Low-field NMR has shown its capability in determining permeability, wettability, connectivity and pore size distributions in porous materials^{1}, which proves a huge potential in oil, geothermal and hydrological industries. Many NMR methods were developed to detect the pore size distribution of rock cores, either using induced internal gradient fields^{2}, or scaling the relaxation distribution to the pore size distribution with an estimated surface relaxivity^{1}. However, these techniques can only be applied if internal magnetic gradient fields are sufficiently high^{2 }or if prior knowledge on the sample exists^{1}. Regarding these constraints, we use a more general approach which allows one to directly determine the pore length scales of rocks using Pulsed Field Gradient (PFG)-NMR at 2 MHz ^{1}H resonance frequency, so as to improve the applicability and reliability of NMR methods for industrial environments.

PFG techniques record the averaged net displacement of mobile spins during the observation time *Δ*. Within a long enough observation time, the pore length (R) can be obtained as the displacements will be determined by the mophology of the porous system^{3,4}. To approach this, the kernel of the numerical inversion and boundary conditions of the diffusion equation has to be chosen accordingly during data processing, in order to take into account the contributions of the restricted diffusion.

Finally, the aforementioned modified PFG technique is combined with a CPMG pusle train which allows one to correlate the pore length scale with the transversal relaxation time *T*_{2} in a two-dimensional experiment. The surface relaxivity *ρ*_{2 }of rock cores is then determined from this 2D correlation map which can be used subsequently for the calibration of in-situ NMR well-logging data.

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- Y.Q. Song, S. Ryu, P. N. Sen, Nature, 406 (2000) 178.
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- P.T. Callaghan, Oxford University Press, New York, 1991.