Induction Log Shoulder-Bed Corrections to Anisotropic Formations and the Effect of Shale Anisotropy in Thinly Laminated Sand/Shale Sequences

Abstract

Summary: We examine induction log responses to layered, dipping, and anisotropic formations analytically. The analytical model is especially helpful in understanding induction log responses to thinly laminated binary formations, such as sand/shale sequences that exhibit macro-scopically anisotropic resistivity. We discuss two applications of the analytical model. In one application, we examine special induction log shoulder-bed corrections for use when thin anisotropic beds are encountered. It is known that thinly laminated sand/shale sequences act as macroscopically anisotropic formations. Hydrocarbon-bearing formations also act as macroscopically anisotropic formations when they consist of alternating layers of different grainsize distributions. When such formations are thick, induction logs accurately read the macroscopic conductivity, from which the hydrocarbon saturation in the formations can be computed. When the laminated formations are not thick, proper shoulderbed corrections (or thinbed corrections) should be applied to obtain the true macroscopic formation conductivity and to estimate the hydrocarbon saturation more accurately. We use the analytical model to calculate the thinbed effect and to evaluate the shoulder-bed corrections. We show that the formation resistivity and, hence, the hydrocarbon saturation are greatly overestimated when the anisotropy effect is not accounted for and conventional shoulder-bed corrections are applied to the log responses from such laminated formations. In another application, we examine the effect of shale anisotropy in thinly laminated sand/shale sequences. How do induction logs respond to such laminated formations when shale laminae are anisotropic? How accurate are the estimates of the sand-laminae resistivity and of the hydrocarbon saturation in these sand laminae? To answer these questions, we used the analytical model to examine the effect of shale lamina anisotropy on induction log responses in thinly laminated formations. We learned that the macroscopic conductivity of a laminated formation is determined uniquely by the sandlaminae conductivity and the anisotropic shale conductivity, if the sand fraction is known. We also found that the sand resistivity estimate depends on the value of shale resistivity and the dip angle, if the shale is assumed to be isotropic and if the sand fraction is known. When the sand fraction is not known, the sand resistivity and the sand fraction can be estimated if the set of horizontal and vertical macroscopic resistivities is known. In this case, the sand resistivity tends to be overestimated if the shale anisotropy is not accounted for. On the other hand, the sand fraction estimate is generally insensitive to the shale anisotropy, except for low sand-laminae resistivity (Rsd/Rsh < 5).