High-pressure catalytic combustion of methane over ...cfg.web.psi.ch/acnf_2004.pdf · 218 M. Reinke et al. / Combustion and Flame 136 (2004) 217–240 Nomenclature b Channel half

f

entallyessible,ies andtivity ands-phase)entaryd numericalgeneouscatalyticreaction

en in themethane

eous andpracticalvalidatedhemes ca-ell as ininedmeasured

Combustion and Flame 136 (2004) 217–240www.elsevier.com/locate/jnlabr/cn

High-pressure catalytic combustion of methaneover platinum: In situ experiments and detailed

numerical predictions

Michael Reinke, John Mantzaras,∗ Rolf Schaeren, Rolf Bombach,Andreas Inauen, and Sabine Schenker

Paul Scherrer Institute, Combustion Research, CH-5232 Villigen PSI, Switzerland

Received 20 June 2003; received in revised form 24 September 2003; accepted 1 October 2003

Abstract

The catalytic combustion of fuel-lean methane/air premixtures over platinum was investigated experimand numerically in the pressure range 4 to 16 bar. Experiments were performed in an optically acclaminar channel-flow catalytic reactor. In situ, spatially resolved Raman measurements of major spectemperature over the reactor boundary layer were used to assess the heterogeneous (catalytic) reacplanar laser-induced fluorescence (LIF) of the OH radical confirmed the absence of homogeneous (gaignition. Numerical predictions were carried out with a two-dimensional elliptic code that included elemheterogeneous and homogeneous chemical reaction schemes. Comparisons between measurements anpredictions have led to the assessment of the high-pressure validity of two different elementary heterochemical reaction schemes for the complete oxidation of methane over platinum. It was shown that thereactivity increased with increasing pressure and that crucial in the performance of the heterogeneousschemes was the capture of the decrease in surface free-site availability with increasing pressure. Evabsence of homogeneous ignition, the contribution of the gaseous reaction pathway to the conversion ofcould not be ignored at high pressures. The delineation of the regimes of significance for both heterogenhomogeneous pathways has exemplified the importance of the preignition gaseous chemistry in manyhigh-pressure catalytic combustion systems. Sensitivity and reaction flux analyses were carried out on aelementary heterogeneous reaction scheme and led to the construction of reduced catalytic reaction scpable of reproducing accurately the catalytic methane conversion in the channel-flow configuration as wa surface perfectly stirred reactor (SPSR) and, when coupled to a homogeneous reaction scheme, the combheterogeneous and homogeneous methane conversions. A global catalytic step could not reproduce thecatalytic reactivity over the entire pressure range 4 to 16 bar. 2003 The Combustion Institute. Published by Elsevier Inc. All rights reserved.

Keywords:High-pressure methane catalytic combustion; In situ Raman measurements; Catalytic reactivity; Reducedheterogeneous reaction schemes

ofin-m

ant

* Corresponding author.E-mail address:[email protected]

(J. Mantzaras).

0010-2180/$ – see front matter 2003 The Combustion Institutdoi:10.1016/j.combustflame.2003.10.003

1. Introduction

The complete and partial catalytic oxidationlower hydrocarbons over noble metals is of primeterest in many industrial applications ranging fropower generation and microreactors to pollut

e. Published by Elsevier Inc. All rights reserved.

http://www.elsevier.com/locate/jnlabr/cnf

218 M. Reinke et al. / Combustion and Flame 136 (2004) 217–240

-

s

Nomenclature

b Channel half height, Fig. 1B Preexponential of global catalytic reac-

tion, Eqs. (13) and (16)cp Specific heat at constant pressureDas Surface Damköhler number, Eq. (20)Dkm Mixture-average species diffusion coef-

ficient, Eq. (7)Ea Effective activation energy, Eqs. (13)

and (16)F,G,H Functions defined in Eqs. (21) and (23)h,h0

k Total enthalpy, chemical enthalpy of thekth gaseous species

Ih,F Fractional heterogeneous fuel conver-sion, Eq. (17)

k Reaction rate coefficient, Eq. (11)Kg Total number of gaseous species, Eq. (5)Ms Total number of surface species, Eq. (6)mF (x) Local fuel mass flow rate per unit

channel depth(z)mh,F (x) Integrated heterogeneous fuel conver-

sion per unit depth(z)L Channel length, Fig. 1Le Lewis number of the fuel (thermal over

species diffusivity)m Sum of surface reactants’ stoichiometric

coefficients, Eq. (11)n Pressure exponent of global catalytic

reaction, Eqs. (13) and (16)P Function defined in Eq. (21)p PressurePr Prandtl numberR Universal gas constantSV Surface-to-volume ratio, Eq. (14)sk Species heterogeneous molar production

rates, Eq. (6)T,T0 Temperature, reference temperature in

Eq. (8)u,UIN Local streamwise velocity, inlet stream-

wise velocityv Transverse velocity

�Vk Species diffusion velocity vector, Eq. (7)wk Gas-phase species molar production

rate, Eq. (5)W Channel width, Fig. 1Wk, �W Gas-phase species molecular weight,

average molecular weightXk Gas-phase species mole fractionYk Gas-phase species mass fractionYF Normalized fuel mass fraction defined

after Eq. (19)x, y, z Streamwise, transverse, and lateral phys

ical coordinates, Fig. 1

Greek symbols

αth Thermal diffusivity, Eq. (20)γk Sticking coefficient, Eq. (11)Γ Surface site density, Eq. (11)ζ Nondimensional streamwise distance,

Eq. (18)θT ,k Species thermal diffusion ratio, Eq. (7)θm Surface species coverage, Eq. (6)λ Thermal conductivityµ Viscosityρ Densityσm Surface species site occupancy, Eq. (6)τ Reactor residence time, Eq. (14)

Subscripts

ads Adsorption, desorptionF Fuelh HeterogeneousIN Inletk,m Indices for gas-phase and surface specieW Wallx, y Streamwise and transverse components

Superscripts

′ Differentiation with respect to the nor-malized transverse coordinate

there-andthe

on

eousom-m-ent

m-m-rald ofet-

n-ctorticstheen-

abatement and chemical synthesis. In particular,complete catalytic oxidation of natural gas hasceived increased attention in decentralized heatpower systems and in stationary gas turbines;latter employ the catalytically stabilized combusti(CST) technology [1,2], whereby ultralow NOx emis-sions can be achieved in a sequential heterogen(catalytic) and homogeneous (gas phase) hybrid cbustion concept. The advancement of catalytic cobustion in power systems requires the developm

of catalysts with increased activity toward the coplete oxidation of methane in fuel-lean air-fed cobustion (methane is the main constituent of natugas), the understanding of the heterogeneous anthe low-temperature homogeneous chemical kinics of methane, and the availability of multidimesional numerical codes that can be used for readesign. Moreover, the hetero/homogeneous kineand their interactions should be investigated underhigh-pressure operating conditions of the aforem

M. Reinke et al. / Combustion and Flame 136 (2004) 217–240 219

ntCSTet-rted

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resssedthethespti-ichen-ay

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tioned combustion systems. Validation of differeelementary homogeneous reaction schemes inover platinum and investigation of the underlying hero/homogeneous chemistry coupling were reporecently in Reinke et al. [3] for CH4/air mixturesat pressures up to 10 bar and in Appel et al.for H2/air mixtures at atmospheric pressure; thassessed homogeneous ignition in a channel-flowalytic reactor using planar laser-induced fluoresce(LIF) of the OH radical and—in conjunction witdetailed numerical predictions—they clearly demostrated substantial differences in the performancevarious elementary gaseous reaction schemes.

Existing elementary heterogeneous chemical retion schemes for the complete [5–7] and partial [6–oxidation of methane over platinum (the catalystinterest in the present study) have relied primaon ultra high vacuum (UHV) surface science danotwithstanding recent advances of in situ surfascience diagnostics [10]. The extension of the deoped reaction schemes to realistic pressures andnical catalysts has necessitated appropriate kinrate modifications in order to bridge the well-know“pressure and materials gap.” These modificatiwere aided by measurements of catalytic ignitiocatalytic extinction, steady fuel conversion, and prouct selectivity in two basic reactor configurationthe nearly isothermal, low-temperature (T � 600◦C),gradientless tubular or annular flow reactor [11,1(fed with highly diluted fuel/oxidizer mixtures inorder to maintain a minimal temperature rise) athe stagnation flow reactor [5,7,13,14]. Although textraction of kinetic data is straightforward in thformer configuration, the nearly isothermal opetion poses inherent limitations in the descriptionprocesses that can be—for certain fuels—thermcontrolled (for example, catalytic ignition). Stagntion flow configurations, on the other hand, have pvided a wealth of data on catalytic ignition/extinctiosteady fuel conversion and product selectivity uder realistic temperatures and mixture compositioThe measurements, in conjunction with numeripredictions from well-established one-dimensiocodes [13,14], have aided considerably the refinemof surface reaction mechanisms. Most experimeinvolved mainly measurements of global quantit(total fuel conversion, surface temperature, etc.)were, therefore, better suited for the descriptionabrupt ignition/extinction transient phenomena ratthan of steady processes where local experimevariations in the gas and/or on the surface couldtentially affect the data interpretation.

In our recent atmospheric-pressure catalytic cobustion studies of H2/air over Pt [4], we introducedthe methodology of in situ spatially resolved Rammeasurements of gas-phase species concentratio

the boundary layer formed over a catalyst, as arect way to assess the catalytic reactivity—as was the gaseous reactivity when combined withLIF—under steady operating conditions. Othersearchers have further adopted similar approacSidwell et al. [15] studied the catalytic combustionCH4/air mixtures over Pd-substituted hexaluminaat atmospheric pressure with spatially resolvedsampling over a stagnation-flow boundary layer. Tvalidity of various heterogeneous reaction schemfor the total oxidation of methane at high pressurelevant to practical systems has not been addrein the literature. In the present study we applyaforesaid established methodology to investigatecatalytic combustion of CH4/air over Pt at pressureup to 16 bar. Experiments were performed in an ocally accessible catalytic channel-flow reactor, whwas operated at sufficiently low temperatures thatsured kinetically controlled methane conversion awfrom the mass-transport limit. Fuel-lean CH4/air pre-mixtures (ϕ = 0.35 to 0.40) were investigated under laminar flow conditions, with surface tempeatures and pressures in the ranges 780 K� T �1250 K and 4 bar� p � 16 bar, respectively. Onedimensional Raman measurements (across the cnel transverse distance) provided the boundary laprofiles of major species and temperature, planarof the OH radical along the streamwise plane of symetry confirmed the absence of homogeneous ition and the ensuing formation of a flame, and, finathermocouples embedded beneath the catalyst yiethe surface temperature distribution. Computatiwere carried out with an elliptic two-dimensionCFD code that included elementary heterogeneand homogeneous chemical reaction schemesdetailed transport. Two recent heterogeneous rtion schemes for the total oxidation of methane oPt [5,7] were investigated, with the main objectivof validating their applicability under high pressurand, subsequently, based on the validated elemtary heterogeneous scheme(s), of developing reduand—if possible—one-step surface reaction mecnisms. Particular objectives were to investigate thefect of pressure on catalytic reactivity, to elucidateinfluence of gaseous chemistry during high-presscatalytic combustion, and to address issues of hpressure reactor performance in light of recent alytical studies that have identified the controlling prameters in channel-flow CST [16,17].

First the test rig, the Raman/LIF measuring teniques, and the numerical model are presented.contribution of the homogeneous pathway to the cversion of methane at high pressures is then eorated, followed by comparisons between measments and numerical predictions that result inassessment of the validity of the tested schemes.


gh-dis-

er-ad tre-on

ticurewasm-ch

eac-0-heas

ednwswithotw-of

osi-

tes,ally,

asce-

redm

eathep

un-heirtheatus-isas

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(upsi-. 1).edes.uresotsotterac-eno ank.ssec-c-

h-

okshanive

ofairsta-

mt 40-ni-tordelet

-m-ss-bar.

Fig. 1. Schematic of the catalytic reactor and the hipressure vessel: (a) side view and (b) cross section. Alltances are in mm. The enclosureL × W × 2b defines thereactor volume.

sitivity and reaction flux analyses elucidate the diffences among the heterogeneous schemes and lethe development of reduced and global catalyticaction mechanisms. Finally, the effect of pressurecatalytic reactor performance is addressed.

