Chemical Engineering Journal

Chemical Engineering Journal 276 (2015) 388 397 Contents lists available at ScienceDirect Chemical Engineering Journal journal homepage: www.elsevier.com/locate/cej Effect of washcoat diffusion resistance in foam based catalytic reactors Jan von Rickenbach a,c, Francesco Lucci b, Chidambaram Narayanan c, Panayotis Dimopoulos Eggenschwiler b, Dimos Poulikakos a, a Laboratory of Thermodynamics in Emerging Technologies, Swiss Federal Institute of Technology, ETH, Zürich, Switzerland b Laboratory for I.C. Engines, Empa, Swiss Federal Laboratories for Materials Testing and Research, Dübendorf, Switzerland c Ascomp GmbH, Zürich, Switzerland article info abstract Article history: Received 3 February 2015 Received in revised form 25 March 2015 Accepted 28 March 2015 Available online 2 April 2015 Keywords: Washcoat diffusion Open cell foam Microkinetic modelling Honeycomb Catalytic CO oxidation Foam based catalytic converters are a promising alternative to the established honeycomb reactors for treatment of pollutants in automotive applications. They provide excellent mass transfer properties at reasonable pressure drop and have the potential to achieve high conversion at smaller external dimensions. The goal of this work is to determine the relative importance of washcoat diffusion resistance in foam based reactors. Catalytic oxidation of CO over Pt is computationally simulated with a volume averaged model. Based on micro-kinetic modelling and the resulting resolution of the reaction-diffusion processes inside the washcoat, the simulations provide a comprehensive picture of the chemistry and transport processes. Washcoat diffusion resistances in foams although often considered negligible are shown to be at least as important as in honeycomb converters, due to the higher external mass transfer coefficients in foams. The computations show a reduction in conversion with respect to the limit of infinitely fast kinetics of 46% for the foam-based reactor after catalytic light-off. The impact of washcoat diffusion resistance on conversion decreases with increasing surface area of the washcoat. An increase in pore size of the washcoat leads to improved conversion. Ó 2015 Elsevier B.V. All rights reserved. 1. Introduction Extruded honeycombs are the established technology for catalytic exhaust gas cleaning in automotive applications [1]. Recently, foam based catalytic converters have been proposed as an alternative technology [2], since they provide a high surface area and efficient mass transfer combined with a low pressure drop. In both reactor types the support material is coated with a washcoat layer containing the precious metal catalyst particles. The washcoat provides a large surface area for the chemical reaction, however, diffusion resistances in the washcoat are often significant and have been shown to reduce the observed reaction rates in honeycomb reactors [3]. The oxidation of CO over a Pt based catalyst is often used as a prototype reaction to study catalytic pollutant conversion [4]. Based on measurements and simulations it is currently believed that catalytic oxidation of CO can be described by three regimes [5]. At low temperatures the conversion is limited by slow chemical reaction rates, which results in low conversion of CO. At high temperatures conversion is limited mainly by external mass Corresponding author. Tel.: +41 44 632 2738; fax: +41 44 632 1176. E-mail address: dimos.poulikakos@ethz.ch (D. Poulikakos). transfer from the bulk fluid to the washcoat surface. Finally, at intermediate temperatures the above mentioned washcoat diffusion resistance can severely reduce the achievable conversion. Not all of these regimes necessarily exist in all reactor configurations [5,6]. Quantifying the importance of washcoat diffusion resistance is of significant practical importance as it will guide the efforts in the optimization of foam based catalytic reactors. For honeycomb reactors washcoat diffusion resistance has been shown to be important for a range of temperatures above light-off and a pure external mass transfer limited regime was not observed [6]. In foams the effects of washcoat diffusion have often been ignored in the experimental [7 10] and numerical literature [11,12]. It is often assumed that conversion in foam based reactors changes from kinetically limited to external mass transfer limited directly [8 10]. In this case the mass transfer limited regime is identified as where the slope in the conversion versus temperature plot decreases [9,10]. Furthermore, external mass transfer coefficients in foams are often obtained experimentally assuming negligible washcoat diffusion resistance [8 10,13]. Even if the assumption of negligible washcoat diffusion in foams is satisfied, the question remains as to why washcoat diffusion resistance in honeycomb reactors is very important, while being negligible in foam based reactors. This is especially surprising since the http://dx.doi.org/10.1016/j.cej.2015.03.132 1385-8947/Ó 2015 Elsevier B.V. All rights reserved.

