FracKfinder: A MATLAB Toolbox for Computing Three-Dimensional Hydraulic Conductivity Tensors for Fractured Porous Media

Fractures in porous media have been documented extensively. However, they are often omitted from groundwater flow and mass transport models due to a lack of data on fracture hydraulic properties and the computational burden of simulating fractures explicitly in large model domains. We present a MATLAB toolbox, FracKfinder, that automates HydroGeoSphere (HGS), a variably saturated, control volume finite-element model, to simulate an ensemble of discrete fracture network (DFN) flow experiments on a single cubic model mesh containing a stochastically generated fracture network. Because DFN simulations in HGS can simulate flow in both a porous media and a fracture domain, this toolbox computes tensors for both the matrix and fractures of a porous medium. Each model in the ensemble represents a different orientation of the hydraulic gradient, thus minimizing the likelihood that a single hydraulic gradient orientation will dominate the tensor computation. Linear regression on matrices containing the computed three-dimensional hydraulic conductivity (K) values from each rotation of the hydraulic gradient is used to compute the K tensors. This approach shows that the hydraulic behavior of fracture networks can be simulated where fracture hydraulic data are limited. Simulation of a bromide tracer experiment using K tensors computed with FracKfinder in HGS demonstrates good agreement with a previous large-column, laboratory study. The toolbox provides a potential pathway to upscale groundwater flow and mass transport processes in fractured media to larger scales.     

Estimating Tortuosity Coefficients Based on Hydraulic Conductivity

While the tortuosity coefficient is commonly estimated using an expression based on total porosity, this relationship is demonstrated to not be applicable (and thus is often misapplied) over a broad range of soil textures. The fundamental basis for a correlation between the apparent diffusion tortuosity coefficient and hydraulic conductivity is demonstrated, although such a relationship is not typically considered. An empirical regression for estimating the tortuosity coefficient based on hydraulic conductivity for saturated, unconsolidated soil is derived based on results from 14 previously reported diffusion experiments performed with a broad range of soil textures. Analyses of these experimental results confirm that total porosity is a poor predictor for the tortuosity coefficient over a large range of soil textures. The apparent diffusion tortuosity coefficient is more reliably estimated based on hydraulic conductivity.     

Assessment of NMR Logging for Estimating Hydraulic Conductivity in Glacial Aquifers

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

A Physically Based Approach for Estimating Hydraulic Conductivity from HPT Pressure and Flowrate

The hydraulic profiling tool (HPT) is widely used to generate profiles of relative permeability vs. depth. In this work, prior numerical modeling results are used to develop a relationship between probe advance rate V (cm/s), probe diameter D (cm), water injection rate Q (mL/min), corrected pressure P_c (psi), and hydraulic conductivity K (feet/d) ((1)) where E is an empirically derived hydraulic efficiency factor. The relationship is validated by 23 HPT profiles that, after averaging K vertically, were similar to slug test results in adjoining monitoring wells. The best fit value of E for these profiles was 2.02. This equation provides a physically based approach for generating hydraulic conductivity profiles with HPT tooling.     

Determination of Hydraulic Conductivity from Grain‐Size Distribution for Different Depositional Environments

Over 400 unlithified sediment samples were collected from four different depositional environments in global locations and the grain‐size distribution, porosity, and hydraulic conductivity were measured using standard methods. The measured hydraulic conductivity values were then compared to values calculated using 20 different empirical equations (e.g., Hazen, Carman‐Kozeny) commonly used to estimate hydraulic conductivity from grain‐size distribution. It was found that most of the hydraulic conductivity values estimated from the empirical equations correlated very poorly to the measured hydraulic conductivity values with errors ranging to over 500%. To improve the empirical estimation methodology, the samples were grouped by depositional environment and subdivided into subgroups based on lithology and mud percentage. The empirical methods were then analyzed to assess which methods best estimated the measured values. Modifications of the empirical equations, including changes to special coefficients and addition of offsets, were made to produce modified equations that considerably improve the hydraulic conductivity estimates from grain size data for beach, dune, offshore marine, and river sediments. Estimated hydraulic conductivity errors were reduced to 6 to 7.1 m/day for the beach subgroups, 3.4 to 7.1 m/day for dune subgroups, and 2.2 to 11 m/day for offshore sediments subgroups. Improvements were made for river environments, but still produced high errors between 13 and 23 m/day.     

