Tensor Hydraulic Conductivity Estimation for Heterogeneous Aquifers under Unknown Boundary Conditions

A physically based inverse method is developed using hybrid formulation and coordinate transform to simultaneously estimate hydraulic conductivity tensors, steady‐state flow field, and boundary conditions for a confined aquifer under ambient flow or pumping condition. Unlike existing indirect inversion techniques, the physically based method does not require forward simulations to assess model‐data misfits. It imposes continuity of hydraulic head and Darcy fluxes in the model domain while incorporating observations (hydraulic heads, Darcy fluxes, or well rates) at measurement locations. Given sufficient measurements, it yields a well‐posed inverse system of equations that can be solved efficiently with coarse grids and nonlinear optimization. When pumping and injection are active, well rates are used as measurements and flux sampling is not needed. The method is successfully tested on synthetic aquifer problems with regular and irregular geometries, different hydrofacies and flow patterns, and increasing conductivity anisotropy ratios. All problems yield stable inverse solutions under increasing head measurement errors. For a given set of observations, inversion accuracy is strongly affected by the conductivity anisotropy ratio. Conductivity estimation is also affected by flow pattern: within a hydrofacies, when Darcy flux component is very small, the corresponding directional conductivity perpendicular to streamlines becomes less identifiable. Finally, inversion is successful even if the location of aquifer boundaries is unknown. In this case, the inversion domain is defined by the location of the measurements.     

Remediation of Heterogeneous Aquifers Subject to Uncertainty

Optimal cost pump-and-treat ground water remediation designs for containment of a contaminated aquifer are often developed using deterministic ground water models to predict ground water flow. Uncertainty in hydraulic conductivity fields used in these models results in remediation designs that are unreliable. The degree to which uncertainty contributes to the reliability of remediation designs as measured by the characterization of the uncertainty is shown to differ depending upon the geologic environments of the models. This conclusion is drawn from the optimal design costs for multiple deterministic models generated to represent the uncertainty of four distinct models with different geologic environments. A multi scenario approach that includes uncertainty into the remediation design called the deterministic method for optimization subject to uncertainty (DMOU) is applied to these distinct models. It is found that the DMOU is a method for determining a remediation design subject to uncertainty that requires minimal postprocessing efforts. Preprocessing, however, is required for the application of the DMOU to unique problems. In the ground water remediation design problems, the orientation of geologic facies with respect to the orientation of flow patterns, pumping well locations, and constraint locations are shown to affect the preprocessing, the solutions to the DMOU problems, and the computational efficiency of the DMOU approach. The results of the DMOU are compared to the results of a statistical analysis of the effects of the uncertainty on remediation designs. This comparison validates the efficacy of the DMOU and illustrates the computational advantages to using the DMOU over statistical measures.     

Numerical Modeling of Emulsified Oil Distribution in Heterogeneous Aquifers

In situ anaerobic bioremediation using edible oil emulsions will be most effective if the oil droplets can be brought into close contact with the contaminant to be treated. However, uniformly distributing oil in heterogeneous aquifers can be difficult. The impact of injection conditions on emulsion distribution in a three-dimensional heterogeneous aquifer is examined using MODFLOW and RT3D. Emulsion retention is simulated using a rate-limited Langmuir isotherm. Volume and flow contact efficiency are shown to be functions of mass of oil injected, injection fluid volume, well spacing, and injection sequence. Regression equations are developed relating dimensionless scaling factors to expected contact efficiency for area treatment and barriers. Cleanup time for uncontacted zones is estimated using a mobile-immobile zone modeling approach.     

