Effect of Wettability on Two-Phase Relative Permeabilities and Capillary Pressures

ABSTRACT The percolation theory of two-phase relative permeability at low capillary numbers (SPE 11015) is further developed to account for the physics of intermediate and mixed wettability in reservoir rocks. The elements of the theory are: a network representation of porespace connectivity; a distribution function description of porespace geometry; capillary pressure (i.e. quasistatic) and wettability criteria of allowability of the invading phase to poresegments according to their throat or body size; a Bethe network approximation to pore space connectivity, to estimate occupancy-conditioned poresize distributions that follow from the preceding elements and lead to occupancy-conditioned distributions of segment volumes (for saturations) and hydraulic conductances (for permeabilities); and a Bethe network transport path conductivity function for creeping flow of each phase that occupies continuously connected pore-segments. Also included is the volume occupied by virtually stationary thin films and pendular structures of the more strongly wetting liquid. Wettability is expressed in the capillary pressure criterion of allowability and acts through the pore-filling sequence in any displacement process. The theory reveals how pore-filling sequences depend on capillary pressure. The theory predicts the saturation-dependent and saturation-history-dependent capillary pressure and relative permeability relations measured by Morrow and coworkers in uniformly wet porous media. Applied to reservoir rock in which a fraction of poresegments previously occupied by oil have become oil-wet, the theory, with that fraction a variable, accounts for the continuous spectrum of capillary pressure and relative permeability curves encountered in reality. Parameter estimation from limited data will be treated elsewhere. The theory is so founded that it can be extended to three-phase relative permeabilities, as will be reported in a sequel.