Exploring an ‘ideal hill': how lithology and transport mechanisms affect the possibility of a steady state during weathering and erosion

We present a model of chemical reaction within hills to explore how evolving porosity (and by inference, permeability) affects flow pathways and weathering. The model consists of hydrologic and reactive-transport equations that describe alteration of ferrous minerals and feldspar. These reactions were chosen because previous work emphasized that oxygen- and acid-driven weathering affects porosity differently in felsic and mafic rocks. A parameter controlling the order of the fronts is presented. In the absence of erosion, the two reaction fronts move at different velocities and the relative depths depend on geochemical conditions and starting composition. In turn, the fronts and associated changes in porosity drastically affect both the vertical and lateral velocities of water flow. For these cases, estimates of weathering advance rates based on simple models that posit unidirectional constant-velocity advection do not apply. In the model hills, weathering advance rates diminish with time as the Darcy velocities decrease with depth. The system can thus attain a dynamical steady state at any erosion rate where the regolith thickness is constant in time and velocities of both fronts become equal to one another and to the erosion rate. The slower the advection velocities in a system, the faster it attains a steady state. For example, a massive rock with relatively fast-dissolving minerals such as diabase – where solute transport across the reaction front mainly occurs by diffusion – can reach a steady state more quickly than granitoid rocks in which advection contributes to solute transport. The attainment of a steady state is controlled by coupling between weathering and hydrologic processes that force water to flow horizontally above reaction fronts where permeability changes rapidly with depth and acts as a partial barrier to fluid flow. Published 2020. This article is a U.S. Government work and is in the public domain in the USA.     

Hydrogeophysical Methods for Analyzing Aquifer Storage and Recovery Systems

Hydrogeophysical methods are presented that support the siting and monitoring of aquifer storage and recovery (ASR) systems. These methods are presented as numerical simulations in the context of a proposed ASR experiment in Kuwait, although the techniques are applicable to numerous ASR projects. Bulk geophysical properties are calculated directly from ASR flow and solute transport simulations using standard petrophysical relationships and are used to simulate the dynamic geophysical response to ASR. This strategy provides a quantitative framework for determining site‐specific geophysical methods and data acquisition geometries that can provide the most useful information about the ASR implementation. An axisymmetric, coupled fluid flow and solute transport model simulates injection, storage, and withdrawal of fresh water (salinity ～500 ppm) into the Dammam aquifer, a tertiary carbonate formation with native salinity approximately 6000 ppm. Sensitivity of the flow simulations to the correlation length of aquifer heterogeneity, aquifer dispersivity, and hydraulic permeability of the confining layer are investigated. The geophysical response using electrical resistivity, time‐domain electromagnetic (TEM), and seismic methods is computed at regular intervals during the ASR simulation to investigate the sensitivity of these different techniques to changes in subsurface properties. For the electrical and electromagnetic methods, fluid electric conductivity is derived from the modeled salinity and is combined with an assumed porosity model to compute a bulk electrical resistivity structure. The seismic response is computed from the porosity model and changes in effective stress due to fluid pressure variations during injection/recovery, while changes in fluid properties are introduced through Gassmann fluid substitution.     

Simulation of Water‐Table Aquifers Using Specified Saturated Thickness

Simulating groundwater flow in a water‐table (unconfined) aquifer can be difficult because the saturated thickness available for flow depends on model‐calculated hydraulic heads. It is often possible to realize substantial time savings and still obtain accurate head and flow solutions by specifying an approximate saturated thickness a priori, thus linearizing this aspect of the model. This specified‐thickness approximation often relies on the use of the “confined” option in numerical models, which has led to confusion and criticism of the method. This article reviews the theoretical basis for the specified‐thickness approximation, derives an error analysis for relatively ideal problems, and illustrates the utility of the approximation with a complex test problem. In the transient version of our complex test problem, the specified‐thickness approximation produced maximum errors in computed drawdown of about 4% of initial aquifer saturated thickness even when maximum drawdowns were nearly 20% of initial saturated thickness. In the final steady‐state version, the approximation produced maximum errors in computed drawdown of about 20% of initial aquifer saturated thickness (mean errors of about 5%) when maximum drawdowns were about 35% of initial saturated thickness. In early phases of model development, such as during initial model calibration efforts, the specified‐thickness approximation can be a very effective tool to facilitate convergence. The reduced execution time and increased stability obtained through the approximation can be especially useful when many model runs are required, such as during inverse model calibration, sensitivity and uncertainty analyses, multimodel analysis, and development of optimal resource management scenarios.     

