A general capillary equilibrium model to describe drainage experiments in heterogeneous laboratory rock cores

Abstract

Macroscopic observations of two-phase flow in porous rocks are largely affected by the heterogeneity in continuum properties at length scales smaller than a typical laboratory sample. The ability to discriminate among the rock properties at the origin of the heterogeneity is key to the development of numerical models to be used for prediction. Here, we present a capillary equilibrium model that represents spatial heterogeneity in dual-porosity porous media in terms of the capillary entry pressure, 1/α, and the irreducible wetting phase saturation, Sir. Both parameters are used to scale local capillary pressure curves by using three-dimensional imagery acquired during multi-rate gas/liquid drainage displacements. We verify the proposed approach by considering the case study of a dual-porosity limestone core and use the spatial variation in Sir as proxy for microporosity heterogeneity. The latter places potentially next-to-leading order controls on the observed fluid saturation distribution, which is strongly correlated to the distribution of 1/α. While microporosity is by and large uniform at the observation scale on the order of 0.1 cm3, the spatial correlation of 1/α is on the order of 1 cm and is therefore not statistically represented in the volume of typical laboratory core samples.