Numerical Analysis of Invasion Patterns During Drainage Process in a Simplified Pore Network Model

Abstract

Immiscible two-phase flows in porous media is of concern for various problems such as underground water pollution by non-aqueous phase liquid and enhanced oil recovery. It is understood that the drainage process in porous media exhibits patterns of either stable displacement, viscous fingering flow or capillary fingering flow depending on the conditions. However, the physical mechanism of the invasion and critical conditions for different invasion patterns have not been universally identified. This study employed a numerical two-phase flow simulation using the Color Gradient Lattice Boltzmann Method (CG-LBM) in a simplified pore network model with different capillary numbers and viscosity ratios between the two fluids. Simulation results confirm that flows for a low capillary number produce the preferential flow for pores with the least threshold pressure, which corresponds to capillary fingering flow. In addition, the retreat of the invading fluid caused by the Haines jump was observed. When the capillary number is higher, these two phenomena were not observed. Flows with a higher capillary number lead the invading fluid to simultaneously displace different pores when its viscosity is higher than that of the invaded fluid (stable displacement), and the viscous fingering flow happens otherwise. These findings suggest that capillary number and viscosity ratio, and occurrence of the preferential flow and Haines jump are key factors that determine invasion patterns.