(386d) Simulation of Hypercompressible Flow of Carbon Dioxide through Porous Media

The transient pressure associated with flow of a compressible fluid through a porous medium satisfies an equation resulting from combination of Darcy's Law, the continuity equation, and equations of state for the fluid and the medium. Such flow equations are nonlinear in nearly all cases of practical interest, as a result of the pressure-dependence of the hydraulic diffusivity, but can be appreciably simplified by application of Kirchhoff-type integral transformations such as the pseudopressure. The pronounced changes in hydraulic diffusivity expected in the vicinity of the critical temperature and pressure - under conditions that are relevant to supercritical fluid extraction and proposed technologies for geosequestration of carbon dioxide - constitute a potentially exacting test of numerical solution schemes. In this paper, we compare the performance of commercial finite-difference and finite-element solvers in calculating porous-medium flow of carbon dioxide, and investigate the possible usefulness of the numerical method of lines in the description of such hypercompressibility effects.