NMR Logging to Estimate Hydraulic Conductivity in Unconsolidated Aquifers by Rosemary Knight1 , David O. Walsh2 , James J. Butler Jr.3 , Elliot Grunewald4 , Gaisheng Liu5 , Andrew D. Parsekian6 , Edward C. Reboulet7 , Steve Knobbe8 , and Mercer Barrows9
Abstract 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.
Introduction The evaluation, management, and protection of our groundwater resources require an ability to obtain reliable estimates of the subsurface properties that control the movement of fluids in the near-surface region (defined here as the uppermost ∼100 m below the surface). Estimates of these properties can be used for assessment of 1 Corresponding
author: Department of Geophysics, Stanford University, Stanford, CA 94305; 650-736-1487; [email protected] 2 Vista Clara Inc., 12201 Cyrus Way, Suite 104, Mukilteo, WA 98275; 425-493-8122; [email protected] 3 Kansas Geological Survey, University of Kansas, Lawrence, KS 66047; (785) 864–2116; [email protected] 4 Vista Clara Inc., 12201 Cyrus Way, Suite 104, Mukilteo, WA, 98275; [email protected] 5 Kansas Geological Survey, University of Kansas, Lawrence, KS 66047; (785) 864–2115; [email protected] 6 1000 E. University Ave., Dept. 3006, University of Wyoming, Laramie, WY 82071; (307) 766–3603; [email protected] 7 Kansas Geological Survey, University of Kansas, Lawrence, KS 66047; (785) 864–2173; [email protected] 8 Kansas Geological Survey, University of Kansas Lawrence, KS 66047; (785) 864–2111; [email protected] 9 6010 Canyonside Rd., La Crescenta, CA 91214; (818) 415–1913; [email protected] Received July 2014, accepted January 2015. © 2015, National Ground Water Association. doi: 10.1111/gwat.12324
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the production potential from aquifers, for the remediation and monitoring of contaminated sites, and for building predictive numerical models of subsurface flow. One such property is hydraulic conductivity (K ) that describes the ease with which water flows in the subsurface. Conventional methods for measuring K involve drilling boreholes, installing wells, and conducting hydraulic tests of varying levels of complexity. There has been considerable recent interest in the use of nuclear magnetic resonance (NMR) logging as a more cost-effective, highresolution method for estimating K in the saturated zone of the near-surface region. While well established as a logging method for obtaining permeability (k ) in petroleum applications, it is only in the last few years that field and laboratory studies have begun to explore the use of NMR logging for estimating K for near-surface applications (Dlubac et al. 2013; Walsh et al. 2013). Major impediments to the use of NMR logging have been the size of the petroleum-industry tools (could not easily fit into the small-diameter wells typically used in nearsurface hydrogeologic investigations), their complexity, and the cost of their use. The recent development of an NMR logging tool specifically designed for nearsurface applications (Walsh et al. 2013) has made NMR logging practical and cost-effective for hydrogeologic applications and triggered significant interest in this technology. NMR logging can be performed in an open
Vol. 54, No. 1–Groundwater–January-February 2016 (pages 104–114)
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hole, or in wells cased with PVC, fiberglass, or other nonconductive materials without suffering any influence from the casing material; the casing does not intersect the sensitive zone of the tool. Logging in steel-cased wells is not possible because the magnetic and conductive properties of the steel block the transmission of the direct current and radiofrequency magnetic fields used to make the measurement. NMR logging tools were first developed in the 1960s for petroleum applications. This was followed by more than 20 years of research to determine how to obtain accurate k estimates from the measured parameters, NMR relaxation times. NMR logging tools were operated by major service and petroleum companies, so a large number of NMR data sets and auxiliary data were available, along with the financial incentive, to dedicate significant resources to further technological developments. What resulted was widespread adoption of the SchlumbergerDoll Research (SDR) equation (Kenyon et al. 1988). The SDR equation contains three empirical constants in the expression relating the NMR measurement to k . If a high level of accuracy is required, site-specific values for these constants are determined by calibrating the NMR-derived k values with permeability estimates obtained with other methods (typically using results from well tests or core samples). Ultimately, the more than 20 years of research have resulted in standard values for these constants that yield reliable estimates of k in sandstones, without the need for local calibration. A recent study of NMR logging in unconsolidated to semi-consolidated near-surface materials (with occasional layers of sandstone and siltstone) found that the use of the SDR equation with the standard constants for sandstone did not provide accurate estimates of k , underestimating k by one to two orders of magnitude (Dlubac et al. 2013). The proposed explanation was that the standard constants were empirically determined using NMR logging and laboratory measurements on consolidated reservoir rocks, not unconsolidated to semi-consolidated near-surface materials. The question that motivated this current study was: For the assessment of near-surface unconsolidated aquifers, do we need site-specific calibration of NMR logging at every site or can we develop, as has been done for petroleum applications, a set of standard constants that provide acceptable accuracy in the NMR-derived estimates of K ? Such a finding would make NMR logging an extremely valuable tool for characterizing groundwater systems. Over the past 3 years, we completed an extensive field study to explore the link between NMR logging and K in unconsolidated near-surface materials. Working at three field sites, two in Kansas and one in Washington, USA, we acquired logs of NMR and K measurements at a total of 10 locations. Initial work at one of the field sites allowed us to develop a statistically based method for calibrating NMR and K measurements to determine the optimal values for the empirical constants (Parsekian et al. 2015). In this study, we used that approach to analyze data from all 10 locations. We present a set of constants
that we suggest could be the standard constants for shallow unconsolidated aquifers. This finding significantly advances the use of NMR logging as a means of determining K for hydrogeologic applications.
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Estimates of Permeability and Hydraulic Conductivity from NMR Logging Measurements NMR is a phenomenon where the nuclei of atoms with an odd number of protons or neutrons are able to absorb and transmit energy at a particular frequency. The odd number results in the formation of a nuclear magnetic moment associated with the nucleus that will respond to perturbations in a magnetic field. For most geologic applications, hydrogen is the atom of interest due to its presence in water and hydrocarbons. In this study, we use NMR logging to measure the response of the hydrogen nuclei in the water-filled region of the pore space of unconsolidated sediments in the shallow subsurface. Details of the NMR logging measurement can be found in the books by Coates et al. (1999) and Dunn et al. (2002). What is obtained from the measurement is an estimate of the water-filled porosity and the NMR relaxation time T 2 of the pore water. The magnitude of T 2 reflects relaxation processes occurring in the bulk pore water and at the surface of the pore space, providing sensitivity of the NMR measurement to the geometry of the pore space. In general, longer relaxation times are observed in larger pores and shorter relaxation times are observed in smaller pores. As such, a measured relaxation time distribution can be related to the distribution of pore sizes in the sampled geologic material. The distribution of relaxation times is often represented using the arithmetic mean of log T 2 , T 2ML , and displayed in a plot using the log T 2ML values. The precise scaling relationship between T 2 and pore size can vary in different lithologies. The key factors that influence this relationship include the geochemistry of the solid surface and the geometry of the pore space. In fine- to medium-grained materials with relatively small pores, surface relaxation tends to occur in the so-called fast-diffusion regime (defined by Brownstein and Tarr 1979), where the scaling between T 2 and pore size is given by the surface relaxivity ρ. The magnitude of ρ has been shown experimentally to be related to the concentration and mineralogy of paramagnetic species on the surface of the pore space (Foley et al. 1996; Bryar et al. 2000; Keating and Knight 2007, 2008, 2010). In coarser materials with relatively large pores, or in materials with high ρ, relaxation occurs in the slowdiffusion regime (defined by Brownstein and Tarr 1979), and is simply controlled by the pore dimension or distance a water molecule must diffuse to reach the pore surface. In very coarse and clean materials, the relaxation in the bulk pore water can become the dominant mechanism. The SDR equation, widely used in petroleum applications to estimate k from NMR logging T 2 measurements, is derived assuming that relaxation occurs in the 105
fast diffusion regime and that bulk-fluid relaxation can be neglected. T 2ML can then be related to the geometry of the pore space as shown in the following expression (Brownstein and Tarr 1979): 1 S =ρ T2ML V
(1)
where S /V is the surface area-to-volume ratio of the pore space. The derivation of the SDR equation adapts the Kozeny–Carman equation (Kozeny 1927; Carman 1956) that relates k of a material to its porosity and S/V . Porosity −1 is obtained from the NMR measurement and T2ML is substituted for the term representing S /V leading to the SDR equation (Kenyon et al. 1988, Straley et al. 1997): kNMR = b φ m (T2ML )n
(2)
where k NMR is the estimated permeability from the NMR data, φ is the NMR-determined porosity (with φ < 1.0), and b, m, and n are empirically determined constants. The exponent n is typically set equal to 2 to be consistent with the exponent on S /V in the Kozeny–Carman equation. When applied to NMR logging in consolidated sandstone reservoirs for petroleum applications, the standard set of constants for estimating permeability in units of millidarcies with T 2ML given in units of milliseconds and n = 2 are: b = 4 mD/ms2 and m = 4 but can vary with local conditions (Allen et al. 2000). The constant b, which is referred to as the lithologic constant, contains information about ρ and all the parameters affecting permeability other than porosity and S /V (e.g., tortuosity). It has been found to range from 4 to 5 mD/ms2 in laboratory studies on consolidated sandstones (Kenyon 1997; Straley et al. 1997) and was found to be 0.1 mD/ms2 for carbonates (Kenyon et al. 1995). While the standard set of constants are commonly used to obtain k, sitespecific calibration can be performed by comparing NMR logs with direct measurements of permeability obtained through other means when high accuracy is required. We can write the SDR equation in terms of hydraulic conductivity K : KNMR = b φ m (T2ML )2
(3)
where K NMR is the value of K estimated from the NMR data. We can then convert the standard constants for reservoir sandstones to the values that they would have if estimating K in units of m/s for a water temperature of 15 ◦ C (used to calculate density and viscosity to convert from permeability to K ) from T 2ML in units of seconds. The standard values become b = 3.4 × 10−2 m/s3 and m = 4. In the study by Dlubac et al. (2013), use of these values in the SDR equation led to estimates of K that were off by up to two orders of magnitude from the values of K measured with flowmeter logging. When the flowmeter data were used to calibrate the SDR equation, the optimal values for the constants for prediction of K in units of m/s from T 2ML in units of seconds were found to 106
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be: b = 2.4 × 10−2 m/s3 , m = 2; or for prediction of k in millidarcies from T 2ML in milliseconds, b decreased from the standard value of 4 to 2.9, and m decreased from the standard value of 4 to 2. When the SDR equation was used with these parameters, the K values estimated from NMR and measured with flowmeter logging showed very good agreement. When the calibration was repeated for the two other commonly used values of m, the following constants were found: m = 1, b = 8.0 × 10−3 m/s3 ; m = 4, b = 2.1 × 10−1 m/s3 (Dlubac et al. 2013). The lithologic constant was increased by an order of magnitude from the standard value with m = 4. The use of the SDR equation with the standard petroleum constants would therefore, on average, underestimate the true K by at least an order of magnitude. The need to calibrate the SDR equation is due to the fact that it is based on the Kozeny–Carman equation, which itself requires calibration to obtain accurate estimates of k . The Kozeny–Carman equation predicts k from measured values of porosity and S /V . The effects of all other properties likely to impact k , such as tortuosity, pore connectivity, and distribution of pore sizes, are lumped into a single parameter. The calibration of both the SDR and Kozeny-Carman equations is a practical way to account for these other properties that may vary among different geological materials but cannot be readily measured or quantified. The other consideration in calibration is variation in the relationship between the measured NMR parameter T 2ML and pore-scale properties. In the derivation of the SDR equation, the S /V term in the Kozeny–Carman −1 . As discussed equation is simply replaced with T2ML before, the precise scaling relationship between T 2ML and pore geometry can vary depending on the surface relaxivity and diffusion regime. The surface geochemistry, and thus ρ, can be highly variable (Kenyon et al. 1988; Howard et al. 1993; Kleinberg et al. 1994), as can the occurrence of fast- and slow-diffusion regimes. The calibration process is intended to account for these factors.
