Kim Spayd, North Carolina State University


Two Phase Flow in Porous Media with Dynamic Capillary Pressure

Abstract: The Buckley-Leverett equation for two phase flow in porous media is modified by including a dependence of capillary pressure on the rate of change of saturation. This model, due to Gray and Hassanizadeh, results in a nonlinear partial differential equation. Phase plane analysis, including a separation function to measure the distance between invariant manifolds, is used to determine when the equation supports traveling waves correspond- ing to undercompressive shocks. The Riemann problem for the underlying conservation law is solved and the structures of the various solutions are confirmed with numerical simulations of the partial differential equation.

Advisor: Michael Shearer (North Carolina State University)