Abstract: Fractured reservoirs have strong inhomogeneity and multi-scale characteristics, and the traditional methods have high requirements on the grid setting during the numerical simulation of discrete fracture groups, which are usually difficult to balance the computational efficiency and accuracy; moreover, the limitations in efficient and elaborate simulation of multi-scale disordered cross-fracture seepage are becoming more and more prominent. Based on the discrete fracture model, each crack is explicitly described. Enrichment functions based on the asymptotic analytical solution are constructed for different scales of factures. And the multi-scale extended finite element method is constructed to simulate the flow characteristics of disordered intersected fracture groups with grid-crack decoupling. The method uses the asymptotic analytical solution to capture the local seepage characteristics of cracks in the grid, avoiding the local refinement at the crack walls and tips by use of unstructured grids, thus effectively reducing the computational amount and improving the computational accuracy. A single fracture model and a large-scale fracture group model are established for simulation. Using this method, the calculation accuracy of normal flux along the crack wall can be improved by more than 80 % when compared with the traditional finite element method; when using coarse grids to simulated a large-scale fracture cluster, the calculation complexity (number of grids and nodes) is reduced by about 90 %, and the error of single well production is maintained at only 5 %, which verifies the accuracy and effectiveness of this method. The method proposed in this paper provides a new idea and method for the simulation of fluid flow in fractured reservoirs and the subsequent solution of a series of complex problems such as two-phase flow, fluid-solid coupling, and fracture propagation.

Key words: multi-scale, extended finite element method, discrete fractures, enrichment functions, flow

摘要： 裂缝性储层具有强非均质性和多尺度特征,传统方法在离散裂缝群数值模拟中对网格设置有较高的要求,通常难以平衡计算效率和精度,在高效且精细模拟多尺度无序交叉裂缝渗流方面的局限性日益凸显。基于离散裂缝模型显示表征每一条裂缝,针对不同尺度裂缝构造基于渐近解析解的加强形函数,建立了一种裂缝和网格解耦的多尺度扩展有限单元法用于模拟无序交叉裂缝群的渗流特征。该方法利用渐近解析解捕捉网格内裂缝局部渗流特征,避免使用非结构网格在裂缝壁面和尖端的局部加密,因此能有效降低计算量,提高计算精度。建立了单裂缝模型和大规模裂隙群模型用于模拟,新方法相较于传统有限单元法将裂缝壁面法向流速的计算精度提高80 %以上;在采用粗网格模拟大规模裂隙群时,在计算量(网格数和结点数)降低约90 %的情况下,单井产量误差保持在仅约5 %,验证了新方法的准确性和有效性。新方法为裂缝性油气藏流体流动模拟以及后续解决两相流、流固耦合、裂缝扩展等一系列复杂问题提供了一种新的思路和方法。

关键词: 多尺度, 扩展有限单元法, 离散裂缝, 加强形函数, 渗流