## 2 Materials and Methods
### Catalyst Model  
The study employed a flow-through monolith oxidation catalyst model for dual-layer washcoat, as proposed by [PERSON] et al. [29]. This model is part of VATS, a virtual environment developed by CMT-Clean Mobility & Thermofluids to simulate ATS coupled with VEMOD, a gas dynamic software for engine modelling [33]. Detailed descriptions of the model for dual-layer washcoat catalysts can be found in [29], which is based on earlier developments focused on deriving explicit solutions for flow transport in catalytic reactors with single-layer washcoats [34; 35] from a 1+1D two-phase approach [36]. The model calculates the concentration of chemical species in the bulk gas along the monolith. It includes convective and diffusive transport mechanisms and accounts for chemical reactivity in dual-layer washcoat structures. The model assumes constant flow properties at the monolith inlet and negligible radial temperature gradients, ensuring consistent behavior across all channels [35], as well as quasi-steady incompressible flow [37; 38]. The chemical species conservation equations, corresponding to a single channel bulk gas (Equation (1)) and washcoat layers (Equations (2) and (3)), are written as:  
\[u_{x}\frac{\partial c_{g}}{\partial x}=-S_{s,g}J_{g,wc_{1}} \tag{1}\]  
\[-\sum_{r_{wc_{1}}}v_{r_{wc_{1}}}R^{m}_{r_{wc_{1}}}=S_{s,wc_{1}}\left(J_{g,wc_ {1}}-J_{wc_{1},wc_{2}}\right) \tag{2}\]  
\[-\sum_{r_{wc_{2}}}v_{r_{wc_{2}}}R^{m}_{r_{wc_{2}}}=S_{s,wc_{2}}J_{wc_{1},wc_ {2}} \tag{3}\]  
In the equations, subscripts \(g\), \(wc_{1}\), and \(wc_{2}\) denote the bulk gas and the two washcoat layers, respectively. The variable \(u_{x}\) indicates the axial velocity of the gas. The term \(R^{m}_{r_{wc_{1}}}\) quantifies the reaction rate of an \(m\)th-order reaction, and \(v_{r_{wc_{1}}}\) are the stoichiometric coefficients, with positive values for products and negative values for reactants. Additionally, \(S_{s}\) refers to the specific surfaces of the gas and each washcoat layer. The terms \(J_{g,wc_{1}}\) and \(J_{wc_{1},wc_{2}}\) describe the fluxes at the interface between the gas and the upper washcoat layer and between the upper and lower washcoat layers, respectively [29]. The fundamentals of the explicit solver lie in the dependence of the interfacial fluxes on the species concentration at every phase, as proposed by [PERSON] et al. [38]. The explicit solution obtained to determine the concentration of the chemical species at the outlet of the monolith is given by Equation (4). Constants \(b\) and \(d\) are functions of specific surfaces, diffusion times, reaction rates, and Sherwood numbers, as detailed in [29]. \[c_{g,out}=\frac{\left(d+bc_{g,in}\right)e^{-S_{s,g}b\tau}-d}{b} \tag{4}\]  
In parallel to the solution of chemical species transport, the energy balance in the gas and solid phases is also addressed due to the influence of substrate temperature on reactivity and outlet gas concentration, as detailed in [29]. Regarding the reaction mechanism, which is listed in Table 4, it presents the comprehensive reaction mechanism along with the corresponding rates for each reaction accounted for in every catalyst layer, including kinetic constants (\(k_{i}\)) derived from the Arrhenius equation. This reaction mechanism covers, as baseline, primary processes such as HC adsorption/desorption (\(R_{1}\) and \(R_{2}\)), CO and HC oxidation with O\({}_{2}\) (\(R_{3}\) and \(R_{4}\)), and NOx interconversion (\(R_{5}\) and \(R_{6}\)), detailed in [28]. Although these reactions address catalyst behavior with excess O\({}_{2}\), they lack sensitivity to H\({}_{2}\) presence. By introducing -OH radicals as intermediates, the influence of H\({}_{2}\) can be covered. [PERSON] and [PERSON] [27] proposed a microkinetic scheme highlighting the significance of the carboxylic pathway. This pathway involves adsorption and desorption steps for various reaction intermediates with a radical nature, including -H, -O, -OH, -COOH, and -HCO [39].