J. von Rickenbach et al. / Chemical Engineering Journal 276 (2015) 388 397 389 Nomenclature A r pre-expontential factor for reaction r (mol, cm, s) a V geometric surface area per unit volume (A sf /DV) (1/m) A sf solid fluid interfacial area in a REV (m 2 ) c i concentration of species i (mol/m 3 for gas phase species and mol/m 2 for surface species) c p heat capacity at constant pressure (J/(kg K)) D i mixture diffusion coefficient of component i (m 2 =s) d wc washcoat pore diameter (m) E a;r activation energy for reaction r (kj/mol) F cat=geo ratio between catalytic active surface area and geometric surface area ( ) DH heat release per mole of CO (J/mol) H phase indicator function (Eq. (A1) ( )) k 0 m Sh/L (1/m) k m;i mass transfer coefficient of species i (m/s), k r reaction rate constant of reaction r (mol, cm, s) L reactor reactor length (m) L macro scale length scale (m) M i molecular weight of component i (kg/mol) N g number of gas phase species ( ) ~n fs normal vector pointing from fluid to the solid N s number of surface species ( ) n wc number of cells in the washcoat n x number of cells in the x-direction R ideal gas constant (J/(mol K)) rr CO CO reaction rate (mol=ðm 2 sþ) S 0 r initial sticking coefficient of reaction r ( ) S r sensitivity of reaction r ( ) _s i molar production rate of species i per unit surface area (mol/(m 2 s)), DT ad adiabatic temperature increase along reactor (K) T temperature (K) t time (s) washcoat thickness (m) t wc u cat characteristic catalyst velocity (Eq. (19)) (m/s), u velocity in the x-direction (m/s) DV volume of the representative elementary control volume (m 3 ), w washcoat coordinate normal to washcoat fluid interface (m) x coordinate (m) Y i mass fraction of component i ( ) Greek letters wc washcoat porosity ( ) macro scale porosity ( ) C Pt surface coverage (mol/m 2 ) m 0 k;r forward stoichiometric coefficient of component k in reaction r ( ) m 00 k;r reverse stoichiometric coefficient of component k in reaction r ( ) q density (kg=m 3 ) h i surface coverage of species i ( ) s wc washcoat tortuosity ( ) v CO conversion (Eq. (20)) Non-dimensional Groups Pe Peclet number Sh Sherwood number Superscripts hi p phase averaged in phase p b bulk value f fluid s surface averaged wc value in the washcoat pore thickness of the washcoat, its specific surface area and Pt loading in both reactor types are typically very similar. The experimental quantification of washcoat diffusion resistance in foams is difficult because the overall conversion of CO is often the only observable quantity. However, it is impossible from the conversion alone to determine whether washcoat diffusion resistance in a reactor is important. Furthermore, the exact properties of the washcoat, such as pore size and washcoat thickness, are difficult to precisely control in an experiment. With simulations on the other hand, the external mass transfer, washcoat diffusion and the elementary reaction steps can be modeled separately and the relative impact of the different phenomena on conversion can be analyzed in great detail. It is also straight-forward to control the washcoat properties and to study the impact of the various washcoat parameters on conversion. Simulations also allow to study quantities not accessible through experiments such as concentration profiles within the washcoat layer which provide interesting insights in the small scale phenomena governing catalytic CO oxidation. A volume averaged reactor model is used to simulate light-off curves in foams and honeycomb reactors. The honeycomb reactor serves as a validation since washcoat diffusion resistance in honeycomb reactors is easier to quantify and its impact on conversion has been shown experimentally [6]. Quantification of washcoat diffusion resistance in honeycomb reactors is significantly more accurate, since external mass transfer can be predicted with analytical methods and simulations due to their relatively simple geometry. The reactor model is used to quantify the washcoat diffusion resistance by comparing simulations assuming instantaneous washcoat diffusion with a model that resolves the reaction diffusion phenomena inside the washcoat. Since the impact of washcoat diffusion on conversion is expected to depend on temperature, ignition and extinction curves are simulated in the temperature range of 300 K to 1000 K. 2. Reactor model The catalytic converter is modeled as a porous medium at two distinct length scales. The macro pores have a characteristic length-scale on the order of L ¼ 1 mm. This corresponds to the pore diameter in a foam and the hydraulic diameter in a honeycomb channel. The honeycomb and the foam are coated with a washcoat to increase the catalyst surface area. The washcoat thickness (t wc ) is on the order of 100 lm. The washcoat itself is modeled also as a porous medium with a characteristic pore diameter on the order of d wc = 10 nm. The relevant scales for the foam and the honeycomb are summarized in Figs. 1 and 2. 2.1. Macro pore governing equations The governing equations for averaged quantities on the macro scale are obtained by averaging the governing equations over a representative elementary volume REV [14]. This corresponds to a cross-sectional average in a honeycomb channel and an average over a sphere with a diameter of order L in the foam. It is assumed

390 J. von Rickenbach et al. / Chemical Engineering Journal 276 (2015) 388 397 Flow L L reactor d wc t wc catalyst support Fig. 1. Two dimensional schematic of a foam based reactor. Not to scale. temperature sensitivity of the reaction rates is high, conversions are lower (<30%), which implies maximum temperature differences below 10 K. These maximum temperature differences are even lower when heat losses to the environment are considered. The pressure drop in foams is of the order of 10 5 Pa/m for foams [8] and 10 4 Pa/m for honeycombs [10] at high superficial velocities of 10 m/s. Incerna Garrido et al. [8] have shown that short reactors (L reactor <1 cm) are needed to measure conversions lower than unity in the external mass transfer limited regime. Therefore, we expect maximum density changes due to varying pressure along the reactor of the order 1%. We consider CO mole fractions less than 1%, therefore a change in density due to composition is considered negligible. Due to the reasons