Mathematical Modeling of Tidal Effects in Groundwater

This paper presents a special use of the linear poroelasticity theory to describe tidally induced groundwater oscillations. Two models of oscillation inducing mechanism make use of this theory to predict groundwater level fluctuations. The numerical solutions of both models are presented and compared with well water level measurement obtained in Police Basin, north-east Bohemia.     

Investigation of Groundwater Contaminant Discharge into Tidally Influenced Surface-Water Bodies: Experimental Results

An investigation of the effect of tidally influenced water elevations on the concentration of groundwater contaminants discharging to a surface-water body is studied using a one-dimensional homogeneous sand column. A constant water level is imposed upstream, and the downstream water level is controlled by a wave generator that controls the hydraulic head to mimic a 12-h tidal fluctuation. The experimental results demonstrate that the tidal fluctuations in the downstream reservoir result in a decrease in average contaminant concentration at the point of discharge to the tidally influenced surface-water body. The further upstream an observation well is located, the smaller the amplitude of the concentration oscillation. Fourier analysis suggests that the dominant frequency of the pressure at different locations along the length of the column is identically two cycles per day and that the concentration data have a dominant frequency of two cycles per day, but also exhibit harmonics.     

Groundwater Fluctuations in Sloping Aquifers Induced by Time-Varying Replenishment and Seepage from a Uniformly Rising Stream

This paper analyses the classical problem of transient surface?Cgroundwater interaction in a stream?Caquifer system under rather realistic conditions. The downward sloping unconfined aquifer is in contact with a constant water level at one end, and a fully penetrating stream at the other end whose water level is rising at a uniform speed. Furthermore, the aquifer is replenished by a vertical time-varying recharge. Closed form analytical expressions for hydraulic head and flow rate in the aquifer are obtained by solving the linearized Boussinesq equation using Laplace transform method. Effects of aquifer parameters on transient water table and flow rate are illustrated with a numerical example. To assess the efficiency of the linearization method, analytical solutions are compared with numerical solutions of the corresponding non-linear equation.     

Investigation of Groundwater Contaminant Discharge into Tidally influenced Surface-water Bodies: Theoretical Analysis

Data from an one-dimensional homogeneous sand column, which is utilized to investigate the effect of tides on the concentration of groundwater contaminants discharging to a surface-water body, demonstrate that the tidal fluctuations in water level elevation create concentration oscillations upgradient of the groundwater discharge locations and there is a resulting decrease in average contaminant concentration at the point of groundwater discharge to a surface-water body. The further upgradient an observation point is located, the smaller the amplitude of the tidally induced concentration oscillations. In addition, an excessive upstream migration of concentration oscillations is observed although there is a net downgradient flow. As the classical groundwater flow and transport model could not reproduce this phenomena, a multi-mobility model is proposed with one highly mobile liquid phase, one less mobile liquid phase and a solid phase. Averaging theory is applied in a first step to develop the macroscopic mass conservation equation from its microscale counterpart and then, in a second step, averaging is again used to reduce dimensionality to one-dimensional governing equations defined along the axis of the column. The simulation confirms the existence of an enhanced tidally induced mixing process and the suitability of our mathematical-physical representation of it.     

Tidal Effects on Groundwater Motions

Assuming a sharp interface between freshwater and seawater within a coastal aquifer, a theory is developed to account for the piezometric head movement of steady and unsteady components in terms of large- and small-time scales. Tidal fluctuations are simulated by a series of decomposed simple harmonic motions in time. Groundwater fluctuation induced by tidal motion is perturbed to the groundwater head of large-time scale. Ghyben–Herzberg formulation is applied for solutions of large-time scale and a unified formulation for various flows of small-time scale is derived (Strack, 1989). Approximate analytical solutions for amplitudes and phase lags of tidal groundwater motions and the freshwater–seawater interface for a coastal aquifer in a circular island are obtained. The induced fluctuation amplitude generally decays in distance with a parameter consisting of hydraulic conductivity, storage coefficient, thickness of aquifer and tidal period. The present approach can be applied to confined and unconfined aquifers, with only freshwater flows or interfacial flows. The theory is verified with some experimental results (Parlange, et al., 1984; Nielson, 1990). It can also used to determine physical parameters of an aquifer by monitoring the groundwater fluctuations due to tidal motions (Carr and van der Kamp, 1969).     