Backward probabilistic model of groundwater contamination in non-uniform and transient flow

Backward location and travel time probabilities, which provide information about the former location of contamination in an aquifer, can be used to identify unknown contamination sources. Backward location probability describes the possible upgradient positions of contamination at a known time in the past, and backward travel time probability describes the time required for contamination to travel from a known upgradient location to an observation point. These probabilities are related to adjoint states of resident concentration, and their governing equation is the adjoint of a forward contaminant transport model. Using adjoint theory to obtain the appropriate governing equation, we extend the backward probability model for conservative solutes to more general non-uniform and transient flow fields. In particular, we address three important extensions, spatially-varying porosity, transient flow and temporally-varying porosity, and internal distributed sources and sinks of solute and water. For the first time we learn that forward and backward location and travel time probabilities are not necessarily equivalent to adjoint states, but are related to them. The extensions are illustrated using a vertically-integrated groundwater model, creating transient flow by a step change in pumping and using areal recharge as an internal distributed source. Both the movement and spread of probabilities are affected. With internal sources of water, there are two interpretations of backward probability, depending on whether or not the source of water is also a source of solute. The results demonstrate how the backward probability model can be applied to other, perhaps more important, non-uniform and transient flow conditions, with time- and space-varying water storage, such as time-varying pumping or unsaturated (or saturated–unsaturated) flow and transport with spatially- and temporally-varying moisture content.     

Time–space fractional governing equations of transient groundwater flow in confined aquifers: Numerical investigation

In order to model non‐Fickian transport behaviour in groundwater aquifers, various forms of the time–space fractional advection–dispersion equation have been developed and used by several researchers in the last decade. The solute transport in groundwater aquifers in fractional time–space takes place by means of an underlying groundwater flow field. However, the governing equations for such groundwater flow in fractional time–space are yet to be developed in a comprehensive framework. In this study, a finite difference numerical scheme based on Caputo fractional derivative is proposed to investigate the properties of a newly developed time–space fractional governing equations of transient groundwater flow in confined aquifers in terms of the time–space fractional mass conservation equation and the time–space fractional water flux equation. Here, we apply these time–space fractional governing equations numerically to transient groundwater flow in a confined aquifer for different boundary conditions to explore their behaviour in modelling groundwater flow in fractional time–space. The numerical results demonstrate that the proposed time–space fractional governing equation for groundwater flow in confined aquifers may provide a new perspective on modelling groundwater flow and on interpreting the dynamics of groundwater level fluctuations. Additionally, the numerical results may imply that the newly derived fractional groundwater governing equation may help explain the observed heavy‐tailed solute transport behaviour in groundwater flow by incorporating nonlocal or long‐range dependence of the underlying groundwater flow field.     

A quasi three-dimensional model for flow and transport in unsaturated and saturated zones: 1. Implementation of the quasi two-dimensional case

A quasi three-dimensional (QUASI 3-D) model is presented for simulating the subsurface water flow and solute transport in the unsaturated and in the saturated zones of soil. The model is based on the assumptions of vertical flow in the unsaturated zone and essentially horizontal groundwater flow. The 1-D Richards equation for the unsaturated zone is coupled at the phreatic surface with the 2-D flow equation for the saturated zone. The latter was obtained by averaging 3-D flow equation in the saturated zone over the aquifer thickness. Unlike the Boussinesq equation for a leaky-phreatic aquifer, the developed model does not contain a storage term with specific yield and a source term for natural replenishment. Instead it includes a water flux term at the phreatic surface through which the Richards equation is linked with the groundwater flow equation. The vertical water flux in the saturated zone is evaluated on the basis of the fluid mass balance equation while the horizontal fluxes, in that equation, are prescribed by Darcy law. A 3-D transport equation is used to simulate the solute migration. A numerical algorithm to solve the problem for the general quasi 3-D case was developed. The developed methodology was exemplified for the quasi 2-D cross-sectional case (QUASI2D). Simulations for three synthetic problems demonstrate good agreement between the results obtained by QUASI2D and two fully 2-D flow and transport codes (SUTRA and 2DSOIL). Yet, simulations with the QUASI2D code were several times faster than those by the SUTRA and the 2DSOIL codes.     