stated above, density changes in the reacting mixture are neglected, which implies that the velocity along the reactor is constant. The volume averaged species equation reads: @hy i i f þ hui f @Y b i @t @x ¼ 1 Z D i ry i ~n fs da; ð3þ DV A sf where A sf is the geometric surface area within the averaging volume and DV is the volume of the averaging volume. Axial diffusion is neglected due to the high Pe number: Flow t wc t wc catalyst support washcoat L washcoat catalyst support d wc Pe ¼ L reactorhui f hd i i f 1 ð4þ The bulk mass fraction (Y b i ) is defined in Appendix A. Dispersion is neglected which implies that the phase averaged mass fraction hy i i f and the bulk mass fraction (Y b i ) are identical. The last term on the right hand side of Eq. (3) is the interfacial mass transfer term and has to be expressed in terms of the bulk mass fraction Y b i. The flux of species to the surface can be written as [16]: 1 DV Z D i ry i ~n fs da ¼ a V k m;i Y b i Y s i A sf ; ð5þ that the reactor can be modeled as a one dimensional system where the averaged quantities vary only along the main flow direction. The volume averaged continuity equation for the macro scale can be expressed as [15]: @ @x hqi f hui f ¼ 0; L reactor Fig. 2. Two dimensional schematic of a honeycomb channel. Not to scale. where hi f indicates a quantity averaged over the fluid volume (see Appendix A). The temperature along the reactor is assumed constant. This is justified for foam-based reactors, where temperature gradients along the reactor are typically less than 10 K for the CO concentrations considered here [10]. In honeycomb reactors higher temperature differences have been measured [10]. The maximum adiabatic temperature difference across the reactor due to the heat release of the reaction at steady state operation can be estimated based on DT ad ¼ DHDYb CO c p M i ; ð2þ where DY CO is the difference of Y CO across the reactor, DH is the heat release per mole of reacted CO and c p is the heat capacity of the gas mixture. In this work conversions range from 0 to 65% which results in a maximum DT ad of 18 K. In the light-off region, where the ð1þ where Y s i is the averaged surface mass fraction of species i (Appendix A) and a V is the geometric surface area per unit volume. The mass transfer coefficient is defined as k m;i ¼ hd ii f Sh ; ð6þ L where Sh is the Sherwood number. The right hand side of Eq. (5) depends on the surface mass fraction of the chemical species (Y s i ), which in turn depends on the reaction rates in the washcoat. 2.2. Micro pore governing equations The reaction rates in the washcoat are evaluated with two different models: In a simplified model, instantaneous washcoat diffusion is assumed and the reaction rates are evaluated at the surface mass fractions (Y s i ). In a more sophisticated model the effect of washcoat diffusion is taken into account. Comparing the two models will allow to quantify the impact of washcoat diffusion on conversion. 2.2.1. Instantaneous washcoat diffusion The diffusion resistance inside the washcoat is neglected and all surface sites are available at the geometric surface of the macro pores. The increased surface area due to the washcoat is taken into account by introducing an additional parameter which describes the ratio of geometrical surface area and the actual available surface area within the washcoat ðf cat=geo Þ [17]. The external mass flux balances the production rate of the chemical species at the fluid-washcoat interface:

J. von Rickenbach et al. / Chemical Engineering Journal 276 (2015) 388 397 391 hqi f k m;i ðy b i Y s i Þ¼ M i _s if cat=geo : We consider a chemical mixture of N g gas phase species and N s surface adsorbed species. The molar production rates of the chemical species can be expressed as [18] _s i ¼ XNr r¼1 ð7þ N ðm 00 ir m0 ir Þk Y gþn s r c m0 jr j ; ð8þ j¼1 where c j is the surface concentration for the surface absorbed species (mol=m 2 ) and the volumetric concentration for the gas phase species (mol=m 3 ) which is evaluated at the solid fluid interface (Y s i ). The reaction rate constants for the reactions among the surface adsorbed species and the desorption reactions are evaluated from [18] k r ¼ A r exp E a;r ; ð9þ RT where the activation energy of the reaction (E a;r ) can depend on the surface coverage of the surface species. The adsorption rate coefficient is expressed in terms of a sticking coefficient: k ads r ¼ S 0 r 1 C sffiffiffiffiffiffiffiffiffiffiffiffi RT ; ð10þ 2pM i where C is the surface site density. The surface coverage of the adsorbed species is defined as H i ¼ c i C : ð11þ Surface transport is neglected and the surface site density is constant. Therefore the governing equation for the surface species is written as C @H i @t ¼ _s i: ð12þ At steady state Eq. (7) for each gas-phase species and Eq. (12) for each surface adsorbed species form a system of non-linear equations with N g þ N s unknowns. A good initial guess is needed to solve this system with an iterative method such as Newton-Raphson. To improve the robustness of the solution process a dimensionally adjusted artificial pseudo time term is added to Eq. (7): hqi f t wc @Y s i @t ¼hqi f k m;i ðy b i Y s i ÞþM i _s if cat=geo : ð13þ The introduction of the artificial pseudo time term does not change the steady state solution which is of interest in this work. 2.2.2. Reaction diffusion washcoat model The washcoat is assumed to form a uniform, flat and thin layer where the species mass fractions vary only in the direction normal to the fluid-solid interface [17]. The fluid density in the washcoat pores is assumed to be constant and transport by convection is neglected due to the small pore diameters. The conservation equation for the volume averaged species mass fractions simplifies to a one dimensional reaction diffusion equation along the washcoat coordinate w: wc @Ywc i q ¼ @ @t @w qwc D wc e;i @ @w Y wc i þ a wc V M i _s i: ð14þ The superscript wc indicates a washcoat quantity. a wc V = F cat=geo/ t wc is the surface area of the washcoat per unit volume and D wc e;i is the effective diffusion coefficient in the washcoat: 1 D wc ¼ s wc 1 þ 1 ; ð15þ e;i wc D i D knud;i where s wc is the washcoat tortuosity and wc the washcoat porosity [17]. The Knudsen diffusion coefficient is defined as D knud;i ¼ d wc 3 sffiffiffiffiffiffiffiffiffi 