Percolation theory of two phase flow in porous media

Abstract

The simultaneous flow of two phases through porous media has long lacked a sound theoretical description, due, in large measure, to the complex geometry and topology of the pore space, and the chaotic, nearly random spatial distribution of the fluids. For some 20 years, a theory of flow through random media, percolation theory, has existed in the field of mathematical physics. In this paper, it is demonstrated that percolation theory describes the distribution of non-wetting fluid in common sandstones and limestones during capillary pressure and relative permeability measurements. In particular, the theory predicts the relative amounts of non-wetting fluid in each of three distinct fluid configurations: isolated, dead-end, and flow effective fluid. Porous media are herein idealized as random mixtures of solid and void to which concepts of percolation theory apply. For sinter-bodies a critical porosity, φ c ⋍ 1 12 , exists, below which the void space is not continuous across the sample. For many natural porous materials, e.g. sandstones and limestones, the dependence of residual non-wetting saturation upon porosity is roughly that which corresponds to the existence of a critical porosity, whose value is again 1 12 . The distribution of the non-wetting phase during two phase flow, in particular, the amount of isolated and dead-end fluid, can be qualitatively predicted by simple graph models. The concepts of dead end and isolated fluid must be considered if relative permeability, capillary pressure, and other descriptors of two phase flow are to be understood.