非结构网格油藏数值模拟方法研究

根据所建立的单个控制体离散形式的物质平衡方程,基于PEBI和CVFE网格,采用任意形式的渗透率张量,建立了相应的数值算法。PEBI网格是一种局部正交网格,其离散形式与有限差分方法相似,流动系数的取值原则和界面渗透率的取法均与有限差分相同。CVFE网格是非正交网格,本文混合运用有限差分和有限元方法计算折算压力梯度,得到与有限差分和PEBI网格不同的离散形式,提出了根据流量符号判定上游的方法,使模型更为合理。模型计算表明,对于形式简单的对角渗透率张量,本文方法可以与九点差分格式相比,精度是可靠的,并且该方法还能模拟完全各向异性渗透率张量,对于精细油藏数值模拟,其应用范围将更为广泛。

STUDY OF UNSTRUCTURED GRIDS IN RESERVOIR NUMERICAL SIMULATION

According to the discrete material balance equation of control volume,a new numerical scheme based on PEBI grid and CVFE grid is provided,where absolute permeability is in tensor form. Because of PEBI grid's orthogonalization,its discrete equation is similar with that of finite difference method. The mobility coefficient and interface permeability can be calculated as same as finite difference method. For CVFE grid,reduced pressure gradient is approximated using finite difference and finite element methods simultaneously,and a new upstream weighting approach is proposed based on the signal of flow term,which is more reasonable. The final discrete form of CVFE grid is different from that of PEBI grid and finite difference method. Numerical model tests show that the method proposed by this paper is as accurate as nine point finite difference when permeability tensor is in diagonal form, and it can simulate more complicated cases when permeability is in full tensor form. Its application prospect is more extensive in fine detailed reservoir simulation.