Computation of continuum percolation threshold for pore systems composed of vugs and fractures

In this research, we study the connectivity of a network composed of pores with different shapes including combinations of vugs and fractures. For this purpose, we have developed a numerical simulation technique to determine the dependence of continuum percolation threshold on the pore-shape distribution for isotropic porous 2D and 3D networks composed by elliptical and spheroidal elements respectively. This technique is based on the following new algorithms: (1) analytical estimation of overlapping between inclusions; (2) partial discretization schemes (elements of a discrete pixel base with one continuous dimension) for numerical calculation of connected-cluster porosity; and (3) determining the percolation-threshold porosity by using Monte Carlo simulations for different relative pore sizes. By approximating the pore shapes by ellipses (2D) and spheroids (3D) and varying their aspect ratios, we can model different types of pores from vugs (spheres) to fractures (oblate spheroids) and channels (prolate spheroids). We have calculated the critical percolation porosity for the following models: (1) a network consisting of elements with constant shapes; (2) a network composed of elements with the uniform logarithmic distribution of aspect ratios; and (3) a network containing elements of two different shapes. To validate the simulation technique, we have compared the modeling results for the first model with a threshold-aspect ratio relationship published previously. Based on the modeling results we have found simple and explicit equations for 2D and 3D models to determine the percolation threshold for pore networks with the bimodal distribution of shapes. The equations use only the element concentrations and percolation-threshold values for each elements shape.