Direct correlation of diffusion and pore size distributions with low field NMR

The time-dependent diffusion coefficient (D) is a powerful tool to probe microstructure in porous media, and can be obtained by the NMR method. In a real porous sample, molecular diffusion is very complex. Here we present a new method which directly measures the relationship between effective diffusion coefficients and pore size distributions without knowing surface relaxivity. This method is used to extract structural information and explore the relationship between D and a in porous media having broad pore size distributions. The diffusion information is encoded by the Pulsed Field Gradient (PFG) method and the pore size distributions are acquired by the Decay due to Diffusion in the Internal Field (DDIF) method. Two model samples were measured to verify this method. Restricted diffusion was analyzed, and shows that most fluid molecules experience pore wall. The D(a) curves obtained from correlation maps were fitted to the Padé approximant equation and a good agreement was found between the fitting lines and the measured data. Then a sandstone sample with unknown structure was measured. The state of confined fluids was analyzed and structural information, such as pore size distributions, were extracted. The D - T1 correlation maps were also obtained using the same method, which yielded surface relaxivities for different samples. All the experiments were conducted on 2MHz NMR equipment to obtain accurate diffusion information, where internal gradients can be neglected. This method is expected to have useful applications in the oil industry, particularly for NMR logging in the future.