Improved Macroscopic Equations Of Two-phaseFlow In Porous Media Based On New Models OfThe Capillary Pressure And Relative Permeability

Abstract

Concepts of percolation theory, universal scaling laws, thin film flow and fractal geometry are used to develop realistic expressions for the capillary pressure and relative permeability curves for the case of two-phase (oil/water) flow in natural porous media (e.g. sedimentary rocks, soils, etc.). Approximate analytical expressions are derived for drainage processes in water-wet porous media, taking into account the gradual changes of fluid distribution and effective conductivities in the pore network and fractal roughness porosity. The geometrical and topological parameters of the pore space as well as the capillary number and the viscosity ratio of the two-fluid system are incorporated in these equations. The new phenomenological models are used to supplement the macroscopic onedimensional equations that have been suitably extended to describe immiscible displacement in porous media in a comprehensive way by taking into account the effects of the current local flowrates of the two fluids on the relative permeabilities and the capillary pressure. The computations (which are considerably more demanding than those of the conventional method) are made with an accurate algorithm that is based on a variational (collocation) principle. Sample computations for several typical cases of porous media and displacement modes are made. Preliminary results indicate that the effects of the current local flowrates on the overall behavior of the displacement process may be substantial. Transactions on Ecology and the Environment vol 17, © 1998 WIT Press, www.witpress.com, ISSN 1743-3541