Contaminant transport in a small deformation aquitard affected by the delayed drainage phenomenon

This paper presents a formulation accounting for the effect of delayed drainage phenomenon (DDP) on the breakthrough of contaminant flux in an aquitard, by considering the movement of soil particles, porosity variation, hydraulic head variation, and transient flow during the consolidation. The water flow equation in an aquitard was based on the Terzaghi's consolidation theory, and the contaminant transport equation was derived on the basis of the mass balance law. Two cases were used to illustrate the effect of DDP on the contaminant transport in an aquitard of small deformation. It is found that the breakthrough time of contaminant in an aquitard is very long, which is mainly ascribed to the low permeability of aquitard and sorption of soil particles. It is also found that the increase of depletion, which is in general induced by the increase of thickness and specific storativity and the decrease of hydraulic conductivity, enhances the impact of DDP on the contaminant transport in an aquitard. A larger delay index (τ₀) of DDP gives a greater delay breakthrough time (DBT) of solute transport in an aquitard, which controls the difference of the breakthrough time of contaminant transport in aquitards with and without the occurrence of DDP. For the cases where advection plays a dominant role during the process of solute transport, τ₀ is almost linearly correlated with DBT, and the ratio of DBT over the breakthrough time without consideration of DDP also approximately shows a linear relationship with the ratio of specific storativity to porosity, given a fixed drawdown in the adjacent aquifer with the sorption being ignored.     

Using MODFLOW code to approach transient hydraulic head with a sharp‐interface solution

Saltwater intrusion problems have been usually tackled through analytical models because of its simplicity, easy implementation and low computational cost. Most of these models are based on the sharp‐interface approximation and the Ghyben–Herzberg relation, which neglects mixing of fresh water and seawater and implicitly assumes that salt water remains static. This paper provides insight into the validity of a sharp‐interface approximation defined from a steady state solution when applied to transient seawater intrusion problems. The validation tests have been performed on a 3D unconfined synthetic aquifer, which include spatial and temporal distribution of recharge and pumping wells. Using a change of variable, the governing equation of the steady state sharp‐interface problem can be written with the same structure of the steady confined groundwater flow equation as a function of a single potential variable (?). We propose to approach also the transient problem solving a single potential equation (using also the ? variable) with the same structure of the confined groundwater flow equation. It will allow solving the problem by using the classical MODFLOW code. We have used the parameter estimation model PEST to calibrate the parameters of the transient sharp‐interface equation. We show how after the calibration process, the sharp‐interface approach may provide accurate enough results when applied to transient problems and improve the steady state results, thus avoiding the need of implementing a density‐dependent model and reducing the computational cost. This has been proved by comparing results with those obtained using the finite difference numerical code SEAWAT for solving the coupled partial differential equations of flow and density‐dependent transport. The comparison was performed in terms of piezometric heads, seawater penetration, transition zone width and critical pumping rates. Copyright © 2014 John Wiley & Sons, Ltd.     

An exact solution of solute transport by one-dimensional random velocity fields

The problem of one-dimensional transport of passive solute by a random steady velocity field is investigated. This problem is representative of solute movement in porous media, for example, in vertical flow through a horizontally stratified formation of variable porosity with a constant flux at the soil surface. Relating moments of particle travel time and displacement, exact expressions for the advection and dispersion coefficients in the Focker-Planck equation are compared with the perturbation results for large distances. The first- and second-order approximations for the dispersion coefficient are robust for a lognormal velocity field. The mean Lagrangian velocity is the harmonic mean of the Eulerian velocity for large distances. This is an artifact of one-dimensional flow where the continuity equation provides for a divergence free fluid flux, rather than a divergence free fluid velocity.     

An exact solution of solute transport by one-dimensional random velocity fields

The problem of one-dimensional transport of passive solute by a random steady velocity field is investigated. This problem is representative of solute movement in porous media, for example, in vertical flow through a horizontally stratified formation of variable porosity with a constant flux at the soil surface. Relating moments of particle travel time and displacement, exact expressions for the advection and dispersion coefficients in the Focker-Planck equation are compared with the perturbation results for large distances. The first- and second-order approximations for the dispersion coefficient are robust for a lognormal velocity field. The mean Lagrangian velocity is the harmonic mean of the Eulerian velocity for large distances. This is an artifact of one-dimensional flow where the continuity equation provides for a divergence free fluid flux, rather than a divergence free fluid velocity.     