2. Experimental

2.1. Reactor configuration and test conditions

The test rig consisted of a channel-flow catalyreactor, which formed a liner inside a high-pressstainless-steel vessel (see Fig. 1). The reactorsimilar to that used in earlier studies [3,4] and coprised two horizontal Si[SiC] ceramic plates, whiwere 300 mm long(L), 110 mm wide, 9 mm thickand placed 7 mm apart(2b). The ceramic plates werchamfered along their 300-mm sides in order tocommodate two 3-mm thick, 12-mm high, and 30mm long quartz glass windows, which formed treactor sidewalls. The lateral window separation w104 mm(W) and the reactor volume was delineatby the 300× 104× 7-mm3 enclosure (see Fig. 1). Icontrast to previous studies [4], the quartz windowere spring-pressed against the ceramic plates (an intervening 1-mm-thick soft ceramic gasket) non their center but on their four edges, thus alloing unobstructed optical access from both sidesthe reactor. Four rectangular ceramic spacers, p

o

tioned at the chamfered corners of the Si[SiC] plamaintained a constant 7-mm plate separation. Finthe entire ceramic-plate and window assembly wmounted on an inconel-steel frame with the aid oframic support rims.

The catalyst surface temperature was monitowith 12 thermocouples on each plate (S type, 1 mthick), positioned along thex–y plane of symmetry.The thermocouples were countersunk 0.9 mm benthe catalytically active surfaces through 8.1-mm-deand 1.2-mm in diameter holes eroded from thecoated ceramic surfaces and were affixed inside tholes with alumina cement. In order to achievedesired kinetically controlled fuel conversion andthe same time to sustain steady catalytic combtion at the relatively low laminar flow rates of thwork, a combined cooling/heating arrangement wadopted: the 110× 9-mm2 entry sides of the ceramiplates were contacted to a water-cooled sectionthe inconel-steel frame, whereas the rear 200 mmthe plates was heated with two adjustable-powerto 2.5 kW) resistive heating coils, which were potioned 15 mm above the thermocouples (see FigA 50-mm-thick fiber ceramic insulation was placon top of the heating coils to minimize the heat lossWith the above arrangement, the surface temperatcould be controlled to sufficiently low levels that nonly allowed for finite-rate surface chemistry but alinhibited the onset of homogeneous ignition; the lawould have complicated the present catalytic retivity studies. The combustion products were drivthrough an insulated cylindrical exhaust section twater-cooled exit segment of the high-pressure taA 3-mm-thick and 50-mm in diameter quartz glawindow positioned along the axis of the exhaust stion provided an additional (streamwise) optical acess.

An oil-free compressor provided dry air and higpressure bottles supplied technical CH4 (>99.5%).Both gases were regulated with two calibrated Bromass-flow controllers, having an accuracy better t0.5%. The air was preheated by a 3-kW resistheater and mixed with methane 25 cm upstreamthe reactor (see Fig. 1a). A high degree of fuel/premixedness was achieved with two sequentialtic Sulzer mixers (type SMV). After mixing, the flowwas straightened in a 40-mm-long packing of 2-min diameter ceramic spheres and in a subsequenmm-long inert ceramic honeycomb, leading to uform velocity and temperature profiles at the reacentry. An additional thermocouple, positioned insione channel of the honeycomb, monitored the intemperature of the mixture.

The high-pressure vessel consisted of a 1.8long and 0.28-m inside diameter cylindrical stainlesteel structure, rated to a maximum pressure of 60


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forealy-withceace

u-

inledzheioneamer-

tankthe

ns-romeng.

The vessel was equipped with two high-pressquartz glass windows (350 mm long, 35 mm thicand 50 mm high, running parallel to the reactor swindows) that provided optical access from both sidof the reactor (see Fig. 1b). In addition, a counterflstreamwise optical access (used for the LIF expiments) was achieved through the reactor exhawindow and a 30-mm-thick and 30-mm in diamehigh-pressure quartz glass window positioned atcenter of the rear flange of the vessel (see Fig.The power supply and thermocouple lines wererected into the reactor via high-pressure feedthrouon four dedicated tank flanges. The tank pressuremeasured with a Fuji-Electric pressure transmiand was regulated through a PID-controlled pnmatic exhaust gas throttle. During the experimena continuous flow of secondary air through a distribtion ring cooled the tank walls and flushed the volubetween the reactor and the high-pressure tank fany undesirable combustion products.

The laminar experimental conditions are givenTable 1 and span the pressure range 4 bar� p �16 bar. Atp < 4 bar the recorded methane Ramsignal was too weak; the same methane signanoise considerations dictated the minimum fuel-to-equivalence ratio (ϕ = 0.35). Safety considerationdetermined the higher equivalence ratio(ϕ = 0.40):largerϕ resulted in high surface temperatures thatdangered long-term catalyst stability. The Reynonumbers of Table 1 were based on the uniformlet properties and the channel hydraulic diame(= 13.1 mm) and were kept below 2000, even thouthe strong flow laminarization induced by the hetransfer from the hot catalytic plates guaranteed lainar flow conditions at considerably higher incomiReynolds numbers [18]. Case 16 was the only oneTable 1 with homogeneous ignition and flame formtion and was included to facilitate the ensuing discsion on catalytic reactivity.

2.2. Catalyst preparation

The inner surfaces of the Si[SiC] plates wecoated with Pt using plasma vapor deposition (PVa 1.5-µm-thick nonporous Al2O3 layer was first de-posited on the ceramic surface, followed by a 2.2-µthick Pt layer. The very thick Pt coating on a noporous structure closely resembled a polycrystalPt surface, and this was verified with independsurface area and surface composition measuremThe surface area was measured with BET in cerawafers 1 mm thick and 75 mm in diameter, coatwith exactly the same PVD procedure as the catalplates of the reactor; fresh samples and samplesposed to the combustion environment of this stuwere analyzed. The total and active surface areas w

Fig. 2. Schematic of the OH planar laser-induced fluorcence (LIF) and Raman setup. All focal lengths are in m

measured with Kr physisorption and CO chemisotion, respectively. Tests with krypton were necessas the nonporous nature of the catalyst resultea very small surface area (practically equal togeometrical area) not measurable with standard2physisorption. The BET measurements confirmedabsence of porous surface structure and, moreoshowed that the total and active surface areas wersame, indicating a surface covered completely wPt. The latter was also verified with independentray photoelectron spectroscopy (XPS) surface coposition analyses of the reactor catalytic plates beand after the combustion experiments; the XPS anses have shown that the surface was coveredPt and that Al or Si did not diffuse on the surfaeven after extended reactor operation. A Pt surfsite density of 2.7 × 10−9 mol/cm2 (the value ofpolycrystalline Pt [5]) was, therefore, used in the nmerical analysis.

2.3. Laser diagnostics

The Raman and planar LIF setup is depictedFig. 2. In the Raman experiment, a frequency-doubNd:YAG pulsed laser (Quantel YG781C20, 20-Hrepetition rate) provided the excitation source. Tpulse energy and duration of the 532-nm radiatwas 180 mJ and 14 ns, respectively. The laser bwas first expanded to a diameter of 2 cm by a sphical lens telescope and then focused through theand reactor side windows into a vertical line insidereactor (∼0.3 mm thick) by anf = 150-mm cylindri-cal lens. The focal line spanned the entire 7-mm traverse channel separation and was 15 mm offset fthex–y symmetry plane (z= 15 mm) to increase thcollection angle and minimize thermal beam steeri


Table 1Experimental conditionsa

Case p (bar) ϕ UIN (m/s) TIN (K) ReIN

1 4 0.40 2.05 624 19262 4 0.35 2.02 633 18543 6 0.40 0.51 587 7964 6 0.36 0.51 590 7905 7 0.40 1.16 624 19076 7 0.35 1.15 627 18707 8 0.36 0.38 587 8008 10 0.40 0.81 621 19159 10 0.35 0.80 627 1869

10 12 0.40 0.66 612 193611 12 0.35 0.68 627 191012 14 0.40 0.55 604 192113 14 0.35 0.55 606 190814 16 0.35 0.45 586 189815 16 0.35 0.46 592 188716 16 0.36 0.44 636 1616

a Pressure, equivalence ratio, inlet velocity, temperature, and Reynolds number.

toren-neslsoat-act

re-

t tophede-l-gthdi-nels-erethe

cat-testi-

roveon

slitns-

nedhetray

id-anich

zeiousager

iedent

for

em-s-ns,

in-ere

m-ly-ofre

thedis-re-micss-

1],andis-asfewthe

Given the large cross-flow aspect ratio of the reac(∼15:1), the combustion processes were two dimsional with no lateral dependence (apart from zoextending up to 15 mm from each window, as adiscussed in previous works [4]). Therefore, the leral offset of the Raman measurements did not impthe forthcoming comparisons with 2-D numerical pdictions. Two 76-mm-diameter lenses (f = 300 mm)collected the scattered light, at a 50◦ angle with re-spect to the sending optical path, and focused ithe entrance slit of a 25-cm imaging spectrogra(Chromex 250i). The dispersed light was recordon an intensified CCD camera (LaVision FlamStar 2F, 576× 384 pixels). The 576- and 384-pixelong CCD dimensions corresponded to wavelenand transverse distance, respectively; in the lattermension, only 250 pixels spanned the 7-mm changap. A holographic notch filter (Kaiser Optical Sytems, HNPF) and an OG-550 colored glass filter wplaced before the spectrograph slit to attenuateintense Rayleigh signal and the stray laser light stered from the mechanical components of therig. As the flow conditions were steady and lamnar, an average of 2000 images was used to impthe signal-to-noise ratio. The spectral dispersionthe CCD camera ranged from 1250 to 5000 cm−1,allowing observation of all major species (O2, N2,CH4, H2O, and CO2); the Raman shift ranged from1388 cm−1 (CO2) to 3652 cm−1 (H2O). To furtherincrease the signal-to-noise ratio, the spectrographwas opened to 0.4 mm; an almost top-hat slit trafer function with a width of about 60 to 80 cm−1

(depending on spectral position) was thus attaithat still allowed for ample spectral separation of tRaman-shifted species lines and the background s

light on the CCD array. The signal-to-noise conserations should not be understated in 1-D Ramcombustion measurements of hydrocarbons, whrequire visible light excitation sources to minimifluorescence interferences. In contrast to our prevatmospheric-pressure H2/air CST studies [4] whereUV excimer laser source provided a much stronRaman signal (owing to itsω4 dependence, withωthe laser light frequency), the present work relheavily on the effect of pressure to achieve sufficisignals: pressures below 4 bar were not amenable1-D Raman measurements of lean (ϕ � 0.4) CH4/airmixtures.

The Raman data were referenced to a room tperature distribution of nitrogen inside the combution channel. The effective Raman cross sectiowhich included transmission efficiencies (i.e., wdows, lenses, filter, spectrometer, and camera), wevaluated by recording the signals of pure CH4, air,and completely burnt exhaust gases of known coposition. The background signal was fitted to a ponomial curve to account for the spectral variationthe stray light. An initial guess of the temperatudistribution inside the channel was derived fromnitrogen signal assuming ideal gas behavior. Thistribution was further used to correct all temperatudependent Raman cross sections. For the diatospecies, theoretical harmonic oscillator Raman crosection variations have been used [19]; for CH4 andH2O the data from Steiner [20] and Eisenberg [2respectively, were employed. The corrected Ramcross sections provided an updated temperaturetribution; a converged temperature distribution wachieved by repeating the entire process for atimes. The Raman signal of methane, which was


de-tod;oorwestun-id-entsnd

icaltics,calRa-

63nur-tio.hean-atblerdLIF

ereRa-LIFRa-that

a-edto ale-

rec-in-othre-tD

ails3,4,

s

sfol-

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-

er-

ate

all

deficient reactant, was of prime interest for thetermination of the catalytic reactivity. In additionCH4, the H2O and O2 Raman lines were evaluatethe CO2 line suffered from low signal-to-noise ratigiven its low concentration (the lowest of all majspecies), its moderate Raman cross section (the loof all species having more than two atoms), and itsfavorable spectral position within a region of conserable background radiation. Raman measuremwere acquired at streamwise intervals of 10 mm (ain some cases 20 mm) by traversing axially an opttable that supported the sending and collecting opincluding the spectrograph (see Fig. 2). The optiarrangement limited the streamwise extent of theman measurements to 15.5 mm� x � 163.5 mm. The250-pixel-long transverse distance was binned topixels, providing ay resolution of 0.11 mm. Ramadata points closer than 0.6 mm to both catalyst sfaces were discarded due to low signal-to-noise ra

For the OH-LIF tests, the second harmonic of tNd:YAG laser pumped a tunable dye laser (Qutel TDL50) with a frequency-doubled radiation285.09 nm and a pulse duration of 10 ns. A traversamirror directed the 532-nm radiation either towathe Raman setup or toward the dye laser and thesetup (Fig. 2). As the experimental conditions whsteady and laminar, simultaneous acquisition ofman and OH-LIF data was not necessary; thewas recorded at regular intervals in-between theman data acquisition. The OH-LIF tests assuredthere was no homogeneous ignition and flame formtion, events that were increasingly likely at elevatpressures [3]. The laser beam was transformed invertical laser sheet by a cylindrical/spherical lens tescope and entered the reactor in a counterflow dition through the tank and reactor-exhaust quartz wdows (see Figs. 1a and 2). The fluorescence of bOH (1–1) and (0–0) transitions at 308 and 314 nm,spectively, was collected at 90◦ through the second seof tank and reactor side windows with another CCcamera, identical to that of the Raman setup. Detof the OH setup have been provided elsewhere [22].