Data Acquisition at Field Sites NMR and K data were acquired at three field sites using direct-push (DP) methods. DP methods acquire high-resolution information about subsurface properties for environmental and engineering applications by driving an instrumented steel rod into the ground using hydraulic rams supplemented with vehicle weight and a highfrequency percussion hammer (McCall et al. 2005). The DP approach avoids the need to drill boreholes for well installation and the handling of drill cuttings, thus reducing the cost and potential environmental impact of subsurface characterization. The use of DP methods in this study gave us a cost-effective, high-resolution, minimal impact approach for obtaining a large set of NMR and K data. The NMR data were acquired at the three field sites using NMR logging technology developed for groundwater applications; the logging tool is referred to NGWA.org
as the Javelin (Walsh et al. 2013). We used the version of the tool designed for deployment with DP technology. The DP NMR logging is performed as follows: (1) a DP machine is used to create a temporary boring by driving hollow 8.26 cm (3.25 in) diameter rods to the maximum depth of investigation; (2) a 6.01 cm (2.38 in) diameter DP NMR logging tool is pushed down the center of the DP rods, using plastic pipe, until it contacts the expendable point at the bottom of the rods; (3) the NMR logging tool is deployed by holding the tool and expendable point in place while the DP rods are retracted about a meter upward, pushing the expendable drill point out the bottom of the drill rods and exposing the lower portion of the NMR probe to the formation (the tool has a collar at its top to prevent it from falling out of the drill point holder); and (4) NMR measurements are performed at 0.5m depth intervals as the DP machine is used to pull both the drill rods and the NMR tool up to the surface; the tool is paused for 5 to 10 min at each measurement depth to acquire the NMR data. Note that fresh water is added to the DP rods prior to and during tool deployment to create positive pressure so that the formation, specifically sand, will not move into the rods, preventing effective deployment. The NMR data acquired at each measurement depth are inverted to obtain the porosity, T 2 distribution, and a single T 2ML value for use in estimation of K . The DP NMR logging tool has a well-defined cylindrical NMR-sensitive zone surrounding the center of the tool. The vertical length of this shell and its radial distance from the center of the tool depend on tool size. The 6.1-cm (2.38 in) diameter tool used in this study has a sensitive shell (i.e., the NMR measurement domain) with a zone length of approximately 0.5 m, and a sensitive zone radial thickness of approximately 1 mm. This shell is at a radial distance of 14 to 15.25 cm (5.5 to 6.0 inches) from the center of the tool. Hydraulic conductivity at the three sites was measured using the DP permeameter (DPP) (Stienstra and van Deen 1994; Lowry et al. 1999; Butler et al. 2007a; Liu et al. 2012). The DPP consists of a short cylindrical screen with two pressure transducers inset into the probe at two distances above the screen. The DPP probe was advanced to the depth at which a K estimate was needed and then a series of short-term injection tests were performed; K was estimated from the spherical form of Darcy’s Law using the injection rate and the injectioninduced pressure responses at the two transducers (see equation 1a in Butler et al. 2007a). The resulting estimate is a weighted average over the vertical interval (approximately 0.4 m in the current tool) between the screen and the farthest transducer within a radial distance of approximately 0.5 m from the center of the tool; material outside of that interval has little influence (Liu et al. 2008). As discussed by Butler et al. (2007a) and Liu et al. (2012), the DPP has significant advantages over other DP or wellbased methods for determination of K . In this study, DPP measurements were made every 0.5 to 1.0 m, resulting in K measurements at the same depth (±0.15 m) as the DP-NMR measurements.
NMR and K data were acquired from three sites: the Geohydrologic Experimental and Monitoring Site (GEMS), a research site of the Kansas Geological Survey (KGS) located in the floodplain of the Kansas River just north of Lawrence, Kansas; the Larned Research Site of the KGS in west-central Kansas; and Leque Island in the Puget Sound lowlands of western Washington. These three sites were selected because (1) the unconsolidated nature of the subsurface was suitable for DP methods, (2) we had prior knowledge of the subsurface hydrostratigraphy, (3) the sites represented three hydrogeologically distinct settings, and (4) we had guaranteed access to the sites and permission to conduct the DP profiling. We note that at all sites we limited ourselves to working with materials with K greater than 1 × 10−8 m/s, as it is very time consuming to acquire DPP data in materials with lower K . GEMS has been the site of extensive research on flow and transport in heterogeneous formations for more than two decades (Butler 2005; Zemansky and McElwee 2005). In this study, we worked in an area, GEMS2, approximately 600 m northwest of the main GEMS site. The shallow subsurface at GEMS2 consists of 9.5 m of primarily clay and silt overlying 11.4 m of a mixture of sand and gravel (Liu et al. 2012); all of the shallow sediments were deposited in a fluvial depositional environment. Initial work was conducted at GEMS and GEMS2 to develop the calibration methods used in the current study (Parsekian et al. 2015). This preliminary work used borehole NMR logging data and multilevel slug test measurements of K in one well at GEMS and borehole NMR logging data in two wells at GEMS2 with adjacent DPP measurements of K . During that study, DPP measurements were also made at three locations for the purpose of assessing variance in the derived K estimate (see Parsekian et al. [2015] for details of that analysis). Our work at GEMS2 focused on the sand and gravel interval between approximately 10 and 20 m below land surface, which is hydraulically confined by the overlying clays and silts and is bounded below by limestone. DPNMR and DPP data were acquired in two areas, referred to as A and C, approximately 360 m apart. In the A Area, DP-NMR measurements were made at two locations, A11 and A1-2, separated by approximately 3 m. One set of DPP measurements were made at a location that was 5.4 m from A1-1 and 7.1 m from A1-2. In the C Area, DP-NMR measurements were acquired at three locations, C1-S, C1SE, and C1-SW, arranged in a triangle approximately 1 m on a side. These C Area DP-NMR data were calibrated to a DPP log located approximately 1 m to the north of this triangle. The Larned site is a research site developed by the KGS for the purpose of studying stream–aquifer interactions and riparian zone processes (Butler et al. 2007b). The depth region of interest at this site was the upper 10 m of sediments and consists of an upper sand and gravel interval, approximately 8 m in thickness, underlain by a 6-m thick clay aquitard. DP-NMR data were acquired at three locations: Larned E, Larned C, and Larned W. These three locations are roughly aligned: Larned C lies
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between the other two locations, 302 m from Larned E, and 430 m from Larned W. DPP logs were obtained, at each of the three locations, 1.5 m from where the DPNMR data were acquired. The Leque Island site served as the third field site for this project. Leque Island is located west of Stanwood, Washington, at the mouth of the Stillaguamish River. The site was historically an intertidal marshland, but was converted for agricultural use in the late 19th century through the construction of dikes. A previous hydrogeologic study of the Leque Island site by the Pacific Groundwater Group (2012) characterized the site as marsh sediments overlying up to 10 m of sandy alluvium, which is underlain by approximately 30 m of silty alluvium. DPNMR data were acquired at two locations, referred to as Leque E and Leque W, separated by 780 m. DPP data were acquired approximately 1 m from each DP-NMR measurement location.
