三维非均匀不稳定渗流方程的二维不均匀粗化算法

在无源汇条件下，根据流过某一个横截面的流体流量等于流过这一横截面内所有精细网格的流体流量之和这一特点提出了粗化网格等效渗透率的计算方法。在粗化区内，利用直接解法求解二维渗流方程，再用这些解合成粗化网格的三维合成解，并由合成解计算粗化网格的等效渗透率。根据精度的要求采用了不均匀网格粗化，在流体流速大的区域采用精细网格。利用所得等效渗透率计算了粗化网格的某三维非均匀不稳定渗流场的压降解，结果表明三维非均匀不稳定渗流方程的二维不均匀粗化解非常逼近采用精细网格的解，但计算的速度比采用精细网格提高了80倍。

2D scale-up method of 3D fluid equation in heterogeneous porous media

If there is no resource or sink in the coarse grid block, the numerical computing method of effective permeability of coarse grid blocks has been given,where the fluid flow rate is the same flowing through the coarse grid block as all fine grid blocks in the coarse grid.The 3D composite results have been obtained by solving 2D fluid equations in porous media,and then using the composite results to compute the effective permeability of coarsen grid.We use the effective permeability to calculate the pressure distribution of the 3D transient fluid equations in heterogeneous porous media.For the whole reservoir we also adopt a nonuniform upscaling approach,i.e.in the high velocity regions using fine grid blocks,in the other regions using coarse grid blocks.The results show that the solutions of scale-up method are very approaching the solutions of adopting fine grid blocks,however,the computation speed of scale-up method is 80 times more than that adopting fine grid blocks.