利用积分方程计算阵列感应测井响应

利用积分方程计算了阵列感应测井仪器各子阵列在轴对称二维地层中的响应,计算中将纵向成层原状地层作为背景地层,从而将计算区域限制在井眼和侵入带内。与数值模式匹配法和有限元素法将全部地层作为求解区域相比,未知量范围和计算量均大大减小,计算精度亦可相应提高。采用改进型逐次逼近解法(MSAM)计算了积分方程,该方法所需内存量小,且可适用于高电导率对比度地层。采用递推算法计算纵向成层背景地层中Green函数及其对空间坐标积分的待定系数,从而大大加快了计算速度。数值算例的结果说明了利用积分方程计算阵列感应测井响应的有效性。

Computation of array induction logging response using integral equations

The response of each sub-array of array induction logging tool in 2-D formation model with cylindrical symmetry was computed using integral equations. The longitudinal layered virgin formation is taken as background medium,and thus the computational region of the method is restricted within the borehole and invasion zone.Compared with numerical mode matching(NMM) method and the finite element method(FEM) which take all the formations as computational region,the range of the unknowns and the computational amount are greatly reduced and the accuracy is accordingly increased.The integral equations were computed by modified successive approximation method(MSAM).The method needs less computer memory requirements and is suitable for high-conductivity-contrast formation.The coefficients of the Green's function in longitudinal layered background medium and the integral of the Green's function with respect to the space coordinates were calculated by recursion algorithm.So the speed is greatly increased.Numerical examples show the effectiveness of integral equations applied for computing array induction logging response.