Numerical simulation of viscous fingering phenomenon in immiscible displacement of two fluids in porous media using Lattice Boltzmann method

Abstract

In the present study, viscous fingering phenomenon, which occurs when a less viscous fluid (e.g. supercritical carbon dioxide) is injected into simplified porous media to displace a more viscous fluid (e.g. crude oil), is investigated by a mesoscopic approach-the lattice Boltzmann method (LBM). Due to its convenience in dealing with complex fluids of different viscosities, the pseudo-potential model is employed to study the effects of the capillary number, Bond number and viscosity ratio between the displaced fluids and displacing fluid; as such effects reflect the competition of viscous force and surface tension and gravity forces during viscous fingering. The numerical procedure is validated against a series of droplet tests, in which surface tension can be determined. By changing the injecting velocity of the displacing fluid and gravitational acceleration, the displacement processes under conditions of different capillary number and Bond number are investigated. The finger pattern is presented in this paper. The effects of capillary number, Bond number and viscosity ratio are discussed in detail. The ability and suitability of the lattice Boltzmann method for simulating multi-component fluids displacement in porous media are proved in our work.