Estimating Flow Using Tracers and Hydraulics in Synthetic Heterogeneous Aquifers

Regional ground water flow is most usually estimated using Darcy's law, with hydraulic conductivities estimated from pumping tests, but can also be estimated using ground water residence times derived from radioactive tracers. The two methods agree reasonably well in relatively homogeneous aquifers but it is not clear which is likely to produce more reliable estimates of ground water flow rates in heterogeneous systems. The aim of this paper is to compare bias and uncertainty of tracer and hydraulic approaches to assess ground water flow in heterogeneous aquifers. Synthetic two-dimensional aquifers with different levels of heterogeneity (correlation lengths, variances) are used to simulate ground water flow, pumping tests, and transport of radioactive tracers. Results show that bias and uncertainty of flow rates increase with the variance of the hydraulic conductivity for both methods. The bias resulting from the nonlinearity of the concentration–time relationship can be reduced by choosing a tracer with a decay rate similar to the mean ground water residence time. The bias on flow rates estimated from pumping tests is reduced when performing long duration tests. The uncertainty on ground water flow is minimized when the sampling volume is large compared to the correlation length. For tracers, the uncertainty is related to the ratio of correlation length to the distance between sampling wells. For pumping tests, it is related to the ratio of correlation length to the pumping test's radius of influence. In regional systems, it may be easier to minimize this ratio for tracers than for pumping tests.     

Estimating the Horizontal Gradient in Heterogeneous, Unconfined Aquifers: Comparison of Three-Point Schemes

At least two approaches may be used to estimate the horizontal components of the hydraulic gradient based on measured heads from three observation points. First, the gradient may be estimated by passing a plane through the measured heads (h-method). Second, if the elevation of the base of the aquifer is known to be spatially constant, an estimate of the gradient may be obtained using the squares of the measured heads (h²- method). In the present study, these methods are examined in application to a heterogeneous system. Using Monte Carlo analysis, we demonstrate that the magnitude of the gradient estimated via the h-method involved significant bias, which increased when the distance separating the wells increased. In contrast, bias in the estimated magnitude of the gradient based on the h²-method decreased with increasing separation among the wells. Estimation variances for both the magnitude and orientation of the gradient also decreased with separation distance. The variance in the orientation was observed to remain relatively high, however, even at relatively large separations among the wells (e.g., 10 integral scales). These results are Interpreted as implying that the best estimate of the gradient for steady flow in an unconfined aquifer is derived from the h²- method with the wells separated by significant distances. These results also demonstrate the uncertainty inherent in estimating the gradient based on limited field data.     

Interpretation of Pumping Tests in Heterogeneous Aquifers with Constant Head Boundary

This paper investigates the impact of heterogeneity of the transmissivity field on the interpretation of steady-state pumping test data from aquifer systems delimited by constant head boundaries such as aquifers adjacent to lakes or rivers. Spatially variable transmissivity fields are randomly generated and used to simulate the drawdown due to a pumping well located at different distances from a constant head boundary. The steady-state drawdown simulated at different observation wells are then interpreted using the Hantush method (Hantush 1959). The numerical simulations show that, in contrast to the case of infinite aquifer domains, the interpreted transmissivity varies depending on well locations and the separation distance between pumping well and boundary relative to the correlation length. The ensemble-averaged estimated transmissivity varies between the geometric mean and the arithmetic mean, and can even exceed the arithmetic mean in a narrow domain adjacent to the boundary. It approaches the geometric mean of the underlying transmissivity field only if the distance between the pumping well is more than 20 times the characteristic length of the transmissivity field.     

Evolution of Heterogeneous Mixed Siliciclastic/Carbonate Aquifers Containing Metastable Sediments

Mixed carbonate and siliciclastic marine sediments commonly become freshwater aquifers in eastern coastal regions of the United States and many other global locations. As these deposits age, the carbonate fraction of the sediment is commonly removed by dissolution and the aquifer can become a solely siliciclastic system or contain zones or beds of pure quartz sand. During aquifer evolution, the sediment grain size characteristics, hydraulic conductivity, and porosity change. An investigation of these changes using mixed carbonate/siliciclastic sediment samples collected from a modern barrier island beach in southern Florida showed that the average mean grain diameter decreased with removal of the carbonate fraction, but the average hydraulic conductivity and porosity increased slightly, but not to statistical significance. This counterintuitive result occurs because of the change in the pore types from a combined shelter and intergranular pore system producing a dual porosity system in the mixed sediments to a single intergranular pore system in the siliciclastic sediment fraction. Within the mixed carbonate/siliciclastic sediment, in the pure carbonate fraction, large shell fractions form grain‐supported large pores, which become filled with sand‐sized quartz as the shell fragments decrease in size or as the sediment becomes compacted. The hydraulic conductivity increases because the shell fragments that were oriented perpendicular to flow caused an increase in the length of the flow path, or a larger scale tortuosity, compared with the flow through pure quartz sand.