8RT ; ð16þ pm i where d wc is an average pore diameter of the washcoat. At the interface of the washcoat with the macro scale pore, the species fluxes due to external mass transfer match the diffusive fluxes to the washcoat which results in a boundary conditions for Eq. (14) at w =0: D wc e;i @Y wc i @w ¼ k m;iðy b i Y s i Þ ð17þ The washcoat impermeable at w = t wc and therefore the species flux there is set to zero: @Y wc i @w ¼ 0: 2.3. Chemical reaction mechanism ð18þ To model catalytic oxidation of CO over Pt we use the CO oxidation part of the mechanism presented by Chatterjee et al. [19] (Table 1). Although the mechanism of Chatterjee et al. [19] has been obtained for a reactor containing Pt and Rh in a 5:1 ratio as active sites it has been shown to accurately predict light off curves over a catalyst containing only Pt particles [4]. The CO 2 adsorption reaction is omitted from the reaction mechanism since CO 2 adsorption rates were found to be negligible due to the low sticking coefficient of CO 2 on Pt. We use a micro kinetic reaction scheme since simplified kinetics, such as Langmuir-Hinshelwood kinetics [20], are only applicable in a narrow range of operating conditions [4]. Table 1 Chemical reaction mechanism for CO oxidation on Pt [19], s Sticking coefficient. Step Reaction A=S 0 ðmol; cm; sþ E a ðkj=molþ Adsorption O 2 adsorption O 2 þ 2PTðSÞ )2OðSÞ 0:07 s CO adsorption CO þ PTðSÞ )COðSÞ 0:84 s Desorption O 2 desorption 2OðSÞ )O 2 þ 2PTðSÞ 3.7E21 232.2 90 h O CO desorption COðSÞ )CO þ PTðSÞ 1E13 136.4 33 h CO CO 2 desorption CO2ðSÞ )CO 2 þ PTðSÞ 1E13 27.1 Surface reaction Forward surface reaction (SR) COðSÞþOðSÞ )CO2ðSÞþPTðSÞ 3.7E20 108 33 h CO Reverse surface reaction (rsr) CO2ðSÞþPTðSÞ )COðSÞþOðSÞ 3.7E21 165.1 + 45 h O

392 J. von Rickenbach et al. / Chemical Engineering Journal 276 (2015) 388 397 Flow direction n wc 3 2 1 washcoat 1 2 3 n x Table 2 Inflow mole fractions. Species Mole fraction ( ) CO 0.003 O 2 0.1 CO 2 0.0 N 2 0.897 Fig. 3. Schematic of the discretization. In the flow direction n x cells are used to discretize Eq. (3). For each of cells in the flow direction n wc cells are used to discretize the species equation in the washcoat (Eq. (14)). 2.4. Numerical solution The convection term in the macro scale species equation (Eq. (3)) and the diffusion term in the washcoat equation (Eq. (14)) are discretized with the finite volume method [21]. In the model assuming instantaneous washcoat diffusion the discretized form of Eq. (3), the equation for the gas phase species at the surface (Eq. (13)) and the equation for the surface species (Eq. (12)) form a system of ODEs with (2N g + N s )n x unknowns, where n x is the number of cells used for the discretization of Eq. (3). For the reaction diffusion washcoat model the system of ODEs is formed by the discretized form of Eq. (3) and Eq. (14) together with Eq. (12) for each surface species in each washcoat cell. The resulting system of ODEs contains n x n wc ðn g þ N s ÞþN g n x unknowns, where n wc is the number of cells used for the discretization of the washcoat equation (Fig. 3). For both models the coupled system of ODE is integrated in time using the ODE solver CVode which is part of the Sundials package [22]. CVode uses variable order Backward Differentiation Formulas (BDF) for the time discretization which are well suited for the stiff problem at hand. A banded preconditioner with upper and lower bandwidth N s þ N g is used to accelerate convergence of the GMRES (generalized minimal residual method) solver in each time step. Material properties and reaction rates are evaluated using the Cantera chemistry library [23]. 3. Cases studied 3.1. Simulation methodology Light-off curves are simulated using the transient model described above. It is well known that catalytic oxidation of CO exhibits hysteresis in CO conversion with respect to temperature and CO mass fraction and the steady-state solution depends on the initial conditions [24]. The simulation starts at a low temperature of 300 K, at which the reactor model is integrated to steady state. The temperature is then step-wise increased. After each increase in temperature, the reactor model is integrated to steady state before the next step increase of temperature occurs. The temperature steps are of the order of 10 K. At 1000 K the temperature is decreased with the same step sizes until the initial temperature is reached. This procedure closely resembles the way light off curves are obtained experimentally. 3.2. Simulation parameters The reactive mixture is modeled as an ideal gas containing O 2 ; CO; N 2 and CO 2. The inflow concentration is given in Table 2. The inflow stream is assumed to contain no CO 2. The remaining simulation parameters can be split into two different groups. Macroscale parameters are likely to be different in foams and honeycomb reactors. These include external mass transfer coefficients, geometric surface area or macroscale porosity. Microscale parameters such as Pt loading or washcoat pore diameter are likely to be independent on the type of reactor and depend only on the washcoating method applied. 3.2.1. Macroscale parameters The mass transfer coefficient is varied by changing the ratio k 0 m ¼ Sh=L. For foams the Sh number depends on the Re number, porosity and pore diameter [8]. The values k 0 m ¼ 4000 m 1, k 0 m ¼ 8000 m 1 and k 0 m ¼ 16; 000 m 1 are used to represent foams at different velocities. These three values for k 0 m correspond to inflow velocities of roughly 0.5 m/s, 2 m/s and 10 m/s for the foams considered in Incerna Garrido et al. [8] at a temperature of 400 K. A typical value for fully developed flow in a honeycomb channel is k 0 m ¼ 3675 m 1 [17] which is represented by k 0 m ¼ 4000 m 1. Since velocity and density are assumed to be constant along the reactor, a characteristic velocity u cat is fixed: u cat ¼ hui f : a V L reactor ð19þ The value of u cat ¼ 1:25 is chosen for all simulations. This results in conversion of close to one at full external mass transfer control for the highest temperatures and external mass transfer coefficients considered. Note that a given value of u cat can be obtained with any reactor type by adjusting the length of the reactor. 