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. And 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 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 is performed based on the proposed model in the end.

A Novel Threshold Pressure Gradient Model and Its Influence on Production Simulation for Shale Oil Reservoirs

“…(1) The porous media are made up of many tortuous parallel cylindrical capillaries, ,, and each capillary consists of three equivalent spherical particles with identical physical properties in a triangular arrangement. − Moreover, under the effects of temperature and effective stress, the area of the triangular arrangement and the thickness of the water film remain constant before and after deformation.…”

Theoretical investigation of threshold pressure gradient in hydrate-bearing clayey-silty sediments under combined stress and local thermal stimulation conditions

“…(1) The porous space in HBCSS is composed of numerous tortuous cylindrical capillaries (Fig. 1) [59,60]. In this study, the Euclidean dimension is considered to be 2, and each pore in HBCSS consists of three equivalent spherical particles arranged in a triangle [53,61,62].…”

An innovative technique to solve a fractal damping Duffing-jerk oscillator

“…A two-scale technique was also used by Ain et al [52] and Yang et al [53] to investigate time-fractional heat transport and Varicella-Zoster virus models, respectively. Also, based on the two-scale fractal calculus, Huang et al [54]. developed a permeability fractal model for a porous medium.…”