## 2 Material and Methods
### Catalyst Model  
A flow-through monolith model [38] comprising a reaction mechanism to deal with CO and HC abatement was employed in this work. The heat transfer was solved by means of a lumped nodal discretization [39], which considered gas to wall heat exchange as well as the heat that is released by the CO and HC oxidation, the heat losses toward the ambient and the effect of the thermal effect due to the ceramic substrate, the mat and the external canning. This way, the substrate temperature variation during every time-step was computed solving the general heat transfer equation by explicit centered finite differences as  
\[\Delta T_{w}=\frac{\Delta t}{c_{w}}\left(\sum_{i}\frac{T_{i}-T_{w}}{r_{i}}+ \dot{q}_{r}\right), \tag{1}\]  
where \(\Delta t\) represents the time-step, \(T\) is the temperature, and \(r\) stands for the thermal equivalent resistance between \(i\) and the substrate. In these terms, the subscript \(i\) represents the gas or internal canning surface. The thermal inertia of the substrate was considered by means of the thermal capacitance (\(c_{w}\)). Finally, \(\dot{q}_{r}\) represents the thermal power that is related to the reaction mechanism. This consisted of the CO and HC oxidation reactions in the presence of O\({}_{2}\), as well as the HC adsorption and desorption on the zeolite washcoat [40]:  
\[\text{CO}+\frac{1}{2}\text{O}_{2}\to\text{CO}_{2} \tag{2}\]  
\[\text{C}_{\text{n}}\text{H}_{\text{m}}+\Big{(}\text{n}+\frac{\text{m}}{4} \Big{)}\text{O}_{2}\to\text{nCO}_{2}+\frac{\text{m}}{2}\text{H}_{2}\text{O} \tag{3}\]  
\[\text{C}_{\text{n}}\text{H}_{\text{m}}+\text{Zeolite}\
eq\text{C}_{\text{n}} \text{H}_{\text{m}}\cdot\text{Zeolite} \tag{4}\]  
The HCs were represented by decane, as the most representative HC compound in diesel applications [41]. The CO and HC conversion efficiencies were determined solving  
Figure 1: Scheme of the engine test bench.  
the one-dimensional chemical species transport assuming quasi-steady flow, flat velocity, and negligible concentration gradients in the washcoat [42], according to [25]:  
\[u_{in}\frac{\partial p_{n}}{\partial x}=-S_{p,gas}k_{m,n}(p_{n}-p_{n,vac}) \tag{5}\]  
\[\sum_{i}\
u_{n}R_{i}+S_{p,wc}k_{m,n}(p_{n}-p_{n,vac})=0 \tag{6}\]  
Equation (5) represents the bulk gas transport, which involves the advective transport of species \(n\) along the monolith channels and its diffusion toward the washcoat interface. Although the use of the mole fraction to write the species conservation equations [25] is convenient in aftertreatment applications [42], the partial pressure (\(p_{n}\)) was considered in this work to make the impact of the gas pressure on the reaction rate explicit. In Equation (5), \(S_{p,gas}\) represents the specific surface, which accounts for the catalytic surface to gas volume ratio, and \(k_{m}\) is the bulk mass transfer coefficient [43]. In a similar way, Equation (6) refers to the species \(n\) balance in the washcoat, with \(S_{p,wc}\) being the washcoat specific surface, i.e., the inverse of the effective washcoat thickness [44] defined as the washcoat volume to catalytic surface ratio. The term \(R\) refers to the reaction rate, which is defined as a function of the reactants partial pressures for every reaction:  
\[R_{ox,n}=\frac{k_{ox,n}}{G_{ox}}p_{O_{2}}p_{n,wc},\ \ \text{where}\ n=\text{CO},\text{HC} \tag{7}\]  
\[R_{ads,HC}=k_{ads,HC}(1-\theta_{HC})\psi_{HC}p_{HC,wc} \tag{8}\]  
\[R_{des,HC}=k_{des,HC}\theta_{HC}\psi_{HC} \tag{9}\]  
In Equations (7)-(9), the kinetic constant \(k\) is defined according to the Arrhenius expression, \(\theta\) and \(\psi\) represent the HC surface coverage and specific storage capacity, respectively, and \(G_{ox}\) is the inhibition term for CO and HC oxidation reactions, as proposed by [PERSON] et al. [45]:  
\[G_{ox}=T_{w}(1+K_{1}p_{CO,wc}+K_{2}p_{HC,wc})^{2}(1+K_{3}p_{CO,wc}^{2}p_{HC,wc }^{2})(1+K_{4}p_{NO,wc}^{0.7}) \tag{10}\]