Journal of Hydrologic Engineering

A novel dimensionless formulation for water flow in two-dimensional variably saturated media is presented. It shows that scaling physical systems requires conservation of the ratio between capillary forces and gravity forces. A direct result of this finding is that for two physical systems to be hydraulically similar, the soil in the smaller system has to be coarser than the soil in the larger system. The new formulation is implemented in a finite-element model that compared favorably with published numerical results with a minimal mass balance error. Bayesian estimation using prior physical information was used to fit the model to experimental data that simulated tidal action in a laboratory beach. Results show that the model is not sensitive to the residual soil moisture or the parameter n in the van Genuchten model, but is sensitive to variation in the saturated hydraulic conductivity and the parameter α in the van Genuchten model. Nomographs based on the dimensionless formulation were used to scale the results of the laboratory beach to the range of natural beaches.

This paper deals with modeling depth-averaged solute transport and lateral-diffusive transfer in a two-layer system of contrasting permeabilities. Two-dimensional transport equations are developed, by averaging the local three-dimensional transport equations vertically across the high- and low-permeability layers. The equations account for interlayer mass transfer and the capacitance of the low-permeability layer to store and release reactive constituents by diffusion. The theory indicates that a first-order rate model can describe the process of interlayer mass transfer under quasi-steady condition. An expression for the mass-transfer rate coefficient α is obtained in terms of the transverse diffusion time (or diffusion rates) across the layers. In particular, the diffusion time in the high-permeability layer is related to transverse-vertical dispersion that accounts for the effect of mechanical mixing on the interlayer mass transfer. For small capacity ratio β< 1 the rate coefficient α shows a linear dependence on the pore-water velocity, and a linear approximation is obtained in terms of a Peclet number, in which the transverse-vertical dispersivity is the characteristic length scale. Application to previously published experimental data highlighted the applicability and limitations of the first-order rate model.

Transverse diffusive transfer of solute mass between regions of mobile and immobile water is a key mechanism causing tailing and reduced peak concentrations. In Part 1, we developed a two-dimensional first-order rate model that describes reactive solute transport averaged across the thickness of a two-layer system. The model describes the capacitance effect of low-permeability layers to store and release solute by diffusive-type mass transfer, under quasi-steady conditions. In this paper, we develop two-dimensional analytical solutions for the first-order rate model in an infinite porous medium, using the methods of Fourier and Laplace transforms and superposition. The solutions consider a rectangular source with (1) an instantaneous release of a contaminant mass and (2) an exponentially decaying source applied at a fixed rate. Simulations show that increased pore-water velocity produces a more dispersed mobile solute and pronounced tailing. Comparison of the theory with the Borden aquifer data indicates that the first-order rate model can describe the early dispersion of the chloride tracer, on the basis of diffusive interlayer mass transfer.

A 2-dimensional finite-element model for density-dependent flow and transport through saturated-unsaturated porous media has been developed. The combined flow and transport model can handle a wide range of real-world problems, including the simulations of flow alone, contaminant transport alone, and combined flow and transport. The conventional finite-element methods and a hybrid Lagrangian-Eulerian finite-element method were incorporated in the transport module. Saltwater intrusion problems and instability caused by denser water on the top were investigated in this paper. Because the fundamental mechanism causing saltwater intrusion most likely is caused by density-induced convection and dispersion, the developed model was used to assess the interplay between density-driven flow and the subsurface media through which the saltwater intrusion occurs. The mathematical formulation of the model is comprised of fluid flow and solute transport equations, coupled by fluid density. In the specific case of saltwater intrusion and unstable brine transport problems, this set of governing equations is nonlinear and requires iterative methods to solve them simultaneously. Three case studies, which include a wide spectrum of physical conditions, show the verification and effectiveness of the model by comparing previously published solutions from other researchers with the simulation results of the present model. Two demonstrated problems examine the model capabilities to handle saltwater intrusion problems through unsaturated-saturated porous media and density-dependent flow and transport under unstable conditions.

An ensemble-averaged prediction equation system for transient subsurface stormflow on sloping impermeable beds in heterogeneous hillslopes is derived by means of the regular perturbation method. The covariance of hydraulic conductivity and flow depth, which emerges during the derivation of the mean flow depth, causes a closure problem. To close the equation system, a second equation is derived for this covariance term. The overall set of ensemble-averaged prediction equations then is solved numerically and their validity is tested by comparing the results against those obtained from a Monte-Carlo simulation for different values of slope and variance of hydraulic conductivity. The comparison of the results suggests that the system of prediction equations gives satisfactory results for coefficient of variation of hydraulic conductivity as high as 1.12 for slopes as steep as 0.3.

