Gasoline direct injection (GDI), because it improves fuel economy, has seen rapid adoption, despite large emissions of harmful nanoparticles. To overcome this shortcoming, Selective Catalytic Reduction Filters (SCRF), a combination of a Selective Catalytic Reduction system (SCR) and a Particulate Filter (PF) meant to reduce both NOx gas and Particulate Matters (PM), have also attracted OEMs’ interest due to lower cost and volume than existing engine exhaust after-treatment systems. Practically speaking, integrating the two technologies consists in depositing a layer of a catalytic washcoat into the PF, but this usually affects negatively the PM capture and back-pressure in the filter. Seeking a possible synergistic effect such that an optimum balance between catalyst effectiveness, PM capture, back-pressure and cost is found is of prime interest. To predict how the washcoat deposition profile can affect the SCRF performance, a four-step numerical model was developed. It consists of: (1) the numerical reconstruction of a representative volume of the porous wall with various washcoat distributions and coat weights based on X-ray computed tomography (CT) data, the computation of both (2) the pressure drop and (3) the NOx catalytic reduction effectiveness through the coated porous wall by solving, using the Lattice Boltzmann Method (LBM), a coupled problem involving the Navier-Stokes equations and an advection-diffusion-reaction equation, and (4) the prediction of the PF filtering performance by means of the solution of a Langevin problem.