Fractal-Based Production Analysis For Shale Reservoir Considering Vertical Cross-Flow

Multi-fractured horizontal wells have been widely used in shale oil development. The induced fracture network around the hydraulic fractures has significant impacts on pressure propagation and fluid migration. In shale formations, the effectiveness of reservoir stimulation is vertical heterogeneous due to the various sedimentary environment. In the horizontal direction, the permeability/porosity and density of the induced fractures are self-similar. No solutions have been achieved combing both the vertical and the horizontal heterogeneities of the stimulated reservoir volume (SRV). In this work, a novel semi-analytical model is proposed to characterize the SRV heterogeneities in both vertical and horizontal directions. The SRV is divided into several layers to characterize the vertical heterogeneities of shale formation. The fractal permeability/porosity and density of induced fractures are introduced to describe the horizontal heterogeneities of each layer. The fractal vertical cross-flow between adjacent layers is considered to depict the flux transfer caused by the vertical heterogeneities. The proposed model is solved in Laplace domain and inversed to the real domain numerically. Then, the model validation and sensitivity studies are conducted. The results show that the fractal vertical cross-flow causes the flow behavior in shale formation transforms from a no-cross-flow system to a vertical homogeneous system. The larger the fractal dimension, the earlier the transformation occurs, and the larger the reservoir seepage capacity. The effects of fractal parameters are obvious at the early and middle stages. This paper provides a more realistic representation of the flow behavior of shale oil in multi-fractured horizontal wells. The new model is beneficial for understanding the flow mechanisms and improving production forecasting of shale oil.