The mixed bond—site percolation problem and its application to capillary phenomena in porous media

Abstract

A mixed percolation problem is proposed with applications to pore network structure and capillary phenomena in porous media. The mixed percolation probability is calculated using random elimination of sites and bonds simultaneously. The percolation probability function and the critical percolation probability, the point of creation of infinite cluster in the lattice, are determined by the fractions of both open sites and bonds. This approach was initiated due to the existence of overlapping distributions of pore body and neck size, and it provides a means for calculating the capillary pressure saturation curve. Drainage and imbibition curves are calculated using the mixed percolation probability and uniform size distributions having various degrees of overlap. The distributions were set such that the probability of finding a neck of a given size is equal to or smaller than that of finding a pore body of a given size. It is found that the breakthrough capillary pressure during drainage is higher as the degree of overlap rises. Nonwetting phase penetration during drainage is more moderate as the degree of overlap rises and is close to a step function at the 0 overlap area. During the imbibition process, the first full pore penetration by the wetting phase occurs at higher pressure as the degree of overlap rises. It is concluded that the mixed percolation problem can provide a means for modeling capillary phenomena in porous media in cases of overlapping pore size distributions.