Modeling and Simulation of

Catalytic Partial Oxidation in Monolith Reactors

Jorge Emanuel Pereira Navalho

July 2, 2013

Abstract

Catalytic partial oxidation of hydrocarbons presents a promising route for synthesis gas and H2 pro-

duction for stationary decentralized and on-board applications. This process o�ers several advantages

over other well-established reforming technologies.

The present work reports the development of a 1D heterogeneous numerical model suitable for cat-

alytic partial oxidation of light hydrocarbons in monolith reactors. The model accounts for a wide

variety of transport and chemical steps occurring in di�erent regions of the catalyst bed. In par-

ticular, radiative heat transfer through the application of the zone method is considered as well as

the interactions between surface chemistry and transport of heat and mass along the porous catalyst

layers.

The model is extensively validated with literature data and also with new experimental results. In this

process a broad range of operating conditions including di�erent fuel compositions namely methane,

propane, surrogates of natural gas and synthetic biogas fuel are considered. Validation of the model

is also performed under non-adiabatic reactor operation. The good agreement observed between

the reference data and the current numerical predictions has allowed to a further application of the

model. Therefore, the role of several reactor design parameters to improve catalyst thermal stability

is assessed. Finally, an uncertainty quanti�cation study on the impact of eight random parameters

required as input data for the model on the �nal solution is provided pointing out the most relevant

uncertainty players on the stochastic model solution.

Keywords: Catalytic partial oxidation, Synthesis gas, Catalyst thermal stability, Zone method,

Parametric uncertainty quanti�cation.

1 Introduction

Catalytic partial oxidation (CPOx) of hydrocarbons as a route to produce synthesis gas (a mixturecomposed mainly of H2 and CO) has received an increasing attention from the beginning of the 1990'safter Schmidt and co-workers [8] reported excellent fuel conversion and synthesis gas selectivity underautothermal and short contact time conditions using rhodium and platinum noble metals over monoliths.

This process has several advantages over other well-established technologies to produce syngas like theenergy intensive steam reforming technology. The catalytic partial oxidation of hydrocarbons (para�ns)is globally described by the following reaction:

CxHy +x

2O2 → xCO +

y

2H2 (∆H◦R < 0) (R1)

In the case of being methane the fuel on Reaction (R1), the partial oxidation is mildly exothermic with aheat of reaction at standard conditions (∆H◦R) of about −36 kJ/mol and a H2/CO molar ratio of 2 whichis optimal for downstream chemical processes (methanol or Fischer-Tropsch synthesis). Besides moreeconomical than methane steam reforming, which globally is a strongly endothermic reaction (∆H◦R =206 kJ/mol), this technology also requires much simpler equipment, shorter residence times (millisecondcontact times) and presents the possibility to scale down (or up) [1] the reformer for a speci�c application,resulting in small reactors with a fast dynamic response due to its low heat capacity being suitable formobile or stationary decentralized applications [7].

Numerical modeling has been used mainly in the last two decades for gaining insight and also toimprove CPOx reactor catalysts and con�gurations. In particular, one-dimensional models have beenbroadly applied in literature to capture the reactor performance in an expedite way [15, 4].

1

In the next section a brief description on the mathematical model and numerical solution procedure isprovided. This is followed by the presentation of a short set of results. The document ends with summaryconclusions.

2 Modeling

2.1 Mathematical model

The mathematical model herein employed is based on a 1D steady-state two-phase model of a �xed bedreactor which accounts for a variety of phenomena. Equations (1) and (2) are the species mass andenergy balance equations of gas phase whereas Equations (3) and (4) are the species mass and energybalance equations of solid phase. The model takes into account di�usion and convection of heat andmass, radiative heat transfer and detailed or global surface chemistry. Homogeneous gas phase reactionsand internal di�usion limitations along the washcoat layer are also included in the model.

