Method for modeling fluid displacements in a porous medium

Abstract

Modelling method for optimizing faster and more realistically the displacement conditions, in a porous medium wettable by a first fluid (water for example), of a mixture of fluids including this wetting fluid and at least another fluid (oil and possibly gas). The method comprises experimental determination of the variation curve of the capillary pressure in the pores as a function of the saturation in the liquid phases, modelling the pores of the porous medium by means of a distribution of capillaries with a fractal section while considering, in the case of a three-phase water (wetting fluid)-oil-gas mixture for example, a stratification of the constituents in the pores, with the water in contact with the walls, the gas in the center and the oil forming an intercalary layer, determination, from this capillary pressure curve, of the fractal dimension values corresponding to a series of given values of the saturation in the liquid phase, modelling the relative permeabilities directly in the form of analytic expressions depending on the various fractal dimension values obtained and in accordance with the stratified distribution of the various fluids in the pores, and using a porous medium simulator in order to determine, from the relative permeabilities, the optimum displacement conditions of the fluids in the porous medium. The method can be applied for petroleum production, soil depollution, etc.