3.2.2. Microscale parameters In honeycombs typical values of F cat=geo are 70 [19] and 25 [17]. Chan et al. [25] and Boll et al. [26] have shown that catalyst aging can be modeled by reducing the value of F cat=geo. F cat=geo ¼ 100 is used as a reference value, with 1, 10 and 500 as parameter variations. The same values are used to represent foams. The molar concentration of surface sites (C) is kept constant, which implies that the number of available surface sites per unit geometric surface area is proportional to F cat=geo. This assumption is consistent with previous studies [25,26]. The washcoat consists of meso-scale pores with pore diameters of the order of 10 nm [27], and a varying number of macropores with diameters from 100 nm to several microns [28]. Experimentally measured diffusion coefficients in washcoats show a large variability. In some studies diffusion coefficients of the order of 10 7 m 2 =s have been measured, which corresponds to a washcoat that contains no or very few macropores [27,29]. In other studies it was found that the macropores contribute significantly to the diffusion process and diffusion coefficients of the order of 10 6 m 2 =s have been measured [28,30]. These large variations suggest that the effective diffusion coefficient depends strongly on the washcoat formulation and the fraction of macropores available for transport [30]. Santos et al. [31] have concluded that washcoat used in automotive catalytic converters is closer the lower values reported by Stary et al. [29]. In the model used here, washcoat porosity, tortuosity and washcoat characteristic pore diameter (d wc ) affect the effective diffusion coefficient in the washcoat. Washcoat porosity is kept constant at 0.35 [17]. To investigate the effect of the effective diffusion coefficient in the washcoat,

J. von Rickenbach et al. / Chemical Engineering Journal 276 (2015) 388 397 393 the pore diameter and the tortuosity are varied. We use d wc ¼ 10 nm [17,27,31,32] and a tortuosity of 8 [27] as reference values. Two additional simulations with a pore diameter of 100 nm are run to investigate the effect of a larger pore diameter. In the two additional cases the tortuosity is 8 and 2 respectively. The lower tortuosity case corresponds to larger effective diffusion coefficients as observed for a washcoat with a significant fraction of macropores. The value of the diffusion coefficients used in the simulations and the values reported in the literature are summarized in Table 4. A constant washcoat thickness of 100 lm is assumed [17,25,27]. 4. Results and discussion 4.1. Code verification and grid convergence The results obtained with the current code were compared to the cases studied by Mladenov et al. [17]. For a honeycomb reactor the model presented here is identical to the plug flow with mass transfer coefficients model (PF-MTC) used by Mladenov et al. [17]. The major species profiles with instantaneous and finite rate washcoat diffusion (Fig. 2 and Fig. 6 in Mladenov et al. [17]) were reproduced and a maximum relative difference in the two implementations of less than 5% was observed. The reference case (full ignition-extinction cycle) was run with different resolutions for the discretization of the washcoat equation and the macroscale species equation. Grid independence was reached with n x ¼ 20 and n wc ¼ 64. The grid for the washcoat discretization is refined near the washcoat fluid interface. Doubling the number of cells for both discretizations showed differences in conversion of less than 1% at all temperatures. 4.2. Conversion assuming infinitely fast kinetics The assumption of infinitely fast kinetics is a useful limiting case to quantify the impact of finite rate chemistry and washcoat diffusion resistance on conversion. Conversion is defined based on CO mass fractions: v ¼ 1 Yb;out CO ; ð20þ Y b;in CO where Y b;in CO and Yb;in CO are the inflow and outflow mass fraction of CO respectively. In the case of infinitely fast kinetics the conversion can be computed analytically based on Eq. (3) and Eq. (5) assuming Y s CO ¼ 0: lnð1 v inf Þ¼ hd COi f k 0 m u cat : ð21þ Note that Eq. (21) predicts an increase in conversion with temperature for fixed u cat and k 0 m due to the temperature dependence of the diffusion coefficient. 4.3. Simulations with instantaneous washcoat diffusion 4.3.1. Light-off curves Fig. 4 shows light-off curves for different values of F cat=geo for the foam based reactor (reference case) under the assumption of instantaneous washcoat diffusion. Light-off curves are plotted with solid lines and are obtained by gradually increasing the temperature as described in Section 3.1. Extinction curves are plotted with dashed lines and are obtained with a gradual reduction of the reactor temperature. The solid black line represents the conversion in the limit of infinitely fast kinetics (v inf ). The light-off and extinction temperatures (T L and T E ) are defined as the temperatures where conversion is equal to 0:5v inf in the two branches respectively. Fig. 4. Conversion at different washcoat surface areas F cat=geo. Instantaneous washcoat diffusion. inf: Conversion assuming infinitely fast kinetics (Eq. (21)). : heating, : cooling. Case F cat=geo ¼ 10 omitted for clarity. The conversion curves show the well known characteristics of catalytic light-off: negligible conversions at low temperature; a steep increase around the light-off temperature (T L ) or a drop around the extinction temperature (T E ); at high temperatures conversion is close to the limit of infinitely fast kinetics. In all cases hysteresis between the heating and the cooling phase is observed and its amplitude, measured as the difference between the light-off and extinction temperatures (T L T E ), increases with the surface area. The hysteresis is due to the two possible steady states in the region between T L and T E : A predominately CO covered state in the ignition branch and a predominantly oxygen covered state in the extinction branch [4]. Since washcoat diffusion resistance is neglected, it is expected that catalytic CO conversion after the light-off (T > T L ) is limited only by external mass transfer. However in Fig. 4 this regime, equivalent to infinitely fast kinetics, is reached only by the cases with F cat=geo P 10. The conversion for F cat=geo ¼ 1, after a strong increase around (T L ), remains below the limit of infinitely fast kinetics for a wide temperature range. This suggests that for F cat=geo ¼ 1 the conversion at high temperatures is still affected by finite rate chemical kinetics. 