Aερg∂Yk,g∂t

+Aερgu∂Yk,g∂x

+∂

∂x(AερgYk,gVk,g) +AaV ρgKmat,k(Yk,g − Yk,w)−Aεωk,gWk = 0 (1)

AερgCp,g∂Tg∂t

+AερguCp,g∂Tg∂x− ∂

∂x

(Aεkg

∂Tg∂x

)+Aερg

KKg∑k=1

Yk,gVk,gCp,k∂Tg∂x

+AaV h(Tg − Ts)

+Aε

KKg∑k=1

ωk,gHk +Aεq′′′Rad = 0

(2)

ξεwρg∂Yk,w∂t

− aV ρgKmat,k(Yk,g − Yk,w)− ωk,wWk = 0 (3)

A(1− ε)ρsCp,s∂Ts∂t− ∂

∂x

(Aks,eff

∂Ts∂x

)−AaV h(Tg − Ts) +A

KKw∑k=1

ωk,wHk +AaV q′′Rad = 0 (4)

The correction velocity formalism is considered in the mass balance equations of gas phase species toassure the overall mass conservation since a non-conservative approach for molecular di�usion evaluationis employed (mixture-averaged formalism). Thermal di�usion relevant for low molecular weight species isincluded in molecular di�usion velocities. External transport coe�cients of species (Kmat,k) and heat (h)are evaluated through proper Sherwood and Nusselt correlations, respectively. The perfect-gas equationof state is employed for the evaluation of the gas mixture density.

In the energy balance equation of solid phase (Equation (4)) radiative heat transfer between surfacewalls is accounted for through the zone method. For honeycomb monoliths, shape factor expressions areemployed to compute direct exchange areas and after total exchange areas (ZjZi) evaluation Equation(5) is applied to determine the net radiative heat �ux from each surface.

q′′

si = εiσT4si −

1

Aiσ

Ns∑j=1

SjSiT4sj +

Ng∑j=1

GjSiT4gj

(5)

For foam monoliths the porous matrix is treated as a pseudo-homogeneous medium de�ned by continuumradiative properties such as an extinction coe�cient and a single scattering albedo. In this case, isotropicscattering and gray media are considered and the net radiative heat �uxes are computed through Equation(6).

q′′′

gi = 4κiσT4gi −

1

Viσ

Ns∑j=1

SjGiT4sj +

Ng∑j=1

GjGiT4gj

(6)

Boundary conditions

At the inlet section of the computational domain Danckwerts type of boundary conditions are consideredfor gas phase balance equations and for the energy balance of solid phase a radiative boundary conditionis applied. At the outlet, vanishing gradients for gas phase temperature and species mass fractions areconsidered and for the energy balance of solid phase a radiative boundary condition is also applied.

2

2.2 Numerical model

The set of governing equations, reliable constitutive relations, underlying assumptions required for modelclosure and boundary conditions are implemented in an in-house version of PREMIX code [11] fromCHEMKIN software packages. A �nite di�erence approach is considered as well as an adaptive meshprocedure. The calculation starts in an initial coarse mesh with uniformly spaced grid points and amodi�ed damped Newton method is used for the iteration process. If the solution lies out of the conver-gence domain the program initiates a time-stepping approach in an attempt to bring the solution to thedomain of convergence of the Newton method by a physically consistent evolution. The adaptive meshprocedure adds new grid points after the achievement of a converged solution in a given mesh locationif this location does not respect the gradient and curvature resolution for each dependent variable to thedegree de�ned by speci�c grid parameters.

Numerical integration of direct exchange areas was performed using the Gauss-Legendre quadraturewith 20 Gauss points for radial and angular directions whereas the Simpson's method with 5 points wasapplied for numerical integration along the axial direction.

Thermodynamic and transport properties are evaluated with CHEMKIN libraries [12, 10] with coe�-cients taken from GRI-Mech 3.0 database [23]. The open-source code CANTERA [2] is employed in thiswork to serve the main code as the kinetic interpreter for surface chemistry.

3 Results

3.1 Zone method veri�cation

The numerical results obtained with the numerical implementation of the zone method are comparedwith benchmark data. The cases herein presented are concerned with cylindrical and conical frustumenclosures. For both cases, the enclosure is composed by black-walled surfaces at 0 K and �lled with anabsorbing/emitting medium at a constant temperature of Tg = 100.0 K. For the cylindrical enclosurecase, the exact solution evaluated by Dua and Cheng [6] and the solutions recently reported by Kim andBaek [13] with the �nite volume method (FVM) and the S8 discrete ordinates method (DOM) are usedfor veri�cation purposes. For the truncated conical the results obtained by Kaminski [9] through theMonte Carlo (MC) method and the results computed by Kim and Baek [13] with the FVM are employed.

