Unified Model of Drainage and Imbibition in 3D Fractionally Wet Porous Media

摘要

We develop a grain based model for capillarity controlled displacement within 3D fractionally wet porous media. The model is based on a novel local calculation of the position of stable interfaces in contact with multiple grains. Each grain can have a different, arbitrary contact angle with the interface. The interface is assumed to be locally spherical for menisci separating the bulk non-wetting and wetting phases. The fluid/fluid interfaces between pairs of grains (surfaces of pendular rings) are assumed toroidal. Because the calculation of interface position is entirely local and grain-based, it provides a single, generalized, geometric basis for computing pore-filling events during drainage as well as imbibition. This generality is essential for modeling displacements in fractionally wet media. Pore filling occurs when an interface becomes unstable in a pore throat (analogous to Haines condition for drainage in a uniformly wet throat), when two or more interfaces come into contact and merge to form a single interface (analogous to the Melrose condition for imbibition in uniformly wet medium), or when a meniscus in a throat touches a nearby grain (a new stability criterion). The analytical solution for stable interface locations generalizes the Melrose and Haines criteria previously validated for pore-level imbibition and drainage events in uniformly wet media. The concept of tracking the fluid/fluid interface on each grain means that a traditional pore network is not used in the model. The calculation of phase saturation or other quantities that are conveniently computed in a network can be done with any approach for defining pore bodies and throats (e.g. Delaunay tessellation, Voronoi tessellation, and medial axis methods). The fluid/fluid interfaces are mapped from the grain-based model to the network as needed. In addition, the model is robust as there is no difference in the model between drainage and imbibition, as all criteria are accounted for both increasing and decreasing capillary pressure. To validate the model, we perform a series of drainage/imbibition experiments (oil/water) on fractionally wetted porous media prepared by mixing oil-wet grains with water-wet grains. In both experimental and simulation results, the drainage/imbibition curves shifts to lower capillary pressure with increasing fraction of oil-wet grains. Using the model, we delineate which pore filling criteria occur as a function of initial wetting phase and wettability of grains. The shape and position of the pressure–saturation curve is shown to be a function of the pore filling types, and hysteresis arises naturally from the model.