Method and apparatus for determining invasion parameters and using said parameters to plot a more accurate resistivity log on an output record

摘要

A system receives output signals from a well tool adapted to be disposed in a wellbore and, after appropriate processing of the signals, generates a set of invasion parameters which are used for plotting a resistivity log on an output record medium. The invasion parameters include Rxo, the flushed zone resistivity; Rt, the uninvaded zone resistivity; and two other parameters not previously known, the "w" parameter and the "N" parameter. "w" represents the midpoint of the transition zone region on the resistivity log and "N" represents a value related to the slope of the resistivity log in the transition zone region. Given the four parameters, Rxo, Rt, w, and N, a more accurate resistivity log may be generated and illustrated on an output record medium. The system uses an iterative procedure wherein physical values of Rxo, Rt, w, and N are selected; in addition, an additional constraint value is selected. A cost function "chi squared", a function of the squares of differences between measured and modeled apparent conductivity (resistivity), is computed. The chi-squared cost function is then minimized. The chi-squared is minimized by first determining if the difference between the new versus old chi-squared changed less than a desired amount a required number of times, and secondly determining if the ratio of the constraint to the chi-squared has resulted in a required a-priori value a required number of times in a row. When the chi-squared is minimized, the parameters utilized to determine the chi-squared are the required invasion parameters used to plot the more accurate and improved resistivity log output record medium, one which reflects a gradual change in resistivity in the transition zone.