Simulation of less‐mobile porosity dynamics in contrasting sediment water interface porous media

Considering heterogeneity in porous media pore size and connectivity is essential to predicting reactive solute transport across interfaces. However, exchange with less‐mobile porosity is rarely considered in surface water/groundwater recharge studies. Previous research indicates that a combination of pore‐fluid sampling and geoelectrical measurements can be used to quantify less‐mobile porosity exchange dynamics using the time‐varying relation between fluid and bulk electrical conductivity. For this study, we use macro‐scale (10 s of cm) advection–dispersion solute transport models linked with electrical conduction in COMSOL Multiphysics to explore less‐mobile porosity dynamics in two different types of observed sediment water interface porous media. Modeled sediment textures contrast from strongly layered streambed deposits to poorly sorted lakebed sands and cobbles. During simulated ionic tracer perturbations, a lag between fluid and bulk electrical conductivity, and the resultant hysteresis, is observed for all simulations indicating differential loading of pore spaces with tracer. Less‐mobile exchange parameters are determined graphically from these tracer time series data without the need for inverse numerical model simulation. In both sediment types, effective less‐mobile porosity exchange parameters are variable in response to changes in flow direction and fluid flux. These observed flow‐dependent effects directly impact local less‐mobile residence times and associated contact time for biogeochemical reaction. The simulations indicate that for the sediment textures explored here, less‐mobile porosity exchange is dominated by variable rates of advection through the domain, rather than diffusion of solute, for typical low‐to‐moderate rate (approximately 3–40 cm/day) hyporheic fluid fluxes. Overall, our model‐based results show that less‐mobile porosity may be expected in a range of natural hyporheic sediments and that changes in flowpath orientation and magnitude will impact less‐mobile exchange parameters. These temporal dynamics can be assessed with the geoelectrical experimental tracer method applied at laboratory and field scales.     

Simulation of long-term transient density-dependent transport in groundwater

A numerical model for the economical simulation of long-term transient response in density-dependent transport problems is introduced. Although a classical Galerkin finite element approach is used, emphasis on optimum efficiency throughout the development results in a scheme that is found to be significantly less costly than comparable existing schemes. This advantage in efficiency increases the scope of simulation problems that can be handled within the constraints of a limited research budget. Some distinctive aspects are the elimination of static quantities in the fluid continuity equation, achieved by the introduction of equivalent freshwater head, and the elimination of numerical integration, achieved by the deliberate choice of linear elements. As a result of this choice, fluid velocities are discontinuous across the element boundaries. It is shown, however, that the solution obtained with discontinuous velocities approaches that obtained with continuous velocities as the grid is refined, and that the two types of solutions give essentially the same results when the elements are in the same size range. The model is applied to simulate the complete transient response for a well-known problem of seawater intrusion in a confined aquifer. The simulation is performed with both the constant dispersion coefficient used by previous researchers, and a more physically realistic velocity-dependent dispersion coefficient. Responses are found to be substantially different for the two types of coefficients, with the velocity-dependent dispersion coefficient producing much slower convergence to a state of dynamic equilibrium, and a much more pointed saltwater toe, which at the bottom of the aquifer tends to a sharp interface at equilibrium. Finally, it is shown by means of large-scale applications that the model is capable of efficiently simulating the long-term transient response in systems of practical significance.     

Analytical Solutions for Water Flow and Solute Transport in the Unsaturated Zone

Analytical solutions for the water flow and solute transport equations in the unsaturated zone are presented. We use the Broadbridge and White nonlinear model to solve the Richards’ equation for vertical flow under a constant infiltration rate. Then we extend the water flow solution and develop an exact parametric solution for the advection-dispersion equation. The method of characteristics is adopted to determine the location of a solute front in the unsaturated zone. The dispersion component is incorporated into the final solution using a singular perturbation method. The formulation of the analytical solutions is simple, and a complete solution is generated without resorting to computationally demanding numerical schemes. Indeed, the simple analytical solutions can be used as tools to verify the accuracy of numerical models of water flow and solute transport. Comparison with a finite-element numerical solution indicates that a good match for the predicted water content is achieved when the mesh grid is one-fourth the capillary length scale of the porous medium. However, when numerically solving the solute transport equation at this level of discretization, numerical dispersion and spatial oscillations were significant.     

