Integration of Capillary and NMR Relaxometry Results: From Linear Calibration to Nonlinear 2D Interpretation

An approach to interpreting pore size distributions (derived from NMR relaxometry, mercury injection, and porous plate methods) based on a nonlinear transformation (quantile alignment, or quantile mapping) is proposed. Unlike conventional linear calibrations of the form r = cT₂ (where r is the pore radius, c is the calibration coefficient, and T₂ is the transverse NMR relaxation time), the proposed method accounts for the geometric heterogeneity of the pore space, enabling a closer match with experimental data when reconstructing capillary pressure curves from NMR results. Based on a dataset of 751 core samples, a correlation was established between the nonlinear transformation parameters and the lithological characteristics of the rocks. An interpretation of the r ~ T₂ ⁿ relationship is proposed, accounting for the link between the pore surface fractal dimension d_s and the exponent n. Based on a limited sample set, ranges of ds values for the considered rock types were estimated through pore-space image analysis using the box-counting method. It is shown that the apparent d_s values derived from the r(T₂ ) dependence are consistent with the ranges determined by the box‑counting method. Using a simple machine learning model (the k-nearest neighbors method) as an example, it is demonstrated that the quality of residual water saturation S_wi recovery from NMR relaxometry data using the considered method corresponds to the quality of S_wi recovery by the cut-off method when trained on the same dataset, with comparable accuracy of saturation estimation at other capillary pressure stages.

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