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点电流源位于井内任意一点时,将在井眼、地层两个区域中求解泊松方程的边值问题化为在半径小于源到井轻距离的圆柱、源到井壁间的圆筒以及地层三个区域中求解拉普拉斯方程的边值问题。电流源的贡献则体现在源所在柱面的边界条件上,由此得到电位的偏心格林函数。水平井中偏心双侧向测井仪器在井内产生的电位可由偏心格林函数沿电极系积分得到,从而求得视电阻率响应。通过数值计算,绘制了深、浅侧向的偏心井眼校正图板。
When the current source is located at any point in the well, the boundary value problem of solving the Poisson’s equation in the borehole and the formation is transformed into a cylinder with a radius less than the source to the well, a cylinder with the source to the sidewall and a formation Solving the Boundary Value Problem of Laplace Equation in Three Regions. The contribution of the current source is reflected in the boundary conditions of the cylinder where the source is located, thereby obtaining the Eccentric Green’s function of the potential. The potential generated in the well by an eccentric double lateral logging instrument in a horizontal well can be obtained by integrating the potential along the electrode system by an Eccentric Green function to obtain the apparent resistivity response. Through numerical calculation, we draw deep and shallow lateral wellbore correction charts.