The submerged archaeology of the North Sea: Enhancing the Lower Palaeolithic record of northwest Europe

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Modelling complete methane oxidation over palladium oxide in a porous catalyst using first-principles surface kinetics† Carl-Robert Florén,∗a Maxime Van den Bossche,b Derek Creaser,a Henrik Grönbeck,b Per-Anders Carlsson,a Heikki Korpic and Magnus Skoglundha

A comprehensive model is developed for complete methane oxidation over supported palladium. The model is based on first-principles microkinetics and accounts for mass and heat transport in a porous catalytic layer. The turnover frequency (TOF) is simulated for wet exhaust gas compositions, exploring the effects of temperature and total pressure on the TOF. Three different temperature regimes are identified each with different dependency on the total pressure. The regimes originate from temperature and pressure dependent coverages of carbon dioxide and water, which are the most abundant surface species hindering methane dissociation at low temperatures. The TOF is controlled by surface kinetics below 400◦ C whereas above 500◦ C and up to 8 atm, internal mass transport is controlling. A combination of kinetics, external and internal mass transport controls the TOF at other reaction conditions. The physically meaningful model paves the way for extrapolation and optimization of catalyst design parameters for high catalytic efficiency.

1 Introduction Heterogeneous catalysts are widely used for production of, e.g., fuels, fertilizers and chemicals as well as for abatement of harmful emissions. Efficient utilization of the catalyst material in industrial processes relies on maintaining reactor control parameters,

∗ Corresponding author. Fax: +46 31 160062; Tel: +46 31 7722925; E-mail: [email protected] a Competence Centre for Catalysis, Department of Chemistry and Chemical Engineering, Chalmers University of Technology, SE-41296 Göteborg, Sweden. b Competence Centre for Catalysis, Department of Physics, Chalmers University of Technology, SE-41296 Göteborg, Sweden. c Wärtsilä Finland Oy, FI-65100 Vaasa, Finland. † Electronic Supplementary Information (ESI) available: [Summary of all elementary steps with kinetic parameters.]. See DOI: 10.1039/b000000x/

e.g., temperature, pressure and feed composition, that are beneficial for the reaction. The choice of suitable operating conditions benefits from a good understanding of the reaction network and its dependence on reaction conditions. The reaction network is often complex and the preferred reaction pathway may change with even a small change of the control parameters, hence, impacting the overall performance of the reactor 1,2 . Detailed models that couple microkinetic reactions with descriptions of mass and heat transport for the reactor at hand provide new possibilities to simulate not only the influence of control parameters on the overall performance but also to link obtained activity and selectivity to detailed mechanistic steps. Natural gas has regained interest as an alternative fuel and the usage is presently increasing both in the transport and energy sectors 3–6 . Lean (oxygen excess) engine combustion of natural gas, which essentially is methane, has some advantages as compared to combustion of common diesel fuels. The low carbon-tohydrogen ratio of methane results in less CO2 emissions per delivered energy unit and the formation of CO, soot and NOx is often lower than for longer hydrocarbons 7 . Methane, however, is a potent greenhouse gas 8 and slipped methane from the combustion process must be carefully handled. The method of choice is commonly supported palladium-based catalytic exhaust aftertreatment systems for complete oxidation of methane 6,9–11 . The thermodynamically favourable phase of palladium below 700◦ C and at oxygen pressures above 10 mbar is a bulk oxide 12,13 . The phase transition temperature from palladium oxide to metallic palladium increases with oxygen pressure 12,13 and the PdO decomposition temperature may be even higher for supported particles. 13–15 . Thus, under realistic lean exhaust gas conditions, i.e., 1-10 vol.-% O2 , palladium is expected to be in an oxidised state 10,16,17 . Catalytic processes can in many cases be more efficient when operated at elevated pressures 18–20 . Nikitin et al. 21 showed that J our na l Na me, [ y ea r ] , [ vol . ] ,1–13 | 1

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the temperature for oxidative hydrocarbon cracking can be lowered by increasing the total pressure. Another reaction is oxidative steam reforming of methane where it has been shown that the reaction rate increases under pressurized conditions 22 . In the case of catalytic combustion of methane for power generation, increased pressure has also been shown to increase the rate of reaction 20,23,24 . Hitherto, however, the literature on lean methane oxidation is scarce at low temperatures, which is relevant for exhaust aftertreatment, and high-pressures. First-principles based microkinetic models have been developed for complete methane oxidation on metallic palladium 25–28 . Further, detailed first-principles based models coupled to mass and heat transport have been developed 29 to elucidate the preferred reaction pathway 30,31 for partial oxidation of methane on Rh. Stotz et al. 28 , coupled the kinetics to mass and heat transport and showed that it is possible to predict concentration profiles along a monolith channel, as well as to capture reaction features observed in experiments. In the present study we develop a comprehensive model for lean oxidation of methane over a layer of porous alumina supported palladium, representing the geometry of a monolith reactor. The surface processes over palladium oxide are described by first-principles microkinetics and coupled to mass and heat transport descriptions for the porous catalyst. The methane turnover frequency (TOF) is simulated as a function of temperature and total pressure for wet conditions. It is shown that the TOF above 500◦ C is governed by the total pressure.