3. Numerical model

3.1. Governing equations and boundary condition

An elliptic, two-dimensional, steady model waused and numerical solution was obtained for thelowing governing equations.

Continuity equation:

(1)∂(ρu) + ∂(ρv) = 0.
∂x ∂y
Momentum equations:

∂(ρuu)

∂x+ ∂(ρvu)

∂y+ ∂p

∂x

− ∂

∂x

[2µ

∂u

∂x− 2

3µ

(∂u

∂x+ ∂v

∂y

)]

(2)− ∂

∂y

[µ

(∂u

∂y+ ∂v

∂x

)]= 0,

∂(ρuv)

∂x+ ∂(ρvv)

∂y+ ∂p

∂y− ∂

∂x

[µ

(∂v

∂x+ ∂u

∂y

)]

(3)− ∂

∂y

[2µ

∂v

∂y− 2

3µ

(∂u

∂x+ ∂v

∂y

)]= 0.

Energy equation:

∂(ρuh)

∂x+ ∂(ρvh)

∂y+ ∂

∂x

(ρ

Kg∑k=1

YkhkVk,x − λ∂T

∂x

)

(4)+ ∂

∂y

(ρ

Kg∑k=1

YkhkVk,y − λ∂T

∂y

)= 0.

Gas-phase species equations:

∂(ρuYk)

∂x+ ∂(ρvYk)

∂y+ ∂

∂x(ρYkVk,x)

+ ∂

∂y(ρYkVk,y)− wkWk = 0,

(5)k = 1,2, . . . ,Kg.

Surface species coverage equations:

(6)∂θm

∂t= σm

sm

Γ− θm

ΓΓ , m= 1,2, . . . ,Ms.

It is understood that only the steady-state solutiof Eqs. (6) are of interest in the present study andgravity is not important for the high Reynolds numbers of Table 1.

The species diffusion velocities�Vk were deter-mined using the mixture average diffusion plus thmal diffusion for the light species [23]:

�Vk = −[Dkm/Xk]∇Xk(7)+ [

DkmθT ,k/(XkT )]∇T .

Finally, the ideal gas and caloric equations of stwere

(8)p = ρRT/W and hk = h0k(T0)+

T∫T0

cp,k dT ,

respectively. The boundary conditions at the gas-winterfaces (y = 0 andy = 2b), were

(ρYkVk,y)y=0 =Wk(sk)y=0,

(9)(ρYkVk,y)y=2b =Wk(sk)y=2b


-up-m-STperaryo-e-ud-m-m-ofp-e inlateuta-

llsns

tand

liedas

inged

eo-

or-

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ic-ch-n,

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mes

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ort-aseverthethe

wasre-igni-

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ureentusnlyseis

cu-(i.e.,igni-es:h-t

and

T (x, y = 0)= TW,L(x),

(10)T (x, y = 2b)= TW,U (x).

TW,L(x) andTW,U (x) were the thermocouple-measured temperature distributions of the lower andper walls, respectively. Equations (10) were an iprovement to previous homogeneous ignition Cworks [3,4] that used the average (between upand lower walls) temperature profile as a boundcondition for simulations over half the channel dmain (0� y � b). The earlier approach was adquate in the aforesaid homogeneous ignition sties, which were characterized by high surface teperatures with random upper/lower wall surface teperature differences—at any given axial position—±8 K. In the present study, however, the lower oerating temperatures and the absence of a flamthe reactor resulted in systematic temperature pdifferences as large as 60 K, necessitating comptions over the entire channel domain (0� y � 2b).No-slip boundary conditions were applied at the wafor both velocity components. The inlet conditiowere uniform profiles for the temperatureTIN (mea-sured), the axial velocityUIN (deduced from the inletemperature and the measured mass-flow rates),the species mass fractions. Finally,v = 0 and zero-Neumann conditions for all other scalars were appat the end of the computational domain, which wtaken atx = 180 mm.

The governing equations were discretized usa finite volume approach and solution was obtainiteratively with a SIMPLER [24] method for thpressure-velocity field; details on the solution algrithm have been provided elsewhere [4,25]. Anthogonal staggered grid of 350× 120 points (inx andy, respectively) with finerx spacing toward the entrance andy spacing toward the wall was sufficieto produce a grid-independent solution. In additto the elliptic model, a simpler and computationafaster parabolic (boundary layer) model was also u(details are given in Ref. [26]), with elementary heero/homogeneous chemical reaction schemes andtailed transport; solution of the discretized algebradifferential set of equations was obtained via maring in x. In the absence of homogeneous ignitiowhich could invalidate the boundary-layer appromation by inducing significant axial gas-phase graents [26], both elliptic and parabolic models yieldexactly the same result. This was not surprising, asparabolic model has been shown [27] to be validpurely heterogeneous combustion at Reynolds nbers as low as 20, a value considerably lower thanReynolds numbers of Table 1.

3.2. Chemical kinetics

Two elementary heterogeneous reaction schefor the total oxidation of CH4 on Pt were investi-gated (see Table 2), further denoted as Deutschmet al. [5] and Vlachos and co-workers [7]. It is worpointing that the scheme of Vlachos has been deoped for both complete and partial catalytic oxidtion applications. The adsorption reactions were cculated as

(11)kads,k = Cγk

Γ m

√RT

2πWk,

with C the Motz correction factor,C = (1 −θPtγk/2)

−1, as proposed in [25]. In Vlachos’ schemno correction was implemented andC = 1 [28]; nev-ertheless, the inclusion of the correction factor hanegligible impact on the performance of this scheunder the conditions of Table 1. In Deutschmanheterogeneous scheme, the reverse rates of reac15–17 (see Table 2) were calculated using theward rate coefficients and surface thermochemdata [29]. The surface site density wasΓ = 2.7 ×10−9 mol/cm2 as discussed in Section 2. Althougthe OH-LIF experiments assured no homogeneousnition for Cases 1–15, the preignition gaseous chistry could not be ignored at high pressures, as wilfurther elaborated in the following section. In our prvious [3] high-pressure homogeneous ignition studof CH4/air over Pt (conducted under mass-transplimited catalytic operation), the elementary gas-phscheme of Warnatz and Maas [30] was validated othe pressure range 1 bar� p � 6 bar; however, a8 bar � p � 10 bar, the scheme overpredicted tmeasured homogeneous ignition distances. Onother hand, the gas-phase scheme of GRI-3.0 [31]shown [3] to be unrealistically fast, as it underpdicted substantially the measured homogeneoustion distances at all pressures (1 bar� p � 10 bar).Ongoing homogeneous ignition studies of our groat pressures of up to 16 bar have shown that the mrecent scheme of Warnatz et al. [32] (further denoas Warnatz) provided very good homogeneousnition predictions in the range 6 bar� p � 16 bar,and progressively earlier predictions as the presswas reduced from 6 to 1 bar. To maintain the prescatalytic reactivity studies free from homogeneopathway contributions, the analysis considered othe initial reactor extent over which the gas-phaparticipation was negligible. The delineation of thextent required computations with either an acrate or at least a conservative gaseous schemea scheme that predicted an earlier homogeneoustion). We have, therefore, opted to use two schemWarnatz [32], which was accurate over the higpressure range 6 bar� p � 16 bar and somewha


Table 2Heterogeneous chemical reaction mechanismsa

Deutschmannb Vlachosc

A (γ ) E Af (γ ) Ef Ab Eb

Adsorption reactions1. CH4 + 2Pt(s)→ CH3(s)+ H(s) 0.01 0.0 1.0 50.2 –2. O2 + 2Pt(s)→ 2O(s) 0.023 0.0 0.03 0.0 –3. O2 + 2Pt(s)→ 2O(s) 4.9×1012 0.0 – – – –4. CH3 + Pt(s)→ CH3(s) – – 1.0 0.0 – –5. CH2 + Pt(s)→ CH2(s)s – – 1.0 0.0 – –6. CH+ Pt(s)→ CH(s) – – 1.0 0.0 – –7. C+ Pt(s)→ C(s) – – 1.0 0.0 – –8. H2 + 2Pt(s)→ 2H(s) 0.046 0.0 0.25 0.0 – –9. H + Pt(s)→ H(s) 1.0 0.0 1.0 0.0 – –

10. O+ Pt(s)→ O(s) 1.0 0.0 1.0 0.0 – –11. H2O+ Pt(s)→ H2O(s) 0.75 0.0 0.7 0.0 – –12. OH+ Pt(s)→ OH(s) 1.0 0.0 1.0 0.0 – –13. CO2 + Pt(s)→ CO2(s) – – 1.0 0.0 – –14. CO+ Pt(s)→ CO(s) 0.84 0.0 1.0 0.0 – –

Pure surface reactions15. H(s)+ O(s)= OH(s)+ Pt(s) 1.0×1013 11.5 1.7×1010 50.6 5.6×1011 102.116. H(s)+ OH(s)= H2O(s)+ Pt(s) 1.0×1013 17.4 3.5×1011 51.9 1.2×1010 77.017. OH(s)+ OH(s)= H2O(s)+ O(s) 1.0×1013 48.2 1.0×1011 79.1 1.0×1011 52.718. C(s)+ OH(s)→ CO(s)+ H(s) – – 1.0×1011 16.7 1.0×1011 168.619. C(s)+ O(s)→ CO(s)+ Pt(s) 1.0×1013 62.8 1.0×1011 18.0 – –20. CO(s)+ Pt(s)→ C(s)+ O(s) 2.7× 109 184.0 1.0×1011 221.8 – –21. CO(s)+ O(s)→ CO2(s)+ Pt(s) 1.0×1013 105.0 1.0×1011 15.1 1.0×1011 88.722. CO(s)+ OH(s)→ CO2(s)+ H(s) – – 1.0×1011 35.1 1.0×1011 56.923. 2CO(s)→ C(s)+ CO2(s) – – 1.0×1011 0.0 1.0×1011 129.724. CH(s)+ O(s)→ CO(s)+ H(s) – – 1.0×1011 0.0 1.0×1011 336.825. CH3(s)+ Pt(s)→ CH2(s)s+ H(s) 1.0×1013 20.0 5.0×1012 107.9 1.0×1011 25.526. CH3(s)+ O(s)→ CH2(s)s+ OH(s) – – 1.0×1011 84.5 1.0×1011 52.327. CH3(s)+ OH(s)→ CH2(s)s+ H2O(s) – – 1.0×1011 77.8 1.0×1011 21.328. CH2(s)s+ Pt(s)→ CH(s)+ H(s) 1.0×1013 20.0 1.0×1011 104.6 1.0×1011 51.029. CH2(s)s+ OH(s)→ CH(s)+ H2O(s) – – 1.0×1011 81.6 1.0×1011 55.230. CH2(s)s+ O(s)→ CH(s)+ OH(s) – – 1.0×1011 83.3 1.0×1011 80.831. CH(s)+ Pt(s)→ C(s)+ H(s) 1.0×1013 20.0 1.0×1011 22.6 1.0×1011 157.332. CH(s)+ OH(s)→ C(s)+ H2O(s) – – 1.0×1011 0.4 1.0×1011 159.433. CH(s)+ O(s)→ C(s)+ OH(s) – – 1.0×1011 6.3 1.0×1011 192.0

(continued on the next page)

he

as-er-ere-usednn/te

n ofec-

ioncat-

am-anesesre-sch-

thedi-

conservative over the range 4 bar� p � 6 bar andGRI-3.0 [31], which was very conservative over tentire pressure range.

The CHEMKIN database was used for the gphase thermochemical [33] and transport propties [23]. Gas-phase and surface reaction rates wevaluated with CHEMKIN [34] and Surface-CHEMKIN [35], respectively. A set of hetero/homogeneoschemes will be further denoted by the assignnames of its components: for example, DeutschmaWarnatz schemes. Finally, the suffix (s) will denoa surface species and the prefix S or R a reactiothe full and the reduced catalytic schemes, resptively.

