Transitional non-Darcy displacement of immiscible fluids due to inertial effect

Abstract This study describes immiscible fluid displacement near a transitional boundary at which inertial effect occurs. We simulated two-phase fluid flow in a 2D micromodel using the lattice Boltzmann method with varying Reynolds numbers ( Re ) (log Re = –2 to 2) and viscosity ratios ( M ) (log M = –2 to 0). To highlight the role of inertial force rather than capillary and viscous forces, the capillary number ( Ca ) was kept constant at log Ca = –5. As Re and M increased, development in the preferential flow became more pronounced with tortuous paths. We found the transitional boundary exists near log Re = –1 to 1 at which residual saturation of the displaced fluid starts to fluctuate and changes 5% - 14% in the transitional regime. In particular, this boundary describes the effect of inertia on immiscible fluid displacement before an increase in the work done due to inertial force occurs.