A discrete‐domain description of multiphase flow in porous media: Rugged energy landscapes and the origin of hysteresis

Abstract We propose a discrete‐domain model to describe mesoscale (many pore) immiscible displacements in porous media. We conceptualize the porous medium and fluid system as a set of weakly connected multistable compartments. The overall properties of the system emerge from the small‐scale compartment dynamics. Our model aims at capturing the rugged energy landscape of multiphase porous media systems, emphasizing the role of metastability and local equilibria in the origin of hysteresis. Under two‐phase displacements, the system behaves hysteretically, but our description does not rely on past saturations, turning points, or drainage/imbibition labels. We characterize the connection between micrometastability and overall system behavior, and elucidate the different nature of pressure‐controlled and rate‐controlled immiscible displacements in porous media.