Density-driven Transport of Volatile Organic Compounds and its Impact on Contaminated Groundwater Plume Evolution

Density-driven advection of gas phase due to vaporization of chlorinated volatile organic compounds (VOCs) has a significant effect on fate and transport of contaminants. In this study, we investigated the effects of density-driven advection, infiltration, and permeability on contaminant plume evolution and natural attenuation of VOCs in the subsurface system. To analyze these effects, multiphase flow and contaminant transport processes were simulated using a three-dimensional Galerkin-finite-element-based model. Trichloroethylene (TCE) is selected as a target contaminant. Density-driven advection of gas phase elevated the potential of groundwater pollution in the saturated zone by accelerating downward migration of vaporized contaminant in the unsaturated zone. The advection contributed to increased removal rates of non-aqueous phase liquid (NAPL) TCE source and reduced dissolved TCE plume development in the downstream area. Infiltration reduced the velocity of the density-driven advection and its influence zone, but raised TCE transfer from the unsaturated to the saturated zone. The variation in soil permeability showed greater impact on contaminant migration within water phase in the saturated zone than within gas phase in the unsaturated zone. Temporal variations of TCE mass within two-dimensional (2D) and three-dimensional (3D) domains under several modeling conditions were compared. These results are important in evaluation of natural attenuation processes, and should be considered to effectively design monitored natural attenuation as a remedial option.     

Salt Water Intrusion in a Three-dimensional Groundwater System in The Netherlands: A Numerical Study

Salt water intrusion is investigated in a coastal groundwater system in the northern part of the province Noord-Holland, The Netherlands. Density dependent groundwater flow is modeled in three-dimensions with MOCDENS3D. This computer code is a version of MOC3D (Konikow et al., 1996) that has been adapted to simulate transient density-driven groundwater flow. Results from the model suggests that in this Dutch hydrogeologic system a severe and irreversible salinisation is already occurring. Within a few tens to hundreds of years, the salinity of the shallow aquifer is estimated to increase substantially. This salinisation process is a result of human activities such as the reclamation of the low-lying areas during the past centuries. Without changing the present boundary conditions, seepage into the low-lying areas will decrease slightly because of predicted increases in groundwater salinity. However, the rate in salt load through the Holocene aquitard into the low-lying areas will increase significantly due to an increase in salinity in the shallow aquifer. In addition, a relative sea level rise of 0.5m per century will intensify the salinisation process, causing an enormous increase in salt load in all low-lying areas in this part of The Netherlands.     

Evaluation of Potential Changes in Groundwater Quality in Response to CO<Subscript>2</Subscript> Leakage from Deep Geologic Storage

Concern has been expressed that carbon dioxide (CO₂) leaking from deep geological storage could adversely impact water quality in overlying potable aquifers by mobilizing hazardous trace elements. In this article, we present a systematic evaluation of the possible water quality changes in response to CO₂ intrusion into aquifers currently used as sources of potable water in the United States. The evaluation was done in three parts. First, we developed a comprehensive geochemical model of aquifers throughout the United States, evaluating the initial aqueous abundances, distributions, and modes of occurrence of selected hazardous trace elements in a large number of potable groundwater quality analyses from the National Water Information System (NWIS) database. For each analysis, we calculated the saturation indices (SIs) of several minerals containing these trace elements. The minerals were initially selected through literature surveys to establish whether field evidence supported their postulated presence in potable water aquifers. Mineral assemblages meeting the criterion of thermodynamic saturation were assumed to control the aqueous concentrations of the hazardous elements at initial system state as well as at elevated CO₂ concentrations caused by the ingress of leaking CO₂. In the second step, to determine those hazardous trace elements of greatest concern in the case of CO₂ leakage, we conducted thermodynamic calculations to predict the impact of increasing CO₂ partial pressures on the solubilities of the identified trace element mineral hosts. Under reducing conditions characteristic of many groundwaters, the trace elements of greatest concern are arsenic (As) and lead (Pb). In the final step, a series of reactive-transport simulations was performed to investigate the chemical evolution of aqueous As and Pb after the intrusion of CO₂ from a storage reservoir into a shallow confined groundwater resource. Results from the reactive-transport model suggest that a significant increase of aqueous As and Pb concentrations may occur in response to CO₂ intrusion, but that the maximum concentration values remain below or close to specified maximum contaminant levels (MCLs). Adsorption/desorption from mineral surfaces may strongly impact the mobilization of As and Pb.     

