Borehole dc resistivity response for a transitional invaded zone

Abstract

A borehole direct‐current resistivity boundary value problem for normal and lateral elctrode configuratin is soved assuming axial symmetry. The borehole mud, a flushed zone, an invaded zone, and an unciontaminated zone are all assumed to be present. A linear transition in resistivity is assumed for the invaded zone. Frobenius extended power series and the method of separation of variables are used to solved the 1-D problem. Single-run borehole resistivity sounding and solution of the inverse problem are suggested fo estimatingthe resisitivity of the uncontaminated zone and the radius of invasion. Finite‐difference modeling is dione to estimate the effect of shoulder beds ion borehole sounding. Some of the computed 1-D and 2-D model apparent reisivity curves are compared with the existing scale model data. The analysis reveals that the mud cake effect is negligible for normal and lateral electrode array and the invasion zone thickness is feflected in the forward models. Apparent resistivity curves with and without a transitional invaded zone are well separated. Resistivity departure curves are well separated for fixed resistivity and variable resistivity invaded zone models. A normal electrode configuration can feel the presence of the shoulder bed in a 2-D model when the bed thickness is about 12 time the electrode separation. One‐dimensional ridge regression inversion the synthetic forward model data is presented to suggest an alternative approach for determining the resistivey of the uncontaminated zone ([Formula: see text]) and the radius of invasion [Formula: see text]. We conclude that (1) a single run borehole sounding with 10 or 12 data points from a normal or lateral log may be used, rather than 3 points from a dual laterolog [Formula: see text] tool, for better estimation of [Formula: see text], and (2) a borehole forward model should include a transitional invaded zone. Finally, an alternative approach for the estimation of the radius of invasion is proposed.