Deriving NMR surface relaxivities, pore size distributions and water retention curves by NMR relaxation experiments on partially de-saturated rocks

Nuclear magnetic resonance (NMR) is a method used over a wide field of geophysical applications to non-destructively determine transport and storage properties of rocks and soils. In NMR relaxometry signal amplitudes correspond directly to the rock's fluid (water, oil) content. On the other hand the NMR relaxation behavior, i.e. the longitudinal (T1) and transverse (T2) NMR relaxation times, can be used to derive pore sizes and permeability as it is linearly linked to the pore's surface-to-volume-ratio and physiochemical properties of the rock-fluid interface by the surface relaxivity ρ_s This parameter, however, is dependent on the type and mineral constituents of the investigated rock sample and thus has to be determined and calibrated prior to estimating pore sizes from NMR relaxometry measurements. Frequently used methods to derive surface relaxivity to calibrate NMR pore sizes comprise mercury injection, pulsed field gradients (PFG-NMR) or grain size analysis. This study introduces an alternative approach to jointly estimate NMR surface relaxivity and pore radii distributions using NMR relaxation data obtained from partially de-saturated rocks. In this, inverse modeling is carried on a linked Young Laplace equation for capillary bundles and the Brownstein and Tarr equations. Subsequently, this approach is used to predict water retention curves of the investigated rocks. The method was tested and validated on simulated and laboratory transverse NMR data. Calculated inverse models are generally in a good agreement with results obtained from mercury injection and drainage measurements. Left: Measured and predicted water retention (pF) curves. Center: NMR relaxometry data, fit and error. Right: Mercury injection data (HgPor, dashed line) and jointly derived pore radii distributions and surface relaxivity by joint inverse modelling