Three‐dimensional, randomized, network model for two‐phase flow through porous media

Abstract A structural model for a porous medium in the form of a randomized, three‐dimensional network is developed that can be used to calculate permeability, capillary pressure as measured under static conditions and during steady‐state flows, and relative permeabilities as measured during steady‐state flows. This randomized network model, expressed in terms of seven free parameters, can be employed to correlate for a given system the single‐phase permeability, the drainage and imbibition capillary pressure curves, and the two drainage relative permeability curves. The subsequent portions of the hysteresis loops for capillary pressure and for the relative permeabilities then can be predicted. The limited data available from the literature for unconsolidated packed beds have been successfully correlated: 100 to 200 mesh sand and uniform 181 μm glass spheres. Data for a bed of sintered 200 μm glass beads also has been successfully described.