2 Methods 2.1 First-principles microkinetic modelling 2.1.1 Electronic structure calculations The electronic structure calculations are performed using density functional theory (DFT) as outlined by Van den Bossche et al. 32 . The plane-wave projector augmented-wave (PAW) code VASP 33–35 is used, with PAW potentials and a kinetic energy cutoff value of 450 eV. All calculations are performed in a (3×1) PdO(101) surface unit cell containing four PdO trilayers (48 substrate atoms), a top view is shown in Figure 1. The structures are relaxed (with the bottom PdO trilayer constrained to bulk positions) until the strongest force in the system is lower than 0.01 eV/Å for local minima and lower than 0.05 eV/Å for transition states. The transition states are obtained with the climbing image nudged elastic band 36,37 as well as the dimer method 38 . The energies are evaluated employing the screened hybrid functional HSE06 39,40 , whereas the structures are obtained using the Perdew, Burke, and Ernzerhof (PBE) functional 41 . Transition state theory is used to describe the kinetics. The possible adsorption sites on the PdO(101) surface are visualised in Figure 1. Here S1 sites are associated with undercoordinated Pd sites and S2 sites with undercoordinated O sites. Both S1 and S2 sites may be of either atop (a) or bridge (b) type. The carbonaceous intermediates that adsorb on S1a are CH3 , CH2 O, CO and CO2 while S1b is the preferred site for adsorption of CH2 , CH, C, CH2 OH, CHO, HOCO, HCOO, CO3 , CO3 HA and CO3 HB . Species that can adsorb on undercoordinated oxygen sites are CH3 (S2a ), CH2 (S2b ), CHO (S2a ) 2|

J our na l Na me, [ y ea r ] , [ vol . ] , 1–13

Fig. 1 Left: Top view of a (3×1) PdO(101) unit cell and the different adsorption sites. Middle: Adsorbed bicarbonate in A-configuration. Right: Adsorbed bicarbonate in B-configuration. Atomic color code: Pd (gray), O (red) for surface atoms, and C (black), O (blue) and H (white) for adsorbed atoms.

and CO (S2b ). The hydrogen-oxygen compounds that adsorb on Pd include H2 O (S1a ), OH (S1b ), O2 (S1b ), O (S1b ) and H (S1a ). When atomic H and O adsorb on an oxygen site, S2a and S2b are preferred respectively. The microkinetic reaction model includes pairing reactions between adsorbed surface species due to strong adsorbate-adsorbate interactions. 2.1.2 Microkinetics model The microkinetic model 32 is complemented with additional elementary steps to consider adsorbed carbon dioxide, carbonates and bicarbonates. Bicarbonates adsorb on S1a sites in either A- or B-type configuration as shown in Figure 1. The reaction network includes 43 different surface species and 80 considered elementary steps. The elementary steps and respective kinetic parameters are shown in Tables 1-3. 2.1.3 Rate coefficients The rate coefficients for surface reaction, k, are calculated according to conventional transition state theory 42,43 between reactant (R) and its transition state (TS) as k=

∆E kB Ts QT S ( )exp(− T S−R ) h ΠR QR kB Ts

(1)

where Ts is the catalyst surface temperature, h is Planck’s constant, Q denotes the partition functions of translational, rotational and vibrational motion, which are assumed to be separable and ∆ET S−R is the difference in electronic energy between the reactants and the transition state 32 . Kinetic gas theory is used to describe the adsorption kinetics, kads , as shown in Eq. 2. S0 Sdyn Asite −Ea kads = √0 exp( ) kB Ts 2πmkB Ts

(2)

where kB is the Boltzmann constant and Ea is the activation energy. The area per adsorption site (Asite ) is set to 1 Å2 and m is the mass of the adsorbed molecule. The sticking coefficient at zero coverage, S00 , is calculated from transition state theory

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no. (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15) (16) (17) (18) (19) (20) (21) (22) (23) (24) (25) (26) (27) (28) (29) (30) (31) (32) (33) (34) (35) (36) (37) (38) (39) (40) (41) (42) (43) (44) (45) (46) (47) (48) (49) (50) (51) (52) (53) (54) (55) (56) (57)

Reaction equation CH4 (g) + S1 -S2 CH4 (g) + OH + S1 CH4 (g) + OH-H + S1 CH4 (g) + OH + S1 + H CH4 (g) + OH-H + S1 + H CH4 (g) + O CH4 (g) + O2 CH3 -H + OH CH3 -H + OH-H CH3 -H + O CH3 -H CH3 + OH CH3 + OH-H CH3 + O CH3 + O2 CH3 + S2 CH3 + S2 CH3 -Vac + S2 CH3 CH3 + O CH3 + OH CH3 + OH-H CH3 CH2 -H + OH CH2 -H + OH-H CH2 -H + S2 CH2 + OH CH2 + OH-H CH2 + O2 CH2 + S2 CH2 + S2 CH2 + S1 CH2 OH + S2 CH2 O + S2 CH2 O + OH CH2 O + OH-H CH2 O CH + S2 CH + S2 CHO-H + OH CHO + S2 CHO + S2 CHO + OH CHO + S1 CHO + OH CHO + S1 CHOO-Vac + S2 CHOO + S2 CHOO + OH CO CO + S2 CO + S1 CO2 -Vac CO + O CO + O2 CO + OH HOCO + S2

                                                        

