A statistical model of apparent pore size distribution and drainage capillary pressure

Apparent pore size distributions of porous media are commonly obtained from capillary pressure measurements. Drainage capillary pressure curves depend on the penetration pressures of pore necks and the interconnectivity of pore space that determines access to the necks. In this paper, a probability distribution function is proposed to describe the apparent pore size distributions of porous media. The distribution function can be integrated directly to obtain the related mathematical model of capillary pressure versus wetting phase saturation. The model parameters, related to entry pressure, pore size sorting factor, characteristic pore neck radius, and retained wetting phase saturation, can be obtained by fitting the model to experimental capillary pressure curves. Examples of determining model parameters from measured data are presented. The physical significance of each parameter is demonstrated by its effect on apparent pore size distributions and capillary pressure drainage curves. The model provides a dimensionless capillary pressure function that corresponds to a generalized form of the Leverett J-function.