Method Used in Data Analysis Our approach was to work with closest pairs of NMR and DPP data to determine the optimal values for the empirical constants in the SDR equation by minimizing the root mean square error (rmse) between log K NMR and log K DPP . We started with each NMR data point and defined a data pair by selecting the closest DPP data point that was at the same depth (±15 cm). If there was not a DPP data point available within that depth tolerance, we did not use the NMR data point in the calibration. Note that the lateral distance between the NMR data points and the corresponding DPP data points varied (as described before) at the 10 locations. We used the SDR equation with n = 2, then determined the optimal values for the lithologic constant (b) for commonly used values of m, 1, 2, and 4. We first worked with datasets containing NMR and DPP data pairs at each of the 10 locations to determine the optimal b values for the SDR equation for each location; then optimized at the level of each of the three field sites, using a dataset containing all the data pairs from all locations at each site to obtain site-specific values. Rather than using the typical optimization approach, which would yield one set of optimal constants for the one dataset containing all data pairs of interest, we used nonparametric bootstrap re-sampling (Efron 1979) to analyze the data following Parsekian et al. (2015). This approach utilizes a large number of random subsets of the K NMR and K DPP data pairs selected from a uniform distribution. Instead of a single optimal value for the SDR constant b for each m (=1, 2, 4), we obtained distributions of optimized SDR b values where the distributions represent the uncertainty in b. We estimated the minimum size of the subset by sensitivity analysis, increasing the size until the normalized standard deviation of b changed by less than 10%. We found this to be satisfied when the size of the subset reached 50% of the dataset size, so we used subsets of that size in all re-samplings of a dataset. We found that a total of 104 re-samplings of a dataset 108
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was able to capture the uncertainty because this number of re-sampling events is greater than the threshold where least-squares residuals become normally distributed (Gong 1986).
Results and Discussion Figure 1 shows examples of the NMR logging data from GEMS2 (Figure 1a), Larned (Figure 1b), and Leque Island (Figure 1c). Shown in the figure are the T 2 distributions and calculated T 2ML values; the latter were used to obtain K from the SDR equation (K NMR ). At all locations we also had DPP measurements of K (K DPP ). The white triangles indicate the depths where we had colocated (within 15 cm) NMR and DPP data that were used in the calibration. In Table 1, we list the b values obtained for each location at the field sites. Also given are the standard deviation (σ ), and the rmse between K NMR and K DPP . While the analysis was performed for values of m = 1, 2, and 4 in the SDR equation, we present the results obtained with m = 1, which provided the lowest rmse. In each case, the reported value is the most common value in the distribution obtained through the bootstrap analysis. As shown in Table 1, the b values range from 5 × 10−2 to 1.2 × 10−1 m/s3 . Of particular interest in this study was the question of transferability of the calibrated constants for the SDR equation. The location-specific calibration allowed us to assess this at the scale of one field site: Could we use calibration at one location to reliably predict K throughout a site? The predicted value of K , using the SDR equation, is linearly related to the value of b. Therefore, the differences seen in b at the different locations indicate the error in the K prediction if the b value determined as optimal at one location is used to calculate K at another location. For example, the b value at GEMS2 A1-1 is approximately 50% greater than the value at GEMS2 C1-S. Therefore, if calibration of the SDR equation was conducted at location A1-1 and used to predict K at location C1-S, 350 m away, K would be 50% higher than predicted using the location-specific b value. In contrast, calibration of the SDR equation at GEMS2 A1-2 would allow us to predict K at C1-SE, also 350 m away, as accurately as we would using the location-specific b value because the same b value was determined for both locations. When we consider the variability in b at each of the three sites, we see similar results: maximum difference in b at any of the sites is about 50%. The ability to predict K within 50% is certainly within the level of accuracy typically expected in estimates of K for hydrogeologic applications. The ultimate objective in this study was not just to explore the transferability of the calibration at the scale of an individual field site, but to address a more critical question: Can we define standard SDR constants that could be used to estimate K from NMR logging in unconsolidated aquifers, regardless of their geographic location? If this were the case, NMR logging could NGWA.org
Figure 1. Examples of acquired NMR data. At each depth, the color displays the distribution of NMR relaxation times, T 2 , where warm colors correspond to high amplitudes. The open circles connected by the solid line indicate T 2ML . (a) Example of NMR data from GEMS2. These data were acquired at location GEMS A1-1. (b) Example of NMR data from Larned. These data were acquired at location Larned C. (c) Example of NMR data from Leque Island. These data were acquired at location Leque East. White triangles show data used in calibration.
Table 1 Value of b for Each Location with Standard Deviation and Root Mean Square Error Location GEMS2 A1-1 GEMS2 A1-2 GEMS2 C1-S GEMS2 C1-SE GEMS2 C1-SW Larned E Larned C Larned W Leque E Leque W
b (m/s3 )
σ (m/s3 )
rmse (m/s)
0.12 0.11 0.08 0.11 0.09 0.11 0.11 0.05 0.11 0.06
0.044 0.031 0.053 0.078 0.064 0.074 0.091 0.025 0.050 0.035
0.0001 0.0004 0.0020 0.0025 0.0021 0.0006 0.0011 0.0001 0.0007 0.0015
Figure 2. Distribution of b values obtained for GEMS2 A1-2.
become a valuable new method for obtaining K estimates for hydrogeologic applications in the same way that it has been widely adopted and accepted as a reliable measure of permeability for petroleum applications. Shown in Table 2
are the b values determined through calibration at the scale of the field site for each of the three sites. In conducting the site-scale calibration, the analyzed data set for each site included the K NMR and K DPP data pairs from all of the locations at that site. We find little difference in the b values at the three sites: 9 × 10−2 m/s3 for the GEMS2 site and 8 × 10−2 m/s3 for both the Larned site and the Leque Island site. The close similarity in the b values suggests that all the parameters affecting the T 2ML –K relationship other than porosity and S /V (e.g., tortuosity, pore connectivity, distribution of pore sizes, and grain surface geochemistry) have a relatively constant impact on the K of sand and gravel across the different unconsolidated sites. This is a very significant result, suggesting that it may be possible to define, as has been done for petroleum applications, standard constants that can be used to obtain reliable estimates of K from NMR
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Table 2 Value of b for Each Field Site with Standard Deviation and Root Mean Square Error Location GEMS2 site Larned site Leque site
b (m/s3 )
σ (m/s3 )
rmse (m/s)
0.09 0.08 0.08
0.021 0.031 0.029
0.0023 0.0003 0.0023
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Figure 3. Distribution of b values obtained at each location at the three sites: (a) GEMS2, (b) Larned, and (c) Leque Island.
logging data in unconsolidated aquifers, without the need for site-specific calibration. An important component of this study was the way in which the calibration was conducted; it provides insights into the uncertainty in the b value obtained at each location. In Figure 2, we show as an example the distribution of b values obtained at the GEMS2 site, location A1-2. While b = 0.12 was reported as the most common value (the peak of the histogram), the range of
values from 0.087 to 0.131 all occurred at a similar high frequency; this range is very close to capturing the entire range of b values found at GEMS2. The distribution in b values can be used to quantify the uncertainty that would result in the K estimate at a location due to the uncertainty in the calibration of the SDR equation. In Figure 3, we show the distribution in b values obtained for all the locations at each of the three sites. The plots in Figure 3 are a graphic display of what is
Figure 4. Comparison at GEMS2 of K DPP and K NMR calculated using the SDR equation. (a) A1-1, (b) A1-2, (c) C1-S, (d) C1-SE, and (e) C1-SW. The dashed lines show the uncertainty in K NMR due to the distribution in b values (±1σ ).
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Figure 5. Comparison at Larned of K DPP and K NMR calculated using the SDR equation. (a) Larned E, (b) Larned C, (c) Larned W. The dashed lines show the uncertainty in K NMR due to the distribution in b values (±1σ ).
presented in Table 1; at any field site, there is very little variation in the optimal value of b across a site; both the peak values and the distributions are very similar at all locations. Comparing the data at the three field sites (i.e., comparing Figures 3a through c), we see the significant result that there is very little difference
in the b distributions from GEMS2, Larned and Leque Island. The b values from the GEMS2 site are in good agreement with those found during the work at three locations at GEMS and GEMS2 by Parsekian et al. (2015). The most common b values found in this previous study (0.05, 0.07, and 0.07) are slightly lower than the value of 0.09 for the GEMS2 site in this study, but the distributions overlap. We attribute the difference in the b values to the fact that different methods were used to acquire the NMR and K data. In the study by Parsekian et al. (2015), the NMR data were acquired using a borehole logging tool with K estimated in one case using multilevel slug tests and in the other two cases using DPP data. In this study, we used DP methods of sampling for NMR and K, resulting in very similar measurement conditions. We used the site-scale b values to compare K NMR and K DPP at all sampled depths at each of the locations. Figure 4 shows the results from GEMS2, Figure 5 shows the results from Larned, and Figure 6 shows the results from Leque Island. In all figures, both the K NMR and K DPP in each data pair are plotted at the measured depth of the NMR data. These estimates of K from the NMR data are calculated using the distribution of b values, which results in the uncertainty in K (i.e., ±1σ from the optimal b value) shown in the figures as dashed lines. In all cases, we see very good agreement between K NMR and K DPP . This approach to displaying uncertainty is not intended to capture measurement error in its entirety, but rather to illustrate that magnitude of error incurred in using a b value that is somewhat different from the optimal
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Figure 6. Comparison at Leque of K DPP and K NMR calculated using the SDR equation. (a) Leque E, (b) Leque W. The dashed lines show the uncertainty in K NMR due to the distribution in b values (±1σ ).
