Determining fractal dimension from nuclear magnetic resonance data in rocks with internal magnetic field gradients

Pore size distributions in rocks may be represented by fractal scaling, and fractal descriptions of pore systems may be used for prediction of petrophysical properties such as permeability, tortuosity, diffusivity, and electrical conductivity. Transverse relaxation time (T-2) distributions determined by nuclear magnetic resonance (NMR) measurements may be used to determine the fractal scaling of the pore system, but the analysis is complicated when internal magnetic field gradients at the pore scale are sufficiently large. Through computations in ideal porous media and laboratory measurements of glass beads and sediment samples, we found that the effect of internal magnetic field gradients was most pronounced in rocks with larger pores and a high magnetic susceptibility contrast between the pore fluid and mineral grains. We quantified this behavior in terms of pore size and Carr-Purcell-Meiboom-Gill (CPMG) half-echo spacing through scaling arguments. We additionally found that the effects of internal field gradients may be mitigated in the laboratory by performing T-2 measurements with different CPMG half-echo spacings and fitting the apparent fractal dimensions determined by the NMR measurements with a model to determine the true pore system fractal dimension.