Shale permeability is low enough to require unconventional stimulation treatment, such as hydraulic fracturing. Hydraulic fracturing is now widely used to achieve a larger stimulated reservoir volume by connecting intrakerogen pores, which are otherwise isolated from one another. It is important to monitor and predict the migration of fracturing fluid. The authors studied fracturing fluid injection in a granite rock in the laboratory and observed a sharp penetration front, implying the motion of the penetration front is advection-dominated. Based on this, they developed a numerical model using the level set method to track the penetration front of fracturing fluid. In the model, auto-correlated Gaussian random fields are generated to represent heterogeneous permeability distributions. Reservoir heterogeneity is measured using the coefficient of variation, which is defined as the ratio between standard deviation of permeability and mean permeability. The correlation length in the horizontal direction is much larger than in the vertical direction, implying a horizontal layered structure. The authors investigated the effect of heterogeneity on penetration front motion. Using the same statistical parameters, numerous realizations of the permeability field are generated. A finite difference reservoir simulator equipped with the weighted Jacobi iteration method was then used to solve for the Darcy flow fields, and the level set simulation was repeated to study the collective behavior of the system. In all simulations, the authors observed linear relationships between time and the first- and second-order spatial moments of the penetration fronts. The time derivatives of the first- and second-order spatial moments were the velocity and dispersion coefficient, respectively. With increasing reservoir heterogeneity, velocity decreased linearly, while the dispersion coefficient increased linearly. These observations imply there is a strong coupling between penetration front motion and reservoir heterogeneity. Therefore, to accurately predict the movement of fracturing fluids, it is necessary to effectively characterize heterogeneity of the host formation. This study is the first to systematically investigate the correlation between fracturing fluid penetration and reservoir heterogeneity using the level set method. It has important applications with respect to optimization of fracturing fluid injection.

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