Jointly deriving NMR surface relaxivity and pore size distributions by NMR relaxation experiments on partially desaturated rocks

Nuclear magnetic resonance (NMR) relaxometry is a geophysical method widely used in bore-hole and laboratory applications to nondestructively infer transport and storage properties of rocks and soils as it is directly sensitive to the water/oil content and pore sizes. However, for inferring pore sizes, NMR relaxometry data need to be calibrated with respect to a surface interaction parameter, surface relaxivity, which depends on the type and mineral constituents of the investigated rock. This study introduces an inexpensive and quick alternative to the classical calibration methods, e. g., mercury injection, pulsed field gradient (PFG) NMR, or grain size analysis, which allows for jointly estimating NMR surface relaxivity and pore size distributions using NMR relaxometry data from partially desaturated rocks. Hereby, NMR relaxation experiments are performed on the fully saturated sample and on a sample partially drained at a known differential pressure. Based on these data, the (capillary) pore radius distribution and surface relaxivity are derived by joint optimization of the Brownstein-Tarr and the Young-Laplace equation assuming parallel capillaries. Moreover, the resulting pore size distributions can be used to predict water retention curves. This inverse modeling approach-tested and validated using NMR relaxometry data measured on synthetic porous borosilicate samples with known petrophysical properties (i.e., permeability, porosity, inner surfaces, pore size distributions)-yields consistent and reproducible estimates of surface relaxivity and pore radii distributions. Also, subsequently calculated water retention curves generally correlate well with measured water retention curves.