For both case studies Figure 1 presents the comparison between the solutions for the non-dimensionalwall heat �ux (−q′′

s /σ.Tref with Tref = Tg) along the non-dimensional enclosure height (z∗) on the

-qs'' /(σ

.Tre

f4

) [-]

0

0.2

0.4

0.6

0.8

1

z* [-]0 0.2 0.4 0.6 0.8 1

κ=0.1 m -1

κ=1.0 m-1

κ=5.0 m-1

Exact (Dua and Cheng, 1975)ZM - Present WorkFVM (Kim and Baek, 2005)S8 DOM (Kim and Baek, 2005)

(a)

z* [-]0 0.2 0.4 0.6 0.8 1

-qs'' /(σ

.Tre

f4

) [-]

0

0.1

0.2

0.3

0.4

0.5

κ=0.1035 m-1κ=0.207 m

-1

κ=1.035

m-1

MC (Kaminski, 1989)ZM - Present WorkFVM (Kim and Baek, 2005)

(b)

Figure 1: Comparison of non-dimensional radial wall heat �ux distribution on the side wall for anabsorbing/emitting medium con�ned in cylindrical (a) and truncated conical (b) enclosures.

3

side wall. A general good agreement is observed between the results obtained with the present thermalradiation method and the results reported in literature for the benchmark studies presented above.

3.2 Simulating catalytic partial oxidation: model validation and process in-

sight

The full-scale reactor model was extensively validated. However, herein only one case study is consideredfor validation purposes. The work reported by Beretta et al. [3] provides the reference data for such casestudy. The internal reactor layout is presented in Figure 2. The CPOx reformer consists in a tubular

Figure 2: Schematic diagram of the physical model. LFHS = LBHS = 1.5 cm; Lcat = 2.0 cm.

vessel with an internal diameter of 2.2 cm in which a washcoated 400 cpsi cordierite honeycomb monolithwith square-shaped cells is sandwiched between two uncoated FeCralloy foams. The catalyst honeycomband the inert foams have a length of 2.0 and 1.5 cm, respectively. The washcoat formulation is assumedto be 4 wt.% Rh/α − Al2O3 with a thickness of 12µm. The geometrical and thermophysical propertiesof the reactor for modeling purposes are shown in Table 1a. A bimodal pore size distribution of thewashcoat layer is presented in Table 1b.

Table 1: Properties of the reactor: (a) geometrical and thermophysical properties; (b) washcoat texturalproperties.

(a)

ε [−] 0.80aV[m−1

]2800.00

dh [m] 1× 10−3

ρcat[kg m−3

]1500.00

ks[W m−1 K−1

]3.00

(b)

δcat [µm] 12.50Macro-pores

εM [−] 0.050rM [nm] 200.00Micro-pores

εµ [−] 0.550rµ [nm] 50.00

Homogeneous reactions were neglected whereas the heterogeneous catalytic reactions were accountedfor through the global molecular kinetic scheme proper for the present catalyst formulation reported byDonazzi et al. [5]. Di�erent external transport correlations were considered for the catalyst and forheat shields. Radiative heat transfer was accounted for only in the energy balance of the solid phasethrough the Lee and Aris correlation [14]. Molecular intraphase di�usion limitations along the porousand isothermal washcoat layer were considered through the simpli�ed washcoat model and the e�ectivedi�usion coe�cients of each di�usive limiting species were computed through the random pore modelwith the washcoat pore structure presented in Table 1b. Dirichlet boundary conditions were consideredfor the gas phase species mass and energy balances at the inlet section (x = −1.5 cm) whereas zeroNeumann boundary conditions were considered for the remaining steady-state di�erential equations atthe inlet and outlet (x = 3.5 cm) sections.

The experimental and numerical results reported by Beretta et al. [3] are concerned with methanecatalytic partial oxidation operating at atmospheric pressure. The reactor feed mixture consists in amethane/air stream with an air ratio (λ) of 0.27, a temperature (Tg,in) of 546 K and a total mass �owrate (m) of 0.18 g.s−1. Figure 3 presents the comparison between the present numerical predictions andthe results reported in [3] for the temperature pro�les and product distribution. Note that the catalyst

4

Tgas - Present WorkTsol. - Present WorkTgas - Ref. (Num.)Tsol. - Ref. (Num.)Tgas - Ref. (Exp.)

Tem

pera

tute

[K]

500

750

1000

1250

x [cm]−1 0 1 2 3

(a)

O2

CH4

CO

H2

0

0.1

0.2

0.3

0.4

Present WorkReference (Num.)