4.3.2. Analysis of the reaction mechanism In order to investigate the impact of finite rate chemistry on CO conversion above light-off for F cat=geo ¼ 1, a sensitivity analysis of the overall reaction rate with respect to temperature is performed. The sensitivity is defined as S T ¼ Drrr CO 2 =rr CO2 ; ð22þ DT=T where Drr r CO 2 is the change in CO 2 production rate by changing the temperature T of the catalytic surface by DT ¼ 0:01T. S T therefore indicates the differential change in reaction rate with a differential change in temperature. The sensitivity is evaluated using the averaged surface concentrations (Y s ) at the inlet. Fig. 5 shows S T and the conversion for the case of F cat=geo ¼ 1. S T is high at low temperatures and drops to zero where the slope in conversion decreases (570 K). At temperatures above 680 K, S T increases again but remains significantly lower than at temperatures below the light-off temperature. The drop in S T at light-off can be understood by identifying the rate limiting steps of the elementary reaction mechanism. The rate limiting steps are identified using the relative sensitivity of the overall reaction rate with respect to the elementary steps: S r ¼ Drrr CO 2 =rr CO2 Dk r =k r ; ð23þ

394 J. von Rickenbach et al. / Chemical Engineering Journal 276 (2015) 388 397 reactions show an exponential temperature dependence. Therefore the change in adsorption rate constant with temperature can be neglected, compared to the change in desorption and surface reaction rate constants. With this simplification it can be concluded that the temperature dependence of the overall reaction rate (S T ) at low temperatures is mainly due to the CO desorption reaction. Above the light-off temperature, the maximum sensitivity of all the desorption reactions and the surface reaction drops by one order of magnitude. This drop in sensitivity of the reactions that have strong temperature dependence explains the strong decrease of S T above the light-off temperature. In other words: The overall reaction rate at high temperature is most sensitive to the CO adsorption rate constants that has only a weak dependence on temperature. Fig. 5. Relative sensitivity of the overall reaction rate with respect to temperature (Eq. (22)). Sensitivity is evaluated at the inlet. v: conversion with instantaneous washcoat diffusion (F cat=geo ¼ 1, heating phase). where Drr r CO 2 is the change in CO 2 production rate by changing the reaction rate constant k r by Dk r ¼ 0:01k r. S r indicates the differential change of the overall reaction rate with a differential change in a reaction rate constant of the elementary step. Fig. 6 shows S r for the most important reactions. The sensitivity with respect to the elementary steps changes sharply in the light-off region. At temperatures below the light-off temperature the sensitivity with respect to CO adsorption is -2, whereas O 2 adsorption sensitivity is equal to one. At temperatures above the light-off temperature, the sensitivity with respect to CO adsorption is positive and O 2 adsorption has a negative sensitivity. The CO desorption reaction has sensitivity of 2 before light-off and above light-off its sensitivity is small and negative. The relative sensitivity of the surface reaction step (SR) and O 2 desorption is small at all temperatures. The sensitivities before light-off are due to a self-inhibition effect of CO: CO adsorption is much stronger than O 2 adsorption and therefore CO blocks most of the available surface sites. It is then clear that an increase in the CO desorption rate constant increases the overall reaction rate (S r ¼ 2), whereas CO adsorption has the opposite effect (S r ¼ 2). Above light-off oxygen blocks the surface sites which leads to opposite sensitivities. The computed surface coverages confirm that this is indeed the case (not shown). The results in Fig. 6 can be used to explain the S T behaviour in Fig. 5. The reaction rate constant for adsorption is proportional to p ffiffiffi T (Eq. (10)), whereas the surface reaction and the desorption 4.4. Simulations with finite rate washcoat diffusion 4.4.1. Light-off curves Fig. 7 presents light-off curves for different values of F cat=geo with finite rate washcoat diffusion. All the simulations are run for the foam based reactor at reference conditions except for the variation in F cat=geo. The case with instantaneous washcoat diffusion and F cat=geo ¼ 100 is also shown for comparison. Note that since the Pt mass per unit washcoat surface area is constant, F cat=geo is proportional to the total amount of Pt in the reactor. Fig. 7 shows that conversion is close to zero at low temperatures and increases rapidly in the light-off region. Conversion above the light-off temperature is lower than the v inf for all values of F cat=geo. The relative reduction compared to v inf decreases with an increase in F cat=geo. Above the light-off region the slope in conversion approaches the slope of v inf for F cat=geo P 100. For the two lower surface areas the slope is slightly lower. Comparing Fig. 7 to the case with instantaneous washcoat diffusion (Fig. 4) three main differences can be identified: Accounting for finite rate washcoat diffusion, the conversion is lower than v inf for all temperatures and all values of F cat=geo. Assuming instantaneous washcoat diffusion, such a reduction was only observed for the lowest surface area considered (F cat=geo ¼ 1). The light-off region in both the heating and the cooling phases is broader with finite rate washcoat diffusion, compared to the case with instantaneous washcoat diffusion. In the beginning of the light-off region during heating, the conversion with finite rate washcoat diffusion is larger than in the case with Fig. 6. Relative sensitivity of the overall reaction rate with respect to the elementary steps (Eq. (23)) (Instantaneous washcoat diffusion, F cat=geo ¼ 1, heating phase). ad: adsorption, de: desorption, SR: surface reaction. Sensitivity is evaluated at the inlet. Fig. 7. Conversion with different washcoat surface areas F cat=geo. Inst wc diff: Case assuming instantaneous washcoat diffusion (F cat=geo ¼ 100). inf: Conversion assuming infinitely fast kinetics (Eq. (21)). : heating, : cooling.

