We report on the results of a two dimensional numerical study using OpenFOAM, of the process of infiltration of a homogeneous porous substrate, moving over a stationary solid cylinder, by an incompressible, isothermal and Newtonian fluid. The motion of the substrate relative to the cylinder causes a pressure build-up in the wedge-shaped region separating them, which forces the fluid to penetrate into the porous material. The analysis assumes Stokes flow outside the substrate and uses Brinkman's equation to describe the flow inside the substrate. The structure of the flow field is characterized by the combination of a drag and an opposing pressure-driven flow, the latter caused by the above mentioned pressure build-up in the wedge. The amount of fluid penetrating into the substrate is found to be affected by various parameters such as the pulling speed, substrate permeability, cylinder diameter and substrate thickness. Based on large numbers of simulations, we correlate the achieved impregnation depth to the above parameters and propose a previously unavailable quantitative relationships expressing the above dependencies. Our results find direct applicability in the modeling of the pin-assisted pultrusion process and are in good agreement with the limited experimental data available in the technical literature.