Gravity‐dominated three‐phase flow in porous media

Abstract This work studies a class of Riemann problems for immiscible vertical three‐phase flow in porous media for the general case in which all fluids have distinct densities and convection occurs solely due to gravity effects. The Riemann solutions were obtained by using conservation law theory, specifically, the “wave curve method” in state space to obtain qualitatively the structure of the solutions in terms of the wave groups. A numerical finite volume scheme of Godunov type was implemented to calculate saturation profiles of the solutions and validate the wave structure obtained through the theory. The solutions for the general “three‐distinct‐densities” case for the special class of Riemann data considered in this work, are proven to be structurally superpositions of simplified EHDs (equal‐high densities) and ELDs (equal‐low densities) solutions, introduced by Rodríguez‐Bermúdez and Marchesin in a previous work. The results in this work are a relevant step toward understanding gravity effects in general three‐phase flow.