Determining the Pore Size Distribution of Rocks by Joint Inversion of NMR Data at Different Water Saturations

Nuclear magnetic resonance (NMR) relaxation is a well-established method to characterize storage and transport properties of rocks due to its sensitivity to pore fluid content and pore sizes. Thereby, the correct estimation of these properties depends on the underlying pore model. Usually, cylindrical or spherical pores are assumed for interpreting NMR relaxation data. For estimating their size, a calibration regarding the mineral parameter surface relaxivity is required.

Mohnke (2014) used NMR measurements at different saturations for deriving surface relaxivity and pore size distribution (psd) simultaneously without the need for calibration. We extendeded this approach by using a model of parallel capillaries with angular cross-section to account for residual water trapped in pore corners of "desaturated" pores (Hiller and Klitzsch 2018).

Aiming at the validation of our approach, we studied carbonate samples and compared the pore size distributions obtained from the NMR joint inversion with those derived from BIB-SEM imaging data. The mean NMR pore size proved to be considerably lower than the mean SEM pore size. We show that the deviation is caused by the capillary bundle assumption used in the joint inversion approach. When adapting our inversion approach by assuming a pore network, both pore size distributions match.

Overall, we introduce a validated method for a direct determination of pore size distribution, pore shape, and surface relaxivity based on NMR measurements without the need for further calibration.