Numerical simulation of three phase porous flow under shock conditions

Abstract

In the context of an existing Lagrangian code, we have developed a stable second order accurate scheme for integrating the time-dependent, mixed Eulerian-Lagrangian, strong conservative form of the governing equations for a 2D, 3 phase (gas, liquid, and solid) multifluid flow. Some of these features are: an explicit-implicit scheme to circumvent the stiffness problem, an exact time integration scheme for the gas and liquid masses, truncation error reduction by splitting the operations of differencing and interpolation, and a robust method of solving systems of highly nonlinear equations.Our results yield correct shock speeds and profiles. We were successful in treating problems with seven orders of magnitude in permeability and three orders of magnitude in the driving velocity. We also show that the gas phase, because of its very low interia, is readily transported as compared to a denser fluid such as water. In highly permeable media, the liquid phase shock can outrun the solid, thereby lowering the effective stress ahead of a lagging solid shock.