High-resolution numerical methods for compressible multi-phase flow in hierarchical porous media. Final report, November 1992--August 1996

The objectives of this project were to develop computationally efficient numerical methods for modeling surfactant flooding in enhanced oil recovery and aquifer remediation. Surfactants have been considered by several oil companies to reduce the large residual oil saturations, and are being seriously considered for cleanup of dense contaminants in aquifers, particularly chlorinated hydrocarbons. The authors employed second-order Godunov methods for the discretization of the conservation laws, and lowest-order mixed finite element methods for the discretization of the pressure equation. They also used dynamically adaptive mesh refinement to concentrate the computational work. The development of the second-order Godunov method required a mathematical analysis of the hyperbolic wave structure; this analysis discovered undesirable features f the model that lead to infinite characteristic speeds. Minor modifications of the model to remove the infinite characteristic speeds improved the stability of the model considerably. The use of adaptive mesh refinement required the development of several techniques for upscaling various physical quantities, and a multigrid iteration for the pressure equation on an adaptively refined grid. Numerical simulations showed that the second-order Godunov method is reasonably effective in preserving sharp fluid fronts, but is too computationally expensive in so complex a fluid model. On the other hand, the same simulations showed that adaptive mesh refinement is very effective in reducing CPU time: computational time for adaptive simulations scale proportional to the total number of grid cells, while uniform grid calculations have computational time that scales with the number of cells times the number of timesteps