Simulating Resistivity Logs of 3D Structures Such As Breakouts, Vugs and Fractures Present in the Borehole Environment

Induction logs produced in three-dimensional (3D) geological environments can be numerically simulated using the integral equation technique. Unlike a differential equation, an integral equation contains a function operated by an integral, however, many problems of physics - mathematics can be worked in both ways. The advantage of the integral equation is that only the heterogeneity is discretized and the boundary conditions are implicit in its formulation. In this article, we have selected some 3D geological objects shown in acoustic log images from a carbonate reservoir of Campos Basin - Southeastern Brazil, aiming to simulate the inductive resistivity log with integral equation. The results reveal that breakouts and fractures can be easily detected, perhaps by the continuity of the tool - induced currents in the geological formations around the well. This is not so in the case of vugs, because of their size and insulation they do not produce electrical currents capable of being registered in the simulated resistivity logs.