Analysis of Linear Encroachment in Two-Immiscible Fluid Systems in a Porous Medium

The flow of two immiscible fluids in a porous medium was analyzed accounting for boundary and inertia effects. This problem was first solved by Muskat using Darcy’s equation for fluid flow in a saturated porous medium. In the present analysis the boundary and inertia effects have been included to predict the movement of the interfacial front that is formed as one fluid displaces the other. In the present work a theoretical study that accounts for the boundary and inertia effects in predicting the movement of the interface for linear encroachment in two immiscible fluid system in a porous material is presented for the first time. The results of the present study when compared with the Muskat’s model show that consideration of the boundary and inertia effects becomes important for low values of mobility ratio (ε<1.0) and higher values of permeability (K>1.0 × 1.0⁻¹⁰ m²).