Direct correlation of internal gradients and pore size distributions with low field NMR

Internal magnetic field gradients Gint, which arise from the magnetic susceptibility difference Δχ between solid matrix and fluid in porous media relate to the pore geometry. However, this relationship is complex and not well understood. Here we correlate internal-gradient distributions to pore-size distributions directly to examine internal gradients in detail at low field NMR. The pore-size distributions were obtained by the method of Decay due to Diffusion in the Internal Field (DDIF), and the internal-gradient distributions were measured with the Carr-Purcell-Meiboom-Gill (CPMG) method. The internal-gradient-pore-size distributions correlation maps were obtained for water in packs of glass beads with different diameter and in a sandstone sample. The relationship between internal gradients and pore structure is analyzed in detail by considering the restricted diffusion of fluids in porous samples. For each case diffusion regimes are assigned by plotting normalized CPMG data and comparing the diffusion lengths, the dephasing lengths and pore diameters. In the free-diffusion limit, the correlation maps reveal the true relationship between pore structure and internal gradients so that Δχ can be approximated from the correlation maps. This limit is met most easily at low field. It provides information about porous media, which is expected to benefit the oil industry, in particular NMR well logging.