4. Results and discussion

4.1. Contribution of the gaseous reaction pathway

The importance of the homogeneous reactpathway and its impact on the assessment of thealytic reactivity are addressed first. Computed strewise profiles of both catalytic and gaseous methconversions are illustrated in Fig. 3 for three caof Table 1 and two different hetero/homogeneousaction schemes: Deutschmann/Warnatz and Deutmann/GRI-3.0. The volumetric gaseous CH4 conver-sion rates of Fig. 3 have been integrated across7-mm transverse distance, so that they could be


heted].

Table 2 (Continued)

Deutschmannb Vlachosc

A (γ ) E Af (γ ) Ef Ab Eb

Desorption reactions34. CH3(s)+ H(s)→ CH4 + 2Pt(s) – – 1.0×1011 23.0 – –35. 2O(s)→ O2 + 2Pt(s) 1.0×1013 213.2–60θO 1.0×1013 213–133.9θO – –36. CH3(s)→ CH3 + Pt(s) – – 1.0×1013 159.0 – –37. CH2(s)s→ CH2 + Pt(s) – – 1.0×1013 284.5 – –38. CH(s)→ CH+ Pt(s) – – 1.0×1013 405.8 – –39. C(s)→ C+ Pt(s) – – 1.0×1013 627.6 – –40. 2H(s)→ H2 + 2Pt(s) 1.0×1013 67.4–6θH 1.0×1013 83.7–25.1θH – –41. H(s)→ H + Pt(s) – – 1.0×1013 251.9–20.1θH – –42. O(s)→ O+ Pt(s) – – 1.0×1013 387.4–107.1θO – –43. H2O(s)→ H2O+ Pt(s) 1.0×1013 40.3 1.0×1013 41.8 – –44. OH(s)→ OH+ Pt(s) 1.0×1013 192.8 1.0×1013 263.6–138.1θO – –45. CO2(s)→ CO2 + Pt(s) 1.0×1013 20.5 1.0×1013 71.1 – –46. CO(s)→ CO+ Pt(s) 1.0×1013 125.5 1.0×1013 142.3–62.8θCO – –

a In all pure surface and desorption reactions, the reaction rate coefficient isk =AT b exp(−E/RT ) with b= 0. The units areA (s−1) andE (kJ/mol) yielding reaction rates in (s−1); to convert to standard surface reaction rate units (mol/cm2 s),A mustbe multiplied byΓ 1−m wherem is the reaction order. In all adsorption reactionsA denotes a sticking coefficient(γ ), exceptin Deutschmann’s reaction S3, wherek = AT b exp(−E/RT ) with b = −0.5 andA in (mol−1 cm3 K0.5s−1); A in S3 must bemultiplied by 1/Γ to convert to standard surface rate units.

b Reactions S2 and S3 are duplicate. Reactions S1, S8, and S14 have a Pt order of 2.3, 1, and 2, respectively.c Parameters are given for the forward(f ) and, when appropriate, for the reverse(b) reactions. The activation energies of t

adsorption and pure surface reactions are valid for an uncovered surface(θPt = 1); at other surface coverage, they were calculausing BOC (bond order conservation) formulae considering interactions of heats of chemisorption, according to Ref. [7

lat-er

cia-nof

ithp-theac-

over-rtlyver-er,h-

sh-

Onmeson.restedre-tly

-. 3lac-blethe

s—steroreaytht de-hatere-h-ostthep-the

tionm ofal-

othig. 4eousingen-ressge-ofby

ldsbar)

rectly compared to the catalytic surface rates; theter referred to the combined contribution of the uppand lower catalytic surfaces. The onset of appreble gaseous CH4 conversion, defined as the positiowhere the gaseous conversion amounted to 5%the corresponding catalytic conversion (shown wthe vertical arrows in Fig. 3), occurred farther ustream in the Deutschmann/GRI-3.0 compared toDeutschmann/Warnatz schemes. In the former retion schemes, the gaseous methane conversiontook the corresponding catalytic conversion shoafter the onset of the appreciable gaseous consion (see, for example, Figs. 3b and 3c). Moreovcontrary to the OH-LIF experiments, the Deutscmann/GRI-3.0 predictions resulted in the establiment of flames anchored atx = 140, 119, and 138 mmfor Cases 1, 13, and 15 of Fig. 3, respectively.the other hand, the Deutschmann/Warnatz schecaptured correctly the absence of flame formatiThe performance of GRI-3.0 at the low temperaturelevant to catalytic combustion has been attributo an unreasonably fast radical pool buildup thatsulted in a rapid methane depletion, predominanvia the step CH4 + OH = CH3 + H2O (see discussion in Reinke et al. [3]). The computations of Figwere repeated with the scheme of Vlachos reping that of Deutschmann; the onset of appreciagaseous conversion shifted farther downstream,

reason being that the former catalytic scheme waas discussed in the next section—considerably fathan the latter and could, therefore, suppress meffectively the contribution of the gaseous pathwby depriving it from fuel. The previous analysis widifferent hetero/homogeneous schemes aimed alineating the streamwise extent of the channel thad negligible gas-phase participation and was, thfore, suitable for catalytic reactivity studies. Notwitstanding the known deficiencies of GRI-3.0, the mconservative estimate was chosen by consideringlength of the channel down to the position of apreciable gaseous conversion as computed withDeutschmann/GRI-3.0 schemes. For the investigaof the hetero/homogeneous processes downstreathis position, however, only predictions with the reistic scheme of Warnatz will be presented.

The measured surface temperature profiles of bupper and lower catalytic plates are presented in Ffor seven selected cases of Table 1. Since the gasreactivity of hydrocarbons increased with increaspressure [36], the surface temperatures were, in geral, reduced at higher pressures in order to suppthe gaseous contribution and the onset of homoneous ignition. The increased gaseous reactivityCH4 at elevated pressures could be readily seencomparing Figs. 3a and 3b: although the Reynonumbers and the inlet temperatures of Cases 1 (4


nse 1;nnelsch-mes.(de-ts toedrti-

g aon-ted,

inap-d toandthatth-ass

faceef-the

uc-es-e ofeeticort-

de-forer-

urescat-ks

on

sedartem-ticre-ownsedous

ablytterre-

ion.ord-14-

ther noflu-n-

15lo-

r-ly,n-ceptoftic

Fig. 3. Computed streamwise profiles of catalytic (C: solidlines) and gaseous (G: dashed lines) methane conversiofor (a) Case 1, (b) Case 13, and (c) Case 15 of Tablthe G conversions have been integrated over the chatransverse direction. The computations refer to the Deutmann/Warnatz and Deutschmann/GRI-3.0 reaction scheThe onset of appreciable gaseous methane conversionfined as the point where the gaseous conversion amoun5% of the catalytic conversion) is indicated by the dashvertical arrow in the former schemes and by the solid vecal arrow in the latter.

and 13 (14 bar) were about the same (indicatinnearly equivalent reactor mass throughput), theset of appreciable gaseous conversion was locairrespective of gaseous scheme, farther upstreamCase 13 compared to Case 1. Moreover, this hpened despite the fact that Case 13 had (compareCase 1) lower surface temperatures (see Fig. 4)higher upstream catalytic conversions (see Fig. 3)led to reduced fuel availability for the gaseous paway. Case 15 (16 bar) had also about the same mthroughput as Cases 1 and 13; however, its surtemperatures were sufficiently low (Fig. 4) and thisfect overtook the positive pressure dependence ofgaseous reactivity. An additional reason for the redtion of the surface temperatures with increasing prsure was an—similar to the gas phase—increasthe catalytic reactivity with increasing pressure (sdiscussion in next section), which shifted the catalyconversion close to the undesirable mass-transplimited operation.

The measured boundary-layer profiles of theficient reactant (methane) were of main interestthe assessment of the catalytic reactivity. The exp

Fig. 4. Measured streamwise profiles of surface temperatfor seven selected cases of Table 1. Solid lines, loweralytic wall; dotted lines, upper wall. The vertical tick maron the horizontal axis indicate the thermocouple positionsboth catalytic walls.

imental requirements for such a task are discuswith the aid of Fig. 5, referring to the three 16-bcases of Table 1. Case 14 had the lowest surfaceperatures (Fig. 4) that resulted in a minimal catalyreactivity, as manifested by the nearly flat and featuless measured methane boundary-layer profiles dto x = 93.5 mm (Fig. 5b). Although such profilewere of limited interest, they nevertheless exemplifithe large differences between the two heterogeneschemes; the scheme of Vlachos was considerfaster than the scheme of Deutschmann, the labeing in relatively good agreement with the measuments as will be further elaborated in the next sectThe onset of appreciable gaseous conversion (accing to the adopted conservative definition) in Casewas located atx = 102 mm. Therefore, the predictions of Figs. 5a and 5b were totally unaffected bychoice of gaseous scheme (GRI-3.0, Warnatz, ogaseous scheme at all) and reflected solely the inence of the catalytic pathway—albeit with a dimiishing impact. The surface temperatures in Casewere high enough as to induce at downstreamcations (Fig. 5d,x = 113.5 mm) a bending in themeasured CH4 boundary-layer profile, which was cadinal in assessing the catalytic reactivity. Fortuitousthe CH4 boundary-layer profiles appeared largely uaffected by the presence of gaseous reactions (exin the wall proximity where the transverse gradientCH4 determined the magnitude of the local cataly


thedis-bolsRa-ch-

tionsesann

ann/in

et-hosporter-ence

on-, foratzith

outthatpre-tic-the

ionsd inr ex-

ith

purehisug-sig-r the

tryand

on

ace

lsoes.

con-ate

porteronsith

usticing-

also

ouspre-es

n-is-oflesatans

eends

ber

et-ctionesheith13

ethem

rredrionver

Fig. 5. Measured and predicted transverse profiles ofmethane mole fractions at two selected streamwisetances for the three 16-bar cases of Table 1. Symare measurements and lines are predictions. Circles,man measurements; solid lines, predictions with Deutsmann/Warnatz schemes; dashed-dotted lines, predicwith Vlachos/Warnatz schemes. In (d) the dotted linare pure heterogeneous predictions with the Deutschmscheme (no gaseous chemistry), in (e) the DeutschmWarnatz and Vlachos/Warnatz predictions coincide, and(f) the dashed lines pertain to two coinciding purely herogeneous predictions with the Deutschmann and Vlacschemes. In (e) the catalytic reactions are mass-translimited, whereas in (f) the methane profile is largely detmined by the gaseous reaction pathway due to the presof a flame in the reactor.

conversion), even at positions downstream of theset of appreciable gaseous conversion. In Fig. 5dexample, predictions with the Deutschmann/Warnschemes (solid line) were in good agreement wthose using only Deutschmann’s scheme withgaseous chemistry (dotted line), despite the factthe gaseous methane conversion in the formerdictions amounted already to 18% of the catalyconversion atx = 113.5 mm (see Fig. 3c). The reason was that the gaseous pathway suppressedcatalytic conversion (see the drop of theC curvesupon the rise of theG curves in Fig. 3) in such away that the sum of catalytic and gaseous converswas close to the pure catalytic conversion attainethe absence of gaseous chemistry; in Case 13, foample, the computed total fractional CH4 conversion(= [mCH4,IN − mCH4(x)]/mCH4,IN) at x = 120 mmwas 16.6% (12.4% catalytic and 4.2% gaseous) w

the Deutschmann/Warnatz schemes and 15.1%catalytic with the Deutschmann scheme alone. Tfortuitous agreement, however, by no means sgested the use of positions downstream of the denated onset of appreciable gaseous conversion foassessment of the catalytic reactivity. The CH4 pro-files of Figs. 5a–5d exhibited only a slight asymmesince the temperature differences between upperlower walls were less than 12 K at any axial positiof Case 14 or 15 (see Fig. 4).

