The preparation of a good espresso goes through various phases: roasting, grinding, blend, extraction etc.. The extraction process is very complex and involves various chemical and physical phenomena. Here, we focus only on the study of water percolation in a porous medium, neglecting the other aspects, such as, for example, the energy balance and chemical reactions. The aim of this work is to study how the described phenomenon can be influenced by the coffee pod geometry and flow direction. In particular, we consider the classical pod geometry and flux direction of the espresso coffee machines, where the flux is from top to bottom, and another one, where the flux of the brewing water is radial, that is, we suppose of having a radial horizontal flux from the central axis to the lateral boundary. In both cases, however, we assume that we are working in the absence of gravity, because it seems plausible to do so, as a first approximation. For the comparison, we use numerical methods based on cellular automata and lattice Boltzmann approaches, due to their flexibility and efficiency, moreover, these models are easy to parallelise when modelling complex phenomena.