【摘要】 若把套管视为一层煤质，便可采用多层径向阶跃媒质模型，对套管井中直流环的场严格求解，得到任一层媒质中的势函数，并由边界条件建立任意相邻两层间势函数的系数递推矩阵。该理论还能用于研究套管井低频似稳场特性、过套管地层电阻单测量方法及套管电导率、厚度等的影响。数值模拟结果表明，套管井中的场按场源距大小分为近场区、中场区和远场区。在中场区，电位二阶导数几乎不随场源距变化，而明显随地层电导率变化。由此确定了通过测量二次电位差求解地层电导率的理论基础。数值模拟结果还表明，二次电位差受套管电导率和厚度影响大，受水泥环电导率影响小。更多还原

【Abstract】 If the case of borehole is considered as a layer of medium, people can make, byusing multi-layer radial-stepped medium model, the strict solution of the field of di-rect current circle in cased borehole to obtain a potential function of any layer; andthen the coefficient recursion matrix for potential functions of any two adjacent lay-ers can be derived from boundary condition- This theory can be also used to knowsome characters of low frequency pseudo-stable field in cased borehole, resistivitymeasure method for formations around the cased borehole, and the effects of bothelectric conductivity and thickness of case. Numerical modeling result shows that interms of field-source distance, field in cased borehole can be divided into near fieldarea, mid field area and far field area. in the mid field area, second-order derivativeof electric potential nearly does not vary with field-source distance, but it changesobviously with formation electric-conductivity. Consequently, the theory can be de-termined of deriving correct formation electric-conductivity from secondary electricpotential difference. Numerical modeling result also says that the secondary electricpotential difference is severely influenced by both electric conductivity and thicknessof case, but slightly affected by electric conductivity of cement.更多还原