Two-Phase Flow in an Unsaturated Porous Medium: How Passive Is the “Passive Phase”?

Abstract. Flow in a partially saturated porous medium is often modeled by assuming that air in the pore space is passive and has little effect on the flow of the infiltrating liquid. This assumption is commonly made when the viscosity of the fluid being displaced (i.e., air) is much smaller than that of the infiltrating fluid, e.g., oil or water. Here, we study, asymptotically and numerically, a one-dimensional problem where the viscosity ratio is indeed small, but the passive-air assumption turns out to be inappropriate. In particular, the porous medium equation obtained in the limit of small viscosity ratio gives solutions that are significantly different to those for the full problem, both qualitatively and quantitatively. This affects the saturation dynamics dramatically: at intermediate times, a corner (or derivative) layer near the infiltration boundary causes a surprisingly large change in saturation everywhere in the domain, while at late times the global filling behavior is algebraically slow, rather than exponentially fast, as is the case when the gas viscosity is neglected completely. Numerical computations are provided to underscore these asymptotic predictions.