CH3 -H CH3 + H2 O CH3 + H2 O + H CH3 -H + H2 O CH3 -H + H2 O + H CH3 + OH CH3 + OOH CH2 -H + H2 O CH2 -H + H2 O + H CH2 OH-H + S1 S1 + CH3 (g) + H CH2 + H2 O CH2 + H2 O + H CH2 OH + S1 CH3 OO + S1 CH2 -H S1 + CH3 CH2 -H + Vac S1 + CH3 (g) CH2 + OH CH2 + H2 O CH2 + H2 O + H S2 + CH3 (g) CH2 OH-H + S1 CH2 OH-H + H + S1 CH2 + H CH2 OH + S1 CH2 OH + H + S1 CH2 OO + S1 CH-H CH2 + S1 CH2 O-Vac CH2 O-H CHO-H CHO + H2 O CHO + H2 O + H S1 + CH2 O(g) C-H CHO + Vac CO + H + H2 O CO + H S1 + CHO CO + H2 O CO2 (g) + H + Vac CO(g) + H2 O CHOO-Vac CO2 (g) + S1 + Vac + H CO2 (g) + S1 + H CO2 (g) + H2 O + S1 S1 + CO(g) S1 + CO CO2 -Vac S1 + CO2 (g) + Vac CO2 (g) + 2 S1 O + CO2 (g) + S1 HOCO + S1 CO2 (g) + S1 + H

and accounts for the change in entropy upon adsorption. Sdyn is an added dynamic sticking coefficient that accounts for the fact that a gas phase molecule has to approach the surface in a favourable orientation to adsorb dissociatively. Sdyn is set to 10−2 for methane and unity for all other species. Reported experimen-

Af 7.6×104 2.8×104 ” ” ” 6.7×104 — 3.6×1012 ” 1.1×1013 1.0×1016 3.6×1012 ” 1.1×1013 — 7.9×1012 4.6×1013 ” 1.0×1016 3.9×1013 4.9×1013 ” 1.9×1017 1.1×1013 ” 3.7×1013 1.1×1013 ” — 1.1×1014 3.7×1013 5.5×1013 5.4×1013 8.8×1012 1.5×1013 ” 4.8×1015 3.5×1013 6.1×1012 2.1×1014 3.9×1014 4.5×1013 2.1×1014 9.2×1012 1.8×1014 1.3×1013 4.4×1014 3.2×1014 4.4×1014 7.7×1015 4.7×1012 8.1×1012 1.9×1014 2.3×1013 5.7×1012 1.1×1013 1.5×1014

Ab 1.8×1014 1.4×1013 ” ” ” 7.7×1013 — 8.3×1013 ” 1.0×1015 2.6×107 8.3×1013 ” 1.0×1015 — 1.5×1014 1.0×1015 ” 2.6×107 7.5×1013 4.0×1013 ” 2.6×107 8.6×1013 ” 1.2×1014 8.6×1013 ” — 1.3×1014 1.2×1014 1.2×1012 1.5×1012 2.8×1014 1.0×1014 ” 1.8×107 6.0×1013 5.3×1012 3.2×1013 2.8×1014 5.2×1013 3.2×1013

4.3×1012

1.9×107 7.8×1012 2.1×1012 1.5×107

6.3×1013

EHSE06 a,f 0.29 0.30 0.24 0.04 0.69 0.33 2.26 1.14 2.08 0.73 2.74 0.83 1.16 0.47 1.11 1.29 1.15 1.44 1.54 0.194* 0.291* 1.15 1.96 0.31 1.11 1.29 0.06 0.19 0.79 1.23 0.22 0.82 0.21 0.69 0.52 0.37 0.55 1.31 0.32 0.33 0.78 0.71 0.58 1.08 0.291* 0.12 1.41 1.83 1.95 1.40 0.45 0.41 0.69 0.194* 1.51 0.32 0.22

EHSE06 a,b 1.32 1.08 0.62 1.32 1.62 1.77 — 1.15 1.03 2.37 0.00 1.14 0.84 3.31 — 1.71 2.09 1.34 0.00 3.30 2.25 2.38 0.00 1.29 1.03 2.15 1.94 1.01 — 1.63 1.97 0.22 0.52 2.19 2.01 0.80 0.00 1.42 2.17 0.00 2.44 1.19 2.88

0.09

0.00 0.07 0.84 0.00

0.53

tal values for methane adsorption on transition metal surfaces are in the interval of 10−4 -10−1 ( 44 and references therein). The reaction rate for each elementary step is calculated by multiplying the rate coefficient, k, with the coverages of reacting surface species. Steady state reaction rates and coverages are obJ our na l Na me, [ y ea r ] , [ vol . ] ,1–13 | 3

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Table 1 Kinetic parameters for the considered elementary steps including carbonaceous intermediates. f and and b denote forward and backward reactions, respectively. The values for the pre-exponential factors (1/s) are calculated at 700 K and 1 bar. The energy barriers are given in eV. Reactants adsorbed on Pd and O sites are in regular and bold font, respectively. Activation energies denoted with * correspond to the barrier for diffusion of the reactants, as the actual reaction is non-activated.

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no. (58) (59) (60) (61)

Reaction equation S1 + CO2 (g) CO2 + O CO2 + OH CO3 HA

   

CO2 CO3 + S1 CO3 HA + S1 CO3 HB

Af 1.5×107 1.0×1013 ” ”

Ab 8.4×1015 1.0×1013 ” ”

EHSE06 a,f 0.00 0.23 0.25 0.87

EHSE06 a,b 0.52 0.80 0.46 1.56

Table 3 Kinetic parameters for the considered elementary steps including Ox Hy intermediates. f and and b denote forward and backward reactions, respectively. The values for the pre-exponential factors (1/s) are calculated at 700 K and 1 bar. The energy barriers are given in eV. Reactants adsorbed on Pd and O sites are in regular and bold font, respectively. Activation energies denoted with * correspond to the barrier for diffusion of the reactants, as the actual reaction is non-activated. no. (62) (63) (64) (65) (66) (67) (68) (69) (70) (71) (72) (73) (74) (75) (76) (77) (78) (79) (80)

