ELECTRICAL-RESISTIVITY MEASUREMENT THROUGH METAL CASING

Methods using dc electrical arrays to measure formation resistivity th rough casing have relied on approximate forms for the current and pote ntial distributions to derive a simple relationship between the format ion resistivity and the transverse resistance calculated from measurem ents of the potential and its second derivative inside the casing. We have derived a numerical solution for the potentials and their derivat ives to examine the accuracy of the approximate forms for casing of fi nite-length, annular zones of varying radius, and for vertical discont inuities such as layers or abrupt changes in annular zone radius. For typical conductivity contrasts between the casing and formation, the a pproximate relationships may be off by as much as 60 percent for long casing and may show variations of 20 to 30 percent as the electrode ar ray moves along the casing. In principle an iterative scheme could be devised to correct the readings if high accuracy was required. The num erical results show that to first order the current flow from the casi ng is radial, and that all the analytic expressions based on this assu mption for evaluating layer resolution and the effects of annular laye rs are valid. An interesting byproduct of this study has been the disc overy that the distortion of the potentials in a nearby well by an ann ular disk (e.g., an injected steam zone) surrounding the current injec tion well is greater if the injection well is cased. Crosswell resisti vity surveys appear feasible if one of the wells is cased.