Method for modelling fluid displacements in a porous environment taking into account hysteresis effects

A modelling method for optimizing displacement conditions, in a porous medium wettable by a first wetting fluid, of a three-phase mixture of fluids including the first wetting fluid and at least a second, non-wetting fluid, comprising:

• determining experimentally a variation curve of capillary pressure in pores of a sample of the porous medium in a presence of the first wetting fluid and of the second non-wetting fluid;
• modelling the pores of the porous medium by a distribution of capillaries with a fractal section by considering a stratified distribution of the fluids in the pores, the first wetting fluid spreading out in contact with walls of the pores and around at least one other fluid;
• determining, from the capillary pressure curve, fractal dimension values corresponding to a series of given values of saturation in liquid phases;
• modelling hysteresis effects that modify mobile saturations of the fluids displaced in the sample according to the number of drainage and imbibition cycles undergone by the sample, involving different non-wetting fluid trapping or untrapping constants according to whether the drainage or the imbibition cycles are carried out;
• modelling relative permeabilities directly in analytic expressions depending on different fractal dimension values which are obtained;
• and
• entering the relative permeabilities into a porous medium simulator and determining, by means of the simulator, optimum displacement conditions for the mixture of fluids in the porous medium.