Effect of pore-space spatial correlations on two-phase flow in porous media

Abstract

The pore space in naturally occurring porous media is often spatially correlated. This work is aimed at developing an understanding of the effect of these correlations on multiphase transport properties. Three different correlation structures, namely, spatially uncorrelated, spherical and fractional Brownian motion (fBm) are used to construct the pore space. Two-phase primary drainage and imbibition capillary pressure and relative permeability curves are calculated from pore-level network simulations. Capillary pressure and relative permeability curves for uncorrelated and spherically correlated media are realization-independent, i.e., variations in these properties from realization to realization tend to vanish for large lattices. This is not true for porous networks based on fBm; variability increases with the Hurst exponent for both primary drainage and imbibition. The percolating cluster during primary drainage for uncorrelated and spherically correlated media is fractal, displaying decreasing density with increase in the system size. The percolating cluster is dense for fBm media studied, displaying scale-invariance. Spatial pore-space correlation has a large impact on imbibition capillary pressure and relative permeability curves. Moreover, the effects of these correlations on the imbibition process are quite different from those observed for primary drainage. The imbibition process for correlated systems is characterized by an increased probability for snap-off with a corresponding decreased probability for piston-like displacement. These mechanisms dictate the residual nonwetting-phase saturation, which generally increases with increasing degrees of pore-size spatial correlation.