Washcoat Internal Diffusion Modeling

In many SCR applications, the thickness and effective diffusivity of the active layer may not allow the simplifying assumption of negligible internal diffusion resistance. In these cases, a more detailed approach which models mass transfer both in the gas phase and in the washcoat/active volume pores is needed. 

The schematic and the basic geometric properties of the monolith channel cross-section are presented in Fig. 13.2 for the cases of a coated and of an extruded monolith. 

The convective mass transfer from the bulk gas to the washcoat/wall surface is now written as  

Following the quasi-steady assumption, the transient accumulation terms are neglected and the species balance inside the catalytic layer is formulated as  

In the catalytic washcoat layer, w — 0 corresponds to the wall boundary while w = —Wc to the external surface of the washcoat. The boundary conditions for the washcoat layer are  

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Figure 13.11a shows conversion efficiency with respect to space velocity at 200 °C where it is evident that diffusion limitations are absent SCR de-NO efi ciency, computed either with the surface reaction or the internal diffusion model, is in complete agreement with the one calculated for the SCRF. On the contrary, washcoat diffusion becomes significant at the temperature of 350 °C (Fig. 13.11b). Examining the SCR curves only, the trends of NO conversions...

In the spatially ID model of the monolith channel, no transverse concentration gradients inside the catalytic washcoat layer are considered, i.e. the influence of internal diffusion is neglected or included in the employed reaction-kinetic parameters. It may lead to the over-prediction of the achieved conversions, particularly with the increasing thickness of the washcoat layer (cfi, e.g., Aris, 1975 Kryl et al., 2005 Tronconi and Beretta, 1999 Zygourakis and Aris, 1983). To overcome this limitation, the effectiveness-factor concept can be used in a limited extent (cf. Section III.D). Despite the drawbacks coming from the fact that internal diffusion effects are implicitly included in the reaction kinetics, the ID plug-flow model is extensively used in automotive industry, thanks to the reasonable combination of physical reliability and short computation times. 

When the internal diffusion effects are considered explicitly, concentration variations in the catalytic washcoat layer are modeled both in the axial (z) and the transverse (radial, r) directions. Simple slab geometry is chosen for the washcoat layer, since the ratio of the washcoat thickness to the channel diameter is low. The layer is characterized by its external surface density a and the mean thickness <5. It can be assumed that there are no temperature gradients in the transverse direction within the washcoat layer and in the wall of the channel because of the sufficiently high heat conductivity, cf., e.g. Wanker et al. 

This intermediate scale affords a preliminary validation of the intrinsic kinetics determined on the basis of microreactor runs. For this purpose, the rate expressions must be incorporated into a transient two-phase mathematical model of monolith reactors, such as those described in Section III. In case a 2D (1D+ ID) model is adopted, predictive account is possible in principle also for internal diffusion of the reacting species within the porous washcoat or the catalytic walls of the honeycomb matrix. 

Exemplary results of modeling processes inside the catalytic layer are presented in Fig. 9. The solid lines show the dependency of the overall effectiveness factor on the relative distribution of the catalyst between the comers and the side regions. The two cases represent two levels of the first-order rate constants, with the faster reaction in case (b). As expected, the effectiveness factor of the first reaction drops as more catalyst is deposited in the comers. The effectiveness factor for the second reaction increases in case (a) but decreases in case (b). The latter behavior is caused by depletion of B deep inside the catalytic layer. What might be surprising is the rather modest dependency of the effectiveness factor on the washcoat distribution. The explanation is that internal diffusion is not important for slow reactions, while for fast reactions the available external surface area becomes the key quantity, and this depends only slightly on the washcoat distribution for thin layers. The dependence of the effectiveness factor on the distribution becomes more pronounced for consecutive reactions described by Langmuir-Hinshelwood-Hougen-Watson kinetics [26]. 

The inlet conditions for the numerical simulations are based on the experimental conditions. The simulations are performed with the three different models for internal diffusion as given in Section 2.3 to analyze the effect of internal mass transfer limitations on the system. The thickness (100 pm), mean pore diameter, tortuosity (t = 3), and porosity ( = 60%) of the washcoat are the parameters that are used in the effectiveness factor approach and the reaction-diffusion equations. The values for these parameters are derived from the characterization of the catalyst. The mean pore diameter, which is assumed to be 10 nm, hes in the mesapore range given in the ht-erature (Hayes et al., 2000 Zapf et al., 2003). CO is chosen as the rate-limiting species for the rj-approach simulations, rj-approach simulations are also performed with considering O2 as the rate-hmiting species. 

