Abstract

Predictive field-scale models of the concurrent flow of three fluids require accurate predictions of five macroscopic flow descriptors: three relative permeabilities and two capillary-pressures as functions of the fluid saturations and saturation history. Since direct measurement of these descriptors is very difficult, and empirical correlations are often unreliable, the use of physically-based pore-scale models has become an appealing alternative. In this paper, we describe the features of our quasi-static pore network model for three immiscible fluids. The model integrates a realistic representation of pore connectivity and morphology, a realistic description of fluid displacement mechanisms, and a sound representation of the wetting properties of the rock. All pore-level displacement mechanisms: piston-type, snap-off, cooperative pore-body filling, and double-displacements are considered with arbitrary contact angles and spreading coefficients. The fluid permeabilities are computed with our accurate expressions for the hydraulic conductance of each fluid in the network ducts of different geometries and for different fluid interface configurations. The proposed model is used to simulate gas injection into permeable rocks that initially contain water and oil after two-phase drainage followed by two-phase imbibition. The gas injection is performed using a cluster-based invasion percolation algorithm with trapping. The strong influence of the two-phase saturation history on the three-phase transport properties of a permeable rock is illustrated by performing a series of gas injections into a sandstone with different initial oil and water saturations, and different microscopic fluid interface configurations.