Percolation model of immiscible displacement in the presence of buoyancy forces

Abstract

We consider the quasistatic displacement of a nonwetting fluid by a wetting one in a porous medium in the presence of buoyancy forces. A simple percolation model of this process is presented and analyzed both theoretically and by Monte Carlo simulation. It is shown that the fact that percolation is a critical phenomenon, with diverging correlation length at the critical point, has a significant effect on the physics of the system, in particular on the dependence of nonwetting phase residual saturation on the density contrast between the phases. An extension of these ideas to the case where the pressure field is generated by viscous rather than buoyancy forces is suggested.