Supercritical fluid flow in porous media: modeling and simulation

The present work aims the modeling and simulation of supercritical fluid flow through porous media. This type of flow appears in several situations of interest in applied science and engineering, as the supercritical flow in porous materials employed in chromatography, supercritical extraction and petroleum reservoirs. The fluid is constituted of one pure substance, the flow is monophasic, highly compressible and isothermal. The porous media is isotropic, possibly heterogeneous, with rectangular format and the flow is two-dimensional. The heterogeneities of porous media are modeled by a simple power law, which describes the relationship between permeability and porosity. The modeling of the hydrodynamic phenomena incorporates the Darcy's law and the equation of mass conservation. Appropriated correlations are used to model, in a realistic form, the density and the viscosity of the fluid. A conservative finite-difference scheme is used in the discretization of the differential equations. The nonlinearity is treated by Newton method, together with the conjugate gradient method. The results of the simulation for pressure and mobility of supercritical and liquid propane flowing through porous media are presented, analyzed and graphically depicted.