The Effect Of Shale Anisotropy On Focused Resistivity Devices

The observed disparity between Laterolog and induction measurements in shales is often attributed to tool imperfection. However, even the current highly accurate Laterolog and Induction devices consistently indicate differences in shales. These differences are particularly pronounced in highly laminated formations characterized as anisotropic and cannot be explained by instrumentation error or borehole effects alone. Because induction devices are only sensitive to the horizontal resistivity of the formation and resistivity devices are sensitive to both horizontal and vertical resistivities, the question arises as the possible relation between formation anisotropy and the observed dissimilarity. Earlier work indicated a significant effect of anisotropy on unfocused normal electrode devices. In the present paper, the effect of anisotropy on Laterologs is completely quantified by means of analytical and numerical solutions to mathematical models. The analytical solution is a natural extension to previous developments which quantifies the different resistive properties of the formation with a simple scaling parameter called the anisotropy coefficient. The numerical solution simulates shales as a fine layering of alternately resistive and conductive zones. Complete agreement was obtained between the predicted results from the two models. The more computationally convenient analytic solution was used to compute the response of the Laterolog device for various hole sizes and mud resistivities for typical shale values of anisotropy coefficients. The computed results indicate a significant departure between the Laterolog responses and the average horizontal resistivity of the formation. In practice, then, a large anisotropy coefficient in shales can easily account for a Laterolog reading up to twenty percent higher in resistivity than the induction tool reading. The study was further expanded to include the effect of apparent dip on the response of laterologs and induction devices.