Case 16 (Figs. 5e and 5f) had the highest surftemperatures and a flame anchored atx ≈ 115 mm,as determined by the OH-LIF experiments and acaptured well by the Deutschmann/Warnatz schemEven though the onset of appreciable gaseousversion occurred atx = 20 mm, the measurementsx = 15.5 mm (Fig. 5e) were of very limited use sincthe catalytic conversion was already mass-translimited, as manifested by the predicted nearly zCH4 concentrations at both walls. The computatioof both Deutschmann and Vlachos schemes (wor without the inclusion of any of the two gaseoschemes) coincided in Fig. 5e; however, no kineinformation could be extracted under such operatconditions. The position of Fig. 5f was well downstream of the onset of homogeneous ignition, asevidenced by the absence of CH4 in extended re-gions close to both channel walls. When the gasescheme was removed, the pure heterogeneousdictions of both Deutschmann and Vlachos schemcoincided (dashed line in Fig. 5f), the catalytic coversion being again mass-transport limited. The dcussion of Fig. 5 has exemplified the importanceoperating conditions that ensured methane profisimilar to those of Case 15. Finally, it is noted ththe surface temperature provided the prime meof controlling the bending of the CH4 boundary-layer profiles. An alternate approach would have bto vary the transport by altering the inlet Reynolnumbers; nevertheless, the CH4 boundary-layer pro-files were much less responsive to Reynolds numchanges.

To understand the coupling between the herogeneous and homogeneous pathways, reaflux analyses were carried out for different casof Table 1, at various streamwise positions. Tgaseous and catalytic carbon fluxes (predicted wthe Deutschmann/Warnatz schemes) for Case(14 bar) atx = 95 mm are presented in Fig. 6; thgas-phase fluxes were obtained by integratingvolumetric gaseous reaction rates over the 7-mtransverse direction and the surface fluxes refeto the contribution of both catalytic walls. Similaflux analyses revealed that all the important reactroutes of Fig. 6 remained unaffected by pressure othe entire range 4 bar� p � 16 bar. Atx = 95 mm the


aly-

nor-H

anined

r the

lidf COtionThe

anneucedro-

verHsch-puta-

f the3b).

be-

nly

ox-

cee asof

re-eenthe

vers of

dpro-7b),at-seeises-aseO

Fig. 6. Homogeneous and heterogeneous reaction flux ansis for Case 13 (14 bar) atx = 95 mm computed with theDeutschmann/Warnatz reaction schemes. All fluxes aremalized with respect to the flux of the gaseous reaction C4→ CH3; only fluxes with relative magnitude greater th0.004 are shown. The gaseous fluxes have been obtaby integrating the volumetric gaseous reaction rates ovechannel transverse direction.

Fig. 7. Computed streamwise profiles of the catalytic (solines) and the gaseous (dashed lines) production rates oand OH obtained with the Deutschmann/Warnatz reacschemes: (a) Case 1 (4 bar) and (b) Case 13 (14 bar).gaseous reaction rates have been integrated over the chtransverse distance. In both cases, the OH (CO) is prod(destroyed) by the catalytic pathway and destroyed (pduced) by the gaseous pathway.

l

Fig. 8. Computed streamwise profiles of the average (othe channel transverse direction) mole fractions of C4,CO, and OH for (a) Case 1 and (b) Case 13; the Deutmann/Warnatz reaction schemes were used in the comtions.

gaseous methane conversion amounted to 36% ocorresponding catalytic conversion (see also Fig.The gaseous pathway converted CH4 predominantlyto CO, the initiating step in the methane breakuping always CH4 + OH = CH3 + H2O. Most of theformed CO was adsorbed on the catalyst and oa small fraction of it was oxidized to CO2 in thegas phase. The adsorbed CO was subsequentlyidized on the surface to CO2(s), which, along withthe CO2(s) produced via the main methane surfaoxidation route, desorbed back to the gas phasCO2. Streamwise profiles of the production ratesCO and OH and the mole fractions of CH4, CO, andOH for Case 13 are illustrated in Figs. 7b and 8b,spectively; the gas-phase rates of Fig. 7 have bintegrated over the 7-mm transverse distance andmole fractions of Fig. 8 have been averaged othe same distance. Using the streamwise profileFig. 8b, a fractional CH4 conversion of 23% couldbe deduced atx = 150 mm; 16% was catalytic an7% gaseous. The gaseous and catalytic pathwaysduced and destroyed, respectively, CO (see Fig.with a positive net production that resulted in thetained low CO levels along the channel length (Fig. 8b). For the very fuel-lean conditions of thstudy, the removal of both CO adsorption and dorption reactions resulted only in a moderate increof the CO levels (in Case 13, for example, the C


ush-

of

ad-theuxath-as, re-

olearoustep-ablently,edac-ut-e

u-bleo-selfaf-romtheous-meit-mi-ousa

ofndsureet-al-e 1un-

for, theled

bu-el-

asen

ch-ans-

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-

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ictedin

and,er-ap-n’s

thehow-erthe

mole fraction increased from 5× 10−4 to 1.2× 10−3

atx = 150 mm) since the oxidation of CO to CO2 wasrerouted efficiently from the catalytic to the gaseopathway. This outcome will be used in the fortcoming reduction of the heterogeneous schemeDeutschmann.

The hetero/homogeneous radical coupling isdressed next. The OH radical was produced bycatalytic pathway (the net OH heterogeneous flwas desorptive) and destroyed by the gaseous pway (see Fig. 7b); the catalytic production rate wsomewhat larger than the gaseous destruction ratesulting in the streamwise increase of the OH mfraction shown in Fig. 8b. It would, therefore, appethat the catalytically produced OH promoted gaseconversion by accelerating the main fuel attack sCH4 + OH = CH3 + H2O. However, the net OH heterogeneous fluxes were too low to have an appreciimpact on the gas-phase pathway and, consequeon the flux analysis of Fig. 6. This was also verifiby removing the OH adsorption and desorption retions from the scheme of Deutschmann and comping anew: the CH4 gas conversion of Fig. 3b and thCH4, CO, and OH levels of Fig. 8b remained virtally unaffected. The gaseous chemistry was still ato build the radical pool without the aid of the hetergeneous pathway. In other words, the catalyst itwas a very poor source of OH as to meaningfullyfect the gaseous pathway under conditions away fhomogeneous ignition and flame propagation. Inpresence of a flame or at the late prehomogeneignition stages, however, the catalyst could becoa very efficient sink of gas-produced OH, inhibing gaseous combustion (see also [3,25]). A silar analysis has shown that the catalytic and gasecoupling of both O and H radicals was minimal,conclusion valid not only under the conditionsthis study but also during homogeneous ignition aflame propagation (see also the atmospheric-presstudies in [25]). The above discussion on the hero/homogeneous chemistry coupling applied, quitatively, at all pressures; Figs. 7a and 8a of Cas(4 bar) exhibited the same trends as their 14-bar coterparts of Figs. 7b and 8b. It is finally noted that,a fixed reactor pressure and surface temperaturecontribution of the gaseous pathway was controlprimarily by the reactor surface-to-volume ratio(SV)and residence time(τ); an increase (decrease) inSV(τ) could suppress effectively the gaseous contrition. The channel-flow reactor of Fig. 1 had a ratively small SV = 2.86 cm−1. The delineation oftheSV–τ regimes leading to an appreciable gas-phcontribution will be dealt in the forthcoming sectioon reduced schemes.

4.2. Comparisons between measurements andpredictions and effect of pressure on catalyticreactivity

Measured and predicted—using both Deutsmann and Vlachos heterogeneous schemes—trverse profiles of the CH4 and H2O mole fractions andof the temperature are presented in Fig. 9 for fivelected cases of Table 1 and four streamwise positfor each case. All predicted profiles of Fig. 9 wetotally unaffected by the presence of gaseous chistry, as they referred to axial positions before theset of appreciable gaseous conversion. The slighmoderate asymmetry in both measured and prediprofiles of Fig. 9 was ascribed to the varying degreetemperature difference between the catalytic plathe lower plate being usually the hottest one (Fig. 4). The CH4 levels in Fig. 9 ranged from 2 t4% per volume over the exploitable transverse exof the experiments (0.6 mm� y � 6.4 mm), resultingin a measurement accuracy of±5%. Over the sametransverse extent, the H2O levels ranged from practically zero about the symmetry plane (y = 3.5 mm)of all upstream axial positions, to 2.5% per voume at the end measurement pointsy = 0.6 mmand y = 6.4 mm. An accuracy of±10% was at-tained in the near wall regions with H2O volumetricconcentrations greater than 0.5%; the lower H2O con-centrations about the channel center resulted in paccuracy; however, these regions were of little intest in the present analysis. The H2O measurementcomplemented the CH4 ones and aided the schemvalidation process, since the near-wall rise of H2Owas directly linked to the catalytic conversion of CH4.The O2 Raman data were of less importance sinthis reactant was in excess, having a boundary-laprofile with a weak near-wall bending. It shouldpointed out that in situ, spatially resolved measuments of species compositions over a catalyst (sas those of Fig. 9) under high pressure have not breported in the literature.

The measured and predicted CH4 and H2O bound-ary-layer profiles were compared against each oin order to assess the performance of the heteroneous schemes. The scheme of Vlachos overpredat all pressures the catalytic reactivity as it resultedsignificantly lower (higher) near-wall CH4 (H2O) lev-els. The scheme of Deutschmann, on the other hyielded an overall good agreement with the expiments at all pressures. The catalytic reactivitypeared to be slightly overpredicted in Deutschmanscheme: the computed CH4 drop and the H2O risenear the wall were somewhat faster compared tomeasurements. The above discrepancies were,ever, within the experimental uncertainty. The propchoice of surface temperatures has exemplified


, Vla-arnatz

ed (dashed

Fig. 9. Comparisons between measured and predicted transverse profiles of temperature and species (CH4 and H2O) molefractions for five cases of Table 1. Four streamwise locations are presented for each case. Measurements: CH4 (circles), H2O(triangles), and temperature (squares). Predictions: CH4 (solid line, Deutschmann/Warnatz schemes; dashed-dotted lineschos/Warnatz schemes) and H2O (dashed-double-dotted lines, Deutschmann/Warnatz schemes; dotted lines, Vlachos/Wschemes). The predicted temperature profiles with the Deutschmann/Warnatz and Vlachos/Warnatz schemes coincidlines). For reasons of clarity, 21 of the 63 transverse measurement points are shown.

es.facetheer-

theHlestheuta-her-e-

ely,fol-e-

ityig-er-

meand

sur-s

large differences between the two reaction schemFor example, in Case 6 that had the highest surtemperatures of all cases of Fig. 9 (see Fig. 4),differences between the two predictions was modate already from the first axial positionx = 15.5 mm.Notwithstanding the large differences betweentwo scheme predictions in their corresponding C4and H2O profiles, the predicted temperature profiwere practically coincident. The reason was thatsurface temperatures were prescribed in the comptions of both schemes and that the changes in the tmal conductivity and heat capacity of a partially r

acted fuel-lean methane/air premixture were, largindependent of the progress of the reaction. Thelowing analysis will focus on the validated heterogneous scheme of Deutschmann.

The effect of pressure on the catalytic reactivis elaborated with the aid of Figs. 9 and 10a. Fure 10a pertains to computations of a surface pfectly stirred reactor (SPSR) [37] using the scheof Deutschmann (no gaseous scheme included)three different pressures: 1, 4, and 16 bar. Theface to volume ratio(SV) in the SPSR computationwas 2.86 cm−1 (equal to the channelSV) and the


e ofn aent

0,SR

ionareres-

d to

ithSRx-

assbartheiv-ceedo-le,of

hatarly

edthial

uresreder

ated

fer-(b)dot-

s-dilyre-

tedason-ac-eddi-es

e ara-ere

thatbarTheinen-es.re-thev-

ur-othane

ith

Fig. 10. (a) Computed heterogeneous (using the schemDeutschmann without inclusion of gaseous chemistry) isurface perfectly stirred reactor (SPSR) at three differpressures. The surface to volume ratio is 2.86 cm−1, theequivalence ratio isϕ = 0.4, and the residence times are 140, and 160 ms at 1, 4, and 16 bar, respectively. (b) SPpredictions of the ratio of the methane catalytic conversat 16 bar to that at 4 bar. The residence times at 4 barsuch that the methane conversion is always 50% and theidence times at 16 bar are a factor of 4 longer comparethose at 4 bar.

residence times were increased proportionally wincreased pressure in order to maintain equal SPmass-flow rates; this mimicked the channel-flow eperiments of Fig. 9 that had a nearly constant mthroughput. TheSPSR residence times at 4 and 16were 40 and 160 ms, respectively, which—usingflow velocities of Table 1—corresponded to an equalent reactor length of about 80 mm. The influenof pressure on catalytic reactivity could be deducdirectly from the SPSR predictions or with apprpriate profile comparisons in Fig. 9. For exampFigs. 9(1b) and 9(8b) indicated that the bendingthe measured CH4 (as well as H2O) profiles nearboth walls was roughly the same: given the fact tthe transverse fluid mechanical transport was nethe same in both cases (for a givenx it scaled withReIN as discussed in Refs. [17,26]), this entailnearly equivalent catalytic reaction rates for bocases according to the diffusion-reaction interfacbalance of Eqs. (9). Since the surface temperatwere lower in the higher pressure Case 8 compato Case 1 (by 40 and 10 K in the upper and lowsurfaces, respectively, see Fig. 4), this necessit

