Bootstrap Calibration and Uncertainty Estimation of Downhole NMR Hydraulic Conductivity Estimates in an Unconsolidated Aquifer

Characterization of hydraulic conductivity ( K ) in aquifers is critical for evaluation, management, and remediation of groundwater resources. While estimates of K have been traditionally obtained using hydraulic tests over discrete intervals in wells, geophysical measurements are emerging as an alternative way to estimate this parameter. Nuclear magnetic resonance ( NMR ) logging, a technology once largely applied to characterization of deep consolidated rock petroleum reservoirs, is beginning to see use in near‐surface unconsolidated aquifers. Using a well‐known rock physics relationship—the Schlumberger Doll Research ( SDR ) equation— K and porosity can be estimated from NMR water content and relaxation time. Calibration of SDR parameters is necessary for this transformation because NMR relaxation properties are, in part, a function of magnetic mineralization and pore space geometry, which are locally variable quantities. Here, we present a statistically based method for calibrating SDR parameters that establishes a range for the estimated parameters and simultaneously estimates the uncertainty of the resulting K values. We used co‐located logging NMR and direct K measurements in an unconsolidated fluvial aquifer in Lawrence, Kansas, USA to demonstrate that K can be estimated using logging NMR to a similar level of uncertainty as with traditional direct hydraulic measurements in unconsolidated sediments under field conditions. Results of this study provide a benchmark for future calibrations of NMR to obtain K in unconsolidated sediments and suggest a method for evaluating uncertainty in both K and SDR parameter values.