Reaction equation H2 O H2 O-OH H2 O-(OH-H) H 2 O + S2 H2 O-OH + S2 H2 O-(OH-H) + S2 O2 (g) + S1 O2 + S1 O2 (g) + Vac O + S1 O + Vac O2 + Vac OH OH-H H2 O(g) + O + S1 H + S1 H + S1 H-H H2

S1 + H2 O(g) OH + S1 + H2 O(g) OH-H + S1 + H2 O(g) OH-H OH-H + OH 2 OH-H O2 2O O O + S2 S1 + S2 O + S2 S1 + OH(g) S1 + OH(g) + H 2 OH OH + Vac H + S2 H 2 + S2 S1 + H2 (g)

                  

tained by solving the following set of coupled differential equations ! δ θi (t) = ∑(νi j r j (θ1 (t), ..., θN (t))) δt j

(3)

k

where θ (t)i is the coverage of surface species i at time t whereas νi j is the stoichiometric coefficient for species i and elementary reaction j. Steady state coverages and reaction rates from Eq. 3 are obtained in each catalyst layer, k, by using the SciPy Python package. Eq. 3 is solved within each iteration for solution of Eq. 4 and 7 in the reactor model.

Af 3.6×1015 ” ” 1.3×1013 ” ” 1.8×107 3.0×1013 1.8×107 2.7×1013 2.3×1013 1.3×1016 2.8×1016 ” 2.3×107 6.7×1013 2.3×1014 1.6×1014 4.6×1014

Ab 2.3×107 ” ” 6.3×1013 ” ” 9.9×1015 2.8×1013 2.2×1016 2.0×1013 6.1×1013 1.1×1014 2.4×107 ” 8.3×1015 1.5×1013 3.2×1013 1.3×1013 7.0×107

EHSE06 a,f 1.38 1.73 1.88 0.13 0.59 0.54 0.00 2.01 0.00 1.16 0.194* 0.73 2.26 3.37 0.00 1.43 1.93 1.49 0.63

EHSE06 a,b 0.00 0.00 0.00 0.23 0.09 0.04 0.58 0.42 1.71 1.17 2.93 1.87 0.00 0.00 1.67 0.294* 0.83 0.29 0.00

that is independent of the number of sublayers, i.e., a solution that converges in terms of average reaction rate. The thickness of each sublayer is systematically increased by 50% starting from the gas-catalyst interface to achieve necessary resolution of regions where gradients are steeper. A schematic representation of the 1D model is shown in Figure 2.

2.2 Reactor model A one-dimensional (1D) model is used to describe the transport phenomena in the gas phase (external) and in the porous catalyst layer (internal). The gas phase is described by laminar flow properties and a film model is applied to describe transport between the bulk gas and the catalyst surface. The catalyst layer is given the physical properties of porous alumina and the active sites are assumed to be evenly distributed within the layer. The density of active sites is calculated for 2 wt.-% completely dispersed palladium. The catalyst layer is discretised for computational purposes into twelve sublayers to resolve internal gradients with sufficient detail during a reasonable computational time. Twelve sublayers are also more than is required to obtain a steady-state solution 4|

J our na l Na me, [ y ea r ] , [ vol . ] , 1–13

Fig. 2 Schematic representation of the porous catalyst layer discretised into sublayers.

The gas composition (concentrations) in the porous catalyst layer is described by a mass balance equation including the effective diffusivity and reaction. The mass balance for component

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Table 2 Kinetic parameters for the considered elementary steps including carbon dioxide, carbonates and bicarbonates. f and and b denote forward and backward reactions, respectively. The values for the pre-exponential factors (1/s) are calculated at 700 K and 1 bar. The energy barriers are given in eV.

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d 2Ci 0 = De f f 2 dz

De f f ,i = (4)

+ νi csite ri (Cs , Ts )

with boundary conditions as

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kc (Ci,b −Ci,s ) = De f f

0=

dCi dz z=0

(5)

dCi dz z=Lwc

(6)

where C is the concentration in gas phase, ν is the stoichiometric coefficient, csite is the density of active sites, r is the reaction rate, Lwc is the porous catalyst thickness and De f f is the effective internal diffusivity as defined in section 2.2.1. Using the Anderson’s criterion 45 for estimation of internal temperature gradients, the catalyst layer can to a good approximation be regarded as isothermal. The only transport of heat generated from the oxidation reaction is, thus, from the catalyst surface at temperature Ts to the bulk fluid at temperature Tg . The corresponding heat balance is described by Eq. 7 0 = hk (Tg − Ts ) +

Z z=Lwc

(7)

νi (−∆Hr )csite ri (Cs , Ts )dz

z=0

where hk is the heat transport coefficient and ∆Hr is the reaction enthalpy. The discretized forms of equations 4-7 that were used for computations are outlined in Azis et al. 46 . 2.2.1 Calculation of mass and heat transport coefficients The mass and heat transport coefficients are calculated using the Sherwood (Sha ) and Nusselt (Nua ) number, respectively. The asymptotic value of 2.98 is used for both the Sha and Nua , which holds for laminar flow 47 . The used correlations are described by Eqs. 8 and 9 kc,i = Sha

Di dh

(8)

hk = Nua

λg dh

(9)

where Di is the diffusivity for component i, dh is the open channel diameter and λg is the thermal conductivity of the bulk gas. The Di is corrected to the catalyst temperature and pressure according to the Fuller-Schettlet-Gidding relationship (Eq. 10). Di = Dre f ,i (

