Calculation of full permeability tensor for fractured anisotropic media

Abstract

Fractured reservoirs’ media consists of matrix and effective fractures. The fracture distribution is complex and variable in these reservoirs with strong characters of anisotropy of reservoirs. This paper introduces a simple, fast and accurate method to test 2D tensor permeability of fractured anisotropy media. Combining numerical simulation results and experiment results, 2D tensor permeability is derived and the variation mechanism of 2D tensor permeability in fractured anisotropic media has been revealed. According to the polar form of elliptic equation, permeability elliptic is derived. With ellipsoidal permeability, the change law of permeability value in principal direction is studied. 3D permeability tensor model for fractured media is proposed on basis of the co-ordinate transformation principle. Based on the quantitative characterization of 3D tensor permeability and Gangi’s permeability stress sensitivity model, a stress-dependent 3D permeability tensor mathematical model for fractured media is established. The method provides a theoretical basis for the determination of percolation parameters in fractured reservoirs, and the results are significant in understanding the fluid flow in fractured anisotropic media.