A characteristic-conservative model for Darcian advection

A numerical method based on the modified method of characteristics is developed for incompressible Darcy flow. Fluid elements modeled as grid cells are mapped back in time to their twisted forms and a strict equality of volumes is imposed between the two. These relations are then cast in terms of potentials using Darcy's law and a nonlinear algebraic problem is solved for potentials. Though a general technique for obtaining Darcy flow, this method is most useful when the solute advection problem also is solved with the modified method of characteristics. The combined technique (referred to as the characteristic-conservative method) using the same characteristics to obtain both velocities and concentrations is then a direct numerical approximation to the Reynolds transport theorem. The method is implemented in three dimensions and a few sample problems featuring nonuniform flow-fields are solved to demonstrate the exact mass conservation property. Inflow and outflow boundaries do not cause any problems in the implementation. In all cases, the characteristic-conservative method obtains velocities that preserve fluid volume and, concentrations that achieve exact local and global mass balance; a desirable property that usually eludes characteristics based methods for solute advection in multidimensional, nonuniform flow-fields.     

Developing Potentiometric Surfaces and Flow Fields with a Head‐Specified MODFLOW Model

Investigating changes in an aquifer system often involves comparison of observed heads from different synoptic measurements, generally with potentiometric surfaces developed by hand or a statistical approach. Alternatively, head‐specified MODFLOW models, in which constant head cells simulate observed heads, generate gridded potentiometric surfaces that explicitly account for Darcy's Law and mass balance. We developed a transient head‐specified MODFLOW model for the stratified Cambrian‐Ordovician sandstone aquifer system of northeastern Illinois to analyze flow within its 275 m deep cone of depression. Potentiometric surfaces were developed using static heads from production wells regardless of open interval; hence assuming no vertical head difference. This assumption was tested against steady‐state, head‐specified models of each sandstone strata for 1980 and 2014. The results indicate that the original conceptual model was appropriate in 1980 but not 2014, where a vertical head difference had developed at the center of the cone of depression. For earlier years, when the head difference was minimal, the transient head‐specified model compared well with a traditional, flow‐specified model. In later years, the transient head‐specified model overestimated removal of water from storage. MODFLOW facilitates the development of a time‐series of potentiometric surfaces and can easily be modified to test the impacts of different conceptual models, such as assumptions on vertical head differences. For this study of a deep confined aquifer, MODFLOW also offers advantages in generating potentiometric surfaces and flow fields over statistical interpolation techniques, although future research is needed to assess its performance in other settings.     

Experimental analysis of pore-scale flow and transport in porous media

A novel, non-intrusive fluorescence imaging technique has been used to quantitatively measure the pore geometry, fluid velocity, and solute concentration within a saturated, three-dimensional porous medium. Discrete numerical averages of these quantities have been made over a representative volume of the medium and used to estimate macroscopic quantities that appear in conventional continuum models of flow and transport. The approach is meant to illustrate how microscopic information can be measured, averaged, and used to characterize medium-scale processes that are typically approximated constitutively. The experimental system consisted of a clear, cylindrical column packed with clear spherical beads and a refractive index-matched fluid seeded with fluorescent tracer particles and solute dye. By illuminating the fluid within the column with a scanning planar laser beam, details of flow and concentration within the pore spaces can be quantitatively observed, allowing for three-dimensional, dimensional, time dependent information to be obtained at good resolution. In time dependent information to be obtained at good resolution. In the current experiment, volumetrically averaged velocities and void-to-volume ratios are first compared with bulk measurements of fluid flux and medium porosity. Microscopic measurements of concentration are then used to construct cross-sectionally averaged profiles, mean breakthrough curves, and direct measurements of the dispersive flux, velocity variance, and concentration variance. In turn, the dispersive flux measurements are compared with mean concentration gradients to provide a basis for confirming the Fickian dispersion model and estimating dispersion coefficients for the medium. Coefficients determined in this manner are compared with others based upon traditional length-scale arguments, mean breakthrough analyses, and curve fits with numerical simulations.     

Environmental tracer transport (H and SF6) in the saturated and unsaturated zones and its use in nitrate pollution management

An important quantity in groundwater protection is the residence time of water in an aquifer. It relates to both the travel time of a pollutant to arrive at a well and the time span required for self-purification of a polluted aquifer after removal of pollutant inputs. Time scales for aquifers can be gained from artificial tracer experiments or from environmental tracer data, the latter offering the only realistic alternative if time scales of years or decades have to be taken into account.