Ts 1.75 Pre f ) ( ) Tre f Ptot

(10)

where Dre f ,i is the diffusion coefficient for component i at standard temperature and pressure. The Knudsen diffusion, Dk , is considered to influence the effective internal diffusion and is estimated according to dp Dk,i = 3

s

1 Di

fD + D1k,i

(12)

where fD is the ratio of the catalyst porosity, ε p , and tortuosity, τ, factors, which is set to 0.1. This value is in the range for reported fD ratios 48,49 . R The reactor model is implemented in a MATLAB (R2015b ) simulation code using ode15s function to find the steady-state solutions for Eq. 4 and 7. The reaction term in the model is determined by the microkinetic reaction model as outlined in section 2.1. 2.3 Methane oxidation simulations The turnover frequency for methane oxidation is explored for a gas composition with 1000 vol.-ppm CH4 , 10 vol.-% O2 , 5 vol.-% H2 O, 5 vol.-% CO2 and balanced with Ar. The simulations are performed for 1, 2, 4, 6, 8 and 10 atm total pressure at constant temperature in the interval 325-625◦ C, in steps of 25◦ C. The monolith channel dimensions represent a 400 cells per square inch cordierite monolith. The thickness of the porous catalyst layer is set to 100 µm and the diameter of the pores to 13 nm. The active site density is set to 0.188 mol/kgcat . To perform simulations of the intrinsic reaction rate, i.e, without influence of mass and heat transport effects, the transport coefficients and effective diffusivity are given the value of 1010 . This results in negligible gradients in TOFs and surface coverages in the porous catalyst layer for all investigated conditions. 2.4 Sensitivity analysis The microkinetic model contains uncertainties originating from its derivation through approximations in the first-principles calculations and transition state theory as well as the chosen sticking coefficients (see section 2.1). Apart from the methane sticking coefficient, these uncertainties have not been evaluated further but could affect the temperature scale or shift the results by ±50◦ C as a preliminary estimate. The macroscopic model includes catalyst properties which affect the observed TOF of methane oxidation. The sensitivity of the model to the three major parameters, methane sticking coefficient, the metal loading and the layer thickness, is studied by varying them individually ±20%, ±0.5 wt.-% and ±20 µm, respectively. The sensitivity is here defined as Sensitivity =

T OFnew T OF

(13)

where T OFnew is the calculated turnover frequency after changing one of the parameters and T OF is the turnover frequency at unchanged conditions.

3 Results and discussion 8Rg Ts Mi π

(11)

where d p is the mean pore diameter, Rg is the gas constant and Mi is the molar mass for component i. The effective internal diffusivity, De f f , is estimated by the Bosanquet correlation

In this section we present and discuss the results of the simulations first in terms of the intrinsic TOF, i.e., the microkinetics without the influence of mass and heat transport effects, and thereafter in terms of the TOF for the full model including also the macroscopic transport effects. J our na l Na me, [ y ea r ] , [ vol . ] ,1–13 | 5

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i is described by Eq. 4.

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The impact of total pressure and temperature on the intrinsic TOF and surface coverages is shown in Figure 3. The TOF increases with increasing temperature for all the investigated total pressures and three temperature regimes for which the TOFs depends differently on the total pressure are observed. The three regimes are from here on be referred to as the low-, intermediateand high-temperature regime. In the low-temperature regime (<420◦ C), the intrinsic TOF exhibits a negative dependence on the total pressure. At 350◦ C, it decreases roughly by an order of magnitude when the total pressure is increased from 1 to 10 atm. Above 475◦ C, in the high-temperature regime, the opposite effect is seen where the TOF instead shows a positive dependence on the total pressure. The negative and positive pressure dependency is most pronounced at the lowest and highest examined gas temperature, respectively. The effect of increasing the temperature is more pronounced at high as compared to low total pressures. A transition regime between the negative and positive total pressure dependencies is present at intermediate temperatures (420-475◦ C). In the intermediate temperature regime, the effect of total pressure on the TOF is relatively low but showing a temperature and pressure dependent maximum.

Fig. 3 Intrinsic TOFs for complete CH4 oxidation on PdO at varying total pressure and temperature.

The general trends in Figure 3 and origin of the three temperature regimes are related to pressure dependent coverages of different surface species. Bicarbonate, adsorbed water, hydroxyl groups, and hydrogen are the most abundant surface species under the examined conditions. Hydrogen adsorbs on S2 sites (undercoordinated oxygen) while the other most abundant surface species adsorb on S1 sites (undercoordinated Pd). The bicarbonates and adsorbed water surface species are found to be most influential on the TOF by hindering the dissociative adsorption of methane on Pd-O sites. The bicarbonates are formed through reaction between adsorbed carbon dioxide and hydroxyl groups. The strong inhibitory effect of H2 O and CO2 is in line with studies by Burch et al. 11 and Ribeiro et al. 50 . In the latter work a reaction order of -2 for CO2 is reported for concentrations above 0.5%. Burch et al. measured a strong inhibitory effect of CO2 6|

