Discrete Inversion Method for Nuclear Magnetic Resonance Data Processing and Its Applications to Fluid Typing and Quantification

A vast amount of petrophysical information can be inferred from continuous longitudinal and transverse time distributions of nuclear magnetic resonance (NMR) data in both laboratory and well-logging settings. As an NMR post-processing step, numerous methods, such as manual cut-offs, Gaussian decomposition, or machine learning techniques, have been developed to partition both 1D and 2D distributions for accurate quantification of pore systems and the fluids contained within. Challenges still remain, partly caused by the continuous distributions themselves, which are derived from the inverse Laplace transformation (ILT) of raw NMR relaxation data. This study develops new post-processing workflows based on the discrete inversion method, demonstrated through applications to fluid typing and quantification for synthetic and shale data. Due to the ill-posed problem of the inversion technique, constraints are applied to obtain stable continuous solutions by the ILT method, which are considered as ground truth but pose challenges for fluid partitioning. The smoothing effects on the continuous solutions are demonstrated by comparison with prior known synthetic datasets, since distributions from actual samples are unknown. We present a comprehensive framework centered around a discrete inversion approach, detailing its successful implementation across various laboratory datasets, its compatibility with ILT, and its enhancement through discrete component optimization. Notably, this methodology exhibits promising results in addressing challenging tasks, including the characterization of shale fluids and the analysis of logging data compromised by low Signal-to-Noise Rations (SNR) conditions Notable limitations of conventional Inverse Laplace Transform (ILT) methods have been identified, primarily manifesting as: (1) excessive smoothing that leads to inconsistent regularization, resulting in substantial peak overlaps and diminished spectral resolution; and (2) considerable uncertainty in estimating short relaxation times, particularly exacerbated by low Signal-to-Noise Ratio (SNR) conditions. Over- smoothing poses particular challenges to subsequent partitioning methods, as it cannot be distinguished from actual distributions, and any inversion inaccuracies propagate into post-processing. In the discrete inversion approach, the number of components is initially estimated using the Bayesian Information Criterion (BIC), and subsequently, neighboring components can be merged to accurately capture broad distributions, taking into account the sensitivity of the data to noise levels. Notably, the components derived from discrete inversion differ fundamentally from those produced by ILT/partitioning workflows, as they inherently eliminate the need for additional partitioning steps, streamlining the analysis process. In the current study, we demonstrated the fluid classification and quantification become trivial once time ranges of fluids are calibrated for a specific shale reservoir. A further advantage of the proposed method lies in its resilience to noisy well- logging data, characterized by low SNR, where it exhibits significantly reduced uncertainty even when noise levels fluctuate, thereby enhancing the reliability of the results. Currently more applications are being developed based on discrete components and continuous distributions from ILT/Anahess.