Vertically Integrated Hydraulic Conductivity: A New Parameter for Groundwater-Surface Water Analysis

Numerical modeling of groundwater-surface water interactions provides vital information necessary for determining the extent of nutrient transport, quantifying water budgets, and delineating zones of ecological support. The hydrologic data that drive these models are often collected at disparate scales and subsequently incorporated into numerical models through upscaling techniques such as piecewise constancy or geostatistical methods. However, these techniques either use basic interpolation methods, which often simplifies the system of interest, or utilize complex statistical methods that are computationally expensive, time consuming, and generate complex subsurface configurations. We propose a bulk parameter termed “vertically integrated hydraulic conductivity” (K_V), and defined as the depth-integrated resistance to fluid flow sensed at the groundwater-surface water interface, as an alternative to hydraulic conductivity when investigating vertical fluxes across the groundwater-surface water interface. This bulk parameter replaces complex subsurface configurations in situations dominated by vertical fluxes and where heterogeneity is not of primary importance. To demonstrate the utility of K_V, we extracted synthetic temperature time series data from a forward numerical model under a variety of scenarios and used those data to quantify vertical fluxes using the amplitude ratio method. These quantified vertical fluxes and the applied hydraulic head gradient were subsequently input into Darcy's Law and used to quantify K_V. This K_V was then directly compared to the equivalent hydraulic conductivity (K_T) assuming an infinitely extending layer. Vertically integrated hydraulic conductivity allows for more accurate and robust flow modeling across the groundwater-surface water interface in instances where complex heterogeneities are not of primary concern.     

Surfactant-Induced Reductions in Soil Hydraulic Conductivity

Surfactant solutions are being proposed for in situ flushing of organic contaminants from soils and aquifers. The feasibility of surfactant additives in remediation may depend in large part on how these chemicals affect the hydraulic conductivity of the porous media. While there is evidence in the literature of conductivity loss during surfactant flushing (Miller et al. 1975; Nash et al. 1987), there has been little research on quantifying the process for unconsolidated sediments. Surfactant-affected hydraulic conductivity reductions were measured in two soils (Teller loam and Daugherty sand). Testing was done with eight surfactants at a variety of concentrations (10^-5 to 10^-l mole/kg), surfactant mixtures, and added solution electrolytes. The Teller was also tested with its organic matter removed. Maximum hydraulic conductivity decreases were 47 percent for the sand and more than two orders of magnitude for the loam. Surfactant concentrations, surfactant mixtures, soil organic content, and added solution electrolytes all affected the degree of conductivity reduction. Results indicate that surfactant-affected hydraulic conductivity losses should be considered prior to in situ remediation and may preclude surfactant use in some fine grain soils.     

Tracer Test Analysis of Anisotropy in Hydraulic Conductivity of Granular Aquifers

A simple method of determining the anisotropy ratio of hydraulic conductivity in near-surface granular aquifers using tracer test and piezometer measurements is presented. Depending on the length of time allowed, the test will yield anisotropy ratios that are representative of the distance traversed by the tracer during the test, up to tens of feet from the injection point for some systems. This method is illustrated with an application to a ground water flow system in northern Wisconsin.     

A Falling-Head Method for Measuring Intertidal Sediment Hydraulic Conductivity

This paper presents an in situ falling-head method for measuring hydraulic conductivity of beach sediments in tidal environment. A polyvinyl chloride (PVC) standpipe was vertically pushed into the submerged beach sediments so that its lower part was filled by a sediment column. During the experiment, the sediments were submerged by sea water and the standpipe top was higher than the sea level. The pipe was fully filled with sea water at the beginning of the experiment. Then the water level time series inside and outside the standpipe were recorded. Analytical solutions were derived to describe the relation among the sediment's hydraulic conductivity and the water levels inside and outside the standpipe and used to analyze the experiment data obtained from the intertidal zone of Puqian Bay, Haikou, Hainan Province, China. The water levels predicted by the analytical solution agreed very well with all the experiment data. Experiments for horizontal hydraulic conductivity estimation were also conducted using L-shaped standpipe which bends from vertical to horizontal in the beach sediments. The averaged hydraulic conductivity anisotropy ratio at the study area is about 2.9. After each in situ experiment, the sediments in the standpipe were stored in a plastic box and transported to university laboratory to measure the hydraulic conductivity using falling-head method. It is found that the in situ hydraulic conductivity averages one order of magnitude greater than the laboratory one, indicating that the original beach surface sediments were loose due to tidal and wave actions and that the samples were significantly compacted during the transportation to laboratory.