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 (T1) and transverse (T2) relaxation time distributions of nuclear magnetic resonance (NMR) data from laboratory and well-logging settings. As an NMR post-processing step, numerous methods, like manual cutoffs or machine learning, partition one-dimensional (1D) and two-dimensional (2D) distributions to quantify pore systems and fluids. Challenges remain, caused by the continuous distributions derived from the inverse Laplace transform (ILT) of raw NMR 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 sets. Due to its ill-posed nature, the ILT method applies constraints to obtain stable, continuous solutions. While often treated as aproxy for ground truth, such solutions pose challenges for fluid partitioning. The smoothing effects inherent to these solutions are demonstrated with synthetic data sets of known ground truth, as true distributions of actual samples are unknown. We present a framework using a discrete inversion approach, detailing its implementation across various laboratory data sets, its compatibility with ILT, and its enhancement through component optimization. This methodology shows promising results for challenging tasks, including the characterization of shale fluids and the analysis of logging data with low signal-to-noise ratio (SNR). Notable limitations of conventional ILT methods include: (1) excessive smoothing, resulting in substantial peak overlap and diminished spectral resolution, and (2) considerable uncertainty in estimating short relaxation times, particularly at low SNR conditions. These oversmoothing challenges subsequent partitioning methods, as smoothed features cannot be distinguished from the true distribution, and inversion inaccuracies are propagated into post-processing. In the discrete inversion approach presented, the number of components is estimated using the Bayesian information criterion (BIC), and neighboring components can be merged to capture broad distributions. These discrete components differ fundamentally from ILT-based results, as they inherently eliminate a separate partitioning step. With this method, we demonstrate that fluid classification and quantification are simplified once fluid relaxation time ranges are calibrated for a reservoir. A further advantage is the method's low bias when analyzing low SNR logging data; while the variance of individual results can be high, this resilience to systematic error enhances the reliability of the average result.