Fig. 11. Computed profiles of the surface coverage (rering to the lower catalyst surface) for (a) Case 1 andCase 13. Solid lines, Deutschmann/Warnatz schemes;ted lines, Vlachos/Warnatz reaction schemes.

an increase of the catalytic reactivity with increaing pressure. The same conclusion could be reareached with the SPSR computations of Fig. 10a: pdictions with the scheme of Deutschmann indicathat the catalytic reactivity increased with pressuremanifested by the corresponding higher methane cversions. Moreover, the increase in the catalytic retivity with increasing pressure was more pronouncat higher temperatures. This was shown with adtional SPSR calculations where the residence timat 4 bar were altered independently as to achievfixed 50% methane conversion at various tempetures. The corresponding methane conversions wthen calculated at 16 bar, using residence timeswere a factor of 4 longer than those computed at 4(to maintain the same reactor mass throughput).ratio of the 16-to-4 bar conversions is illustratedFig. 10b, clearly showing the weaker pressure depdence of the catalytic reactivity at lower temperatur

The origin of the differences between the twoaction schemes and the impact of pressure oncatalytic reactivity is elaborated with the surface coerage of Fig. 11, referring to the lower catalytic sfaces of Cases 1 and 13. The initiation step in bschemes was the dissociative adsorption of meth(reaction S1): CH4 + 2Pt(s)→ CH3(s)+ H(s). In thescheme of Deutschmann S1 had an order of 2.3 wrespect to Pt, so that the adsorption rate of CH4 was

(12)sads,CH = kads,CH [CH4][Γ θPt]2.3,
4 4


en inthe-. 4),re-cor-d)es

ow-as-m-eenandres

ingropeddersen inuctn

hde-

t-verliern-

totheurely,’s

ture

dity

13reionce.

thattedtive

of

are

re-

p-senot

r ofple,pri-16.fordif-d 9

ag-ant

ltingn-s-

in-ch-s ofar-eadrage(s)er-

lue

meof

both

e-telyen

with kads,CH4 given in Eq. (11). The main surfaccoverage was O(s) and free sites (Pt(s)) as seeFig. 11. For a given case and reaction scheme,O(s) dropped with increasingx due to the corresponding increase of the surface temperature (see Figwhich promoted the desorption of O(s) and the cation of free sites. As the pressure increased, theresponding increase in the O2 partial pressure resultein further adsorption of O2 and hence to higher O(sand lower Pt(s) coverage for both reaction schem(see Fig. 11); in the scheme of Deutschmann, hever, the reduction of the Pt(s)/O(s) ratio with increing pressure was much more pronounced. It is ephasized that the Pt(s) and O(s) differences betwFigs. 11a and 11b reflected the effect of pressurenot the (small) differences in surface temperatuTW (x) andϕ; this was verified by replacingTW (x)

andϕ of Case 13 with those of Case 1 and computanew. To facilitate the ensuing discussion, the dof θPt with increasing pressure will be representas [θPt] ∝ p−β , with β a positive number that neenot be a constant but a function of local parametsuch as surface temperature and coverage. As seEq. (12), the methane adsorption rate was a prodof the positive [CH4] ∝ p gas-phase concentratiodependence and the negativep−n surface coveragedependence (in Deutschmann’s schemen = 2.3β).The exponentn was always smaller than unity, sucthat the catalytic reactivity had a positive pressurependencep1−n, the specific value ofn being veryimportant inrestrainingthe rate of increase of the caalytic reactivity with increasing pressure. The abopressure dependence was also recognized in eaempirical global reaction steps [38] proposed for egineering applications,

(13)sCH4 = Bp−n exp(−Ea/RT )[CH4],with a constant exponentn = 0.4 and Ea = 77kJ/mol. The scheme of Deutschmann appearedhave the proper local pressure inhibition throughp−n term that resulted in the capture of the pressdependence of the catalytic reactivity. Interestingthesads,CH4 ∝ [θPt]2.3 dependence in Deutschmannscheme that was, in turn, responsible for the capof the correct local exponentn was derived from at-mospheric pressure experiments; its apparent valiat pressures as high as 16 bar is worth noting.

A heterogeneous reaction flux analysis for Caseat x = 95 mm is shown in Fig. 12; the fluxes wecalculated with the Deutschmann/Warnatz reactschemes and referred to the lower catalyst surfaFlux analyses of different cases have revealedthe dominant pathways of Fig. 12 were unaffecby pressure. The initiating step was the dissociaadsorption of CH4 to H(s) and C(s) and of O2 toO(s), the main surface steps were the reaction

Fig. 12. Heterogeneous reaction flux analysis (the unitsmol/cm2 s) for Case 13 (14 bar) atx = 95 mm, referringto the lower catalytic plate. The Deutschmann/Warnatzaction schemes were used.

O(s) with H(s) and C(s) to form OH(s)/H2O(s) andCO(s)/CO2(s), respectively, and, finally, the desortion of H2O(s) and CO2(s) led to the main gaseouproducts H2O and CO2. The dominant pathways weralso the same in the scheme of Vlachos and areshown here. There were differences in the ordesignificance of certain surface pathways; for examH2O(s) in Deutschmann’s scheme was producedmarily via S17 whereas in Vlachos’ scheme via SHowever, the above differences were not crucialthe overall scheme behavior. The performanceferences of the two schemes shown in Figs. 5 anreflected strongly differences between the CH4 andO2 adsorption/desorption reactions: the relative mnitude of these two steps determined the dominPt(s) and O(s) coverage and, hence, the resucatalytic reactivity inhibition through the aforemetioned p−n dependence. When only the O(s) deorption (reaction S35) of Vlachos’ scheme wasterchanged with the corresponding one of Deutsmann’s scheme, the computed SPSR conversionthe former scheme were improved significantly, pticularly at T < 1100 K. The reason was that thactivation energy of S35 in Vlachos’ scheme ha much stronger dependence on the O(s) cove(see Table 2), which resulted in a more efficient Odesorption and, therefore, in a higher Pt(s) covage and in a higher catalytic reactivity (smaller vaof the exponentn). When all the CH4 and O2 ad-sorption and desorption reactions of Vlachos’ schewere interchanged with the corresponding onesDeutschmann’s scheme, the SPSR predictions ofschemes coincided.

4.3. Reduced heterogeneous schemes

It is of main interest to provide reduced heterogneous reaction schemes that could predict accurathe catalytic methane conversion. Moreover, wh


per-atz-linessionsi-

em-era-

ttedhent to

pli-

, theadeus

im-ouse olat-meho-the-in

ince-ver

PSRnd

time

torin arre-tora-

e-ture;tici-ason-at,e

al-to

yver

ica-ph

ro-antata-ivene.u-ringn-are,si-hatd atatalsoi-m-

cal

oftic;ithe)%

tre-the

thetionly-d

Fig. 13. (a) Computed methane conversions in a surfacefectly stirred reactor (SPSR) with the Deutschmann/Warnreaction schemes andϕ = 0.4: the solid lines are the total (gaseous and catalytic) conversions and the dottedthe catalytic conversions. The onset of gaseous conver(shown with the vertical arrows) is favored at longer redence times(τ ) or smaller surface-to-volume(SV) ratios.(b) Delineation of the regimes of significant gas-phase chistry participation. For a given reactor pressure and tempture the area above each line delineates theτ andSVregimesfor which gas-phase contribution can be neglected; dolines, 1 bar; dashed lines, 4 bar; solid lines, 16 bar. Tshaded area presents an estimate of the regimes relevacatalytically stabilized combustion (CST) gas turbine apcations.

coupled to the homogeneous scheme of Warnatzreduced heterogeneous schemes should predictquately not only the catalytic but also the gaseomethane conversion—whenever the latter is ofportance. The validated elementary heterogenescheme of Deutschmann and the gaseous schemWarnatz were used in the reduction process: theter has been shown (in conjunction with the scheof Deutschmann) to reproduce well the onset ofmogeneous ignition in the channel reactor overpressure range 6 bar� p � 16 bar and to underestimate homogeneous ignition only moderatelythe range 4 bar� p � 6 bar (see the discussionSection 3.2). The first step in the reduction produre was the delineation of the parameter range o

-

f

which the gaseous pathway could be neglected. Spredictions of the total (catalytic plus gaseous) acatalytic methane conversions versus residenceare illustrated in Fig. 13a for variousSV’s. The ver-tical arrows defined the maximum allowable reacresidence times: longer residence times resultedgaseous conversion that exceeded 5% of the cosponding total conversion. Computations similarthose of Fig. 13a were used to construct the pametric plot of Fig. 13b. The lines in Fig. 13b corrsponded to a fixed reactor pressure and temperain the regions above each line the gaseous parpation could be safely ignored, while in the arebelow the gaseous contribution should always be csidered. The line leveling in Fig. 13b indicated thabove a certain value ofSV (that depended on threactor pressure and temperature), the maximumlowable residence times were extremely sensitivesmall changes inSV. The plot of Fig. 13b was nearlindependent of the particular equivalence ratio othe experimental range 0.35� ϕ � 0.40. The shadedrectangle provided an estimate of the regimes applble to gas turbines. It is understood that the graof Fig. 13b (based on ideal reactor predictions) pvided a rough delineation of the regimes of significgas-phase participation. A technical supported clyst would have a porous substrate with an effectarea significantly larger than the geometrical oThis would necessitate modeling of intrapolar diffsion and assessment of its importance by compathe intrapolar diffusion times with the in-channel covective and diffusion time scales; such issueshowever, outside the scope of this work. The potion of the shaded rectangle in Fig. 13b indicated tthe gas phase participation could not be neglectep � 16 bar andT � 1000 K, an operating range thencompasses many practical systems. This wasverified with additional 2-D computations in techncally relevant catalytic channel geometries. For exaple, in a channel with diameter of 2 mm (geometriSV= 20 cm−1), a length of 100 mm,TIN = 673 K,UIN = 5 m/s (residence time∼20 ms),p = 16 bar,and a fixed wall temperatureTW = 1200 K, the com-putations yielded a fractional methane conversion45% out of which 6% was gaseous and 39% catalywhen the channel diameter was reduced to 1 mm wSV= 40 cm−1 (all other parameters being the samthe total fractional conversion was 84% with 10gaseous and 74% catalytic contributions.

In the regions of Fig. 13b with insignificangaseous participation, the sole requirement of theduced heterogeneous scheme was to reproducecatalytic methane conversion. The reduction ofscheme of Deutschmann was aided by the reacflux analysis of Fig. 12 and the sensitivity anasis (SA) of Fig. 14. The SA of Fig. 14 was carrie


wayostge-on inase

xpo-

fingticsixet-eseost

orp--tooisti-S33

the

ithhe

ipa-ionab-

heyterre-

ofthec-

tion

et-e ofhemeousthes of

eac-R7and

evi-ins anrp-ec-

andre-et-

d ofand20me.ex-of

s ofcon-3bn.full

% atin

Fig. 14. Sensitivity analysis of the heterogeneous pathfor Cases 1 (4 bar) and 13 (14 bar) of Table 1. The six msensitive reactions of Table 2 are shown for the heteroneous scheme of Deutschmann. The percentage reductithe methane catalytic conversion is computed for an incre(black bars) or decrease (gray bars) of the reaction preenential coefficient by a factor of 10.

out by multiplying (dividing) the preexponential oeach reaction by a factor of 10 and then comput(without inclusion of gaseous chemistry) the catalymethane conversion along the channel anew. Themost significant reactions are illustrated for each herogeneous scheme; the order of significance of threactions remained unaffected by pressure. The msensitive reactions in both schemes were the adstion/desorption of CH4 and O2, which were the ratelimiting steps. The pure surface reactions werefast to affect the methane conversion; charactercally, a decrease of the rate of reactions S15 toin Deutschmann’s scheme by a factor of 103 did notalter appreciably the catalytic conversion. Hence,consecutive reactions

CH4S1−→ CH3(s)

S25−→CH2(s)S28−→CH(s)

S31−→ C(s)+ 4H(s)

were combined to the single step:

(R1)CH4 + 5Pt(s)→ C(s)+ 4H(s).

Reaction R1 had the same kinetic parameters wS1 (the slowest reaction of the chain), including treaction order of 2.3 with respect to Pt(s).

