CALCULATION OF GUARD ELECTRODE RESPONSE CURVES

Abstract

In the existing theories of guard electrode logging, the electrode is approximated by a prolate spheroid. All equipotential surfaces are assumed to be concentric prolate spheroids and the current nappes are bounded by hyperboloids. This picture ignores the refraction of current at the boreface and at the boundary of invaded zones of porous formations. A new approach to guard electrode theory has been formulated in which the electrode is represented by a series of spheres having the same diameter as the electrode. The boreface and invaded zone boundary are considered to be cylindrical. The current from each sphere is calculated from the condition that all spheres must be at the same potential and the potential distribution is found by superposition of the fields due to the individual currents. For small drill holes in otherwise homogeneous formations of moderate resistivity the prolate spheroid approximation gives results that are identical with those of the present theory. For larger holes, invaded formations and large resistivity contrasts, the prolate spheroid method is shown to give varying degrees of error in the calculated apparent resistivities.