Inversion of Multiple Tool Invasion Model for Resistivity Log Interpretation

Log analysts are experts at combining many wireline mea- surements to locate producible hydrocarbon zones. This a paper describes an optimal method to combine resistiv- ity measurements and multi-array induction data, such as provided by the Array Induction Imager Tool (AlTI). This results in an improved estimate of the radial conductiv- ity profile. The method extends an earlier single tool in- vasion model (Howard, 1992). The method combines in- duction and current electrode tool data without bias with respect one of the two type of measurements. Nonbias results from the definition of the X2 cost function, which is minimized to determine the estimated invasion param- eters. It has a quadratic resistivity term, while the in- u.ctiIon data enters as quadratic terms in conductivity. In this way resistive zone parameter estimates in a log tend depend relatively more on the resistivity measurement, and conversely, more conducting intervals weight the in- duction measurement more heavily. Because resistivity and conductivity are reciprocals, nonlinear minimization is needed. The dynamically constrained Levenburg Mar- quardt method (DCLM) (Howard, 1992) is a nonlinear minimization algorithm which easily accommodates the un- biased approach, Here only the only resistivity tool in- cluded is Micro-SFL1 (MSFL). Comparisons of with and without MSFL augmented estimation in thick bed simu- lations show that when Rro/ Rt > 1, MSFL improves the solution.