Transient Two-Phase Capillary Flow in Porous Media

The dynamics of two-phase capillary displacement in a finite one-dimensional system following a step change in pressure of one phase at one end is considered. Darcy's law and the equation of continuity for each phase together with the capillary pressure-saturation relation are the fundamental equations describing the flow system. The resulting system of differential equations is linearized by assuming a linear relationship between the capillary pressure and the saturation as well as constant conductivity values of both phases (these assumptions are valid for small step changes in pressure). Solutions of the linearized problem are found and presented in some detail. In the limiting case as the conductivity of one phase becomes much greater than the other, the solution reduces to the (known) single-phase solution.