A new fracture permeability model: Influence of surrounding rocks and matrix pressure

Abstract

An appropriate fracture permeability model needs to include terms that characterize the effects of surrounding rocks and varying matrix pore pressure. This paper describes the use of Eshelby's inhomogeneity theory to derive equations that can be used to predict fracture permeability behavior for different shapes of reservoirs whose elastic properties differ from the surrounding rocks. In the equations, permeability is affected by two factors: reservoir volumetric strain and matrix volumetric strain. Reservoir volumetric strain is determined by properties of both the reservoir and surrounding rock. Matrix volumetric strain is controlled by fracture pressure as well as matrix pressure. When fracture permeability is significantly greater than matrix permeability, pressure drop first occurs in fractures and then matrix pressure decreases. In this case, fracture permeability first decreases and then increases. The increase of permeability is related to the matrix pressure drop and the bulk modulus ratio between the matrix and the grains. Results show that the smaller the initial fracture porosity, matrix modulus, shear modulus ratio between the reservoir and surrounding rocks, Poisson's ratio of the reservoir and shape factor of the reservoir, the stronger the stress-sensitivity of fracture permeability during hydrocarbon production. It is also found that when shear modulus of the reservoir is the same as that of surrounding rocks, fracture permeability is independent of reservoir shapes. The model is suitable for heterogeneous reservoirs and can be embedded into the reservoir numerical software to more accurately simulate the development of fractured reservoirs.