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Table 3 Compilation of b Values m =1 b (m/s3 )
Source of Values
Material Type
Standard constants for petroleum applications1 Petroleum applications, reported range2 Study of High Plains Aquifer3
Consolidated sandstones
This study—optimized for each location This study—optimized for each site
m =4 b (m/s3 ) 3.4 × 10−2 3.4 × 10−2 to 4.25 × 10−2 2.1 × 10−1
Consolidated sandstones Un/semi-consolidated sediments with minor sandstone and siltstone Unconsolidated sediments
5 × 10−2 to 1.2 × 10−1
8 × 10−1 to 5.7
Unconsolidated sediments
8 × 10−2 to 9 × 10−2
1.24 to 3.42
8.0
× 10−3
1 Allen et al. (2000). 2 Kenyon (1997) and Straley et al. (1997). 3 Dlubac et al. (2013) and Dlubac (2013).
value. This is the case that would be encountered when using global empirical constants rather than site-specific calibrated values. Our results highlight the dramatic improvement in estimating K that is realized by using the constants determined through our calibration, rather than simply using the standard values for b and m determined and used for petroleum applications. Use of those standard values would result in predictions that underestimate K by approximately two orders of magnitude. We suggest that this is due to the fact that those values were determined as optimal for consolidated sandstone reservoirs, while the b values obtained in this study are optimal for unconsolidated aquifers. In Table 3, we compare reported b values for the lithologic constant when m = 1, found to be the optimal result in this study, and for m = 4, the standard value for petroleum applications. The table includes the standard b values and reported range of values for consolidated sandstones for petroleum applications (Kenyon 1997; Straley et al. 1997); the values reported for the High Plains aquifer (Dlubac 2013; Dlubac et al. 2013); and the values found in this study. We observe that as the material type becomes more consolidated (from bottom to top of the table), b decreases by about an order of magnitude in going from unconsolidated to un/semi-consolidated material and then another order of magnitude in going to consolidated material. While more studies such as this are needed to provide additional data for Table 3, this study provides the significant first step needed in defining the constants that can be used to obtain estimates of K from NMR logging in unconsolidated aquifers.
Conclusions The NMR relaxation time measured during NMR logging can provide reliable estimates of K in sand and gravel aquifers, but equations used to obtain K require empirically determined constants. While standard values of the constants for sandstone reservoirs are widely used 112
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in petroleum applications, we found that the use of these values would underestimate K in unconsolidated aquifers by approximately two orders of magnitude. We worked at three sites, studying the top approximately 10 to 20 m of unconsolidated sediments at each site. Calibration at individual locations within a site showed some variability in the lithologic constant (b), but never greater than a difference of a factor of 2. The use of bootstrap analysis to conduct the calibration provided a distribution of the b values that allowed us to account for the uncertainty in K NMR due to the uncertainty in b. The most significant result of this study was the discovery that the optimal value of b was essentially the same at the three sites. This encouraging result suggests that it might be possible to determine a standard set of constants, as has been done for petroleum applications, for NMR determination of the hydraulic conductivity of near-surface sediments. In this study, we have used the SDR equation, the derivation of which assumes that relaxation occurs in the fast-diffusion regime. In sands and gravels, as the pore size increases, it is quite possible that this assumption would be violated and NMR relaxation would move into the slow-diffusion regime. The impact on the SDR equation, if relaxation occurs in the slow-diffusion regime, is to change the exponent on the T 2ML term from a value of 2 to 1. While there is no simple way to evaluate field data to determine the diffusion regime, it is straightforward to calibrate the SDR equation with the exponent equal to 2 or 1, and evaluate the agreement between the predicted and measured values of K . Improved agreement with the exponent equal to 1 would suggest the presence of slow diffusion; this form of the SDR equation and the corresponding b (as determined through calibration) could then be used to estimate K . A second assumption made in the derivation of the SDR equation is that bulk fluid relaxation is so slow, compared to T 2ML , that it can be neglected. But in materials with large pore sizes, such as well-sorted NGWA.org
gravels, T 2ML can approach the bulk fluid relaxation time of the pore water (∼1 to 3 s). In this case, the contribution of bulk fluid relaxation is likely to reduce the sensitivity of the T 2ML measurement to variations in K at large values. Recent technological advances have resulted in NMR logging systems ideally suited for application to nearsurface hydrogeologic problems (Walsh et al. 2013). As use of NMR logging increases, datasets such as the one presented here can be utilized to improve our understanding of the optimal way to transform acquired NMR logging data into estimates of hydraulic conductivity in unconsolidated aquifers. This, in turn, will help the hydrogeological community better realize the potential of this technology.
Allen, D., C. Flaum, T.S. Ramakrishnan, J. Bedford, K. Castelijns, C. Fairhurst, and R. Ramamoorthy. 2000. Trends in NMR logging. Oilfield Review 12, no. 3: 2–19. Brownstein, K.R., and C.E. Tarr. 1979. Importance of classical diffusion in NMR studies of water in biological cells. Physical Review 19, no. 6: 2446–2453. Bryar, T., C. Daughney, and R. Knight. 2000. Effects of paramagnetic iron (III) species on nuclear magnetic resonance relaxation of saturated sands. Journal of Magnetic Resonance 142: 74–85. Butler, J.J. Jr. 2005. Hydrogeological methods for estimation of hydraulic conductivity. In Hydrogeophysics, ed. Y. Rubin and S. Hubbard, 23–58. Dordrecht, The Netherlands: Springer. Butler, J.J. Jr., P. Dietrich, V. Wittig, and T. Christy. 2007a. Characterizing hydraulic conductivity with the direct-push permeameter. Ground Water 45, no. 4: 409–419. Butler, J.J. Jr., G.J. Kluitenberg, D.O. Whittemore, S.P. Loheide II, W. Jin, M.A. Billinger, and X. Zhan. 2007b. A field investigation of phreatophyte-induced fluctuations in the water table. Water Resources Research 43: W02404. DOI:10.1029/2005WR004627. Carman, P.C. 1956. Flow of Gases Through Porous Media. New York: Academic Press Inc. Coates, G.R., L. Xiao, and M.G. Prammer. 1999. NMR Logging Principles and Applications. Houston, Texas: Halliburton Energy Services. Dlubac, K. 2013. The relationship between nuclear magnetic resonance and permeability in near-surface unconsolidated materials. Ph.D. thesis, Stanford University. Dlubac, K., R. Knight, Y. Song, N. Bachman, B. Grau, J. Cannia, and J. Williams. 2013. The use of NMR logging
to obtain estimates of hydraulic conductivity in the high plains aquifer, Nebraska, USA. Water Resources Research 49: 1871–1886. DOI:10.1002/wrcr.20151. Dunn, K.J., D.J. Bergman, and G.A. Latorraca. 2002. Nuclear Magnetic Resonance—Petrophysical and Logging Applications. Pergamon Press. Efron, B. 1979. Bootstrap method: Another look at the jackknife. Ann. Stat. 7: 1–26. Foley, I., S.A. Farooqui, and R.L. Kleinberg. 1996. Effect of paramagnetic ions on NMR relaxation of fluids at solid surfaces. Journal of Magnetic Resonance 123: 95–104. Gong, S. 1986. Cross-validation, the jackknife, and the bootstrap: Excess error estimation in forward logistic regression. Journal of the American Statistical Association 81: 108–118. Howard, J.J., W.E. Kenyon, and C. Straley. 1993. Proton magnetic resonance and pore size variations in reservoir sandstones. SPE Formation Evaluation 8, no. 3: 194–200. Keating, K., and R. Knight. 2007. A laboratory study to determine the effect of iron-oxides on proton NMR measurements. Geophysics 72, no. 1: E27–E32. Keating, K., and R. Knight. 2008. A laboratory study of the effects of magnetite on NMR relaxation rates. Journal of Applied Geophysics 66: 188–196. Keating, K., and R. Knight. 2010. A laboratory study of the effect of Fe(II)-bearing minerals on NMR relaxation measurements. Geophysics 75: XF71–XF82. Kenyon, W.E. 1997. Petrophysical principles of applications of NMR logging. The Log Analyst 38, no. 2: 21–43. Kenyon, W.E., P.I. Day, C. Straley, and J.F. Willemsen. 1988. A three-part study of NMR longitudinal relaxation properties of water saturated sandstones. SPE Formation Evaluation 3: 622–636. Kenyon, W.E., R.L. Kleinberg, C. Straley, G. Gubelin, and C. Morriss. 1995. Nuclear magnetic resonance imaging—Technology for the 21st century. Oilfield Review 7, no. 3: 19–33. Kleinberg, R.L., W.E. Kenyon, and P.P. Mitra. 1994. Mechanism of NMR relaxation of fluids in rRock. Journal of Magnetic Resonance, Series A 108: 206–214. Kozeny, J. 1927. Uber kapillare Leitung des Wassers im Boden. Sitzungsberichte der Akademie der Wissenschaften in Wien 136: 271–306. Liu, G., G.C. Bohling, and J.J. Butler Jr. 2008. Simulation assessment of the direct-push permeameter for characterizing vertical variations in hydraulic conductivity. Water Resources Research 44: W02432. DOI:10.1029/2007WR006078. Liu, G., J.J. Butler Jr., E.C. Reboulet, and S. Knobbe. 2012. Hydraulic conductivity profiling with direct-push methods. Grundwasser 17: 19–29. DOI:10.1007/s00767-011-01829. Lowry, W., N. Mason, V. Chipman, K. Kisiel, and J. Stockton. 1999. In-situ permeability measurements with direct push techniques: Phase II topical report. SEASF-TR-98207 Report to DOE Federal Energy Technology Center, 102 pp. DOI:10.3997/1873-0604.2005023 McCall, W., D.M. Nielsen, S. Farrington, and T.M. Christy. 2005. Use of direct-push technologies in environmental site characterization and ground-water monitoring. In The Practical Handbook of Environmental Site Characterization and Groundwater Monitoring, 2nd ed., ed. D.M. Nielsen, 345–472. Boca Raton, Florida: CRC Press. Pacific Groundwater Group. 2012. Hydrogeologic evaluation of proposed Leque Island restoration. http://www.epa.gov/ region10/pdf/water/ssa/camano/ppg_leque_hg_eval_1212. pdf (accessed September 2013). Parsekian, A.D., K. Dlubac, E. Grunewald, J.J. Butler, R. Knight, and D.O. Walsh. 2015. Bootstrap calibration and uncertainty estimation of downhole NMR hydraulic conductivity
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Acknowledgments This material is based on work supported, in part, by the U.S. Department of Energy under Grant DESC0004623. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the Department of Energy. The authors thank the Washington Department of Fish and Wildlife for providing access to the Leque Island field site, and Mr. Tom Campbell for assistance with direct push drilling at the Leque Island field site. We also wish to thank the reviewers for their helpful comments.