H2OCO2

0

0.02

0.04

0.06

0.08

0.1

x [cm]−1 0 1 2 3

Mol

e Fr

actio

n [-]

(b)

Figure 3: Comparison between predicted results and the results reported in [3]: (a) solid and bulk gastemperature pro�les; (b) bulk gas product distribution pro�les.

section starts at x = 0.0 cm (see Figure 2). A good agreement between the numerical predictions and thereference data is observed.

An in-depth discussion on the model validation for this case study was previously reported by Navalhoet al. [17]. In such reference the in�uence of the catalyst loading, inlet feed gas temperature and mixturestoichiometry on reactor performance (syngas selectivity and fuel conversion) is investigated as well. Thepresent model was also successfully validated under non-adiabatic regimes over a wide range of operatingconditions for methane and natural gas surrogates [21, 18, 16] as well as for clean model biogas mixtures[22].

3.3 Improving catalyst thermal stability

Catalyst thermal stability during catalytic partial oxidation is an issue that concerns its application.Several authors have considered the catalyst thermal stability a major challenge in catalytic partialoxidation operation [3]. This is mainly due to the high surface temperatures (hot-spot) that establishnear the catalyst inlet section. Very high surface temperatures, say above 1000 ◦C can trigger catalystdeactivation mechanisms such as sintering of metal crystallites and support phase changes.

An investigation was conducted in current work on the role of several design parameters in the catalystthermal performance. For a honeycomb monolith reactor, thermophysical and geometrical parameters,catalyst loading and the length of the front heat shield were considered. Regarding foam monoliths, astrategy was proposed and analyzed, as far as the author is aware for the �rst time: conical-shaped foammonolith reactor [20].

The e�ect of metal loading on the thermal behavior of a honeycomb catalyst is herein brie�y discussed.To conduct this study it was considered the physical model presented in Figure 4 that is composed bytwo 400 cpsi cordierite honeycomb substrates with an external diameter of 2.4 cm. Equal thermophysicaland geometrical properties are assumed for the uncoated front heat shield and for the catalyst monolith.Square-shaped channels with a total hydrodynamic porosity of 80% are considered. A washcoat layermade out of 4 wt.% Rh/α−Al2O3 is considered as well. A continuous material transition from the inert tothe catalytic monolith is assumed as well as a stepwise appearance for the washcoat layer at x = 0.0 cm.The reference operating condition is de�ned by an inlet preheated feed stream at 600 K and 1 atm withan air ratio of 0.30 (O/C molar ratio of about 1.2) and a total volumetric �ow rate of 10 NL/min.

An increase in the catalyst loading was properly accounted for in the model through an increase in thecatalytic volumetric fraction as well as a consistent increase in the washcoat thickness. The geometricalproperties of the honeycombs were kept constant to the reference geometrical parameters along this study.

5

Figure 4: Schematic diagram of the physical model. LFHS = 2.0 cm; Lcat = 3.0 cm.

Figure 5a shows that a signi�cant decrease in the maximum surface temperature can be attained byincreasing the thickness of the deposited catalyst layer. The e�ect of the catalyst loading is practicallyinsensitive during the whole front heat shield length but not along the catalyst domain.

203.58 mg610.73 mg1.22 g1.83 g

Tem

pera

ture

[K]

600

800

1000

1200

1400

x [cm]−2 −1 0 1 2 3

Tem

pera

ture

[K]

11751200122512501275130013251350

x [cm]0 0.1 0.2 0.3 0.4 0.5

Tsol.Tgas

(a)

203.58 mg610.73 mg1.22 g1.83 gO2

0

0.025

0.05

0.075

0.1

0.125

0.15

CH4

0

0.05

0.1

0.15

0.2

0.250.3

x [cm]0 0.25 0.5 0.75 1 1.25 1.5

Bulk gasWall

Mol

e Fr

actio

n [-]

(b)

Figure 5: E�ect of catalyst loading: (a) temperature pro�les; (b) O2 and CH4 molar pro�les.

