Fractal analysis of dimensionless capillary pressure function

The dimensionless capillary pressure function J(SW) was used to eliminate the capillary pressure difference between different strata and to describe similar lithologic reservoirs. Based on the existing function J(SW) and the fractal geometry theory, a fractal model to describe the pore structure of the lithology is presented. The proposed fractal expression for the J(SW) function reveals that when the microstructural parameters (fractal dimension for pore area, the fractal dimension for tortuosity, and the ratio of the maximum pore diameter to the minimum pore diameter) are respectively equal or close for porous samples (with different permeabilities, porosities, interfacial tensions and wetting angles), the values of the J(SW)function vs. saturation coincide each other for wetting phase. In addition, a new dimensionless function G(SW), which is based on the ratio of the average capillary diameter to the critical capillary diameter, is proposed to describe the relationships among the structural parameters of similar lithological porous media and saturation as well as the dimensionless capillary pressure function J(SW).