J. von Rickenbach et al. / Chemical Engineering Journal 276 (2015) 388 397 395 instantaneous washcoat diffusion. This increase in conversion due to finite rate washcoat diffusion is a known phenomenon and is due to the negative reaction order of the overall reaction with respect to CO [33]. Hysteresis effects with finite rate washcoat diffusion are weaker than in the case of instantaneous washcoat diffusion. 4.4.2. Washcoat concentration profiles In Fig. 8 CO concentration profiles are shown in the first 10 lm of the washcoat during the heating phase at the inflow for three different temperatures (reference case). The main reaction zones are indicated with boxes. The reaction zone is defined as the region where the CO 2 production rate is larger than 0.1 of the maximum CO 2 production rate at any point in the washcoat. The concentration profiles at 480 K and 500 K are in the light-off region. At both temperatures the reaction zone is confined to a small region in the washcoat. In the region between the reaction zone and w = 0 the concentration profiles are linear. At a higher temperature of 600 K the reaction zone starts at w = 0 and is thinner than at the lower two temperatures. At 480 K and 500 K the reaction rate between w = 0 and the reaction zone is low. The simulations show that this is due to self-inhibition of CO. On the other side of the reaction zone reaction rates are small due to low CO concentrations. At 600 K no self-inhibition is observed and the CO concentration decreases exponentially along the washcoat coordinate. At all three temperatures only a small fraction of the washcoat is utilized for the reaction. Finite rate washcoat diffusion therefore effectively reduces the utilizable active surface area of the washcoat, which causes a reduction in conversion compared to the case with instantaneous washcoat diffusion. Even for the lowest temperature shown (480 K), the main reaction zone is within first 10 lm of the washcoat. This implies that conversion does not depend on the washcoat thickness as long as the washcoat has a reasonable thickness (>10 lm), if the surface area per unit washcoat volume (a wc V ) remains constant. 4.5. Effect of external mass transfer The difference between the foam and the honeycomb reactor is parametrized with the external mass transfer coefficient. The reference mass transfer coefficient (Sh/L = k 0 m = 8000 m 1 ) represents a foam based reactor at a velocity of approximately 2 m/s. The honeycomb is represented by k 0 m ¼ 4000 m 1, whereas k 0 m ¼ 16; 000 m 1 represents a foam based reactor at higher velocities. Studying the effect of the external mass transfer coefficients on conversion therefore allows to draw conclusions on the relative importance of washcoat diffusion resistance in the two reactor types. Fig. 9 shows the conversion for the three external mass transfer coefficients considered. All the other parameters are at their reference values (Table 3). Above the light-off temperature, an increased external mass transfer coefficient increases conversion. Table 5 shows the ratio of conversion with finite rate washcoat diffusion (v) to the conversion with infinitely fast kinetics (v inf )at 600 K taken from Fig. 9. The ratio v=v inf decreases with an increase in the external mass transfer coefficient. This implies that the relative reduction in conversion due to washcoat diffusion resistance is more important in foams compared to honeycomb reactors since mass transfer coefficients in foams are higher at relevant operating conditions. In contrast to honeycomb reactors, the importance of washcoat diffusion in foams is difficult to investigate experimentally, since external mass transfer coefficients are difficult to measure Fig. 9. Conversion with different external mass transfer coefficients k 0 m. : with washcoat diffusion, : Conversion assuming infinitely fast kinetics (Eq. (21)). Table 3 Simulation parameters. Parameter Reference case Variation u cat 1.25 k 0 m (m 1 ) 8000 4000,16,000 F cat=geo ( ) 100 1,10,500 d wc (nm) 10 100 s wc ( ) 8 2 wc ( ) 0.35 t wc (lm) 100 C ðmol=m 2 Þ 2.72E 5 Table 4 Effective washcoat diffusion coefficients of CO reported in the literature and the values used in the simulations. All the values are reported at standard conditions. Fig. 8. CO mass fraction profiles in the washcoat Y wc CO at the inflow (Y b CO ¼ 0:003) for different temperatures around light-off. Heating phase, Reference case (foam reactor). Only the first 10 lm of the washcoat are shown. The boxes indicate the reaction zones. Outside the boxes the reaction rate is less than 10% of the maximum reaction rate. Reference Hayes et al. [27] 0.074 [29] 0.27 [30] 1 [28] 1.4 6 Simulation d wc ¼ 10 nm, s ¼ 8 0.064 d wc ¼ 100 nm, s ¼ 8 0.25 d wc ¼ 100 nm, s ¼ 2:0 1.6 D wc e;co (m2 =s) 10 6 D wc e;co (m2 =s) 10 6