The thermal behavior observed by increasing the catalyst loading is justi�ed with an increase in thekinetic rate of CH4 consumption due to the endothermic steam reforming reaction. Figure 5b presentsthe pro�les of the reactant species (O2 and CH4) for the di�erent catalyst loadings considered. O2

consumption is fully controlled by external mass transfer and therefore is blind to the enhancement ofsurface chemistry rates due to an increase in the catalyst content (see O2 pro�les in Figure 5b). However,the same does not happen with CH4 that presents di�erent molar pro�les for di�erent catalyst loadings.Therefore, the rate of heat release from exothermic O2 consumption reactions is alike for all catalystloadings but the rate of heat consumption (through methane steam reforming) is accelerated resulting inan overall decrease in the temperatures along the catalyst bed.

An increase in the catalyst loading besides allowing for a signi�cant decrease in the maximum surfacetemperature also allows for a reduction in the required residence time to attain thermodynamic equilib-rium conditions (see Figure 5a). However, a limit seems to appear for such bene�cial e�ects as the catalystloading increases. For instance the increase from 1.22 g to 1.83 g did not promote relevant changes inthe reactor performance. This may suggest that an ine�cient utilization of the washcoat layer starts toappear due to internal mass transport limitations properly accounted for in the model formulation.

6

3.4 On the uncertainty quanti�cation in methane catalytic partial oxidation

The results presented in the previous sections are regarded as deterministic because all parameters re-quired as input data for the model formulation were assumed to be fully known, without presenting anyrandom behavior. However, in practice some uncertainty level is always inherently present in such param-eters and simple sensibility studies do no not provide any insight on the e�ect of uncertainty propagationfrom the input model parameters to the output model solution.

As far as the author is aware, catalytic partial oxidation was not yet subjected to a parametric un-certainty quanti�cation. Therefore, the present section focuses on the uncertainty quanti�cation of eightrandom parameters required as input for 1D modeling of methane catalytic partial oxidation withina highly dense foam monolith reactor. Parameters related with geometrical properties, reactor ther-mophysics and catalyst loading are taken as uncertain. The non-intrusive spectral projection (NISP)approach based on polynomial chaos expansion is applied to propagate the random input data throughthe model and quantify its impact on the �nal solution. The study that follows is mainly based on thework recently submitted for publication [19].

The reactor is composed by two main regions, the catalytically inactive front heat shield (FHS) andthe catalyst monolith, with 1.0 cm and 2.0 cm of length, respectively, and with an outer diameter of 1.7cm (see Figure 6). Both reactor structures are composed by α−Al2O3 foams with 80 ppi. Onto thecatalyst substrate walls a thin Rh/α−Al2O3 washcoat layer (δcat < 10 µm) is assumed to be deposited.A perfect linkage between both foam monoliths are considered and consequently no thermal resistanceat x = 0.0 cm for solid conduction is taken into account.

Figure 6: Schematic diagram of the physical model. LFHS = 1.0 cm; Lcat = 2.0 cm.

Catalytic partial oxidation at atmospheric pressure and steady-state conditions of a methane-airmixture with an air ratio of 0.31 (O/C ratio of about 1.2), a total volumetric �ow rate of 10 NL min−1

and an inlet mixture temperature of 600 K is considered the reference operating condition to explorethe uncertainty propagation through the model. Figure 7 presents the deterministic model solution fortemperature (gas and solid), gaseous species (wall and bulk gas) and surface species pro�les computedwith the mean values for all input uncertain parameters.

The most relevant model input uncertain parameters are: the geometrical properties such as porosity(ε), surface area to total reactor volume (aV ) and pore diameter (Dp); the ratio between catalytic andgeometrical surface area (Fcat/geo); the solid conductivity (ks); the solid tortuosity (τ); and the radiativeproperties of the cellular structure (β and ω). The variability ranges and mean values adopted forsuch random parameters are physically founded and well-supported by literature data. Moreover, twouncertainty ranges (URs) for the eight random parameters are de�ned: the reference and the extended.Both have equal mean values but the extended UR takes a double value for the standard deviation of alluncertain parameters expect the single scattering albedo. The standard deviation of the single scatteringalbedo was increased by a factor of 1.5 in the extended UR.

