Nuclear magnetic resonance relaxometry for pore size distribution in porous media: Accounting for diffusional coupling

Among numerous microstructure detection techniques, nuclear magnetic resonance (NMR) relaxometry has been extensively employed to investigate the microstructure and water distribution owing to its rapid and non-destructive benefits. However, this method may break down when the diffusion coupling of water molecules in adjacent pores becomes pronounced during the relaxation process. The pore size distribution (PSD) obtained with relaxation time distribution may give erroneous results, and the estimation of permeability and adsorbed water content would also have a significant deviation from reality. In this study, how the diffusion coupling effect appears during the relaxation process is analyzed, and a binary pore model is proposed to simulate the diffusion coupling of water molecules in soil. PSD of soil is categorized into three distinct peaks corresponding to small pores, large pores and isolated large pores, respectively. Then, by considering the coupling effect of diffusion between small pores and large pores and utilizing the proposed pore model, calculation and data processing methods, we derive the simulated PSDs via NMR relaxometry at various diffusion coefficients and surface relaxivities for four clays. The simulated PSDs are compared with measured PSDs via mercury intrusion porosimetry. The results show that as the diffusion coupling coefficient β increases, Peak 1 for small pores (or intra-aggregate pores) and Peak 2 for large pores (or inter-aggregate pores) in simulated PSD progressively merge into a singular peak. When β is larger than 40, there will be significant errors in simulated PSD, which tends to underestimate the volumes of small pores and overestimate their size.