety, V. Perrichon,M. Primet, M. Chevrier, C. Gouthier and F. Mathis,“Characterization of Model Three-Way Catalysts”;J. Catal., 186, 414 (1999).
/13/ O. Deutschmann, R. Schmidt, F. Behrendt andJ. Warnatz, “Numerical Modeling of Catlytic Ignition”;Twenty-Sixth Symposium (International) onCombustion, The Combustion Institute, 1747, Pittsburgh(1996).
/14/ D.K. Zerkle, M.D. Allendorf, M. Wolf andO. Deutschmann, J. Catal. (submitted).
and CO-NO Reactions over Single Crystals andSupported Rhodium Catalysts”; J. Catal., 100, 360(1986).
/16/ E.I. Altman and R.J. Gorte, “A Temperature-Programmed Desorption Study of NO on Rh ParticlesSupported on α-Al2O3{0001}”, J. Catal., 113, 185 (1988).
/17/ E. S. J. Lox and B. H. Engler in G. Ertl, H. Knoetzingerand J. Weitkamp (Eds.), "Handbook of HeterogeneousCatalysis"; VCH Verlagsgesellschaft Weinheim, Vol. 4,1586 (1997).
NOTATION
cp,i specific heat at constant pressure of species id channel (tube) diameterDi, m diffusion coefficient of species i in the mixture,F ratio between catalytic active surface area and
geometric surface areahi enthalpy of species iKs number of elementary surface reactions (including
adsorption and desorption)Mi molar mass of the species iNg number of gas phase speciesNs number of adsorbed speciesp static pressureRi net rate of production of species i due to chemical
adsorption and desorption processes/ chemicalsource term
ii Ms�
surface mass fluxes
T temperaturet timeu axial velocityv radial velocityYi mass fraction of species iz axial spatial coordinate
irj diffusive flux
vst Stefan velocityΓ surface site densityεik parameter for coverage dependent activation
energyΘi surface coverages (fraction of surface sites
covered by species i)λox lambda value
thermal conductivity of the mixtureµ viscosityµik parameter for coverage dependent reaction orderνik,νjk' stoichiometric coefficientsρ densityXi concentration of an adsorbed speciesτ number of occupied adsorption sites of species i
