Predicting the Probability and Degree of Preferential Flow in Porous Media from Pore-Network Geometric and Topological Properties

Solving the flow through a porous medium is central to many technological applications spanning oil recovery, groundwater remediation and geotechnical engineering. The calculations involved in this task become computationally expensive as accuracy and domain size increase. Pore network models are a growingly popular and efficient alternative to numerical simulations. Such models can preserve the connectivity and pore size distribution of the medium, but generally fail to predict differences in flow distribution and occurrence of preferential flow. We hypothesize that local variations of pore size and length (geometry), along with their spatial correlation between neighboring pores (topology), control local channel velocities and overall flow arrangement. Here, we present the identified quantitative relationship between pore structural traits (combining geometric and topologic properties) and local velocities, which can be used as flow field predictors. This relationship is obtained by combining complimentary flow simulations and pore-network structural analyses in detailed two-dimensional polydispersed porous media, which are analyzed with advanced statistical regression models to identifying the structure-function relationship. Newly found insights advise on the metrics necessary to parameterize pore network models that more efficiently capture the subtleties in flow distribution, thus permitting inference of flow arrangement and preferential channel localization from inexpensive structural information.