双水平集逼近油藏模型特征的数值模拟方法  

Simulation of reservoir model characterization approximation of binary level set method

作　　者：姚昌辉[1] 贾尚晖[2] 

机构地区：[1]郑州大学数学系,北京530001 [2]中央财经大学应用数学学院,北京100875

出　　处：《中国科学：数学》2012年第5期455-472,共18页Scientia Sinica：Mathematica

基　　金：国家自然科学基金(批准号:11101384;11101381和10971203)资助项目

摘　　要：本文使用双水平集函数逼近油藏模型特征,构造出Uzawas算法进行数值模拟.对于两相流渗透率的数值求解问题,可以通过测量油井数据和地震波数据来实现.将构造出来的带限制的最优化问题使用变异的Lagrange方法求解.如果使用双水平集函数逼近渗透率函数,则需要对Lagrange函数进行修正,从而将带限制的最优化问题转化成无限制的最优化问题.由于双水平集函数的优越性,进一步构造出最速梯度下降Uzawas算法和算子分裂格式Uzawas算法进行求解对应的最优化子问题.数值算例表明设计的算法是高效的、稳定的.In this paper,Uzawas algorithms by steepest gradient descent scheme and operator splitting scheme for dynamic reservoir characterization by a binary level set approach are explored.The permeability of two-phase porous media flow can be recovered by the augmented Lagrangian optimization method with well data and seismic time-lapse data.After adding the constraint functions to the augmented Lagrangian optimization functional,the saddle points can be found by steepest gradient descent scheme and operator splitting scheme,which is based on the essence of binary level set method with few difficulties.In the end,the numerical examples demonstrate that the given algorithms will be efficient,stable when the permeability is recovered.

关 键 词：油藏模型 双水平集 历史匹配问题 渗透率 

分 类 号：P618.13[天文地球—矿床学]