| 自然电位测井的数学模型 |
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| 引用本文： | 蔡志杰. 自然电位测井的数学模型[J]. 数学建模及其应用, 2014, 3(4): 1-7 |
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| 作者姓名： | 蔡志杰 |
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| 作者单位： | 首都师范大学数学科学学院检测成像工程研究中心，北京 100048;首都师范大学数学科学学院检测成像工程研究中心，北京 100048;首都师范大学数学科学学院检测成像工程研究中心，北京 100048 |
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| 基金项目： | 国家自然科学基金(批准号：19972010)资助的课题. |
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| 摘 要： | 自然电位测井是石油开发中一种常用而重要的测井方法。自然电位函数的数学模型可归结为具有间断交界面条件的椭圆型等位面边值问题,在交界面交汇点处,自然电位的跳跃通常不满足相容性条件,此时,这个边值问题不存在分块H1*解,不能使用有限元素法直接求解。本文介绍这一测井方法的数学模型及数值求解方法。
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| 关 键 词： | 自然电位测井；等值面边值问题；相容性条件；有限元素法 |
| 收稿时间： | 2004-02-14 |
| 修稿时间： | 2004-03-22 |
Mathematical Model for the Spontaneous Potential Well-logging |
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| Cai Zhi-Jie. Mathematical Model for the Spontaneous Potential Well-logging[J]. , 2014, 3(4): 1-7 |
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| Authors: | Cai Zhi-Jie |
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| Abstract: | In the paper, an open cavity is divided into two parts: closed part and open part. The closed part means the closed cavity, and the open part is equi valent to the absorbing traveling boundary. According to Maxwell theory, there exists a coupling equation between the modes of the closed cavity and those of the open part.Utilizing the method, the X-band six-cavity transit time oscillator is calculated; the calculated frequency and the Q value of the working mode are very close to the measured values. |
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| Keywords: | spontaneous potential well-logging equi-valued boundary value problem compatibility condition finite element method |
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