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estimates in an unconsolidated aquifer. Groundwater 53, no. 1: 111–122. DOI:10.1111/gwat.12165. Stienstra, P., and J.K. van Deen. 1994. Field data collection techniques—Unconventional sounding and sampling methods. In Engineering Geology of Quaternary Sediments, ed. N. Rengers, 41–55. Balkema. Straley, C., D. Rossini, H.J. Vinegar, P. Tutunjian, and C.E. Morriss. 1997. Core analysis by low-field NMR. The Log Analyst 38, no. 2: 84–94.
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Walsh, D., P. Turner, E. Grunewald, H. Zhang, J.J. Butler, E. Reboulet, S. Knobbe, T. Christy, J.W. Lane, C.D. Johnson, T. Munday, and A. Fitzpatrick. 2013. A small-diameter NMR logging tool for groundwater investigations. Groundwater 51, no. 6: 914–926. DOI:10.1111/gwat.12024. Zemansky, G.M., and C.D. McElwee. 2005. High-resolution slug testing. Ground Water 43: 222–230. DOI:10.1111/j.17456584.2005.0008.x.
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Abstract 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.
Introduction The evaluation, management, and protection of our groundwater resources require an ability to obtain reliable estimates of the subsurface properties that control the movement of fluids in the near-surface region (defined here as the uppermost ∼100 m below the surface). Estimates of these properties can be used for assessment of 1 Corresponding
author: Department of Geophysics, Stanford University, Stanford, CA 94305; 650-736-1487; [email protected] 2 Vista Clara Inc., 12201 Cyrus Way, Suite 104, Mukilteo, WA 98275; 425-493-8122; [email protected] 3 Kansas Geological Survey, University of Kansas, Lawrence, KS 66047; (785) 864–2116; [email protected] 4 Vista Clara Inc., 12201 Cyrus Way, Suite 104, Mukilteo, WA, 98275; [email protected] 5 Kansas Geological Survey, University of Kansas, Lawrence, KS 66047; (785) 864–2115; [email protected] 6 1000 E. University Ave., Dept. 3006, University of Wyoming, Laramie, WY 82071; (307) 766–3603; [email protected] 7 Kansas Geological Survey, University of Kansas, Lawrence, KS 66047; (785) 864–2173; [email protected] 8 Kansas Geological Survey, University of Kansas Lawrence, KS 66047; (785) 864–2111; [email protected] 9 6010 Canyonside Rd., La Crescenta, CA 91214; (818) 415–1913; [email protected] Received July 2014, accepted January 2015. © 2015, National Ground Water Association. doi: 10.1111/gwat.12324
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the production potential from aquifers, for the remediation and monitoring of contaminated sites, and for building predictive numerical models of subsurface flow. One such property is hydraulic conductivity (K ) that describes the ease with which water flows in the subsurface. Conventional methods for measuring K involve drilling boreholes, installing wells, and conducting hydraulic tests of varying levels of complexity. There has been considerable recent interest in the use of nuclear magnetic resonance (NMR) logging as a more cost-effective, highresolution method for estimating K in the saturated zone of the near-surface region. While well established as a logging method for obtaining permeability (k ) in petroleum applications, it is only in the last few years that field and laboratory studies have begun to explore the use of NMR logging for estimating K for near-surface applications (Dlubac et al. 2013; Walsh et al. 2013). Major impediments to the use of NMR logging have been the size of the petroleum-industry tools (could not easily fit into the small-diameter wells typically used in nearsurface hydrogeologic investigations), their complexity, and the cost of their use. The recent development of an NMR logging tool specifically designed for nearsurface applications (Walsh et al. 2013) has made NMR logging practical and cost-effective for hydrogeologic applications and triggered significant interest in this technology. NMR logging can be performed in an open
Vol. 54, No. 1–Groundwater–January-February 2016 (pages 104–114)
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hole, or in wells cased with PVC, fiberglass, or other nonconductive materials without suffering any influence from the casing material; the casing does not intersect the sensitive zone of the tool. Logging in steel-cased wells is not possible because the magnetic and conductive properties of the steel block the transmission of the direct current and radiofrequency magnetic fields used to make the measurement. NMR logging tools were first developed in the 1960s for petroleum applications. This was followed by more than 20 years of research to determine how to obtain accurate k estimates from the measured parameters, NMR relaxation times. NMR logging tools were operated by major service and petroleum companies, so a large number of NMR data sets and auxiliary data were available, along with the financial incentive, to dedicate significant resources to further technological developments. What resulted was widespread adoption of the SchlumbergerDoll Research (SDR) equation (Kenyon et al. 1988). The SDR equation contains three empirical constants in the expression relating the NMR measurement to k . If a high level of accuracy is required, site-specific values for these constants are determined by calibrating the NMR-derived k values with permeability estimates obtained with other methods (typically using results from well tests or core samples). Ultimately, the more than 20 years of research have resulted in standard values for these constants that yield reliable estimates of k in sandstones, without the need for local calibration. A recent study of NMR logging in unconsolidated to semi-consolidated near-surface materials (with occasional layers of sandstone and siltstone) found that the use of the SDR equation with the standard constants for sandstone did not provide accurate estimates of k , underestimating k by one to two orders of magnitude (Dlubac et al. 2013). The proposed explanation was that the standard constants were empirically determined using NMR logging and laboratory measurements on consolidated reservoir rocks, not unconsolidated to semi-consolidated near-surface materials. The question that motivated this current study was: For the assessment of near-surface unconsolidated aquifers, do we need site-specific calibration of NMR logging at every site or can we develop, as has been done for petroleum applications, a set of standard constants that provide acceptable accuracy in the NMR-derived estimates of K ? Such a finding would make NMR logging an extremely valuable tool for characterizing groundwater systems. Over the past 3 years, we completed an extensive field study to explore the link between NMR logging and K in unconsolidated near-surface materials. Working at three field sites, two in Kansas and one in Washington, USA, we acquired logs of NMR and K measurements at a total of 10 locations. Initial work at one of the field sites allowed us to develop a statistically based method for calibrating NMR and K measurements to determine the optimal values for the empirical constants (Parsekian et al. 2015). In this study, we used that approach to analyze data from all 10 locations. We present a set of constants
that we suggest could be the standard constants for shallow unconsolidated aquifers. This finding significantly advances the use of NMR logging as a means of determining K for hydrogeologic applications.
