摘要
目前,油藏数值模拟主要采用的方法如有限元方法、有限容积法等在油藏数值计算时均需要较长的计算时间,很大程度上限制了油藏注采的实时预测与快速动态模拟.该文以一种高效的数据处理方法(最佳正交分解(POD)方法)为基础,对油藏油、水两相流抽取特征函数,并对油藏两相流模型进行Galerkin投影得到新的低阶计算模型.数值计算表明,POD方法所得到的特征向量能量具有最优的特征,能以较少的特征向量捕捉到数学模型中较大的“能量”,因此能最大限度地描述油藏的特征(压力、饱和度),对油藏偏微分方程模型起到较好的降阶作用.结论表明,低阶模型的计算结果与隐压显饱(IMPES)所得计算结果吻合较好,且能节省更多的计算时间,因此能较好地在油藏注采数值模拟中进行历史拟合与仿真计算.
At present,the main methods used in reservoir numerical simulation,such as the finite element method and the finite volume method,require long calculation times,which limit their implementation in the real-time prediction and the reservoir production.An efficient data-processing method that based on the POD(proper orthogonal decomposition)was proposed to obtain the empirical coefficients and eigenfunctions of the oil-water 2-phase flow in the reservoir,and build a new low-order Galerkin calculation model.The numerical calculation indicates that,with the POD,the calculated eigenvector energy has proper features.Only a small number of eigenvalues can capture most of the energy,completely describe the reservoir characteristics(pressure,saturation),and help reduce the order of the partial differential equations.The calculation results of the low-order model are in good agreement with those from the IMPES,with much time saved.The proposed method applies well to history matching in numerical simulation of reservoir injection and production.
作者
贾欣鑫
王雷
张浩
孙小玲
段利亚
王鑫
JIA Xinxin;WANG Lei;ZHANG Hao;SUN Xiaoling;DUAN Liya;WANG Xin(Institute of Oceanographic Instrumentation,Qilu University of Technology(Shandong Academy of Sciences),Qingdao,Shandong 266061,P.R.China)
出处
《应用数学和力学》
CSCD
北大核心
2021年第9期891-899,共9页
Applied Mathematics and Mechanics
基金
国家自然科学基金(61702308,51504146)
山东省重大科技创新工程(2018YFJH0705)。
关键词
油藏数值模拟
低阶模型
油水两相
最佳正交分解
numerical simulation of reservoir
low-order model
oil-water 2-phase
proper orthogonal decomposition
