Forward modeling of ultra-long spacing electrical logs

Ultra-Long Spacing Electrical Logs (ULSEL) are Normal type logging devices with very large electrode spacings, used to investigate resistive or conductive anomalies located far away from a borehole. Such kind of electrical investigations are also used to control the drilling of relief wells, by estimating the distance between them and a cased blowout well, in order to intercept it and terminate the eruption. In this respect, the conductive casing in the target well affects the ULSEL apparent resistivity response recorded in a relief well if the distance between the wells is comparable with the investigation radius of the logging device. Qualitative and quantitative interpretations of ULSEL results, such as trajectory corrections and distance estimations, may be accomplished by comparing the apparent resistivity log actually recorded with the theoretical response of a multilayered geoelectrical model, which is representative for the formations crossed by the borehole. The paper presents a forward modeling algorithm and software that can be used to simulate this response, not only for ULSEL but also for conventional investigation devices, such as the Normal (Potential) and Lateral (Gradient) electrode arrays. The simulation is carried out by solving in cylindrical coordinates the Laplace differential equation for the electrical field's potentials, using a matrix representation and a numerical solution for the fundamental system of boundary conditions.