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.     

NMR Logging to Estimate Hydraulic Conductivity in Unconsolidated Aquifers

Nuclear magnetic resonance (NMR) logging provides a new means of estimating the hydraulic conductivity (K) of unconsolidated aquifers. The estimation of K from the measured NMR parameters can be performed using the Schlumberger‐Doll Research (SDR) equation, which is based on the Kozeny–Carman equation and initially developed for obtaining permeability from NMR logging in petroleum reservoirs. The SDR equation includes empirically determined constants. Decades of research for petroleum applications have resulted in standard values for these constants that can provide accurate estimates of permeability in consolidated formations. The question we asked: Can standard values for the constants be defined for hydrogeologic applications that would yield accurate estimates of K in unconsolidated aquifers? Working at 10 locations at three field sites in Kansas and Washington, USA, we acquired NMR and K data using direct‐push methods over a 10‐ to 20‐m depth interval in the shallow subsurface. Analysis of pairs of NMR and K data revealed that we could dramatically improve K estimates by replacing the standard petroleum constants with new constants, optimal for estimating K in the unconsolidated materials at the field sites. Most significant was the finding that there was little change in the SDR constants between sites. This suggests that we can define a new set of constants that can be used to obtain high resolution, cost‐effective estimates of K from NMR logging in unconsolidated aquifers. This significant result has the potential to change dramatically the approach to determining K for hydrogeologic applications.     

Assessment of NMR Logging for Estimating Hydraulic Conductivity in Glacial Aquifers

Glacial aquifers are an important source of groundwater in the United States and require accurate characterization to make informed management decisions. One parameter that is crucial for understanding the movement of groundwater is hydraulic conductivity, K. Nuclear magnetic resonance (NMR) logging measures the NMR response associated with the water in geological materials. By utilizing an external magnetic field to manipulate the nuclear spins associated with ¹H, the time-varying decay of the nuclear magnetization is measured. This logging method could provide an effective way to estimate K at submeter vertical resolution, but the models that relate NMR measurements to K require calibration. At two field sites in a glacial aquifer in central Wisconsin, we collected a total of four NMR logs and obtained measurements of K in their immediate vicinity with a direct-push permeameter (DPP). Using a bootstrap algorithm to calibrate the Schlumberger-Doll Research (SDR) NMR-K model, we estimated K to within a factor of 5 of the DPP measurements. The lowest levels of accuracy occurred in the lower-K (K < 10⁻⁴ m/s) intervals. We also evaluated the applicability of prior SDR model calibrations. We found the NMR calibration parameters varied with K, suggesting the SDR model does not incorporate all the properties of the pore space that control K. Thus, the expected range of K in an aquifer may need to be considered during calibration of NMR-K models. This study is the first step toward establishing NMR logging as an effective method for estimating K in glacial aquifers.     

The Influence of Topology on Hydraulic Conductivity in a Sand-and-Gravel Aquifer

A field experiment consisting of geophysical logging and tracer testing was conducted in a single well that penetrated a sand-and-gravel aquifer at the U.S. Geological Survey Toxic Substances Hydrology research site on Cape Cod, Massachusetts. Geophysical logs and flowmeter/pumping measurements were obtained to estimate vertical profiles of porosity ϕ, hydraulic conductivity K, temperature, and bulk electrical conductivity under background, freshwater conditions. Saline-tracer fluid was then injected into the well for 2 h and its radial migration into the surrounding deposits was monitored by recording an electromagnetic-induction log every 10 min. The field data are analyzed and interpreted primarily through the use of Archie's (1942) law to investigate the role of topological factors such as pore geometry and connectivity, and grain size and packing configuration in regulating fluid flow through these coarse-grained materials. The logs reveal no significant correlation between K and ϕ, and imply that groundwater models that link these two properties may not be useful at this site. Rather, it is the distribution and connectivity of the fluid phase as defined by formation factor F, cementation index m, and tortuosity α that primarily control the hydraulic conductivity. Results show that F correlates well with K, thereby indicating that induction logs provide qualitative information on the distribution of hydraulic conductivity. A comparison of α, which incorporates porosity data, with K produces only a slightly better correlation and further emphasizes the weak influence of the bulk value of ϕ on K.     

Comparison of Hydraulic Conductivity Values Obtained from Aquifer Pumping Tests and Conservative Tracer Tests

Afield site was established in an area of glacial outwash near Des Moines, Iowa. Hydraulic conductivity (K) of the outwash was measured in various ways including six pumping tests and two natural-gradient Cl^- tracer tests. The velocity of the conservative tracer was converted to K using measured gradients and effective porosity determined from two radial-convergent Cl^- tracer tests.
K values measured from the conservative tracer tests are approximately one-tenth to one-twentieth the average pumping-test value. Thus the K relevant to solute transport does not reflect the K measured by pumping tests. This discrepancy may be caused by the different scale and dimensionality of the two test types. Dispersion may prevent solutes from flowing exclusively within smaller high-conductivity paths which strongly affect the K measured by pumping tests.     

