三维强化采油渗流耦合系统隐式迎风分数步差分方法的收敛性分析

Convergence analysis of an implicit upwind difference fractional steps method of three-dimensional enhanced oil recovery percolation coupled system

对强化(化学)采油数值模拟中的渗流耦合系统问题,本文提出隐式迎风分数步差分格式,利用变分形式、能量方法、差分算子乘积交换性理论、高阶差分算子的分解、微分方程先验估计的理论和技巧,得到最佳阶l2模误差估计.该方法已成功应用到强化采油数值模拟的生产实践中,并且得到了很好的数值模拟效果.

A type of implicit upwind difference fractional steps scheme is presented for the percolation coupled system of enhanced （chemical） oil recovery simulation in this paper. An optimal-order error estimate is discussed in l2-norm by introducing many theories and techniques such as variation form, energy method, product exchange theory of difference operators, splitting of high-order difference operators, priori estimates method of differential equations. This numerical method has been applied successfully in enhanced oil recovery simulation in actual oilfields and gives rise to satisfying simulation results.