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Estimates of Permeability and Hydraulic Conductivity from NMR Logging Measurements NMR is a phenomenon where the nuclei of atoms with an odd number of protons or neutrons are able to absorb and transmit energy at a particular frequency. The odd number results in the formation of a nuclear magnetic moment associated with the nucleus that will respond to perturbations in a magnetic field. For most geologic applications, hydrogen is the atom of interest due to its presence in water and hydrocarbons. In this study, we use NMR logging to measure the response of the hydrogen nuclei in the water-filled region of the pore space of unconsolidated sediments in the shallow subsurface. Details of the NMR logging measurement can be found in the books by Coates et al. (1999) and Dunn et al. (2002). What is obtained from the measurement is an estimate of the water-filled porosity and the NMR relaxation time T 2 of the pore water. The magnitude of T 2 reflects relaxation processes occurring in the bulk pore water and at the surface of the pore space, providing sensitivity of the NMR measurement to the geometry of the pore space. In general, longer relaxation times are observed in larger pores and shorter relaxation times are observed in smaller pores. As such, a measured relaxation time distribution can be related to the distribution of pore sizes in the sampled geologic material. The distribution of relaxation times is often represented using the arithmetic mean of log T 2 , T 2ML , and displayed in a plot using the log T 2ML values. The precise scaling relationship between T 2 and pore size can vary in different lithologies. The key factors that influence this relationship include the geochemistry of the solid surface and the geometry of the pore space. In fine- to medium-grained materials with relatively small pores, surface relaxation tends to occur in the so-called fast-diffusion regime (defined by Brownstein and Tarr 1979), where the scaling between T 2 and pore size is given by the surface relaxivity ρ. The magnitude of ρ has been shown experimentally to be related to the concentration and mineralogy of paramagnetic species on the surface of the pore space (Foley et al. 1996; Bryar et al. 2000; Keating and Knight 2007, 2008, 2010). In coarser materials with relatively large pores, or in materials with high ρ, relaxation occurs in the slowdiffusion regime (defined by Brownstein and Tarr 1979), and is simply controlled by the pore dimension or distance a water molecule must diffuse to reach the pore surface. In very coarse and clean materials, the relaxation in the bulk pore water can become the dominant mechanism. The SDR equation, widely used in petroleum applications to estimate k from NMR logging T 2 measurements, is derived assuming that relaxation occurs in the 105
fast diffusion regime and that bulk-fluid relaxation can be neglected. T 2ML can then be related to the geometry of the pore space as shown in the following expression (Brownstein and Tarr 1979): 1 S =ρ T2ML V
(1)
where S /V is the surface area-to-volume ratio of the pore space. The derivation of the SDR equation adapts the Kozeny–Carman equation (Kozeny 1927; Carman 1956) that relates k of a material to its porosity and S/V . Porosity −1 is obtained from the NMR measurement and T2ML is substituted for the term representing S /V leading to the SDR equation (Kenyon et al. 1988, Straley et al. 1997): kNMR = b φ m (T2ML )n
(2)
where k NMR is the estimated permeability from the NMR data, φ is the NMR-determined porosity (with φ < 1.0), and b, m, and n are empirically determined constants. The exponent n is typically set equal to 2 to be consistent with the exponent on S /V in the Kozeny–Carman equation. When applied to NMR logging in consolidated sandstone reservoirs for petroleum applications, the standard set of constants for estimating permeability in units of millidarcies with T 2ML given in units of milliseconds and n = 2 are: b = 4 mD/ms2 and m = 4 but can vary with local conditions (Allen et al. 2000). The constant b, which is referred to as the lithologic constant, contains information about ρ and all the parameters affecting permeability other than porosity and S /V (e.g., tortuosity). It has been found to range from 4 to 5 mD/ms2 in laboratory studies on consolidated sandstones (Kenyon 1997; Straley et al. 1997) and was found to be 0.1 mD/ms2 for carbonates (Kenyon et al. 1995). While the standard set of constants are commonly used to obtain k, sitespecific calibration can be performed by comparing NMR logs with direct measurements of permeability obtained through other means when high accuracy is required. We can write the SDR equation in terms of hydraulic conductivity K : KNMR = b φ m (T2ML )2
(3)
where K NMR is the value of K estimated from the NMR data. We can then convert the standard constants for reservoir sandstones to the values that they would have if estimating K in units of m/s for a water temperature of 15 ◦ C (used to calculate density and viscosity to convert from permeability to K ) from T 2ML in units of seconds. The standard values become b = 3.4 × 10−2 m/s3 and m = 4. In the study by Dlubac et al. (2013), use of these values in the SDR equation led to estimates of K that were off by up to two orders of magnitude from the values of K measured with flowmeter logging. When the flowmeter data were used to calibrate the SDR equation, the optimal values for the constants for prediction of K in units of m/s from T 2ML in units of seconds were found to 106
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be: b = 2.4 × 10−2 m/s3 , m = 2; or for prediction of k in millidarcies from T 2ML in milliseconds, b decreased from the standard value of 4 to 2.9, and m decreased from the standard value of 4 to 2. When the SDR equation was used with these parameters, the K values estimated from NMR and measured with flowmeter logging showed very good agreement. When the calibration was repeated for the two other commonly used values of m, the following constants were found: m = 1, b = 8.0 × 10−3 m/s3 ; m = 4, b = 2.1 × 10−1 m/s3 (Dlubac et al. 2013). The lithologic constant was increased by an order of magnitude from the standard value with m = 4. The use of the SDR equation with the standard petroleum constants would therefore, on average, underestimate the true K by at least an order of magnitude. The need to calibrate the SDR equation is due to the fact that it is based on the Kozeny–Carman equation, which itself requires calibration to obtain accurate estimates of k . The Kozeny–Carman equation predicts k from measured values of porosity and S /V . The effects of all other properties likely to impact k , such as tortuosity, pore connectivity, and distribution of pore sizes, are lumped into a single parameter. The calibration of both the SDR and Kozeny-Carman equations is a practical way to account for these other properties that may vary among different geological materials but cannot be readily measured or quantified. The other consideration in calibration is variation in the relationship between the measured NMR parameter T 2ML and pore-scale properties. In the derivation of the SDR equation, the S /V term in the Kozeny–Carman −1 . As discussed equation is simply replaced with T2ML before, the precise scaling relationship between T 2ML and pore geometry can vary depending on the surface relaxivity and diffusion regime. The surface geochemistry, and thus ρ, can be highly variable (Kenyon et al. 1988; Howard et al. 1993; Kleinberg et al. 1994), as can the occurrence of fast- and slow-diffusion regimes. The calibration process is intended to account for these factors.
Data Acquisition at Field Sites NMR and K data were acquired at three field sites using direct-push (DP) methods. DP methods acquire high-resolution information about subsurface properties for environmental and engineering applications by driving an instrumented steel rod into the ground using hydraulic rams supplemented with vehicle weight and a highfrequency percussion hammer (McCall et al. 2005). The DP approach avoids the need to drill boreholes for well installation and the handling of drill cuttings, thus reducing the cost and potential environmental impact of subsurface characterization. The use of DP methods in this study gave us a cost-effective, high-resolution, minimal impact approach for obtaining a large set of NMR and K data. The NMR data were acquired at the three field sites using NMR logging technology developed for groundwater applications; the logging tool is referred to NGWA.org
as the Javelin (Walsh et al. 2013). We used the version of the tool designed for deployment with DP technology. The DP NMR logging is performed as follows: (1) a DP machine is used to create a temporary boring by driving hollow 8.26 cm (3.25 in) diameter rods to the maximum depth of investigation; (2) a 6.01 cm (2.38 in) diameter DP NMR logging tool is pushed down the center of the DP rods, using plastic pipe, until it contacts the expendable point at the bottom of the rods; (3) the NMR logging tool is deployed by holding the tool and expendable point in place while the DP rods are retracted about a meter upward, pushing the expendable drill point out the bottom of the drill rods and exposing the lower portion of the NMR probe to the formation (the tool has a collar at its top to prevent it from falling out of the drill point holder); and (4) NMR measurements are performed at 0.5m depth intervals as the DP machine is used to pull both the drill rods and the NMR tool up to the surface; the tool is paused for 5 to 10 min at each measurement depth to acquire the NMR data. Note that fresh water is added to the DP rods prior to and during tool deployment to create positive pressure so that the formation, specifically sand, will not move into the rods, preventing effective deployment. The NMR data acquired at each measurement depth are inverted to obtain the porosity, T 2 distribution, and a single T 2ML value for use in estimation of K . The DP NMR logging tool has a well-defined cylindrical NMR-sensitive zone surrounding the center of the tool. The vertical length of this shell and its radial distance from the center of the tool depend on tool size. The 6.1-cm (2.38 in) diameter tool used in this study has a sensitive shell (i.e., the NMR measurement domain) with a zone length of approximately 0.5 m, and a sensitive zone radial thickness of approximately 1 mm. This shell is at a radial distance of 14 to 15.25 cm (5.5 to 6.0 inches) from the center of the tool. Hydraulic conductivity at the three sites was measured using the DP permeameter (DPP) (Stienstra and van Deen 1994; Lowry et al. 1999; Butler et al. 2007a; Liu et al. 2012). The DPP consists of a short cylindrical screen with two pressure transducers inset into the probe at two distances above the screen. The DPP probe was advanced to the depth at which a K estimate was needed and then a series of short-term injection tests were performed; K was estimated from the spherical form of Darcy’s Law using the injection rate and the injectioninduced pressure responses at the two transducers (see equation 1a in Butler et al. 2007a). The resulting estimate is a weighted average over the vertical interval (approximately 0.4 m in the current tool) between the screen and the farthest transducer within a radial distance of approximately 0.5 m from the center of the tool; material outside of that interval has little influence (Liu et al. 2008). As discussed by Butler et al. (2007a) and Liu et al. (2012), the DPP has significant advantages over other DP or wellbased methods for determination of K . In this study, DPP measurements were made every 0.5 to 1.0 m, resulting in K measurements at the same depth (±0.15 m) as the DP-NMR measurements.