Figure 8a shows the stochastic solid temperature pro�les for ensemble mean, standard deviation anderror bars with a con�dence interval (CI) of 95% for both uncertainty ranges. It shows that the reactorzones with the highest uncertain levels are observed in the FHS, few millimeters upstream the catalystentrance, and downwards in the central part of the catalyst domain and this behavior is independent ofthe uncertainty range considered. In the former region values up to 150 K and 75 K are observed withinthe upper and lower limits of the error bars for the extended and reference URs, respectively. Noticethat the uncertainty on the stochastic solid temperature pro�les near the inlet and outlet reactor sectionstends to become almost negligible due to the absence of uncertain boundary conditions and to the lowimportance of the energy interphase transport term, in particular near the catalyst outlet section drivenby the approximation to thermodynamic equilibrium.

7

CatalystShieldHeatFront

(a)

Tem

pera

ture

[K]

600800

1000

1200

1400

Tsol

Tgas

(b)

CH4

O2

H2OCO2

COH2

Mol

ar fr

actio

n [-]

00.1

0.2

0.3

0.4

Rh(s)CO(s)C(s)H(s)O(s)OH(s)H2O(s) (c)

Surf

ace

cove

rage

[-]

10−610−510−410−310−210−1100101

x [cm]−1 −0.5 0 0.5 1 1.5 2

Bulk speciesWall species

Figure 7: Deterministic model solution pro�les evaluated with mean values: (a) solid and gas tempera-tures; (b) composition of gaseous species (bulk gas and at the bulk gas/wall interface); (c) coverages ofthe most abundant surface species.

σ [K]

0

10

20

30

40

50

Reference URExtended URMean valueσ

T s [K

]

600

800

1000

1200

1400

x [cm]−1 −0.5 0 0.5 1 1.5 2

(a)

1st Order

aV2

ε2

Fcat/geo.aVFcat/geo

2

aV.εks.ε

2nd Order εaVFcat/geoksτβωDp

T s e

xpan

sion

coe

ffici

ents

(CiT s) [

K]

−80

−60

−40

−20

0

20

x [cm]−1 −0.5 0 0.5 1 1.5 2

(b)

Figure 8: Stochastic solution pro�les of solid temperature: (a) ensemble mean, standard deviation anderror bars with 95% CI for the reference and extended URs; (b) most relevant expansion mode coe�cientsfor the reference UR.

The NISP method allows the uncertainty quanti�cation of each input random parameter on the total�nal stochastic solution. Therefore, in Figure 8b it can be seen the �rst-order and the major contributivesecond-order expansion mode coe�cients for the reference UR. The parameters ε, aV , Fcat/geo and ksare the dominant input uncertain sources regarding the solid temperature pro�le. Along the FHS theporosity dominates over the remaining parameters because of its direct impact in the heat di�usion termof the solid phase. Solid tortuosity and thermal conductivity that also have a direct in�uence on thedi�usive term present a lower importance than porosity. In the catalyst region, aV and Fcat/geo are byfar the most important parameters. Uncertainty in radiative heat transfer parameters does not play animportant role on the achieved solution despite the large uncertainty prescribed for these parameters.

8

This is not a surprising remark since the highly dense nature of the employed 80 ppi foam assigns anegligible e�ect for radiative heat transport comparing with solid conduction. The low values registeredfor second-order coe�cients comparing with the �rst-order coe�cients allow one to anticipate a goodstochastic convergence.

Regarding gas temperature pro�les, Figure 9a presents for both URs the stochastic mean values,standard deviations and the error bars for a CI of 95%. Slightly after the catalyst inlet section theuncertainty in the gas temperature pro�le achieves its maximum value. Figure 9b demonstrates thatthe speci�c surface area is the parameter that more contributes to this high uncertainty level because ofits in�uence on the external heat transport term. Parameters that do not play any direct in�uence inthe gas phase energy balance (Equation (2)), such as τ , ks, Fcat/geo, β and ω are also responsible forthe uncertainty registered in the gas temperature pro�les through the external transport term. At the

σ [K]

0

10

20

40

50

60

Reference URExtended URMean valueσ

T g [K

]

600

800

1000

1200

1400

x [cm]−1 −0.5 0 0.5 1 1.5 2

(a)

2nd Order1st Order

aV2

Fcat/geo.aVaV.εε2

Fcat/geo2

ks.ετ.ε

aVεFcat/geoksτDpβω

T g e

xpan

sion

coe

ffici

ents

(CiT g

) [K

]

−50

−25

0

25

50

75

x [cm]−1.5 −1 −0.5 0 0.5 1 1.5 2

(b)

Figure 9: Stochastic solution pro�les of gas temperature: (a) ensemble mean, standard deviation anderror bars with 95% CI for the reference and extended URs; (b) most relevant expansion mode coe�cientsfor the reference UR.