J our na l Na me, [ y ea r ] , [ vol . ] , 1–13

in dry feeds at lower temperatures. Water is in Ref. [ 11 ] suggested to have a stronger inhibitory effect than CO2 . Inhibitory effects of CO2 have also been reported for methane oxidation on LaMnO3 -based perovskite catalysts 24 . Figure 4a-d shows the coverage for bicarbonate (A- and B-type, see Figure 1), adsorbed water, hydroxyl and free Pd-O site pairs. The coverages are correlated. A high coverage of the adsorbates corresponds to a low availability of free Pd-O site pairs and vice versa. In the low-temperature regime, a competing adsorption process of bicarbonate and water on S1 sites explains the low activity for methane oxidation. Below 400◦ C, bicarbonate species are dominant on the surface at S1 sites and hence blocking the Pd-O site pair for methane dissociation. At temperatures above 400◦ C but still within the low-temperature regime, adsorbed water is favoured over bicarbonates on the surface and the negative dependency of the total pressure on TOF is a combination of effects from the two adsorbates. Thus, increasing the total pressure at temperatures within the low-temperature regime enhances the hindering effect of bicarbonate and adsorbed water. As the temperature is raised, the bicarbonates and water species are more prone to desorb from the active surface sites. The higher gas phase entropy keeps the surface relatively free from hindering surface species in the high-temperature regime even at higher total pressures (Figure 4d), which explains the positive dependency of the total pressure on the TOF at high temperatures. As a result from the different pressure dependencies, the TOF is more sensitive to temperature variations at high as compared to low total pressure. Therefore, the transition or intermediate temperature regime is more narrow at high compared to low total pressure. A correltion is also present between the coverage of adsorbed water and hydroxyl groups. The surface hydroxyl groups can be formed through the decomposition of adsorbed CHx species with a surface oxygen and by dissociation of water. The increasing coverage of hydroxyl groups, from 1 atm and 400◦ C to 10 atm and 475◦ C, is due to an increased TOF (decomposition of CHx ) together with the presence of adsorbed water on the catalyst surface. At 1 atm and 400◦ C, where the TOF is roughly two orders of magnitude lower, the coverage of hydroxyl groups mainly originates from dissociation of water. 3.2 Impact of mass and heat transport on the TOF The impact of mass and heat transport on the TOF was studied using the full model. The predicted TOFs shown in Figure 5 are volume averaged over the catalyst sublayers. The three temperature regimes present for the intrinsic TOFs are also observed after including transport resistance, although the trends are shifted to lower temperatures. The intermediate temperature regime spans a narrower range between 400-430◦ C and the high-temperature regime starts at about 450◦ C. Notably, a reduced TOF is predicted when transport limitations are included. The effects of transport phenomena are more pronounced at high temperatures primarily due to the higher internal and external mass transport resistances, which tend to counteract the positive effect of increased total pressure in the high-temperature regime. The significance of internal and external mass transport resistance was evaluated by

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3.1 Impact of total pressure and temperature on the intrinsic TOF

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Fig. 4 Equilibrium coverages of bicarbonate (a), water (b), hydroxyl (c) and free Pd-O site pairs (d) on S1 sites on PdO for complete CH4 oxidation.

comparing the ratio of diffusion and reaction time constants 51 . The ratios offer no sharp criteria for determining the rate controlling step but are used to describe the observed effects on the reaction rate. The significance of internal diffusion resistance was assessed from the ratio of the methane diffusion time constant over the observed reaction time constant (twc /tr ). Here, tr is calculated from the simulated observed reaction rate. In this specific case with a porous catalyst layer of slab geometry, the ratio is the same as the Weisz modulus 52 . The ratio is shown in Figure 6a for the simulated reaction conditions.

Fig. 5 Volume averaged TOFs over the catalyst sublayers with transport resistances for CH4 oxidation on PdO at varying total pressure and temperature.

The result in Figure 6a shows that internal transport resistances exhibit a similar three-regime appearance with different pressure dependencies. The internal resistance increases with temperature due to the enhanced turnover frequencies. Interestingly, the internal diffusion resistance is less significant at higher total pressures in the low-temperature regime despite the inverse proportionality of diffusion on pressure according to Eq. 10. The trend is due to the fact that the decrease in TOF from increasing pressure, originating from hindering bicarbonate surface species, has a higher impact here compared to the decrease in effective diffusivity. The effect of total pressure on the internal diffusion significance is different in the high-temperature regime (>430◦ C) where transport resistances affect the reaction rate. Here, as the total pressure increases the TOF increases while the gas diffusivity decreases resulting in a more prominent Knudsen diffusion. Both these effects contribute to a more significant internal transport resistance. At high temperatures and pressures, it is indicated that internal mass transport resistance is a major contributor to the reduction of TOF. This is reinforced by the steep concentration gradients of methane inside the catalyst layer (see Figure ESI.1 in ESI). The gradients at these conditions are mainly explained by the increased TOF with increasing temperature and to a lesser extent by the decreasing gas diffusivity with increasing total pressure. The influence of external mass transport resistance was evaluated by comparing the diffusion time constant of methane in the monolith channel to the reaction time constant (td /tr ). The ratio is analogous to Mear’s criterion for spherical particles 53 . The ratio is shown in Figure 6b and indicates that external mass transport can be neglected in the low-temperature J our na l Na me, [ y ea r ] , [ vol . ] ,1–13 | 7

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Fig. 6 The ratio of diffusion time and reaction time for internal (twc /tr ) (a) and external (td /tr ) (b) mass transport for complete CH4 oxidation on PdO at varying total pressure and temperature.