In many cases, the influence of internal diffusion is considered negligible and the modeling steps 2 and 4 are lumped into the reaction rate of step 3. The surface reaction model approximates the washcoat with a solid-gas interface where it is assumed that aU reactions take place. In this case, there is no concentration gradient in the washcoat and therefore only one surface species concentration is defined. 

We first assessed the impact of internal diffusion limitations in the PGM layer. For this purpose a simulation study was performed progressively increasing the PGM washcoat thickness, from 10 pm up to 71 pm. From the analysis of NH3 concentration profiles a dramatic impact of dififiisional limitations was apparent indeed only the surface of this layer is effectively active due to the extremely high reactions rates of the PGM catalyst. For this reason, we developed a Layer -I- Surface Model (LSM) of dual-layer ASC where we treat the PGM layer as a surface, while we retain the rigorous description of coupled reaction/dififusion in the SCR layer, based on the previous ID -I- ID model of SCR monolithic converters [12,25,26]. Indeed, avoiding the description of diffusion phenomena in the PGM layer enables the direct inclusion of the PGM reactivity in the SCR converter model by simply modifying the inner boundary conditions of the species differential mass balances in the SCR layer, i.e., those now at the interface with the PGM phase. Treating the PGM layer as a surface thus enabled a simple extension of the ID -I- ID SCR converter model to simulate dual-layer catalytic systems too. 

For the detailed study of reaction-transport interactions in the porous catalytic layer, the spatially 3D model computer-reconstructed washcoat section can be employed (Koci et al., 2006, 2007a). The structure of porous catalyst support is controlled in the course of washcoat preparation on two levels (i) the level of macropores, influenced by mixing of wet supporting material particles with different sizes followed by specific thermal treatment and (ii) the level of meso-/ micropores, determined by the internal nanostructure of the used materials (e.g. alumina, zeolites) and sizes of noble metal crystallites. Information about the porous structure (pore size distribution, typical sizes of particles, etc.) on the micro- and nanoscale levels can be obtained from scanning electron microscopy (SEM), transmission electron microscopy ( ), or other high-resolution imaging techniques in combination with mercury porosimetry and BET adsorption isotherm data. This information can be used in computer reconstruction of porous catalytic medium. In the reconstructed catalyst, transport (diffusion, permeation, heat conduction) and combined reaction-transport processes can be simulated on detailed level (Kosek et al., 2005). 

Instantaneous diffusion oo-approach) model assumes that the catalyst is virtually distributed at the gas/washcoat interface so that there is infinitely fast mass transport within the washcoat. This model eliminates the washcoat parameters, such as its thickness and porosity, and the diameters of the inner pores. Therefore, oo-approach does not account for internal mass transport limitations that are due to a porous layer. It means that mass fractions of gas-phase species on the surface are obtained by the balance of production or depletion rate with diffusive and convective processes (Deutschmann, 2008 Kee et al., 2001 Wamatz, 1992). Thus, the net production rate of each chemical species due to surface reactions can be balanced with the diffusive flux of that species at the gas-surface boundary, assuming that no deposition or ablation of chemical species occurs on/from the catalyst surface ... 

Compressible ID stagnation-point flow analysis forms the basis of the equation system presented below. It was found that the prediction of the effect of internal mass transfer limitations in the catalytic washcoat of the SFR configuration is crucial to derive microkinetic data from SFR experiments (Karadeniz, 2014 Karadeniz et al., 2013) our model is extended to include the diffusion limitations due to a porous layer. It should be noted that the CFiEMKIN code has no abihty to account for internal mass transport in the catalytic coating. 

The scope of this paragraph is to analyze the impact of internal washcoat diffusion on the performance of zeolite-based catalysts both by experimental and simulation results. In the first part, an experimental study of mass transfer limitations in Fe- and Cu-zeolite catalysts performed by Metkar et al. [40] is presented. The authors investigated catalysts with different washcoat loadings, washcoat thicknesses, and lengths under various SCR reactions in order to identify the presence of diffusion limitations throughout an extended temperature range. In the second part, the flow-through catalyst model, presented in Sect. 13.2, was employed to reproduce the test conditions of the fore-mentioned experiments. 

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