Representative elementary volumes for various characteristics of two-phase flows in porous media: A statistical approach

Abstract

This article presents a systematic study of the influence of two-phase flowpatterns on the representative elementary volume for various displacement characteristics. This paper considers both drainage and imbibition regimes and related patterns such as compact displacement, viscous, and capillary fingering. As two-phase flow characteristics, the displacement efficiency and interfacial contact areas between the invaded fluid and the displaced fluid, as well as between the invaded fluid and solid particles, are considered. Not limited to displacement patterns, we study the effect of capillary number on the minimum REV size. The findings of this paper are based on numerical simulations performed in two-dimensional artificially created porous structures using the Monte-Carlo movement algorithm. The main conclusions are validated on 3D X-ray computed tomography images of natural sandstones. Two-phase immiscible displacement in a porous medium is modeled using the lattice Boltzmann equations with the multi-relaxation time collision operator in combination with the color-gradient method describing interfacial phenomena and wetting effects. Minimum REV sizes have been identified using statistical data collected from a large number of numerical simulations in two-dimensional samples. Coefficient of variation and average value of the investigated property have been used to identify REV. The results show that REV for two-phase flow in porous media depends on the displacement pattern. Minimum REV sizes for viscous fingering and compact displacement are close. The accuracy of predicting the displacement efficiency for viscous fingering and compact displacement modes is much higher than for capillary fingering. Minimum REV sizes for interfacial contacts are lower than for displacement efficiency.