自然电位测井的数学模型

Mathematical Model for the Spontaneous Potential Well-logging

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。

The spontaneous potential well-logging is one of the common and important techniques in petroleum exploitation.The spontaneous potential satisfies an elliptic equivalued surface boundary value problem with discontinuous interface conditions.In general,the jumps of the spontaneous potential do not satisfy the compatibility condition at the joint points of the interfaces.In this case,there does not exist a piecewise H1*solution to this boundary value problem,thus the finite element method cannot be applied to get numerical solution directly.In this paper,we introduce the mathematical model and numerical method for this well-logging method.