In the absence of significant gas-phase partiction, the radical (OH, O, and H) adsorption/desorptreactions could be ignored. Furthermore, in thesence of H2 in the reactant stream, the H2 adsorp-tion/desorption reactions could be removed, as tdid not have any noticeable impact on H(s). Wawas formed primarily via S17 (see Fig. 12) and, thefore, S16 was disregarded; in any case, inclusioneither S17 or S16 was sufficient to accommodatewater formation given the fact that all surface reations were much faster compared to the adsorp

Table 3Reduced heterogeneous schemea

R1 CH4 +5Pt(s)S1−→C(s)+ 4H(s)

R2 O2 + 2Pt(s)S2−→2O(s)

R3 O2 + 2Pt(s)S3−→2O(s)

R4 H2O+ Pt(s)S11−→H2O(s)

R5 H(s)+ O(s)S15= OH(s)+ Pt(s)

R6 OH(s)+ OH(s)S17= H2O(s)+ O(s)

R7 C(s)+ 2O(s)S19−→CO2(s)+ 2Pt(s)

R8 2O(s)S35−→O2 + 2Pt(s)

R9 H2O(s)S43−→H2O+ Pt(s)

R10 CO2(s)S46−→CO2 + Pt(s)

R11 OH+ Pt(s)S12−→OH(s)

R12 OH(s)S44−→OH+ Pt(s)

R13 CO+ O(s)+ Pt(s)S14−→CO2(s)+ Pt(s)

a The reduced scheme R1–R10 is valid for purely herogeneous combustion and stems from the full schemDeutschmann (see Table 2). The augmented reduced scR1–R13 can be used for combined catalytic and gasecombustion. The reduced reactions (R reactions) havesame kinetic rate parameters to the indicated S reactionthe full scheme of Deutschmann. R1 and R13 have a rtion order with respect to Pt(s) of 2.3 and 2, respectively.and R13 have a reaction order with respect to O(s) of 10, respectively.

and desorption reactions. Finally, as discussed prously in Section 4.1, under fuel-lean conditions andthe absence of gaseous chemistry, the catalyst waextremely poor producer of CO; therefore, the adsotion/desorption of CO were ignored and the cons

utive surface steps C(s)S19−→CO(s)

S21−→CO2(s) werecombined to:

(R7)C(s)+ 2O(s)→ CO2(s)+ 2Pt(s).

R7 had the same kinetic parameters as S19,a reaction order of one with respect to O(s). Theduced scheme of Deutschmann valid for purely herogeneous applications (see Table 3) consiste10 reactions R1–R10 and 11 species (4 gaseous7 surface) in comparison to the 24 reactions andspecies (9 gaseous and 11 surface) of the full scheThe reduced scheme reproduced at all pressurescellently the predicted channel transverse profilesFig. 9 and the SPSR catalytic methane conversionFig. 10a; the same applied to the SPSR methaneversions under the operating conditions of Fig. 1that were pertinent to purely catalytic combustioThe differences between the reduced and thescheme predictions were, for example, less than 1any transverse position of Fig. 9 and less than 0.4%the SPSR catalytic conversions of Figs. 10a and13b.


tic-ro-on-int of

4.1,cialr-astheof

ionady

, re-is-

ons.. 12her

nedin-e-in

ac-ndemeat-thate.

ytic

ca-m-es.re-

ast

seone of[37]

ce-

re-tive

us-sur-

effec-lots

theisex-re

anddis-on-nn.w-the

enannnot

isge

ri-n inm

Under conditions of appreciable gaseous paripation, the reduced catalytic scheme should repduce the catalytic as well as the gaseous fuel cversion and—although not of particular emphasisthe present investigation—should capture the onsehomogeneous ignition. As discussed in Sectionthe OH adsorption/desorption reactions were cruin describing the inhibiting role of the catalyst duing gaseous ignition. It was further stated that CO wproduced by the gaseous and consumed mainly bycatalytic pathway and that for the lean conditionsthis study removal of the CO adsorption/desorptreactions did not have a strong impact on the alrelow CO levels and the ensuing CH4 conversion. Thelack of the CO heterogeneous reactions, howeversulted in 10–15% shorter homogeneous ignition dtances due to the somewhat higher CO concentratiInclusion of the CO adsorption step (as seen in Figthe CO desorption was less important) could furtimprove homogeneous ignition predictions:

(R13)CO+ O(s)+ Pt(s)→ CO2(s)+ Pt(s).

R13 was not an elementary reaction and combithe adsorption and surface oxidation of CO in a sgle, Eley–Rideal-type reaction. The reaction paramters of R13 were those of S14, the slowest stepthe CO surface oxidation chain; therefore, the retion order with respect to Pt(s) and O(s) was two azero, respectively. The augmented reduced schshown in Table 3 (reactions R1–R13) predicted calytic and gaseous SPSR methane conversionswere in good agreement with those of the full schemIn addition, predictions (augmented reduced catalscheme/Warnatz) of the CH4 boundary-layer profilesin the channel-flow reactor at far downstream lotions were also in good agreement with those coputed with the Deutschmann (full)/Warnatz schemThe same applied also to homogeneous ignition pdictions in the channel-flow reactor; details on the lissue are outside the scope of the present work.

Global catalytic combustion steps similar to thoof Eq. (13) (applicable to pure catalytic combustiapplications) were also investigated. In the absencgaseous reactions, the SPSR governing equationbecomes

(14)(YCH4,IN − YCH4)/τ = (SV/ρ)sCH4WCH4,

with τ andSV the reactor residence time and surfato-volume ratio, respectively. Using Eq. (13) forsCH4and further considering that[CH4] = ρYCH4/WCH4,Eq. (14) yields for a fixed pressure,SVandτ :

(15)log(YCH4,IN/YCH4 − 1)∝ −Ea/RT .Computed SPSR plots of log(YCH4,IN/YCH4 − 1)

versus 1/T for the scheme of Deutschmann are psented in Fig. 15a for three pressures; the effec

Fig. 15. (a) Plots of log(YIN,CH4/YCH4 − 1) versus 1/Tcomputed in a surface perfectly stirred reactor (SPSR)ing the heterogeneous scheme of Deutschmann. Theface-to-volume ratio, the CH4/air equivalence ratio, and thresidence times at each pressure are as in Fig. 10. (b) Etive activation energies calculated from the slope of the pof Fig. 15a, according to Eq. (15).

activation energies (calculated from the slope ofplots of Fig. 15a) are presented in Fig. 15b. Itclearly seen that in Deutschmann’s scheme thereists no constantEa over the temperature and pressuranges of interest:Ea varied from 65 to 185 kJ/mol,increasing strongly with decreasing temperaturemoderately with increasing pressure. The abovecussion has shown that a global step was not csistent with the validated scheme of DeutschmaNevertheless, for engineering applications the folloing global step is proposed, yielding the best fit toSPSR computations,

(16)sCH4 = B(p/p0)−n exp(−Ea/RT )[CH4],

with B = 1.27× 105 cm/s, n = 0.53, Ea = 84 kJ/mol, andp0 = 1 bar. SPSR comparisons betwethe global step and the full scheme of Deutschmare provided in Fig. 16 (gaseous chemistry wasincluded); the agreement in methane conversionbetter than±15% over the extended pressure ran1 bar� p � 16 bar.

4.4. High-pressure reactor performance

In recent studies [17] we developed analytical cteria for heterogeneous and homogeneous ignitio2-D plane channel-flow configurations with unifor


in aeme

lls.tionfin-ntepe-rgeed.n-inoustoofer-and

ion

in,

m-

e

ly

.

at-

stistr-)

,inal

Fig. 16. Computed methane heterogeneous conversionssurface perfectly stirred reactor (SPSR). Solid lines, schof Deutschmann; dotted lines, global step of Eq. (16).

incoming properties and isothermal catalytic waThe approach was based on a parametric descripof the chemically frozen gaseous state for the deition of catalytic ignition and on matched activatioenergy asymptotics for gaseous ignition. A one-scatalytic reaction (first order with respect to the dficient reactant, as in Eq. (16)) and a one-step laactivation energy gaseous reaction were employAlthough the isothermal catalytic wall-boundary coditions were not typical in CST, except possiblya second-stage catalytic module, the heterogenepart of the analytical formulation was rich enoughprovide, in conjunction with the one-step reactionEq. (16), useful insights on high-pressure reactor pformance issues such as catalytic fuel conversioncatalytic ignition distance.

The fractional heterogeneous fuel conversIh,F (x)= mh,F (x)/mF,IN was shown to be [17]

(17)

Ih,F (ζ )= 1

Le

ζ∫0

1√2Prζ

(1/YF,IN)(Y′F )f r,W dζ,

where mF,IN = ρINYF,INUINb was the incomingfuel mass-flow rate over half the channel domamh,F (x) the integrated (down to positionx) heteroge-neous conversion on one catalytic wall,Le the Lewisnumber of the deficient reactant (fuel),ζ the Graetznumber [39] based on the incoming Reynolds nuberRe,

(18)ζ = x/(bRePr), Re= ρINUINb,

µIN

and (1/YF,IN)(Y′F)f r,W the normalized transvers

gradient of the fuel at the wall [17],

(1/YF,IN)(Y′F )f r,W =

[(GPDas)−1

(19)+ [(1/YF,IN)(Y

′F )f r,W

]−1Das→∞

]−1,

with Yk = (WF /νkWk)Yk andνk the stoichiometriccoefficient of thekth species. In Eq. (19),Das was acharacteristic surface Damköhler number

(20)Das = bBp−n exp(−Ea/RTW )

αth,IN,

where αth,IN was the inlet thermal diffusivity andG,P , and[(1/YF,IN)(Y ′

F )f r,W ]Das→∞ were mono-tonically increasing functions ofζ , the last functionbeing the normalized fuel wall gradient at infinitefast surface chemistry:

G= Le√

2Prζ

(TW

TIN

)−1,

P = 1+ 0.158

(TW

TIN

)−1.12Le0.32Da0.75

s ζ0.13,

and[(1/YF,IN)(Y

′F )f r,W

]Das→∞

= (0.43+ 0.45ζ0.35)Le1/3+0.19ζ0.35

(21)× Pr1/3+0.24ζ0.2(TW

TIN

)0.77ζ0.2

,

with TW /TIN the wall-to-inlet temperature ratioEquations (19) and (21) were valid up toζ = 0.16,which corresponded to a maximum fractional calytic fuel conversion (Das → ∞) of Ih,F ∼ 0.43for a diffusionally neutral fuel(Le = 1). Such max-imum fuel conversions were well within the intereof practical CST reactors [1], which usually consof two catalytic modules with combined fuel convesions ofIh,F ∼ 0.5. Substituting Eqs. (19) and (21in Eq. (17), the fractional fuel conversion becomes

(22)Ih,F (ζ )=ζ∫

0

[F(ζ,Das)+H(ζ )

]−1dζ,

with F(ζ,Das) andH(ζ ) the functions:

F(ζ,Das)= (TW /TIN)/(PDas),

(23)

H(ζ )= Le(2Prζ )1/2/[(1/YF,IN)(Y

′F )f r,W

]Das→∞.

In the limit of infinitely fast surface chemistryF(ζ,Das) = 0; substituting Eqs. (23) and (21)Eq. (22), the leadingζ dependence of the fractionfuel conversion is shown to beIh,F (ζ )∝ ζ0.85. Since


nc-balliden-ef

thetant

8)),xedinichassthens.

s-in-ithalna-rs)sureportc-en-

ytict ofas

m-per-sureouldper-gas

ed),

q.

nge

-nelnal

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Fig. 17. Fractional methane catalytic conversion as a fution of pressure, computed from Eq. (17) using the glostep of Eq. (16). Four different cases are plotted (socurves), characterized by different ranges of the nondimsional parameterζ . The top horizontal axis provides thsurface Damköhler numbersDas . The area to the right othe dashed-dotted line delineates the regimes over whichfractional catalytic fuel conversion is, in each case, conswithin 5%.

