An analysis of NMR-permeability scaling rules by numerical MRI

The correlation of NMR relaxation response and fluid permeability relies on a deterministic relationship between self-diffusion at the 100 micron (individual pore) scale and flux at a significantly larger scale (core plug, whole core). Previous work considered averaging rules for the NMR relaxation response in terms of average relaxation times. In addition to standard assumptions of pore isolation, constant surface relaxivity, and fast diffusion, a permeability averaging rule is implicitly assumed at the finest scale. New developments in MRI adding a Laplace dimension allow characterizing the heterogeneity of V/S. It is then possible to apply the NMR-permeability correlations at different scales and compare permeability estimates based on full scale measurements with upscaled (" averaged") values of local measures. In this work I analyse MRI responses with locally resolved Laplace dimension, numerically derived for a set of Xray-CT images of sandstones and carbonates, and comment on appropriate averaging rules for the different rock classes. It is shown that applying the correct averaging rule reduces the scatter of NMR-permeability correlations. I also apply geostatistical techniques and compare geostatistics of V/S obtained from segmented Xray-CT images with simulated MRI images. The inclusion of MRI data in the NMR interpretation process might increase the predictive power of NMR-permeability correlations by including information about the best averaging rules to use.