Method of simulating the response of a through-casing electrical resistivity well logging instrument and its application to determining resistivity of earth formations

摘要

A method of simulating response of a through casing electrical resistivity well logging instrument to a set of simulated earth formations, cement and casing. A model of the earth formations, casing, cement and a configuration of electrodes on the instrument is initialized. Space surrounding the instrument is divided into segments. Conductance of each of the segments is calculated. A system of linear equations describing the electrical potential at each junction of segments is set up. The system expresses the balance of electrical current at each junction disposed outside the instrument and satifies the conditions that the potential on an outer surface of the space is zero, that the current normal to an insulating part of the instrument is zero, and that the potential is substantially equal at all junctions contained within one of the electrodes. The system of linear equations is solved by the conjugate gradient method with Incomplete Cholesky preconditioning. The electrical potential at each one of the electrodes is calculated so that an apparent resistivity as would be indicated by the instrument in the modeled earth formations can be determined.