非均质地层中自然电位测井的数学模型和数值方法

潘克家; 谭永基; 胡宏伶

非均质地层中自然电位测井的数学模型和数值方法

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

基金项目: 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)

详细信息

作者简介:
潘克家(1981- )男,湖南宁乡人,博士(联系人.Tel:+86-21-61445354;E-mail:kjpan@yahoo.cn).

中图分类号: TN011
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- 被引次数: 0
出版历程
- 收稿日期: 2008-06-17
- 修回日期: 2008-12-03
- 刊出日期: 2009-02-15

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

School of Mathematical Sciences, Fudan University, Shanghai 200433, P. R. China;

摘要

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．
- 自然电位测井 /
- 椭圆交界面问题 /
- 数学模型 /
- 数值模拟
Abstract: 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. lluthemwre, a jump ooaidition 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.
- spontaneous potential log /
- elliptic interface problems /
- mathematical model /
- numerical simulation

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参考文献(14)

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