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Volume 38 Number 6
  • E-ISSN: 1365-2478

Abstract

A

A mathematical formulation for the electric potential from point current‐sources coaxial with a metal casing has been obtained. The excitation caused by the axial point‐sources will produce currents in the pipe. By assuming that the pipe can be divided into many cylindrical ring segments with constant axially‐directed current, the solution of the fields inside and outside the pipe can be formulated in an integral form. The integral equation applied to the segmented pipe yields a set of simultaneous linear equations which are solved for the currents in the pipe; these are then used to calculate the potentials anywhere outside the pipe in the medium.

This solution has been used to study the distribution of the potentials in a half‐space for a single current‐source at and beyond the bottom of a finite length of casing. For a casing 0.1 m in radius and 0.006 m in wall thickness with a conductivity of 106 S/m, in a half‐space of 10‐2 S/m, it was found that only in a region very near the pipe does the pipe exert substantial influence on the fields of a point‐source 100 casing diameters beyond the end of the pipe. It appears that cross‐hole resistivity surveys can be implemented without corrections for the casing if the source is located at least 50–100 casing diameters beyond the end of the casing. Hole‐to‐surface surveys are much more affected by the pipe. For a pipe‐source separation of 100 casing diameters, the surface measurements must not be closer than a half pipe length for a 5% or less field distortion.

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2006-04-27
2024-04-20

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