Modelagem de perfis de indução no domínio do tempo por diferenças finitas

Abstract

A new approach of modeling the response of the induction tool in a borehole in the time domain is presented. Here I have solved electromagnetic field diffusion equation in a horizontally stractified medium by finite difference method. The transmitter loop is excited by the step function current. The receiver loop is positioned coaxially in the borehole above the transmitter at a fixed distance. The solution of the difusion equation takes into account the primary and secondary fields. The primary field is obtained analytically and the secondary is calculated by the Alternating Direction Implicit method. The resulting tri-diagonal system is solved by the recursive algorithm proposed by Claerbout. Finally, the electric field in the receiver is computed at different positions of the tool in a borehole and these values are plotted against the depth of measurement. The results obtained show that measuring electric field in the time domain is very eficient to detect the bed boundaries, even if the beds are very thin.