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

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.