FHS entrance (x = −1.0 cm), a negligible uncertainty is noticed and explained through the absence ofrelevant thermal gradients. This makes the Danckwerts boundary condition applied on the gas phaseenergy balance to behave as a Dirichlet boundary condition. Also noticeable is the uncertainty decayas the to thermodynamic equilibrium is reached, i.e., in sections located farther away from the catalystinlet section.

4 Conclusions

A steady-state 1D heterogeneous numerical model was developed for catalytic partial oxidation of lighthydrocarbons and biofuels in monolith reactors. The model accounts for a wide variety of transportmechanisms as well as for homogeneous gas phase and heterogeneous chemistry. The zone method ofradiative heat transfer analysis was developed and coupled to the main model to evaluated the rates ofradiative heat exchange between monolith walls. Mass and heat transfer limitations along the porouscatalyst layers were also properly accounted for. The following conclusions can be drawn:

• the zone method was veri�ed against benchmark studies. Good agreement between numericalresults and the reference data was observed for all cases employed;

• the overall full-scale monolith reactor model was validated with experimental data taken from theopen literature. Moreover, new experimental data performed in non-adiabatic honeycomb monolithreactors was employed for model validation. A wide range of operating conditions including di�erentfuel compositions, viz. methane, propane, simple surrogates of natural gas and clean model biogaswas considered for validation purposes. The model has shown a predictive behavior for all the cases;

9

• an investigation was carried out on the role of speci�c reactor design parameters in the catalyst ther-mal stability. Reactor thermophysical and geometrical parameters, catalyst loading and the lengthof the front heat shield were considered. Conical-shaped foam monolith reactors were proposedexhibiting a better thermal performance than the traditional cylindrical-shaped foam monolithreactors widely applied in catalytic combustion applications;

• an uncertainty quanti�cation study was carried out based on the application of the developedmodel (deterministic model) along with the non-intrusive spectral projection approach based onpolynomial chaos expansion (stochastic model). This study, performed by the �rst time, focused onthe uncertainty quanti�cation of eight random parameters required as input for the deterministicmodel. The variability ranges adopted for such random parameters are physically founded andwell-supported by literature data. The uncertainty role performed by such parameters on the �nalstochastic solution cannot be ruled out in speci�c sections of the catalyst bed, in particular nearthe catalyst entrance section. Porosity, speci�c surface area and catalyst loading were pointed outas the main uncertainty players on the stochastic temperature and bulk species pro�les.

Throughout this work the developed model has proven to be a robust, e�cient, fast and a suitabletool for design assistance of CPOx-based reformers.

10

Nomenclature

A cross-sectional reactor area

Ai area of surface zone i

Cp speci�c heat capacity at constant pressure

Hk molar enthalpy of species k

KK total number of species

Kmat,k interphase mass transport coe�cient

L length

Ng total number of volume zones

Ns total number of surface zones

T temperature

Vk di�usion velocity of species k; volume ofzone k

Wg mean molecular weight of the bulk gas mix-ture

Wk molecular weight of species k

Yk mass fraction of species k

ZiZj total exchange area between zones i and j

aV speci�c surface area

cXj expansion mode coe�cient number j of XPC expansion

dh hydraulic diameter of monolith channels

h interphase heat transport coe�cient

k thermal conductivity

q′′′Rad net radiative heat �ux from the gaseous mix-ture

q′′Rad net radiative heat �ux from the solid phase

r radius

t time

u axial mean �ow velocity (interstitial �ow ve-locity)

x axial reactor coordinate

Greek Letters

β extinction coe�cient

δcat washcoat thickness

ωk,g net molecular production/consumption rateof bulk gas species k due to homogeneousreactions

ωk,w net molecular production/consumption rateof wall species k due to surface reactions

ε porosity

εi emissivity of surface zone i

κi absorption coe�cient of volume zone i

ω single scattering albedo

ρ mass density

σ Stefan-Boltzmann constant; standard devi-ation

Subscripts

µ micro-pores

cat catalyst/washcoat

g gas phase; gas phase species in the bulk gas�ow

gi volume zone i

k species k

M macro-pores

s solid phase; adsorbed species

si surface zone i

w wall species (gas phase species at the gas/wallexternal interface); washcoat

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