New Methods for Modeling Laterolog Resistivity Corrections

Abstract

The paper presents methods for laterolog response modeling. In Coulomb's charges method, Laplace's equation is solved for the electric field distribution in rock medium with internal boundaries between different resistivity layers. There, the boundary problem is reduced to Fredholm integral equation of the second kind. The second method uses a finite element array to model apparent resistivity from laterolog. The task is treated as DC problem and the Laplace equation is solved numerically. The presented methods were applied to borehole data covering a typical stratigraphic section of the Fore-Sudetic Monocline in southwestern Poland. Apparent resistivity was calculated using the Coulomb's charges method and alternatively modeled using a finite element method which gave similar results. Then, a series of linear corrections for borehole, shoulder bed, and filtration effects for apparent resistivity obtained by the Coulomb's charges method demonstrated the feasibility of calculating true resistivity of virgin and invaded zones. The proposed methods provide a flexible solution in modeling which can be adapted to other logs.