Fig. 7 Surface to gas temperature difference (Ts -Tg ) (a) and effectiveness factor (b) for complete CH4 oxidation on PdO at varying total pressure and temperature.

regime. Further, comparing the ratios for internal and external mass transport resistances indicates that external mass transport resistance only affects the activity at high temperature and high total pressure. At other conditions, the ratio for internal mass transport resistance is at least one order of magnitude higher and obscures the effects of external mass transport resistances. The observation is reinforced by Figure 7a-b. Figure 7a shows the temperature difference between the surface of the catalyst layer and the bulk gas phase. Figure 7b shows the effectiveness factor, determined as the reaction rate volume averaged over the catalyst layers divided by the reaction rate at gas phase conditions. The temperature difference, caused by heat transport resistance is highest at high temperature and pressure due to the reaction exotherm. The increased surface temperature could conceivably lead to an effectiveness factor higher than unity, however this is not observed here due the severe net effects of mass transport resistances at high pressure and temperature. The temperature gradient does however serve to moderate the decrease in the effectiveness factor with pressure at the highest temperatures. In the low-temperature regime the effectiveness factor is close to unity as both the TOF at gas phase conditions and transport affected TOFs are low due to adsorbed water and bicarbonate species. As the temperature is raised the effectiveness factor decreases as a result of the stronger dependence of intrinsic TOF on temperature than the transport rates.

To predict whether reaction rate, internal or external mass transport controls the observed reaction rate, a criterion based on the time constants was defined. The time constant for either reaction rate, internal or external mass transport must be at least one order of magnitude higher than both the two other time constants to be assumed to be controlling. At conditions were the time constants do not fulfil the criterion, a mixed region of kinetics, internal and external mass transport is expected. To further distinguish differences within the mixed region and identify where one resistance can be disregarded, another criterion was defined by requiring that a time constant must be at least one order of magnitude lower than the other two to be insignificant. The resulting regions are displayed in Figure 8 which reinforces the previous discussions of intrinsic and mass transport affected turnover frequencies. In the low-temperature regime a kinetically controlled region is present, due to the hindering effect of adsorbed carbon dioxide and water. As the temperature is raised and inhibiting surface species desorb, mass transport phenomena become significant. Internal mass transport control is expected in the high-temperature regime up to a total pressure of 8 atm. At higher pressures external mass transport resistance becomes more pronounced, as previously discussed, and a mixed region of internal and external mass transport control can instead be expected. External mass transport resistance never meets the criterion of being controlling the observed reaction rate. However, conceptu-

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0.06

0.05

0.04

0.03

0.02

0.01

0.00 300

350

400

450

500

550

600

Temperature [°C]

Fig. 8 The controlling regions for for complete CH4 oxidation on PdO at varying total pressure and temperature.

3.2.1 Turnover frequency for varying partial pressures of CO2 and H2 O The effect of CO2 and H2 O on the transport affected turnover frequency for methane oxidation was investigated by varying the CO2 and H2 O concentrations between 2, 5 and 8 vol.-%. The TOFs are shown in Figure 9 at a total pressure of 1 atm and varying reaction temperatures. The black line shows the observed reaction rate for the standard gas composition, i.e as outlined in section 2.3. At an increased concentration of CO2 , a slight reduction in activity is noted at temperatures within the lowtemperature regime. The opposite effect is seen when the concentration of CO2 is decreased due to a lower coverage of bicarbonates. This reinforces the previously discussed hindering effect in the low-temperature regime due to a high coverage of bicarbonates. Within the high-temperature regime carbon dioxide has no effect on the turnover frequency due to an insignificant coverage and follows that of standard gas composition. However, for varied concentration of H2 O the turnover frequency is affected over the entire temperature range. Increasing the concentration of water decreases the turnover frequency due to the increased coverage and as a result its hindering effect (Figure 4d). Decreasing the concentration of water results in increased turnover frequency over the entire temperature range because of a lower coverage of inhibiting surface species. 3.3 Sensitivity analysis The sensitivity of the model is evaluated by varying the methane sticking coefficient, the metal loading and the catalyst layer thickness. Upon varying the methane sticking coefficient in the microkinetic model, the same trends for temperature and total pressure are displayed and the behaviour of the catalyst surface is

Fig. 9 Turnover frequency for complete methane oxidation on PdO with 1000 ppm CH4 , 10% O2 , 5% CO2 and 5% H2 O (black), 8% CO2 and 5% H2 O (solid red), 2% CO2 and 5% H2 O (dashed red), 8% H2 O and 5% CO2 (solid blue), 2% H2 O and 5% CO2 (dashed blue) for varying temperature. All percentages are by volume.

maintained. However, the volume averaged TOF displays a positive dependence on the sticking coefficient and is affected for all reaction conditions. Figure 10a and b shows the effect of increasing and decreasing the methane sticking coefficient on the TOF for methane oxidation on PdO, respectively. The volume averaged TOF is most sensitive to the methane sticking coefficient at combinations of either low temperature-high total pressure or high temperature-low total pressure. The TOF is in these regions, as previously discussed, controlled by kinetics and internal mass transport, respectively. In the kinetically controlled region, the reaction rate depends sensitively on the sticking coefficient of methane. A lowering of the sticking coefficient yields a lower rate, whereas an increased sticking coefficient also increases the rate. In the internal mass transport control region, where the total coverage is low, the volume averaged reaction rate increases with increased methane sticking coefficient. This is rationalized by a relatively unhindered methane adsorption. Instead, lowering the sticking coefficient has an opposite effect and results in decreased volume averaged reaction rate and allows for additional adsorption of water and bicarbonate. After varying the metal loading and catalyst layer thickness, the trends for temperature and total pressure are not affected except for being shifted a few degrees (<10◦ C), due to an affected observed reaction rate, and again show a maintained behaviour of the modeled catalyst surface. While the trends are reproduced, the observed TOF is affected over the entire temperature and pressure range. The sensitivity to catalyst properties is highest at high temperatures and total pressures when varying the metal loading. Figure 11a-b shows the effect of increasing and decreasing the metal loading on the TOF for methane oxidation, respectively. The sensitivity is higher at high temperature and total pressure because of a larger effect on the transport resisJ our na l Na me, [ y ea r ] , [ vol . ] ,1–13 | 9

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ally such a region could be expected at even higher temperatures and pressures.

