A two-scale fractal permeability model for vuggy porous media

Abstract

A vug is a small cavity in a porous medium that is relatively larger than interparticle pore spaces. Vuggy porous media are common in carbonate petroleum reservoirs and karst aquifers. Although small, the vugs can significantly affect the porosity and permeability of a rock. The real rock cores and outcrops indicate that the cumulative size distributions of interparticle pores and vugs both follow the fractal scaling law. In this paper, a two-scale fractal permeability model for natural vuggy porous media is developed based on the fractal characteristics of interparticle pores and vugs. In the proposed model, the interparticle pores of rock matrix are described as a bundle of tortuous capillary tubes. The vugs are embedded in rock matrix and are regarded as equipotential bodies, which change the tortuosity of matrix capillary tubes. Then, different matching relations between matrix capillary tubes and vugs are conducted to predict the permeability of a vuggy porous medium. The results show that the predicted permeability varies within a certain range. The maximum permeability is the case of larger vugs matching with the larger capillary tubes, and the minimum permeability is the converse case. The most probable permeability is calculated based on a set of random matching relations by using the Monte Carlo method. The validity of the proposed model is verified by comparing with experimental results and reference data in the literature. The parameter sensitivity analysis indicates that the fractal dimension of capillary tubes and their tortuosity, and the maximum diameter of capillary tubes and vugs have significant effects on the predicted permeability.