Geophysical Well Log Multifractal Analysis and PLS-DA Modeling for Enhanced Oil–Gas Discrimination

Accurate identification of reservoir fluids is essential for effective exploration and production in the petroleum industry. Traditional petrophysical methods often struggle to distinguish between oil and gas, particularly in geologically complex formations. This study applies advanced fractal and multifractal analyses to geophysical well log data to improve fluid discrimination. Fractal measurements—such as box dimension, regularization dimension, and multifractal spectrum attributes (including spectrum width, peak singularity strength, minimum and maximum singularity strengths, corresponding spectrum values, and the C value)—were evaluated for their ability to differentiate fluids based on distinct log signatures. Partial Least Squares Discriminant Analysis (PLS-DA), a multivariate statistical modeling technique, was employed to uncover patterns between these features and fluid types. A dataset of 1085 geophysical well logs, including gamma ray, acoustic, density, neutron porosity, resistivity, photoelectric factor, and gamma ray spectroscopy measurements, was used to extract attributes. The PLS-DA model achieved strong performance, with Q² cumulative predictive ability values above 0.8, R²Y cumulative explained variance in the response matrix values exceeding 0.9, R²X cumulative explained variance in the predictor matrix values above 0.85, and AUC (area under the receiver operating characteristic curve) scores over 0.95 in both training and validation. A key outcome is a Classification Function that combines multiple attributes into a single score, enhancing prediction accuracy and interpretability. The methodology also quantifies the relative importance of each attribute, offering insight into the petrophysical processes reflected in well logs. This integrated approach provides a robust, interpretable, and data-driven solution for improved fluid identification in petroleum reservoirs.