The Discrete Fracture Network (DFN) model has been widely used in the reservoir numerical simulation. Traditional numerical methods usually require mesh to conform with fractures, often facing the difficulty of balancing calculation accuracy and efficiency. In order to overcome the inherent limitations of traditional numerical methods, this paper proposes a multi-scale extended finite element method (MXFEM). In this method, computational grids are decoupled from fractures, so grids are completely independent of fractures. And there is no need to use unstructured grids for local refinement, which greatly improves the computational efficiency. MXFEM uses the asymptotic analytical solutions of the pressure field as new enrichment functions to enrich the local standard pressure approximation space, which not only helps to accurately capture the pressure characteristics of fractures or fracture sections of different scales, but also greatly improves the convergence and accuracy of the method. By comparing with the results of the finite element method, the effectiveness of MXFEM is verified. Finally, MXFEM is applied to a numerical example to study the effect of hydraulic fracture cluster spacing and width on production.


Reservoir numerical simulation has become an important technical method for oil and gas reservoirs development and is widely used in all stages of development. Fractured reservoirs usually have strong heterogeneity and obvious multi-scale characteristic. Especially for unconventional reservoirs, such as shale and tight sandstone reservoirs, natural fractures are widely developed and distributed in disorder. In order to increase production, hydraulic fracturing is commonly used, which forms large-scale artificial fractures and connects part of natural fractures, which aggravate the heterogeneity and multi-scale characteristic of the reservoir. In this kind of reservoirs, the complex fracture network composed of artificial fractures and natural fractures has a significant impact on fluid flow and production. Therefore, accurate description of fractures is essential for numerical simulation.

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