NMR and K data were acquired from three sites: the Geohydrologic Experimental and Monitoring Site (GEMS), a research site of the Kansas Geological Survey (KGS) located in the floodplain of the Kansas River just north of Lawrence, Kansas; the Larned Research Site of the KGS in west-central Kansas; and Leque Island in the Puget Sound lowlands of western Washington. These three sites were selected because (1) the unconsolidated nature of the subsurface was suitable for DP methods, (2) we had prior knowledge of the subsurface hydrostratigraphy, (3) the sites represented three hydrogeologically distinct settings, and (4) we had guaranteed access to the sites and permission to conduct the DP profiling. We note that at all sites we limited ourselves to working with materials with K greater than 1 × 10−8 m/s, as it is very time consuming to acquire DPP data in materials with lower K . GEMS has been the site of extensive research on flow and transport in heterogeneous formations for more than two decades (Butler 2005; Zemansky and McElwee 2005). In this study, we worked in an area, GEMS2, approximately 600 m northwest of the main GEMS site. The shallow subsurface at GEMS2 consists of 9.5 m of primarily clay and silt overlying 11.4 m of a mixture of sand and gravel (Liu et al. 2012); all of the shallow sediments were deposited in a fluvial depositional environment. Initial work was conducted at GEMS and GEMS2 to develop the calibration methods used in the current study (Parsekian et al. 2015). This preliminary work used borehole NMR logging data and multilevel slug test measurements of K in one well at GEMS and borehole NMR logging data in two wells at GEMS2 with adjacent DPP measurements of K . During that study, DPP measurements were also made at three locations for the purpose of assessing variance in the derived K estimate (see Parsekian et al. [2015] for details of that analysis). Our work at GEMS2 focused on the sand and gravel interval between approximately 10 and 20 m below land surface, which is hydraulically confined by the overlying clays and silts and is bounded below by limestone. DPNMR and DPP data were acquired in two areas, referred to as A and C, approximately 360 m apart. In the A Area, DP-NMR measurements were made at two locations, A11 and A1-2, separated by approximately 3 m. One set of DPP measurements were made at a location that was 5.4 m from A1-1 and 7.1 m from A1-2. In the C Area, DP-NMR measurements were acquired at three locations, C1-S, C1SE, and C1-SW, arranged in a triangle approximately 1 m on a side. These C Area DP-NMR data were calibrated to a DPP log located approximately 1 m to the north of this triangle. The Larned site is a research site developed by the KGS for the purpose of studying stream–aquifer interactions and riparian zone processes (Butler et al. 2007b). The depth region of interest at this site was the upper 10 m of sediments and consists of an upper sand and gravel interval, approximately 8 m in thickness, underlain by a 6-m thick clay aquitard. DP-NMR data were acquired at three locations: Larned E, Larned C, and Larned W. These three locations are roughly aligned: Larned C lies
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between the other two locations, 302 m from Larned E, and 430 m from Larned W. DPP logs were obtained, at each of the three locations, 1.5 m from where the DPNMR data were acquired. The Leque Island site served as the third field site for this project. Leque Island is located west of Stanwood, Washington, at the mouth of the Stillaguamish River. The site was historically an intertidal marshland, but was converted for agricultural use in the late 19th century through the construction of dikes. A previous hydrogeologic study of the Leque Island site by the Pacific Groundwater Group (2012) characterized the site as marsh sediments overlying up to 10 m of sandy alluvium, which is underlain by approximately 30 m of silty alluvium. DPNMR data were acquired at two locations, referred to as Leque E and Leque W, separated by 780 m. DPP data were acquired approximately 1 m from each DP-NMR measurement location.
Method Used in Data Analysis Our approach was to work with closest pairs of NMR and DPP data to determine the optimal values for the empirical constants in the SDR equation by minimizing the root mean square error (rmse) between log K NMR and log K DPP . We started with each NMR data point and defined a data pair by selecting the closest DPP data point that was at the same depth (±15 cm). If there was not a DPP data point available within that depth tolerance, we did not use the NMR data point in the calibration. Note that the lateral distance between the NMR data points and the corresponding DPP data points varied (as described before) at the 10 locations. We used the SDR equation with n = 2, then determined the optimal values for the lithologic constant (b) for commonly used values of m, 1, 2, and 4. We first worked with datasets containing NMR and DPP data pairs at each of the 10 locations to determine the optimal b values for the SDR equation for each location; then optimized at the level of each of the three field sites, using a dataset containing all the data pairs from all locations at each site to obtain site-specific values. Rather than using the typical optimization approach, which would yield one set of optimal constants for the one dataset containing all data pairs of interest, we used nonparametric bootstrap re-sampling (Efron 1979) to analyze the data following Parsekian et al. (2015). This approach utilizes a large number of random subsets of the K NMR and K DPP data pairs selected from a uniform distribution. Instead of a single optimal value for the SDR constant b for each m (=1, 2, 4), we obtained distributions of optimized SDR b values where the distributions represent the uncertainty in b. We estimated the minimum size of the subset by sensitivity analysis, increasing the size until the normalized standard deviation of b changed by less than 10%. We found this to be satisfied when the size of the subset reached 50% of the dataset size, so we used subsets of that size in all re-samplings of a dataset. We found that a total of 104 re-samplings of a dataset 108
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was able to capture the uncertainty because this number of re-sampling events is greater than the threshold where least-squares residuals become normally distributed (Gong 1986).
Results and Discussion Figure 1 shows examples of the NMR logging data from GEMS2 (Figure 1a), Larned (Figure 1b), and Leque Island (Figure 1c). Shown in the figure are the T 2 distributions and calculated T 2ML values; the latter were used to obtain K from the SDR equation (K NMR ). At all locations we also had DPP measurements of K (K DPP ). The white triangles indicate the depths where we had colocated (within 15 cm) NMR and DPP data that were used in the calibration. In Table 1, we list the b values obtained for each location at the field sites. Also given are the standard deviation (σ ), and the rmse between K NMR and K DPP . While the analysis was performed for values of m = 1, 2, and 4 in the SDR equation, we present the results obtained with m = 1, which provided the lowest rmse. In each case, the reported value is the most common value in the distribution obtained through the bootstrap analysis. As shown in Table 1, the b values range from 5 × 10−2 to 1.2 × 10−1 m/s3 . Of particular interest in this study was the question of transferability of the calibrated constants for the SDR equation. The location-specific calibration allowed us to assess this at the scale of one field site: Could we use calibration at one location to reliably predict K throughout a site? The predicted value of K , using the SDR equation, is linearly related to the value of b. Therefore, the differences seen in b at the different locations indicate the error in the K prediction if the b value determined as optimal at one location is used to calculate K at another location. For example, the b value at GEMS2 A1-1 is approximately 50% greater than the value at GEMS2 C1-S. Therefore, if calibration of the SDR equation was conducted at location A1-1 and used to predict K at location C1-S, 350 m away, K would be 50% higher than predicted using the location-specific b value. In contrast, calibration of the SDR equation at GEMS2 A1-2 would allow us to predict K at C1-SE, also 350 m away, as accurately as we would using the location-specific b value because the same b value was determined for both locations. When we consider the variability in b at each of the three sites, we see similar results: maximum difference in b at any of the sites is about 50%. The ability to predict K within 50% is certainly within the level of accuracy typically expected in estimates of K for hydrogeologic applications. The ultimate objective in this study was not just to explore the transferability of the calibration at the scale of an individual field site, but to address a more critical question: Can we define standard SDR constants that could be used to estimate K from NMR logging in unconsolidated aquifers, regardless of their geographic location? If this were the case, NMR logging could NGWA.org
Figure 1. Examples of acquired NMR data. At each depth, the color displays the distribution of NMR relaxation times, T 2 , where warm colors correspond to high amplitudes. The open circles connected by the solid line indicate T 2ML . (a) Example of NMR data from GEMS2. These data were acquired at location GEMS A1-1. (b) Example of NMR data from Larned. These data were acquired at location Larned C. (c) Example of NMR data from Leque Island. These data were acquired at location Leque East. White triangles show data used in calibration.
Table 1 Value of b for Each Location with Standard Deviation and Root Mean Square Error Location GEMS2 A1-1 GEMS2 A1-2 GEMS2 C1-S GEMS2 C1-SE GEMS2 C1-SW Larned E Larned C Larned W Leque E Leque W
b (m/s3 )
σ (m/s3 )
rmse (m/s)
0.12 0.11 0.08 0.11 0.09 0.11 0.11 0.05 0.11 0.06
0.044 0.031 0.053 0.078 0.064 0.074 0.091 0.025 0.050 0.035
0.0001 0.0004 0.0020 0.0025 0.0021 0.0006 0.0011 0.0001 0.0007 0.0015
Figure 2. Distribution of b values obtained for GEMS2 A1-2.
become a valuable new method for obtaining K estimates for hydrogeologic applications in the same way that it has been widely adopted and accepted as a reliable measure of permeability for petroleum applications. Shown in Table 2
are the b values determined through calibration at the scale of the field site for each of the three sites. In conducting the site-scale calibration, the analyzed data set for each site included the K NMR and K DPP data pairs from all of the locations at that site. We find little difference in the b values at the three sites: 9 × 10−2 m/s3 for the GEMS2 site and 8 × 10−2 m/s3 for both the Larned site and the Leque Island site. The close similarity in the b values suggests that all the parameters affecting the T 2ML –K relationship other than porosity and S /V (e.g., tortuosity, pore connectivity, distribution of pore sizes, and grain surface geochemistry) have a relatively constant impact on the K of sand and gravel across the different unconsolidated sites. This is a very significant result, suggesting that it may be possible to define, as has been done for petroleum applications, standard constants that can be used to obtain reliable estimates of K from NMR
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Table 2 Value of b for Each Field Site with Standard Deviation and Root Mean Square Error Location GEMS2 site Larned site Leque site
b (m/s3 )
σ (m/s3 )
rmse (m/s)
0.09 0.08 0.08
0.021 0.031 0.029
0.0023 0.0003 0.0023
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Figure 3. Distribution of b values obtained at each location at the three sites: (a) GEMS2, (b) Larned, and (c) Leque Island.
logging data in unconsolidated aquifers, without the need for site-specific calibration. An important component of this study was the way in which the calibration was conducted; it provides insights into the uncertainty in the b value obtained at each location. In Figure 2, we show as an example the distribution of b values obtained at the GEMS2 site, location A1-2. While b = 0.12 was reported as the most common value (the peak of the histogram), the range of
values from 0.087 to 0.131 all occurred at a similar high frequency; this range is very close to capturing the entire range of b values found at GEMS2. The distribution in b values can be used to quantify the uncertainty that would result in the K estimate at a location due to the uncertainty in the calibration of the SDR equation. In Figure 3, we show the distribution in b values obtained for all the locations at each of the three sites. The plots in Figure 3 are a graphic display of what is
Figure 4. Comparison at GEMS2 of K DPP and K NMR calculated using the SDR equation. (a) A1-1, (b) A1-2, (c) C1-S, (d) C1-SE, and (e) C1-SW. The dashed lines show the uncertainty in K NMR due to the distribution in b values (±1σ ).
