Dynamic effects for two‐phase flow in porous media: Fluid property effects

Traditional descriptions of multiphase flow in porous media rely on an extension of Darcy's law along with relationships between capillary pressure ( P c ), saturation ( S ), and relative permeability ( K r ). New theories have been proposed which suggest that P c relationships should include a dynamic coefficient (τ) (Hassanizadeh and Gray, Water Resour Res . 1993;29:3389–3405) to indicate how “quickly” or “slowly” flow equilibrium is reached. While validity of these theories must be examined, it is also necessary to determine the significance of τ and its range of values. In this article, we analyze the significance of τ depending on fluid properties. We address the ways in which they cause nonuniqueness of dynamic two‐phase flow in porous media and, hence, dynamic effect. Simulations are conducted for quasi‐static and dynamic flow of perchloroethylene (PCE) in water saturated domains. The data are then fitted to the dynamic P c relationships to obtain values of τ. The effects of flow directions and, viscosity and density ratios are discussed. To consider the lumped effects of various fluid properties, τ– S relationships are examined for silicone oils. The results are interpreted by examining the correlation between τ and a mobility coefficient, m . We discuss a scaling relationship that shows the dependence of τ on fluid and material properties.