Quasi‐steady vertical two‐phase flows in porous media

Abstract

Two‐phase flows in which the pressure profile is essentially constant are called quasi‐steady. One‐dimensional quasi‐steady flows have the remarkable property that volumetric flux is essentially independent of position and is a function of time alone. Such volumetric fluxes are (to within an additive constant) inversely proportional to the spatial mean value of flowing viscosity. Consequently, the evolution of such a system is controlled by global properties of viscosity. Vertical two‐phase quasi‐steady flows evolving from an initial steady flow to another final steady flow are analyzed, and the corresponding theory is matched to output from a numerical simulator. Good agreement between the theory and simulator is demonstrated for simple shocks and expansion waves.