Finite Element Analyses in Surface Water and Groundwater: An Overview of Investigations at the U.S. Army Engineer Waterways Experiment Station

This paper highlights the finite element hydrodynamic and transport modeling developments being conducted by the U.S. Army Engineer Waterways Experiment Station (WES) and its partnering organizations. The WES developments in support of surface water, groundwater, and watershed management are presented. A particular facet of these developments, the creation of integrated, comprehensive modeling systems which greatly increase the productive use of WES hydroenvironmental models, is discussed. Future development directions, including the use of scalable high performance computing resources, are also provided.     

Interaction between Wells and a Groundwater Stream

The interaction between a natural contaminated groundwater stream and a flow induced by wells is investigated. When the flow is potential, the boundaries of the regions protected from the contaminated stream are determined for several configurations of their location and all possible flow diagrams. Dimensionless critical well flow rates corresponding to transition from one diagram to another are found.     

Calculation of Groundwater Flows in Coastal Pressurized Reservoirs

A model of a fresh groundwater flow through a rectangular horizontal pressurized reservoir toward a salt-water sea (basin, reservoir, trench, etc.) is examined within the framework of two-dimensional steady-state flow theory. In order to study the model, a mixed multi-parameter boundary value problem of the theory of analytic functions is formulated and solved using the Polubarinova-Kochina method. The structure and the characteristic features of the simulated process and the effect of all the determining physical parameters of the model on the nature of the flow are analyzed using the analytic dependences obtained and numerical calculations. An approximate hydraulic solution of the problem is compared with the exact solution obtained.     

Notes on Groundwater Age in Forward and Inverse Modeling

Several example applications of the groundwater age equation are used to derive some basic results about age in aquifers and to draw linkages among published results involving temporal moments and aquifer–aquitard diffusive mass transfer. We then describe a brief numerical study of an inverse problem in which hydraulic conductivities are identified using both piezometric head and groundwater age data where inclusion of age data helps to reduce evidential nonuniqueness. This reflects the global representation of flow process contained in age data, and that the value of age data in inverse identification of flow properties depends on the paths taken by the sampled groundwater. Paper presented at PORO2007, the 7th North American Workshop on Applications of the Physics of Porous Media, Puerto Vallarta, Mexico, 2–6 November, 2007.     

Some Analytical Solutions for Groundwater Flow and Transport Equation

This paper presents the use of symmetry reduction method resulting in new exact solutions for the groundwater flow and transport equation. It is assumed that the radionuclides are transported by advection-diffusion in a single fracture and diffusion in the surrounding rock-matrix. The application of one-parameter group reduces the number of independent variables, and consequently the governing PDE of (1+2)-dimension reduces to set of ODEs which are solved analytically. This enables us to present some new exact time-dependent solutions of the advection-diffusion equation.     

Groundwater flow in a medium with periodic inclusions

A study is made of the problem of two-dimensional confined steady flow through a porous reservoir whose percolation coefficient is a step function, while the homogeneity zones are rectangular inclusions (blocks) and a matrix (fractures). The velocity distributions, streamlines, isochrones of the motion of marked particles, and their time of passage through the elementary cell are found for this doubly periodic structure under conditions of continuity of the fluid head and the normal component of the flow on the phase contact boundary. Conclusions concerning the convective component of the longitudinal and transverse dispersion are drawn on the basis of these essentially two-dimensional hydrodynamic characteristics. The exact solutions obtained are compared with the results of numerical calculations carried out by the finite-difference method.Kazan'. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 5, pp. 139–148, September–October, 1995.     

