Pore-scale study of the anisotropic effect on immiscible displacement in porous media under different wetting conditions and capillary numbers

Abstract

This article investigates the effect of anisotropy on two-phase flows in porous media (both drainage and imbibition) under various wetting angles and capillary numbers. The focus is on the applied results useful to petroleum engineering. Mathematical modeling based on lattice Boltzmann equations in combination with multi-relaxation time and color-gradient model is used as a research tool. This paper proposes a new method for creating digital models of porous media, based on a combination of a quartet structure generation set and Monte-Carlo algorithms. The advantage is the ability to control both heterogeneity and anisotropy. This paper presents visual phase diagrams of the invasion patterns in anisotropic samples as a function of wetting angle and capillary number. The results show that the ratio between capillary and viscous forces is highest for the sample with favorable anisotropy, which has the biggest permeability, and decreases on going to unfavorable anisotropy (lowest permeability). This effect leads to the finding that boundary capillary numbers, which determine the transition between crossover mode and invasion patterns (viscous and capillary fingering, and compact displacement), are shifted towards lower values as anisotropy increases. The images of fluid distributions are numerically described using fractal dimension and displacement efficiency. It was found that the anisotropic effect is most pronounced at capillary fingering and does not significantly affect the invasion characteristics in the imbibition mode. The sensitivity of the fractal dimension and displacement efficiency to a change in the wetting angle is maximal at favorable anisotropy and decreases on going to unfavorable anisotropy. During drainage, the fractal dimensions, estimated for favorable and unfavorable anisotropy, show opposite trends depending on the capillary number. In the imbibition mode, there is an increase in the fractal dimension with an increase in the capillary number for all porous structures. In addition, this paper investigates the anisotropy effect on the «injected fluid - skeleton » interfacial length under different wetting and dynamic conditions. It was shown that the anisotropy has no significant effect on this parameter, and the best interaction efficiency was found with a compact displacement, and the least with a viscous fingering. Also, the influence of the no-flow and periodic boundary conditions on the invasion characteristics is examined. The results show that boundary conditions do not significantly affect the invasion in the sample with favorable anisotropy for any wetting angles. Periodic boundary conditions negatively influence the displacement efficiency for samples with isotropic and unfavorable structures at drainage, but no noticeable effect was found during imbibition. • The anisotropic effect is most pronounced with capillary fingering. • Anisotropy does not significantly affect invasion during imbibition. • Anisotropy has no significant effect on the «injected fluid - skeleton » interface. • Boundary conditions do not affect invasion with favorable anisotropy for any wettability.