Effects of Improper Characterization of Aquifer Thickness on Estimates of Hydraulic Conductivity from Pumping Tests

Pumping test data for surficial aquifers are commonly analyzed under the assumption that the base of the aquifer corresponds to the bottom of the test wells (i.e., the aquifer is truncated). This practice can lead to inaccurate hydraulic conductivity estimates, resulting from the use of low saturated thickness values with transmissivity estimates, and not accounting for the effects of partially penetrating wells. Theoretical time-drawdown data were generated at an observation well in a hypothetical unconfined aquifer for various values of saturated thickness and were analyzed by standard curve-matching techniques. The base of the aquifer was assumed to be the bottom of the pumping and observation wells. The overestimation of horizontal hydraulic conductivity was found to be directly proportional to the error in assumed saturated thickness, and to the (actual) ratio of vertical to horizontal hydraulic conductivity (K_v/K_h). Inaccurately high estimates of hydraulic conductivity obtained by aquifer truncation can lead to overestimates of ground water velocity and contaminant plume spreading, narrow capture zone configuration estimates, and overestimates of available ground water resources.     

Near Surface Electrical Characterization of Hydraulic Conductivity: From Petrophysical Properties to Aquifer Geometries—A Review

This paper reviews the recent geophysical literature addressing the estimation of saturated hydraulic conductivity (K) from static low frequency electrical measurements (electrical resistivity, induced polarization (IP) and spectral induced polarization (SIP)). In the first part of this paper, research describing how petrophysical relations between electrical properties and effective (i.e. controlling fluid transport) properties of (a) the interconnected pore volumes and interconnected pore surfaces, have been exploited to estimate K at both the core and field scale is reviewed. We start with electrical resistivity measurements, which are shown to be inherently limited in K estimation as, although resistivity is sensitive to both pore volume and pore surface area properties, the two contributions cannot be separated. Efforts to utilize the unique sensitivity of IP and SIP measurements to physical parameters that describe the interconnected pore surface area are subsequently introduced and the incorporation of such data into electrical based Kozeny–Carman type models of K estimation is reviewed. In the second part of this review, efforts to invert geophysical datasets for spatial patterns of K variability (e.g. aquifer geometries) at the field-scale are considered. Inversions, based on the conversion of an image of a geophysical property to a hydrological property assuming a valid petrophysical relationship, as well as joint/constrained inversion methods, whereby multiple geophysical and hydrological data are inverted simultaneously, are briefly covered. This review demonstrates that there currently exists an opportunity to link, (1) the petrophysics relating low frequency electrical measurements to effective hydraulic properties, with (2) the joint inversion strategies developed in recent years, in order to obtain more meaningful estimates of spatial patterns of K variability than previously reported.     

Measuring a Low Horizontal Hydraulic Gradient in a High Transmissivity Aquifer

High transmissivity aquifers typically have low hydraulic gradients (i.e., a flat water table). Measuring low gradients using water levels can be problematic because measurement error may be greater than the true difference in water levels (i.e., a low signal-to-noise ratio). In this study, the feasibility of measuring a hydraulic gradient in the range of 10⁻⁶ to 10⁻⁵ m/m was demonstrated. The study was performed at a site where the depth to water from land surface ranged from 40.1 to 94.2 m and the aquifer transmissivity was estimated at 41,300 m²/d (hydraulic conductivity of 18,800 m/d). The goals of the study were to reduce measurement error as much as practicable and assess the importance of factors affecting water level measurement accuracy. Well verticality was the largest source of error (0.000 to 0.168 m; median of 0.014 m), and geodetic survey of casing elevations was the next most important source of error (0.002 to 0.013 m; median of 0.005 m). Variability due to barometric pressure fluctuations was not an important factor at the site. Hydraulic heads were measured to an accuracy of ±0.0065 m, and the average hydraulic gradient was estimated to be 8.0 × 10⁻⁶ (±0.9 × 10⁻⁶) m/m. The improvement in accuracy allowed for two reversals in the groundwater flow direction to be identified, after which the gradient averaged 2.5 × 10⁻⁵ (±0.4 × 10⁻⁵) m/m. This study showed it is possible to sufficiently control sources of error to measure hydraulic gradients in the 10⁻⁶ to 10⁻⁵ m/m range.