非均质油藏多尺度混合有限元数值模拟方法

Multiscale mixed finite element numerical simulation for heterogeneous reservoirs

采用多尺度混合有限元方法研究了强非均质油藏中的油水两相渗流问题。与传统有限单元法相比,多尺度有限单元法的基函数具有能反映单元内参数变化的优点,因此这种方法能在大尺度上捕捉解的小尺度特征从而获得较精确的解。笔者阐述了多尺度混合有限元方法的基本原理,推导得到了油水两相渗流问题的多尺度混合有限元计算格式。数值计算结果表明,相对于传统的网格粗化技术,多尺度混合有限元能够捕捉小尺度上的非均质特征而具有更高的计算精度;而相对于普通混合有限元方法,多尺度混合有限元方法在保证计算精度的同时能够减少计算量。

The water/oil two-phase seepage in severely heterogeneous reservoirs was studied by applying the multiscale mixed finite element method（MsMFEM）.Compared with conventional finite element methods,the MsMFEM has an advantage of the basic function capable of reflecting changes in parameters within elements.Therefore,this method can gain a more accurate solution in large scale by capturing fine-scale features of the solution.The present paper explicitly described fundamental principles of the MsMFEM and deduced multiscale mixed finite element computing formulae for the water/oil two-phase seepage.The result of numerical calculations shows that compared with conventional reservoir upscaling techniques,the MsMFEM can get a higher degree of computing accuracy by capturing heterogeneous features in fine-scale.Thus,this method is superior to the most of conventional mixed finite element methods not only in reducing the calculated amount but also in improving computing accuracy.