Pore network models for porous media with applications to filtration

We model the void space of a non deformable porous material as a randomly-generated network of pores with circular cross-section. Motivated by applications in membrane filtration, we consider flow of a particle-laden solution through the pore network. Suspended particles are of two distinct types, which deposit within the material via distinct mechanisms: (i) small particles that are transported and attracted to pore walls, where they adhere and shrink the pores; and (ii) large particles that are transported by flow through the network until they reach a pore too small to transit, which is then blocked. We use statistically-averaged simulations to probe how the geometric details of the pore network (e.g. porosity, tortuosity, pore connectivity, pore size distribution) influence global features of the flow over time. We demonstrate how our model can be used to make specific design recommendations depending on the context. In filtration, for example, one would like to determine pore network characteristics that maximize total throughput of fluid over the network lifetime while maintaining particle concentration in the outflow below some threshold. We present sample results for this scenario.