ζ is inversely proportional to pressure (see Eqs. (1a pressure increase in a catalytic channel of a figeometry and inlet velocity would always resulta decrease of the fractional fuel conversion, whis a direct consequence of the higher reactor mthroughput. However, this was not necessarilycase under finite-rate surface chemistry conditioSinceDas ∝ p1−n (considering thep−1 dependenceof the thermal diffusivity in Eq. (20)), for alln < 1 thefunction F(ζ,Das ) decreased with increasing presure and, therefore, the integrand of Eq. (22)creased with increasing pressure; in conjunction wthe drop ofζ with increasing pressure, the integrof Eq. (22) could become (under a proper combition of geometric and surface reaction parameteindependent of pressure over an extended presrange. For a system away from the mass-translimit, this simply implied that the increased reator mass throughput was counterbalanced by thehanced reactivity that led to the increased catalfuel conversion at higher pressures. The attainmenpressure-independent fractional fuel conversion whighly desirable in many practical systems, for exaple, gas turbines, as it resulted in a constant temature rise across the catalytic reactor during presramps and load changes. The above reasoning calso explain the nearly pressure-independent temature rise reported recently [40] in a subscale

turbine honeycomb-type catalytic reactor (Pd-basoperated at 5 bar� p � 15 bar.

Calculated fractional fuel conversions from E(22) are illustrated in Fig. 17, forn = 0.53, 4 bar�p � 16 bar,TW /TIN = 2 and typical for fuel-leanCH4/air mixturesLe= 0.95 andPr = 0.7. Four casesare presented, each characterized by a different raof nondimensional distancesζ and the sameDas fora given pressure:Das = 8 atp = 16 bar, while at dif-ferent pressuresDas scaled according to Eq. (20). Depending on the surface reactivity and on the changeometrical parameters, a nearly constant fractiofuel conversion could be attained over a specific psure range for each case. The higher the fractiofuel conversion of each case, the narrower the psure range over which a constant value ofIh,F couldbe maintained. Since in practical systems the surtemperature is directly linked to the catalytic reactity, an even broader pressure range of constantIh,Fcould be achieved compared to the range predictethe analysis of Eq. (22), which considered the surftemperature decoupled from the kinetics.

The light-off distance (catalytic ignition distancis also of prime interest in practical systems andminimization is a major reactor design goal. Withthe context of isothermal channel catalytic wallscatalytic ignition criterion was presented [17],

(24)Das,ig = (TW/TIN )3/2Le−2/3ζ−1/2.

The ignition criterion of Eq. (24) was a good aproximation to the rigorous criterion presented ain [17] and provided the nondimensional light-off ditance(ζ ) required to achieve a fuel conversion∼50%of the maximum attainable (mass-transport limitDas → ∞) conversion. Forn = 0.5, the physicallight-off distance was independent of pressure (Eqs. (24), (20), and (18)); it could be further reducwith increasing pressure ifn < 0.5. The reason fothis behavior was that, even though in the develing section of a channel the local transverse transrates increased with increasing Reynolds number (hence with pressure), the surface reactions couldcope with this augmentation provided that the calytic reactivity increased at an appropriate pressudependent rate.

5. Conclusions

The catalytic reactivity of fuel-lean methane/amixtures over Pt was assessed with in situ Rammeasurements of major species and temperatura channel-flow catalytic reactor operated at pressand temperatures in the ranges 4 bar� p � 16 barand 780 K� T � 1250 K, respectively. The experments were compared with 2-D numerical predictio


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that included elementary hetero/homogeneous rtion schemes and detailed transport. The followingthe key conclusions of this study.

1. The measured catalytic reactivity increased wincreasing pressure over the entire range 4 bar� p �16 bar. Predictions with two heterogeneous reacschemes, those of Deutschmann and Vlachos, hshown that both schemes captured the increase inalytic reactivity with increasing pressure. Howevonly the former scheme yielded a quantitative agrment with the measurements over the aforesaid psure range.

2. Crucial for the correct prediction of the mesured catalytic reactivity was the ability of the hetegeneous reaction schemes to capture the reductiosurface free-site coverage (and the correspondingcrease in oxygen coverage) with increasing pressThis effect restrained the rate of increase of the calytic reactivity with increasing pressure.

3. The gas-phase pathway could not be ignorehigh pressures. Even in the absence of homogenignition, the gaseous preignition chemistry could cotribute significantly to the fuel conversion at higpressures. The regimes of reactor residence timesurface-to-volume ratio(SV), over which the impacof the gaseous reaction pathway was important, wdelineated with computations in a surface perfecstirred reactor. It was shown that the numerical sulations of practical high-pressure catalytic combtion systems should consider the gaseous cheminotwithstanding the typically largeSV of these sys-tems.

4. Using the heterogeneous scheme of Deutsmann, a reduced catalytic reaction scheme wasrived, valid for purely heterogeneous combustion. Tscheme was capable of predicting accurately thealytic methane conversion in the absence of gasechemistry. A second, augmented reduced catalscheme for combined hetero/homogeneous comtion was also derived, which was capable of repducing the catalytic and gaseous fuel conversionwell as the onset of homogeneous ignition.

5. A global catalytic step could not reproduce tmeasured catalytic reactivity over the entire pressrange 4 bar� p � 16 bar. However, a best-fit globastep has been derived for engineering applicatioyielding catalytic methane conversions in an SPwithin ±15% of those computed with the validatescheme of Deutschmann, over the extended presrange 1 bar� p � 16 bar.

6. It was shown that, under a certain combinatof catalytic reactivity and geometrical reactor paramters, the fractional methane catalytic conversion (ahence, the temperature rise across a channel-flowactor) could become independent of pressure, wall other operating parameters (inlet velocity and

let temperature) were fixed. This property was higdesirable during pressure ramps and load changemany practical systems, such as gas-turbine catareactors.

Acknowledgments

Support was provided by the Swiss Federal Ofice of Energy (BFE), Swiss Federal Office of Eduction and Technology (BBT), and Alstom of Switzeland. We thank Dr. J. Wambach, Dr. F. Raimondi, aMs. F. Geiger for the XPS and BET analyses.

References

[1] R. Carroni, V. Schmidt, T. Griffin, Catal. Today 7(2002) 287–295.

[2] A. Schlegel, P. Benz, T. Griffin, W. WeisensteiH. Bockhorn, Combust. Flame 105 (1996) 332–340

[3] M. Reinke, J. Mantzaras, R. Schaeren, R. BombaW. Kreutner, A. Inauen, Homogeneous IgnitionHigh-Pressure Combustion of Methane/Air over Plinum: Comparison of Measurements and Detailed Nmerical Predictions, Proc. Combust. Inst. 29 (201021.

[4] C. Appel, J. Mantzaras, R. Schaeren, R. BombaA. Inauen, B. Kaeppeli, B. Hemmerling, A. Stampanoni, Combust. Flame 128 (2002) 340–368.

[5] O. Deutschmann, L.I. Maier, U. Riedel, A.H. Stroemman, R.W. Dibble, Catal. Today 59 (2000) 141–150

[6] A.B. Mhadeshwar, P. Aghalayam, V. PapavassilioD.G. Vlachos, Surface Reaction Mechanism Develment for Platinum Catalyzed Oxidation of MethanProc. Combust. Inst. 29 (2002) 997.

[7] P. Aghalayam, Y.K. Park, N. Fernandes, V. Papavsiliou, A.B. Mhadeshwar, D.G. Vlachos, J. Catal. 2(2003) 23–38.

[8] D.A. Hickman, L.D. Schmidt, AIChE 39 (1993) 11641177.

[9] O. Deutschmann, L.D. Schmidt, AIChE 44 (1992465–2477.

[10] H. Haerle, A. Lehnert, U. Metka, H.R. Volpp, LWillms, J. Wolfrum, Chem. Phys. Lett. 293 (1998) 2632.

[11] P. Ciambelli, V. Palma, S.F. Tikhov, V.A. SadykoL.A. Isupova, L. Lisi, Catal. Today 47 (1999) 199–20

[12] G. Groppi, W. Ibashi, E. Tronconi, P. Forzatti, CheEng. J. 82 (2001) 57–71.

[13] O. Deutschmann, R. Schmidt, F. Behrendt, J. WarnNumerical Modeling of Catalytic Ignition, Proc. Combust. Inst. 26 (1996) 1747.

[14] Y.K. Park, P. Aghalayam, D.G. Vlachos, J. Phys. CheA 103 (1999) 8101–8107.

[15] R.W. Sidwell, H. Zhu, R.J. Kee, D.T. WickhamC. Schell, G.S. Jackson, Catalytic Combustion of Pmixed Methane-Air on a Palladium-Substituted Hexluminate Stagnation Surface, Proc. Combust. Inst.(2002) 1013.


99)

02)

ch,r-ds.s,

art

für

li,ofofns,

n,orns-a-

w,

st.

us--u-

tz,

,

ng,

ys-u-

r-B,

-of

89-

in:usIn-

nal

ss,

A.l-Re-

es,

-ort

ss,

al.

[16] J. Mantzaras, P. Benz, Combust. Flame 119 (19455–472.

[17] J. Mantzaras, C. Appel, Combust. Flame 130 (20336–351.

[18] C. Appel, J. Mantzaras, R. Schaeren, R. BombaB. Kaeppeli, A. Inauen, An Experimental and Numeical Investigation of Turbulent Catalytically StabilizeChannel Flow Combustion of Hydrogen/Air Mixtureover Platinum, Proc. Combust. Inst. 29 (2002) 1031

[19] A. Brockhinke, P. Andresen, K. Kohse-HöinghauAppl. Phys. B 61 (1995) 533–545.

[20] B. Steiner, Ph.D. thesis, The University of Stuttg(2002).

[21] S. Eisenberg, Diploma thesis, Max-Planck-InstitutStrömungsforschung, Göttingen (1995).

[22] U. Dogwiler, J. Mantzaras, P. Benz, B. KaeppeR. Bombach, A. Arnold, Homogeneous IgnitionMethane/Air Mixtures over Platinum: ComparisonMeasurements and Detailed Numerical PredictioProc. Combust. Inst. 27 (1998) 2275.

[23] R.J. Kee, G. Dixon-Lewis, J. Warnatz, M.E. ColtriJ.A. Miller, A Fortran Computer Code Package fthe Evaluation of Gas-Phase Multicomponent Traport Properties, Report No. SAND86-8246, Sandia Ntional Laboratories, 1996.

[24] S. Patankar, Numerical Heat Transfer and Fluid FloHemisphere, New York, 1980, p. 131.

[25] U. Dogwiler, P. Benz, J. Mantzaras, CombuFlame 116 (1999) 243–258.

[26] J. Mantzaras, C. Appel, P. Benz, Catalytic Combtion of Methane/Air Mixtures over Platinum: Homogeneous Ignition Distances in Channel Flow Configrations, Proc. Combust. Inst. 28 (2000) 1349.

[27] L.L. Raja, R.J. Kee, O. Deutschmann, J. WarnaL.D. Schmidt, Catal. Today 59 (2000) 47–60.

[28] V.D. Vlachos, personal communication.

[29] J. Warnatz, M.D. Allendorf, R.J. Kee, M.E. ColtrinCombust. Flame 96 (1994) 393–406.

[30] J. Warnatz, U. Maas, Technische VerbrennuSpringer-Verlag, New York, 1993, p. 101.

[31] GRI-3.0, Gas Research Institute,http://www.me.berkeley.edu/gri_mech, 1999.

[32] J. Warnatz, R.W. Dibble, U. Maas, Combustion, Phical and Chemical Fundamentals, Modeling and Simlation, Springer-Verlag, New York, 1996, p. 69.

[33] R.J. Kee, F.M. Rupley, J.A. Miller, The Chemkin Themodynamic Data Base, Report No. SAND87-8215Sandia National Laboratories, 1996.

[34] R.J. Kee, F.M. Rupley, J.A. Miller, Chemkin II: A Fortran Chemical Kinetics Package for the AnalysisGas-Phase Chemical Kinetics, Report No. SAND8009B, Sandia National Laboratories, 1996.

[35] M.E. Coltrin, R.J. Kee, F.M. Rupley, Surface ChemkA Fortran Package for Analyzing HeterogeneoChemical Kinetics at the Solid Surface-Gas Phaseterface, Report No. SAND90-8003C, Sandia NatioLaboratories, 1996.

[36] I. Glassman, Combustion, third ed., Academic PreLondon, 1996, p. 156.

[37] H.K. Moffat, P. Glarborg, R.J. Kee, J.F. Grcar, J.Miller, Surface PSR: A Fortran for Modeling WelStirred Reactors with Gas and Surface Reactions,port No. SAND91-8001, Sandia National Laboratori1993.

[38] G.C. Snow, W.V. Krill, E.K. Chu, R.K. Kendall, Mechanisms and Kinetics in Catalytic Combustion, RepNo. EPA-600/9-84-002, 1984, p. 105.

[39] W.M. Kays, Crawford, Convective Heat and MaTransfer, third ed., McGraw–Hill, New York, 1993p. 128.

[40] R. Carroni, T. Griffin, J. Mantzaras, M. Reinke, CatToday 83 (2003) 157–170.

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