油藏数值模拟中BILU0-GMRES方法的应用

Applications of BILU0-GMRES in reservoir numerical simulation

在油藏数值模拟中通常需要将数学模型转化为大规模线性方程组,求解这些方程组将耗费大量的时间。考虑到黑油模型的物理特性,将其在油藏节点上离散得到的子阵视为构成系数矩阵的基本元素,利用块不完全LU0(BILU0)预处理方法与块广义极小残量法(BGMRES)相结合,迭代求解方程组得到BILU0-GMRES方法。该方法具有更强的稳定性和收敛性,它能提高系数矩阵迭代的速度,减少迭代收敛的次数,并且矩阵规模越大,这种优势越明显。对严重非均质边底水油藏SPE9的测试结果表明,块预处理GMRES方法具有较高的精度,能够准确模拟油藏的开发过程并对生产动态作出预测。

Mathematical models in reservoir numerical simulation usually have to be translated into large-scale linear equations, and it takes lots of time to solve them. Taking physical characteristics of the black oil model into account, sub-matrices （block） can bedisper sed from reservoir nodes as integral elements that constitute a coefficient matrix, herein the sub-matrix scale is determined by control e- quations and unknowns. The block incomplete LU0 （BILU0） preconditioning was combined with the block generalized minimal residual method （BGMRES） to iteratively solve the equations, and the comparison illustrated that the BILU0 GMRES method obtained is of greater stability and convergence, it can accelerate the iteration speed of a coefficient matrix and reduce the frequency of iterative conver- gence, moreover, the greater the scale of a matrix, the better the advantage of this approach. The testing performed on a reference example （sPEg） of a reservoir with severely heterogeneous edge and bottom water indicated that the block II.U0 GMRES method is of higher accuracy and it can well and truly simulate the development process of a reservoir and predict the production performance precisely.