396 J. von Rickenbach et al. / Chemical Engineering Journal 276 (2015) 388 397 Table 5 Ratio of conversion with finite rate washcoat diffusion to the limit of infinitely fast kinetics at 600 K. (Fig. 9). k 0 m (m 1 ) independently. Giani et al. [13] have shown that conversion at temperatures above light-off depends on the washcoating method applied. We believe this is an indication that washcoat diffusion resistances in foams are important above the light-off temperature as shown in our simulations. Comparing foams and honeycomb reactors side by side clearly highlights that there is no reason to assume that washcoat diffusion resistance is negligible in foams, an assumption widely used in the foam literature [8,9,13]. 4.6. Effect of the effective washcoat diffusion coefficient v/v inf 4000 0.74 8000 0.64 16,000 0.54 The effective diffusion coefficient in the washcoat can be estimated only with a large uncertainty, which can have a significant effect on the diffusion resistance in the washcoat (see Section 3.2.2). It is therefore interesting to investigate the sensitivity of conversion with respect to the effective diffusion coefficient. Here we vary the washcoat pore diameter and the washcoat tortuosity. Fig. 10 shows the impact of different washcoat pore diameters (d wc ) on conversion. All simulation parameters except the pore diameter are fixed at reference values (foam reactor). A case with a decreased tortuosity of 2 and a pore diameter of 100 nm is also shown. Fig. 10 shows that the qualitative shape of the light-off curve is unaffected by the effective diffusion coefficient in the washcoat. Conversion at all temperatures increases with an increase in the effective diffusion coefficient. For the largest effective diffusion coefficient studied (s ¼ 2; d wc = 100 nm) the impact of washcoat diffusion resistance is minor. This shows that an optimized washcoat structure with a large fraction of macro-pores can significantly reduce the effect of washcoat diffusion. Plotting the reaction rates along the washcoat coordinate for various washcoat diffusion coefficients shows that a larger diffusion coefficient broadens the zone of significant reaction. That is to say that the width of the boxes as shown in Fig. 8 increases with the pore diameter (not shown for brevity). Therefore a larger part of the washcoat is utilized for the reaction which leads to improved conversion for larger effective washcoat diffusion coefficients. 5. Conclusions Light-off curves for catalytic oxidation of CO over Pt were simulated in foam based reactors and honeycombs with a volume averaged model in order to assess the impact of washcoat diffusion resistance on conversion. The chemical reactions were modeled with a multi-step reaction mechanism. Simulations considering finite rate chemistry and finite rate washcoat diffusion were compared to simulations assuming instantaneous washcoat diffusion and the limit of infinitely fast kinetics. The main conclusions from these simulations are as follows: For both reactor types conversion does not reach the limit of infinitely fast kinetics, even at the highest temperature simulated (1000 K), when finite rate washcoat diffusion is considered and the number macro-pores in the washcoat is insignificant. The difference between the actual conversion and the conversion in the limit of infinitely fast kinetics remains roughly constant above the light-off temperature. The effect of washcoat diffusion is expected to be even more pronounced in foam based reactors compared to honeycomb reactors, since external mass transfer coefficients in foams at relevant conditions are significantly higher than in honeycomb reactors. This implies that optimizing the washcoat structures to reduce the diffusion resistance has the potential to significantly improve the performance of foam based catalytic reactors. Increasing the specific surface area of the washcoat reduces the impact of washcoat diffusion resistance above the light-off temperature. However, even with the highest specific surface area considered (F cat=geo ¼ 500), the washcoat diffusion resistance remains significant at all temperatures. The washcoat diffusion resistance can be reduced with a washcoat that contains a large fraction of macropores which significantly enhance the diffusion process. A high catalytic activity (F cat=geo P 100) combined with a large fraction of macro pores results in a difference between the infinitely fast chemistry limit and the case of finite washcoat diffusion of less than 10%. Assuming instantaneous washcoat diffusion the conversion reaches the infinitely fast chemistry limit within less than 100 K after light off if the specific surface areas are high (F cat=geo P 10). For a washcoat with a low specific surface area (F cat=geo ¼ 1), finite chemistry effects remain visible up to temperatures as high as 800 K, even if washcoat diffusion is assumed to be instantaneous. The temperature dependence of the overall reaction rate above light-off is significantly weaker than before light-off. The decrease in temperature dependence after light-off is explained with a drop in sensitivity of the elementary steps that have a highly temperature dependent rate constant. The oxidation reaction occurs in a narrow zone within the washcoat. Outside of this reaction zone the washcoat is inactive due to the self-inhibition of CO or low CO concentrations. Acknowledgement Support has been provided by the Kompetenzzentrum für Energie und Mobilität CCEM via Project Number 704 and the Swiss Federal Office for the Environement FOEN (BAFU), 3003 Bern, Switzerland Appendix A. Volume averaging definitions Fig. 10. Conversion with different washcoat pore diameters and different washcoat tortuosities. inf: Conversion assuming infinitely fast kinetics (Eq. (21)). : heating, : cooling. The porous medium consists of a fluid phase and a solid phase. The indicator function of phase p is defined as

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