Effect of Elevated Velocity of Particles in Groundwater Flow and Its Role in Colloid-facilitated Transport of Radionuclides in Underground Medium

Colloid-facilitated transport of radionuclides by groundwater can increase the level of ecological hazard from radioactive contaminant migration in geological medium. The reason for this is that the migration velocity of a radioactive colloid can be higher than that of radionuclides carried by the groundwater as a solute. On the basis of their field and laboratory studies, a few researchers have concluded that the velocity of the colloid can even exceed the interstitial velocity of the groundwater by a few times. A theoretical analysis of this effect is carried out in this article. The analysis is based on the assumption that the only mechanism responsible for the effect is caused by a redistribution of the colloid in a cross section of the groundwater flow in a representative volume to such domains of the cross section where the local velocity of the flow is higher than the average velocity over the whole cross section. This redistribution can be caused by drift forces arising as a result of the Magnus effect. The influence of these drift forces on a particle’s movement is considered in two extreme cases; that of relatively large and relatively small colloid particles. Particles are considered relatively small if the thermal motion of water molecules exerts a decisive influence on the particles’ movement. Otherwise the particles are considered as being relatively large. It is shown that in the case of relatively large particles this redistribution can be caused by the instability of their movement. The redistribution in the case of relatively small particles can be caused by an influence of the drift forces on characteristics of Brownian motion. It follows from the results of the theoretical analysis that an influence of the drift forces in both cases does not lead to an increase in the particles’ migration velocity at near-horizontal direction of the groundwater flow. Data from experimental studies of the elevated velocity of colloids in porous medium are analyzed. It is shown that some findings of colloidal migration velocity exceeding the interstitial velocity of the groundwater are a result of misinterpretation of experimental results.     

Hydrodynamic Investigation of Certain Groundwater Flows in Coastal Pressurized Aquifers

Mathematical models of certain fresh groundwater flows through a semi-infinite pressurized aquifer toward a salt-water sea (basin, reservoir, etc.) are examined within the framework of two-dimensional steady-state flow theory. In order to study the models, mixed boundary value problems of the theory of analytic functions are formulated and solved using the Polubarinova-Kochina method. Algorithms for calculating the flows are developed on the basis of these models for situations in which groundwater streams arrive at the sea from one side or from below. Both the structure and the characteristic features of the simulated processes and the effect of all the physical characteristics of the models on the nature of the flow are analyzed in detail using the exact analytic dependences obtained and numerical calculations. The calculation results for the two inflow schemes are compared and features of the flows that depend on the initial position of the fluid contact are discussed.     

Applying Dispersive Changes to Lagrangian Particles in Groundwater Transport Models

Method-of-characteristics groundwater transport models require that changes in concentrations computed within an Eulerian framework to account for dispersion be transferred to moving particles used to simulate advective transport. A new algorithm was developed to accomplish this transfer between nodal values and advecting particles more precisely and realistically compared to currently used methods. The new method scales the changes and adjustments of particle concentrations relative to limiting bounds of concentration values determined from the population of adjacent nodal values. The method precludes unrealistic undershoot or overshoot for concentrations of individual particles. In the new method, if dispersion causes cell concentrations to decrease during a time step, those particles in the cell having the highest concentration will decrease the most, and those with the lowest concentration will decrease the least. The converse is true if dispersion is causing concentrations to increase. Furthermore, if the initial concentration on a particle is outside the range of the adjacent nodal values, it will automatically be adjusted in the direction of the acceptable range of values. The new method is inherently mass conservative.     

Two-Valued Solutions in the Problem of Salt Precipitation during Groundwater Evaporation

The problem of the evaporation of groundwater containing a dissolved admixture is studied. It is shown that in the salt precipitation regime the solution is nonunique. At critical parameter values the solutions merge and in a certain region the solution of the problem disappears. The nonexistence of a solution corresponds to clogging of the pore space with precipitated salt.