Understanding the behavior of aerosol droplets in porous media is of importance for many applications. For instance, in order to quantify filtration efficiency of porous filters, it is essential to know the dynamics of the droplets in such environments. For porous filters, the filtration efficiency is affected by a number of factors such as the 'intensity' of the flow, the size of the particles and the inner structure. We perform direct numerical simulation of the fluid flow and the particle dynamics in a structured porous medium. The mathematical model is based on an Euler-Lagrange description of gas-particle flow, where we employ one-way coupling of the phases. For computing the gas flow we solve the incompressible Navier-stokes equations, by using a symmetry preserving finite volume discretization method. The porous structure of the computational domain is handled with an immersed boundary (IB) method. By assuming that the particles move as a result of stokes drag, we track the trajectories of the particles. A large number of particles is embedded in the flow and their deposition on the surface of the filter is monitored. We investigate the dependence of filtration efficiency on the Reynolds number and the particle inertia.