Using time-dependent random resistor networks to capture the dynamics of flow in disordered porous media

The heterogeneous microstructure of a disordered porous medium determines the pore-level flow. Any changes to the micro-structure in a porous medium, such as solute retention during polymer flow (effectively "clogging" some pores in the network), affects the pore-level flow and alters the bulk behavior. In order to better understand the effect of microstructure on flow behavior, we study a model based on a disordered network of tubes, mathematically equivalent to a random resistor network. We show that this approximate model captures the observed velocity distribution in experiments on glass beadpack. We model the dynamics of structural changes during polymer retention, and show that the (dynamic) resistor network produces flow velocity distributions and bulk properties consistent with the experiments.