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Figure 5. Comparison at Larned of K DPP and K NMR calculated using the SDR equation. (a) Larned E, (b) Larned C, (c) Larned W. The dashed lines show the uncertainty in K NMR due to the distribution in b values (±1σ ).
presented in Table 1; at any field site, there is very little variation in the optimal value of b across a site; both the peak values and the distributions are very similar at all locations. Comparing the data at the three field sites (i.e., comparing Figures 3a through c), we see the significant result that there is very little difference
in the b distributions from GEMS2, Larned and Leque Island. The b values from the GEMS2 site are in good agreement with those found during the work at three locations at GEMS and GEMS2 by Parsekian et al. (2015). The most common b values found in this previous study (0.05, 0.07, and 0.07) are slightly lower than the value of 0.09 for the GEMS2 site in this study, but the distributions overlap. We attribute the difference in the b values to the fact that different methods were used to acquire the NMR and K data. In the study by Parsekian et al. (2015), the NMR data were acquired using a borehole logging tool with K estimated in one case using multilevel slug tests and in the other two cases using DPP data. In this study, we used DP methods of sampling for NMR and K, resulting in very similar measurement conditions. We used the site-scale b values to compare K NMR and K DPP at all sampled depths at each of the locations. Figure 4 shows the results from GEMS2, Figure 5 shows the results from Larned, and Figure 6 shows the results from Leque Island. In all figures, both the K NMR and K DPP in each data pair are plotted at the measured depth of the NMR data. These estimates of K from the NMR data are calculated using the distribution of b values, which results in the uncertainty in K (i.e., ±1σ from the optimal b value) shown in the figures as dashed lines. In all cases, we see very good agreement between K NMR and K DPP . This approach to displaying uncertainty is not intended to capture measurement error in its entirety, but rather to illustrate that magnitude of error incurred in using a b value that is somewhat different from the optimal
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Figure 6. Comparison at Leque of K DPP and K NMR calculated using the SDR equation. (a) Leque E, (b) Leque W. The dashed lines show the uncertainty in K NMR due to the distribution in b values (±1σ ).
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Table 3 Compilation of b Values m =1 b (m/s3 )
Source of Values
Material Type
Standard constants for petroleum applications1 Petroleum applications, reported range2 Study of High Plains Aquifer3
Consolidated sandstones
This study—optimized for each location This study—optimized for each site
m =4 b (m/s3 ) 3.4 × 10−2 3.4 × 10−2 to 4.25 × 10−2 2.1 × 10−1
Consolidated sandstones Un/semi-consolidated sediments with minor sandstone and siltstone Unconsolidated sediments
5 × 10−2 to 1.2 × 10−1
8 × 10−1 to 5.7
Unconsolidated sediments
8 × 10−2 to 9 × 10−2
1.24 to 3.42
8.0
× 10−3
1 Allen et al. (2000). 2 Kenyon (1997) and Straley et al. (1997). 3 Dlubac et al. (2013) and Dlubac (2013).
value. This is the case that would be encountered when using global empirical constants rather than site-specific calibrated values. Our results highlight the dramatic improvement in estimating K that is realized by using the constants determined through our calibration, rather than simply using the standard values for b and m determined and used for petroleum applications. Use of those standard values would result in predictions that underestimate K by approximately two orders of magnitude. We suggest that this is due to the fact that those values were determined as optimal for consolidated sandstone reservoirs, while the b values obtained in this study are optimal for unconsolidated aquifers. In Table 3, we compare reported b values for the lithologic constant when m = 1, found to be the optimal result in this study, and for m = 4, the standard value for petroleum applications. The table includes the standard b values and reported range of values for consolidated sandstones for petroleum applications (Kenyon 1997; Straley et al. 1997); the values reported for the High Plains aquifer (Dlubac 2013; Dlubac et al. 2013); and the values found in this study. We observe that as the material type becomes more consolidated (from bottom to top of the table), b decreases by about an order of magnitude in going from unconsolidated to un/semi-consolidated material and then another order of magnitude in going to consolidated material. While more studies such as this are needed to provide additional data for Table 3, this study provides the significant first step needed in defining the constants that can be used to obtain estimates of K from NMR logging in unconsolidated aquifers.
Conclusions The NMR relaxation time measured during NMR logging can provide reliable estimates of K in sand and gravel aquifers, but equations used to obtain K require empirically determined constants. While standard values of the constants for sandstone reservoirs are widely used 112
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in petroleum applications, we found that the use of these values would underestimate K in unconsolidated aquifers by approximately two orders of magnitude. We worked at three sites, studying the top approximately 10 to 20 m of unconsolidated sediments at each site. Calibration at individual locations within a site showed some variability in the lithologic constant (b), but never greater than a difference of a factor of 2. The use of bootstrap analysis to conduct the calibration provided a distribution of the b values that allowed us to account for the uncertainty in K NMR due to the uncertainty in b. The most significant result of this study was the discovery that the optimal value of b was essentially the same at the three sites. This encouraging result suggests that it might be possible to determine a standard set of constants, as has been done for petroleum applications, for NMR determination of the hydraulic conductivity of near-surface sediments. In this study, we have used the SDR equation, the derivation of which assumes that relaxation occurs in the fast-diffusion regime. In sands and gravels, as the pore size increases, it is quite possible that this assumption would be violated and NMR relaxation would move into the slow-diffusion regime. The impact on the SDR equation, if relaxation occurs in the slow-diffusion regime, is to change the exponent on the T 2ML term from a value of 2 to 1. While there is no simple way to evaluate field data to determine the diffusion regime, it is straightforward to calibrate the SDR equation with the exponent equal to 2 or 1, and evaluate the agreement between the predicted and measured values of K . Improved agreement with the exponent equal to 1 would suggest the presence of slow diffusion; this form of the SDR equation and the corresponding b (as determined through calibration) could then be used to estimate K . A second assumption made in the derivation of the SDR equation is that bulk fluid relaxation is so slow, compared to T 2ML , that it can be neglected. But in materials with large pore sizes, such as well-sorted NGWA.org
gravels, T 2ML can approach the bulk fluid relaxation time of the pore water (∼1 to 3 s). In this case, the contribution of bulk fluid relaxation is likely to reduce the sensitivity of the T 2ML measurement to variations in K at large values. Recent technological advances have resulted in NMR logging systems ideally suited for application to nearsurface hydrogeologic problems (Walsh et al. 2013). As use of NMR logging increases, datasets such as the one presented here can be utilized to improve our understanding of the optimal way to transform acquired NMR logging data into estimates of hydraulic conductivity in unconsolidated aquifers. This, in turn, will help the hydrogeological community better realize the potential of this technology.
Allen, D., C. Flaum, T.S. Ramakrishnan, J. Bedford, K. Castelijns, C. Fairhurst, and R. Ramamoorthy. 2000. Trends in NMR logging. Oilfield Review 12, no. 3: 2–19. Brownstein, K.R., and C.E. Tarr. 1979. Importance of classical diffusion in NMR studies of water in biological cells. Physical Review 19, no. 6: 2446–2453. Bryar, T., C. Daughney, and R. Knight. 2000. Effects of paramagnetic iron (III) species on nuclear magnetic resonance relaxation of saturated sands. Journal of Magnetic Resonance 142: 74–85. Butler, J.J. Jr. 2005. Hydrogeological methods for estimation of hydraulic conductivity. In Hydrogeophysics, ed. Y. Rubin and S. Hubbard, 23–58. Dordrecht, The Netherlands: Springer. Butler, J.J. Jr., P. Dietrich, V. Wittig, and T. Christy. 2007a. Characterizing hydraulic conductivity with the direct-push permeameter. Ground Water 45, no. 4: 409–419. Butler, J.J. Jr., G.J. Kluitenberg, D.O. Whittemore, S.P. Loheide II, W. Jin, M.A. Billinger, and X. Zhan. 2007b. A field investigation of phreatophyte-induced fluctuations in the water table. Water Resources Research 43: W02404. DOI:10.1029/2005WR004627. Carman, P.C. 1956. Flow of Gases Through Porous Media. New York: Academic Press Inc. Coates, G.R., L. Xiao, and M.G. Prammer. 1999. NMR Logging Principles and Applications. Houston, Texas: Halliburton Energy Services. Dlubac, K. 2013. The relationship between nuclear magnetic resonance and permeability in near-surface unconsolidated materials. Ph.D. thesis, Stanford University. Dlubac, K., R. Knight, Y. Song, N. Bachman, B. Grau, J. Cannia, and J. Williams. 2013. The use of NMR logging
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Acknowledgments This material is based on work supported, in part, by the U.S. Department of Energy under Grant DESC0004623. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the Department of Energy. The authors thank the Washington Department of Fish and Wildlife for providing access to the Leque Island field site, and Mr. Tom Campbell for assistance with direct push drilling at the Leque Island field site. We also wish to thank the reviewers for their helpful comments.
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