Robust estimation of reservoir shaliness by iteratively reweighted factor analysis

Abstract

We suggest a statistical method for the simultaneous processing of electric, nuclear, and sonic-logging data using a robust iteratively reweighted factor analysis (IRFA). After giving a first estimate by Jöreskog’s approximate method, we refine the factor loadings and factor scores jointly in an iterative procedure, during which the deviation between the measured and calculated data is weighted in proportion to its magnitude for giving an outlier-free solution. We show a strong nonlinear relation between the first factor and the shale volume of multimineral hydrocarbon formations. We test the noise rejection capability of the new statistical procedure by making synthetic modeling experiments. The IRFA of simulated well-logging data including a high amount of noise gives a well log of the shale volume purified of large errors. Case studies from Hungary and the USA show that the results of factor analysis are consistent with that of independent deterministic modeling and core data. The statistical workflow can be effectively used for the processing of not normally distributed and extremely noisy well-logging data sets to evaluate the shale content and derived petrophysical properties more accurately in reservoir rocks.