Study of resistivity sondes by scale modeling and three-dimensional finite element method

The electric resistivity of a rock formation is essential for evaluation of the hydrocarbon saturation. Many sophisticated logging tools have been developed and used to measure this resistivity. Studying the responses of these tools in complex geometries can improve log interpretation by increasing the accuracy of the resistivity profile.; Two independent techniques to study the responses of resistivity tools in complex geometries are introduced here. First, scale modeling is used to allow reasonably sized tools and formations to be housed in a laboratory. Sand slabs are used to model resistive beds. The true resistivity of such slabs was determined by measuring the resistivity of samples of the slabs using the four-terminal method. An experimental study of two types of the shallow laterolog in high and low contrast zones is presented first. A second experimental study of a shallow laterolog in dipping beds follows. The effects of dip and eccentric tool positions are shown for certain cases. This suggests that a sectorized tool of the laterolog type can be designed to measure dips and detect bed boundaries and fractures. In this proposed tool, current, monitor and focusing electrodes are divided into multiple sectors. In this way, sectorized resistivity information might be gathered at each logging position.; In the second technique, a numerical method is used to study resistivity tools in complex geometries. A three-dimensional theoretical model using the finite-element method is presented and the intricacy of finite-element programming is explained. This method minimizes the total energy of the system. The volume of interest is subdivided into a finite number of elements in space. Numerical minimization of the total power is carried out using the Rayleigh-Ritz procedure. The electric potential is then calculated at each node by solving a linear system of equations. Resistivity logs computed using the finite element method are compared with logs generated by the integral equation method and an excellent agreement is shown.