"A Novel NMR Echo-Based Fractal Method"

"Hydrocarbon mobility is a critical parameter in shale reservoir evaluation. Although NMR T1-T2 measurements are highly sensitive to fluid properties, conventional mobility assessment typically relies on empirical interpretation schemes or additional laboratory experiments, which limit quantitative applicability. In this study, a novel fractal framework directly derived from NMR echo data is proposed to characterize hydrocarbon mobility in shale reservoirs. By bypassing T1-T2 spectral inversion, the proposed method avoids uncertainties associated with ill-posedness and regularization, and directly extracts intrinsic scaling characteristics from the raw echo data. Numerical simulations demonstrate that the echo-based fractal parameters exhibit stronger sensitivity to hydrocarbon mobility than those derived from inverted T1-T2 spectra, while maintaining low sensitivity to noise and NMR acquisition parameters (Echo spacing and polarization time). Core experiments further confirm that the echo-derived fractal dimension shows strong quantitative correlation with geochemical indicators, including S1, OSI, and TOC, and effectively differentiates movable hydrocarbons from pyrolytic components. Overall, the proposed method provides a robust and inversion-independent approach for quantitative evaluation of shale hydrocarbon mobility."