Interval inversion of well-logging data for automatic determination of formation boundaries by using a float-encoded genetic algorithm

Abstract

In the paper a real-valued genetic algorithm is presented for solving the non-linear well-logging inverse problem. The conventional way followed in the interpretation of well-logging data is the formulation of the inverse problem in each measuring point separately. Since barely less number of unknowns than data are estimated to one point, a set of marginally overdetermined inverse problems have to be solved, which sets a limit to the accuracy of estimation. Describing the petrophysical (reservoir) parameters in the form of series expansion, we extend the validity of probe response functions used in local forward modeling to a greater depth interval (hydrocarbon zone) and formulate the so-called interval inversion method, which inverts all data of the measured interval jointly. Assuming an interval-wise homogeneous petrophysical parameter distribution, significantly smaller number of unknowns than data have to be determined. The highly overdetermined inverse problem results in accurate and reliable estimation of petrophysical parameters given for the whole interval instead of separate measuring points. For measuring the storage capacity of the reservoir, the formation thickness is also required to be estimated. As a new feature in well logging inversion methodology, the boundary coordinates of formations are treated as new inversion unknowns and determined by the interval inversion method automatically. Instead of using traditional linear inversion techniques, global optimization is used to avoid problems of linearization related to the determination of formation thicknesses. In the paper, synthetic and field examples are shown to demonstrate the feasibility of the interval inversion method.