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Fig. 10 Sensitivity of the TOF for complete CH4 oxidation on PdO for increased methane sticking coefficient (a), decreased methane sticking coefficient (b). Red areas represent conditions where the model is the most sensitive.

tances. An increased metal loading results in a decreased volume averaged TOF to 84% of the initial value due to significant mass transport resistances less methane can be transported to each site at higher site density. In the same manner, a lower metal loading results in an increased volume averaged TOF by 24% due to the reduced mass transport resistances. The effect of varying the catalyst layer thickness exhibits a characteristic reminding of the three temperature regimes as shown in Figure 11c-d. Upon varying the layer thickness the model is most sensitive at atmospheric pressures and intermediate to high temperatures. It should however be noted that the difference between intermediate and high temperature is marginal. The sensitivity analysis shows that the absolute TOFs are quite sensitive to the metal loading and the layer thickness. As a result it is important to experimentally determine these in order to obtain a correct estimation of the methane conversion, especially at high temperatures where the effects of transport resistances are most pronounced.

adsorbates. The observed TOF is shown to be controlled by kinetics below 400◦ C and by internal mass transport above 500◦ C up to a total pressure of 8 atm. The external mass transport resistance is at the examined conditions never influential enough to be identified as controlling the observed TOF. The effects of external mass transport resistance can, however, be seen at high temperature and pressure. For other reaction conditions a combination of kinetics, external and internal mass transport controls the reaction rate of complete methane oxidation. The model paves the way for further studies to identify the bottleneck of complete methane oxidation and to reach higher catalytic efficiencies.

5 Conflicts of interest

4 Concluding remarks The comprehensive model developed in this study is based on first-principles kinetics and includes structural parameters for a catalytic layer representing the geometry of a coated monolith substrate. The geometry can be varied in order to optimize the catalyst design for complete methane oxidation on palladium oxide in ambient and pressurized conditions. The model shows that the reaction rate for complete oxidation of methane at high temperatures can be considerably enhanced by increasing the total pressure. Furthermore, the chemical potential of gas phase H2 O and CO2 needs to be sufficiently low to keep the active surface sites available for methane to dissociatively adsorb as the total pressure is increased. At the simulated conditions, the required temperature region is referred to as the high-temperature regime and found to be above 475◦ C for intrinsic conditions and 450◦ C for mass and heat transport affected cases. At these temperatures, the coverage of bicarbonates and adsorbed water hindering the dissociative adsorption of methane on the Pd-O site pair is low. The TOF for methane oxidation shows a negative dependence on the total pressure if the reaction temperature is insufficient, here below 400◦ C, to maintain a required desorption rate of inhibiting our na l Na me, [ y ea r ] , [ vol . ] ,1–13 10 | J

There are no conflicts to declare.

6 Acknowledgements

The authors would like to give special thank to M.Sc.(Eng.) J. Leinonen at Wärtsilä Finland Oy for involvement with valuable ideas and fruitful discussions. This work has been performed within the Competence Centre for Catalysis, which is hosted by Chalmers University of Technology and financially supported by the Swedish Energy Agency and the member companies AB Volvo, ECAPS AB, Haldor Topsøe A/S, Scania CV AB, Volvo Car Corporation AB, and Wärtsilä Finland Oy. Additional support from the Swedish Research Council is acknowledged as well as computational resources at C3SE (Göteborg) via SNIC grant.

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Fig. 11 Sensitivity of the TOF for complete CH4 oxidation on PdO at increased metal loading (a), decreased metal loading (b), increased washcoat thickness (c) and decreased washcoat thickness (d). Red areas represent conditions where the model is the most sensitive.

7 Notations Asite C csite cp D De f f Dk dh dp Ea fD ∆Hr h hk k kads kB kc Lwc M m Nua Q Ptot Rg r

adsorption site area, Å2 concentration, mole m−3 site density, mole m−3 wc heat capacity, J kg−1 K−1 binary diffusivity, m2 s−1 effective diffusivity, m2 s−1 Knudsen diffusivity, m2 s−1 open channel diameter, m mean pore diameter, m activation energy, eV ratio of catalyst porosity to tortuosity, reaction enthalpy, J mole−1 Planck’s constant, J s heat transport coefficient, W m−2 rate coefficient for surface reaction, Hz adsorption rate constant, s Pa−1 Boltzmann constant, J K−1 mass transport coefficient, m s−1 porous catalyst thickness, m molecular mass, g mole−1 mass of adsorbed molecule, kg asymptotic Nusselt number, partition function, total pressure, Pa gas constant, J mole−1 K−1 reaction rate, Hz site−1

S00 Sdyn Sha T t z

sticking coefficient at zero coverage, dynamic sticking coefficient, asymptotic Sherwood number, temperature, K time, s axis perpendicular to porous catalyst surface

Greek letters Γ λ ρcat

lumped mass transport coefficient, m s−1 thermal conductivity, W m−1 K−1 catalyst density, kg m−3

Subscripts g i k R r ref s TS wc

gas component index catalyst layer index reactant state reaction reference surface transition state washcoat

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