It has been known for a number of years that dispersivities increase with the scale of a ground-water dispersion experiment, but little appears to be known about the effect of this scale dependency on solutions of the dispersion equation. Solutions of the dispersion equation with dispersivities that increase directly with the first power of the flow length are obtained here for unsteady flow from instantaneous sources and for steady flow from continuous sources in one, two, and three spatial dimensions. When compared with corresponding solutions for constant dispersivity models, these solutions show less dispersion at smaller values of x and more dispersion at larger values of x. In addition, points of maximum concentration for an instantaneous source move with slightly slower speeds, and concentrations upstream from the initial source release point are exactly zero for all time. The chief advantage of using these solutions is that they are likely to hold over a range of values for x, whereas constant dispersivity solutions are accurate only for the single value of x used to calculate dispersivities.

Temporal moments analysis is used to study the impact of chemical heterogeneity on the one-dimensional transport of a pollutant that undergoes linear kinetic adsorption. We make an important simplifying assumption by considering that the aquifer is physically homogeneous, but chemically heterogeneous. The aquifer is assumed to be comprised of distinct reactive and nonreactive zones; in the reactive zones the pollutant undergoes linear kinetic adsorption. The distribution of reactive sites along the porous medium is characterized using two different approaches, stochastic and deterministic. A Bernoulli random process is used in the first approach, whereas a Fourier series is used in the second. In the stochastic approach the adsorption rate constant is also allowed to vary randomly. An approximate analytical solution for the temporal moments of the stochastic problem and an exact solution for the periodic problem are obtained. Temporal moments derived from this analysis are used to compute effective parameters (velocity and dispersion) as a function of the distance from the initial contaminant injection. Our results show that the overall effective dispersion coefficient is a sum of three terms accounting for the processes of equilibrium adsorption, kinetic adsorption, and chemical heterogeneity, respectively. We examine the impact of the adsorption rate parameter upon overall spreading and show that the magnitude of this rate parameter governs the relative contribution of chemical heterogeneity. A comparison between the effective parameters for the stochastic and periodic problem and the sensitivity of the results to physical and chemical parameters are also addressed.

Intrinsic biodegradation of petroleum hydrocarbons in the subsurface has gained increased acceptance as a remedial alternative where the risk of exposure is within acceptable standards. However, methods to predict reliably the rate and extent of biodegradation at contaminated sites have not been established. Laboratory microcosm and in situ column experiments were conducted in a petroleum-contaminated aquifer undergoing intrinsic biodegradation to (1) document that anaerobic biodegradation of benzene, toluene, ethylbenzene, and xylene (BTEX) isomers occurred, (2) determine the rate and pattern of BTEX biodegradation, and (3) compare measured decay rates in laboratory and in situ microcosm results with contaminant concentrations along the length of the plume. Both methods verified that indigenous microorganisms have the capability to biodegrade anaerobically BTX under ambient conditions. However, microcosms constructed with aquifer material from different areas of the plume showed significant variability in rate and extent of contaminant biodegradation. In experiments conducted in the same area of the plume, the biodegradation rate for the individual compounds measured in both in situ columns and microcosms was over 10 times higher than the rate calculated from field monitoring. Thus, these methods should not be used to infer field-scale decay rates.

A canal drawdown experiment was used in conjunction with borehole flowmeter measurements to determine the following hydrologic parameters: (1) the transmissivity (T) and hydraulic conductivity (K) of the Biscayne Aquifer in southeast Florida; (2) the separate hydraulic conductivities of the Miami Limestone (K_M) and the Fort Thompson Formation (K_F)–the two geologic formations making up the Biscayne Aquifer; and (3) the conductance (C) controlling water seepage between the Biscayne Aquifer and the L-31W borrow canal (the canal in which the drawdown experiment was carried out). While the canal drawdown experiment alone would have yielded T and K, also making borehole flowmeter and aquifer thickness measurements allowed determination of K_M and K_F. Two methods of data analysis were used; one based on the Dupuit equation, the other on a previously published set of equations developed specifically for computing the C value required for a regional numerical ground-water flow model. The two methods were in good agreement (within 20% of each other), and averaging results from them gave T= 1.0 × 10⁵ m²/day, K= 7,590 m/day, K_M= 14,900 m/day, and K_F= 4,050 m/day. Estimates of C from the two methods were also similar, although the exact value derived from the second method would necessarily depend on the size of the model grid cell for which the value was calculated. The methods applied here illustrate an effective means for measurement of field-scale hydrologic parameters and confirm the importance of canal sediments in controlling ground-water exchange with the L-31W canal on the eastern boundary of Everglades National Park.