In this work a combination of micro-CT, image-based modeling and CFD has been applied to investigate the phenomena occurring at the micro-scale level in two different porous substrates: open-cell foams and unstructured filtering media. These substrates are of interest in the internal combustion engine field for application in after-treatment systems. Open-cell foams allow achieving a higher ratio between reactants conversion and pressure drop across the catalyst. compared to traditional honeycombs. On the other hand, unstructured filtering media, made of cordierite or SiC, are commonly applied for the manufacturing of Diesel Particulate Filters. Micro-CT technology was adopted to reconstruct the actual microstructure of the porous media, allowing to characterize its main geometrical properties and to generate a computational mesh for CFD simulations. A CFD investigation pointed out how the microscopic geometry influences the pressure drop under different flow conditions. Moreover, a conjugate heat transfer model is applied for investigating the convection between the fluid and the solid. The aim of this analysis is to enhance the understanding of the phenomena occurring at the micro-scale in order to extract useful information for the optimization of the properties of the substrates to be applied in after-treatment devices.