Numerical investigation of inertial, viscous, and capillary effects on the drainage process in porous media

Abstract

The drainage process in porous media, where a non-wetting fluid displaces a wetting fluid, has been studied by considering viscous and capillary effects. However, inertial effects on the drainage process had not been widely studied until recently. Here, we numerically simulate the drainage process in a randomly generated two-dimensional porous medium using the color-gradient lattice Boltzmann method, for capillary numbers Ca=10−3 and 10−5 and Reynolds numbers Re from 0.1 to 50 to demonstrate inertial effects for both larger and smaller capillary numbers. The effects on saturation, interfacial lengths, and capillary pressure during the displacement process and the invasion patterns are analyzed. The results indicate an increase in saturation of the invading non-wetting fluid as the inertial effects become larger. Larger inertia increases the fluid interfacial length for Ca=10−3, whereas it does not affect the interfacial length for Ca=10−5. In regard to capillary pressure, Ca=10−3 produces a larger capillary pressure for larger inertial effects. For Ca=10−5, the capillary pressure fluctuates around the mean threshold capillary pressure of the porous medium, and inertial effects are minor during most of the invasion. In addition, an analysis of the invasion sequence reveals that a more compact invasion is produced by larger inertial effects, and for Ca=10−5, going against the capillary fingering dynamics, a continuous invasion from the inlet region is observed. This study adds the effects of inertia to the well-known viscous–capillary interplay and extends our understanding of the invasion process in porous media.