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On the relationship between effective permeability and stress for unconventional rocks: Analytical estimates from laboratory measurements

2018; Elsevier BV; Volume: 56; Linguagem: Inglês

10.1016/j.jngse.2018.06.026

2212-3865

Hui‐Hai Liu, Huangye Chen, Yanhui Han, Shannon L. Eichmann, Anuj Gupta,

Enhanced Oil Recovery Techniques

Permeability measurements show that unconventional rock is considerably stress sensitive because the matrix permeability is likely controlled by micro cracks and bedding structures in unconventional reservoirs. While there are a number of laboratory studies in the literature on the dependency of core-scale permeability on effective stress for unconventional rocks, how to determine the corresponding large-scale stress-dependency relationship (of more interest to practical applications) from the laboratory measurements has not been systematically investigated. This work proposes a method to estimate such a large-scale relationship from laboratory measurements. Based on the stochastic approach commonly used for parameter upscaling, we derived relationships between the large-scale effective permeability and the stress for the two- and three-dimensional isotropic porous media. The development is based on the empirical observation that at core scale permeability is an exponential function of effective stress. The developed large-scale relationships can be written in terms of the same mathematical form as the local-scale relationship except parameters in the large-scale relationships correspond to effective ones. The effective stress sensitivity parameter (that characterizes the stress-dependency) is simply the expected value of that at the local scale, or the arithmetic average of local values, for the two-dimensional flow problem and a function of effective stress for the three-dimensional problem. Because of its dominant two-dimensional flow along beddings (resulting from the fact that vertical permeability is significantly smaller than the horizontal one), the relationship for the two-dimensional flow case is valid for unconventional rocks. Nevertheless, we demonstrate that for typical local-scale parameter values from unconventional rocks (e.g., Barnett shale and a carbonate source rock), the relationships obtained for two- and three-dimensional problems give the essentially same results.