Multifractal estimation of NMR T_(2) cut-off value in low-permeability rocks considering spectrum kurtosis: SMOTE-based oversampling integrated with machine learning

The transverse relaxation time (T_(2)) cut-off value plays a crucial role in nuclear magnetic resonance for identifying movable and immovable boundaries, evaluating permeability, and determining fluid saturation in petrophysical characterization of petroleum reservoirs. This study focuses on the systematic analysis of T_(2) spectra and T_(2) cut-off values in low-permeability reservoir rocks. Analysis of 36 low-permeability cores revealed a wide distribution of T_(2) cut-off values, ranging from 7 to 50 ms. Additionally, the T_(2) spectra exhibited multimodal characteristics, predominantly displaying unimodal and bimodal morphologies, with a few trimodal morphologies, which are inherently influenced by different pore types. Fractal characteristics of pore structure in fully water-saturated cores were captured through the T_(2) spectra, which were calculated using generalized fractal and multifractal theories. To augment the limited dataset of 36 cores, the synthetic minority oversampling technique was employed. Models for evaluating the T_(2) cut-off value were separately developed based on the classified T_(2) spectra, considering the number of peaks, and utilizing generalized fractal dimensions at the weight <0 and the singular intensity range. The underlying mechanism is that the singular intensity and generalized fractal dimensions at the weight <0 can detect the T_(2) spectral shift. However, the T_(2) spectral shift has negligible effects on multifractal spectrum function difference and generalized fractal dimensions at the weight >0. The primary objective of this work is to gain insights into the relationship between the kurtosis of the T_(2) spectrum and pore types, as well as to predict the T_(2) cut-off value of low-permeability rocks using machine learning and data augmentation techniques.