Continuum-Scale Modeling of Multiphase Flow in Porous Media From a New Microscopic Theory of Hysteresis

We present continuum modeling of multiphase flow in macroscopic porous media based on a new microscopic hysteresis theory that provides physics-based macroscopic parameters and state variables to capture essential pore-scale features. We propose accessivity to characterize the network connectivity of different-sized pores in a porous medium, and radius-resolved saturations to characterize the distribution of fluid phases within. Developing a statistical theory for quasistatic immiscible drainage-imbibition in arbitrary cycles, we arrive at simple models that naturally arrest hysteresis in capillary pressure and relative permeability. Existing models use empirical case-based modifications to capture hysteretic data and rectify the curvatures of their predictions, which fails to make a physical connection to the medium microstructure. Employing the proposed conceptual framework, here we then develop a novel multiphase flow simulator for macroscopic porous media, where the new constitutive relationships for both capillary pressure and relative permeability consistently link the continuum model to the microscopic state of fluid phases in a porous medium of a given microstructure.