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.     

Hydraulic Gradient Comparison Method to Estimate Aquifer Hydraulic Parameters Under Steady-State Conditions

The hydraulic gradient comparison method is an inverse method for estimation of aquifer hydraulic conductivity (or trans-missivity) and boundary conductance for a ground water flow model under steady-state conditions. This method, following formal optimization techniques, defines its objective function to minimize differences between interpreted (observed) and simulated hydraulic gradients, which results in minimization of differences between observed and simulated hydraulic heads. The key features of this method are that (1) the derived optimality conditions have an explicit form with a clear hydrology concept that is con-sistent with Darcy's law, and (2) the derived optimality conditions are spatially independent as they are a function of only local hydraulic conductivity and local hydraulic gradient. This second feature allows a multidimensional optimization problem to be solved by many one-dimensional optimization procedures simultaneously, which results in a substantial reduction in computation time. The results of the numerical performance testing on a heterogeneous hypothetical case confirm that minimizing gradient residuals in the entire model domain leads to minimizing head residuals. Application of the method in real-world projects requires rigorous conceptual model development, use of a global calibration target, and an iterative calibration proess. The conceptual model development includes interpretation of a potentiometric surface and estimation of other hydrologic parameters. This method has been applied to a wide range of real-world modeling projects, including the Rocky Mountain Arsenal and Rocky Flats sites in Colorado, which demonstrates that the method is efficient and practical.     

Electrical Resistivity Characterization of Anisotropy in the Biscayne Aquifer

Electrical anisotropy occurs when electric current flow varies with azimuth. In porous media, this may correspond to anisotropy in the hydraulic conductivity resulting from sedimentary fabric, fractures, or dissolution. In this study, a 28‐electrode resistivity imaging system was used to investigate electrical anisotropy at 13 sites in the Biscayne Aquifer of SE Florida using the rotated square array method. The measured coefficient of electrical anisotropy generally ranged from 1.01 to 1.12 with values as high as 1.36 found at one site. The observed electrical anisotropy was used to estimate hydraulic anisotropy (ratio of maximum to minimum hydraulic conductivity) which ranged from 1.18 to 2.83. The largest values generally were located on the Atlantic Coastal Ridge while the lowest values were in low elevation areas on the margin of the Everglades to the west. The higher values of anisotropy found on the ridge may be due to increased dissolution rates of the oolitic facies of the Miami formation limestone compared with the bryozoan facies to the west. The predominate trend of minimum resistivity and maximum hydraulic conductivity was E‐W/SE‐NW beneath the ridge and E‐W/SW‐NE farther west. The anisotropy directions are similar to the predevelopment groundwater flow direction as indicated in published studies. This suggests that the observed anisotropy is related to the paleo‐groundwater flow in the Biscayne Aquifer.     

Aquifer Properties Determined from Two Analytical Solutions

In the analysis of pumping test data, the quality of the determined aquifer parameters can be greatly improved by using a proper model of the aquifer system. Moench (1995) provided an analytical solution for flow to a well partially penetrating an unconfined aquifer. His solution, in contrast to the Neuman solution (1974), accounts for the noninstantaneous decline of the water table (delayed yield). Consequently, the calculated drawdown in these two solutions is different under certain circumstances, and this difference may therefore affect the computation of aquifer properties from pumping test data. This paper uses an inverse computational method to calculate four aquifer parameters as well as a delayed yield parameter, α₁ from pumping test data using both the Neuman (1974) and Moench (1995) solutions. Time-drawdown data sets from a pumping test in an unconfined alluvial aquifer near Grand Island, Nebraska, were analyzed. In single-well analyses, horizontal hydraulic conductivity values derived from the Moench solution are lower, but vertical hydraulic conductivity values are higher than those calculated from the Neuman solution. However, the hydraulic conductivity values in composite-well analyses from both solutions become very close. Furthermore, the Neuman solution produces similar hydraulic conductivity values in the single-well and composite-well analyses, but the Moench solution does not. While variable α₁, seems to play a role in affecting the computation of aquifer parameters in the single-well analysis, a much smaller effect was observed in the composite-well analysis. In general, specific yield determined using the Moench solution could be slightly higher than the values from the Neuman solution; however, they are still lower than the realistic values for sand and gravel 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.     

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.