An Enhanced Percolation Model for the Capillary Pressure-Saturation Relation

This chapter discusses an enhanced percolation model for the capillary pressure–saturation relation. Analysis of immiscible flow in porous media requires constitutive relationships between fluid content(s), fluid pressure(s), and relative permeabilities. Laboratory measurement of these relationships, especially, for the case of more than two fluid phases, is an expensive and time-consuming undertaking. An enhanced percolation model offers a theoretical framework in which these relationships can be predicted based on measurement of simple fluid and matrix properties. An application of this technique to the hysteretic relationship between capillary pressure and saturation for a two-fluid system is presented. Fundamental to the present work is construction of a topologically complex, yet mathematically tractable model of pore space. This takes the form of a regular geometric pattern of spherical nodes connected by cylindrical bonds. Specification of bond and node radii, bond length, and the pattern of interconnectedness serves to completely define the geometry of the pore space.