Intrinsic Permeability of Heterogeneous Porous Media

Providing a sound appraisal of the nature of the relationship between flow(Q) and pressure drop (Δ P) for porous media is a long-standingfundamental research challenge. A wide variety of environmental, societal andindustrial issues, ranging, e.g., from water-soil system remediation tosubsurface energy optimization, is affected by this critical issue. While suchdependence is well represented by the Kozeny-Carman formulation for homogeneousmedia, the fundamental nature of such a relationship (Q vs Δ P) withinheterogeneous porous systems characterized by a broad range of pore sizes isstill not fully understood. We design a set of controlled and complex porousstructures and quantify their intrinsic permeability through detailed highquality microfluidics experiments. We synthesize the results upon deriving anoriginal analytical formulation relating the overall intrinsic permeability ofthe porous structure and their key features. Our formulation explicitly embedsthe spatial variability of pore sizes into the medium permeability through aconceptualization of the system as a collection of smaller scale porous mediaarranged in series. The resulting analytical formulation yields permeabilityvalues matching their experimentally-based counterparts without the need ofadditional tunable parameters. Our study then documents and supports the strongrole played by the micro-structure on the overall medium permeability.