Models and methods for predicting hydraulic conductivity in near-surface unconsolidated sediments using nuclear magnetic resonance

Nuclear magnetic resonance (NMR) logging provides a relatively new approach for estimating the hydraulic conductivity K of unconsolidated aquifers. We have evaluated results from model validation and uncertainty quantification using direct-push measurements of NMR mean relaxation times and K in sands and gravels at three field sites. We have tested four models that have been proposed for predicting K from NMR data, including the Schlumberger-Doll research, Seevers, and sum-of-echoes equations, all of which use empirically determined constants, as well as the Kozeny-Godefroy model, which predicts K from several physical parameters. We have applied four methods of analysis to reanalyze NMR and K data from the three field sites to quantify how well each model predicted K from the mean log NMR relaxation time T-2ML given the uncertainties in the data. Our results show that NMR-estimated porosity does not improve prediction of K in our data set for any model and that all of the models can predict K to within an order of magnitude using the calibrated constants we have found. We have shown the value of rigorous uncertainty quantification using the methods we used for analyzing K-NMR data sets, and we have found that incorporating uncertainty estimates in our analysis gives a more complete understanding of the relationship between NMR-derived parameters and hydraulic conductivity than can be obtained through simple least-squares fitting. There is little variability in our data set in the calibrated constants we find, given the uncertainty present in the data, and therefore we suggest that the constants we find could be used to obtain first-order estimates of hydraulic conductivity in unconsolidated sands and gravels at new sites with NMR data available.