基于聚类分析的降阶模型在低渗透油藏数值模拟中的应用

Reduced-order Model Based on Cluster Analysis in Numerical Simulation of Low Permeability Reservoir

基于全隐式法求解考虑低渗透油藏流动过程中启动压力梯度影响的二维油水两相流动数学模型;利用本征正交分解法从获取的快照中提取基函数,将原模型投影到基函数展成的低维子空间中构造相应的降阶模型;考虑到依据等时间间隔获取的快照的缺陷,利用CVT-Lloyd算法对快照进行聚类分析.实例计算表明:通过本征正交分解法构造降阶模型能很好地对原模型进行近似;通过基于聚类分析处理快照后,一方面减少数据冗余,生成空间分布更均匀的快照集合从而提高降阶模型的精度,另一方面过少的聚类数可能导致快照信息的缺失,影响最后模型的精度.

A mathematical model for numerical simulation of 2D wateroil phase reservoir concerning startup pressure gradient is solved with full implicit finite difference scheme. A reducedorder model is established by projecting original model in low dimension space formed by basis functions, which is produced from collected snapshots; CVTLloyd algorithm is employed in cluster analysis to tackle with flaws from collecting snapshots of same time interval. Computational results show that reducedorder model established based on POD is able to approximate the original model effectively. With cluster analysis, data reduction is eliminated, which could create uniform snapshots in space resulting in enhanced accuracy of reduceorder model. On the other hand, extremely limited clustering groups may lead to loss of information and thus impairing accuracy of reducedorder model.