Understanding NMR relaxometry of partially water-saturated rocks

Abstract. Nuclear Magnetic Resonance (NMR) relaxometry measurements are commonly used to characterize the storage and transport properties of water-saturated rocks. These assessments are based on the proportionality of NMR signal amplitude and relaxation time to porosity (water content) and pore size, respectively. The relationship between pore size and NMR relaxation time depends on pore shape, which is usually assumed to be spherical or cylindrical. However, the NMR response at partial water saturation for natural sediments and rocks differs strongly from the response calculated for spherical or cylindrical pores, because these pore shapes cannot account for water menisci remaining in the corners of de-saturated angular pores. Therefore, we consider a bundle of pores with triangular cross-sections. We introduce analytical solutions of the NMR equations at partial saturation of these pores, which account for water menisci of de-saturated pores. After developing equations that describe the water distribution inside the pores, we calculate the NMR response at partial saturation for imbibition and drainage based on the deduced water distributions. For this pore model, NMR amplitude and NMR relaxation time at partial water saturation strongly depend on pore shape even so the NMR relaxation time at full saturation only depends on the surface to volume ratio of the pore. The pore-shape-dependence at partial saturation arises from the pore shape and capillary pressure dependent water distribution in pores with triangular cross-sections. Moreover, we show the qualitative agreement of the saturation dependent relaxation time distributions of our model with those observed for rocks and soils.