Accounting for fluid rheology in a hydrophobization model of the hysteresis of relative permeabilities

A complex mathematical model for hysteresis of relative permeabilities based on percolation theory is developed. The model take into account the change in the surface properties of the pore space and the rheology of percolating fluids during the transition from drainage to impregnation, which gives rise to hysteresis. It is shown that accounting for the change in the rheology of the percolation fluids, along with accounting for the hydrophobization of the surface of the pore space, provides a better agreement between the calculated and experimental curves of relative permeabilities.