非均质地层中自然电位测井的数学模型和数值方法  

Mathemtical Model and Numerical Method for Spontaneous Potential Log in Heterogeneous Formations

作　　者：潘克家[1] 谭永基[1] 胡宏伶[2] 

机构地区：[1]复旦大学数学科学学院,上海200433 [2]湖南师范大学数学与计算机科学学院,长沙410081

出　　处：《应用数学和力学》2009年第2期203-212,共10页Applied Mathematics and Mechanics

基　　金：国家自然科学基金资助项目(10431030);上海市自然科学基金资助项目(08ZR1401100)

摘　　要：针对非均质地层中电阻率非分块常数,提出一个新的自然电位测井模型.自然电位满足具有交界面跳跃的椭圆边值问题.证明了该椭圆边值问题弱解的存在唯一性;提出一种捕捉交界面电位跳跃的有限差分方法求解此类问题,数值例子验证了该方法的可靠性和有效性.A new spontaneous potential log model for the case when formation resistivity is not piecewise constant was introduced. The spontaneous potential satisfies an elliptic boundary value problem with jump conditions on interfaces. It was proved that the elliptic interface problem has a unique weak solution. Furthermore, a jump condition capturing finite difference scheme was proposed and applied to solve such elliptic problems. The validity and effectiveness of the proposed method were demonstrated through numerical examples.

关 键 词：自然电位测井 椭圆交界面问题 数学模型 数值模拟 

分 类 号：TN011[电子电信—物理电子学]