Different tracers show different time scales due to their different transport mechanisms especially in the unsaturated zone. While solute tracers are moved advectively with the seepage water, gas tracers pass the unsaturated zone diffusively through the air phase. Depending on the properties of the unsaturated zone (hydraulic properties, thickness) this difference in behavior can be used to separate the subsurface transport process into the unsaturated and the saturated parts.

In a field study in Germany, SF₆ and ³H were used as environmental tracers. Both have a relatively well-known input function. Interpretation of data from observation wells by a box model approach led to spatially and temporally varying residence times. This was an indication that the influence of the unsaturated zone could not be neglected. While the gas tracer SF₆ shows only residence times in the saturated zone, the tracer ³H reflects the whole travel time of water including both the unsaturated and saturated zones. Using a one-dimensional plug-flow model for the unsaturated zone combined with a detailed two-dimensional flow and transport model for the saturated zone leads to a holistic and consistent interpretation of the measured tracer concentrations. The observed pattern of old water under thick loess cover and younger water under areas where the fractured basalt aquifer crops out is reproduced after adjusting only two parameters: the effective porosity of the saturated aquifer and the product of field capacity and thickness of the unsaturated zone. While the effective porosity of the saturated zone is adjusted by means of the SF₆ data, the field capacity of the loess layer is adjusted by means of the ³H observations. The thickness of the unsaturated zone is deduced from geological and pedological maps. All flow data are obtained from a calibrated flow model, which is based on geological data, observed heads and pumping tests only.

The transport model for the saturated zone was calibrated by fitting the porosity by means of gaseous tracer concentrations (SF₆). The combined saturated–unsaturated zone model was then calibrated by fitting the field capacity of the unsaturated zone by means of ³H concentrations. With this model it was possible to verify the observed NO₃ concentrations at the drinking water wells and to develop predictions for their future development under various scenarios of fertilizer input reduction in specific areas.     

Can a Time Fractional‐Derivative Model Capture Scale‐Dependent Dispersion in Saturated Soils?

Time nonlocal transport models such as the time fractional advection‐dispersion equation (t‐fADE) were proposed to capture well‐documented non‐Fickian dynamics for conservative solutes transport in heterogeneous media, with the underlying assumption that the time nonlocality (which means that the current concentration change is affected by previous concentration load) embedded in the physical models can release the effective dispersion coefficient from scale dependency. This assumption, however, has never been systematically examined using real data. This study fills this historical knowledge gap by capturing non‐Fickian transport (likely due to solute retention) documented in the literature (Huang et al. 1995) and observed in our laboratory from small to intermediate spatial scale using the promising, tempered t‐fADE model. Fitting exercises show that the effective dispersion coefficient in the t‐fADE, although differing subtly from the dispersion coefficient in the standard advection‐dispersion equation, increases nonlinearly with the travel distance (varying from 0.5 to 12 m) for both heterogeneous and macroscopically homogeneous sand columns. Further analysis reveals that, while solute retention in relatively immobile zones can be efficiently captured by the time nonlocal parameters in the t‐fADE, the motion‐independent solute movement in the mobile zone is affected by the spatial evolution of local velocities in the host medium, resulting in a scale‐dependent dispersion coefficient. The same result may be found for the other standard time nonlocal transport models that separate solute retention and jumps (i.e., displacement). Therefore, the t‐fADE with a constant dispersion coefficient cannot capture scale‐dependent dispersion in saturated porous media, challenging the application for stochastic hydrogeology methods in quantifying real‐world, preasymptotic transport. Hence improvements on time nonlocal models using, for example, the novel subordination approach are necessary to incorporate the spatial evolution of local velocities without adding cumbersome parameters.     

Transport of variable-density solute plumes in beach aquifers in response to oceanic forcing

A comprehensive numerical study was undertaken to investigate transport of a variable-density, conservative solute plume in an unconfined coastal aquifer subject to high and low frequency oceanic forcing. The model combined variable-density saturated flow for groundwater and solute transport, and wave hydrodynamics from a 2D Navier–Stokes solver. A sinusoidal tidal signal was specified by implementing time-varying heads at the seaward boundary. The solute plume behavior was investigated under different oceanic forcing conditions: no forcing, waves, tide, and combined waves and tide. For each forcing condition, four different injected solute densities (freshwater, brackish water, seawater, brine) were used to investigate the effects of density on the transport of the injected plume beneath and across the beach face. The plume’s low-order spatial moments were computed, viz., mass, centroid, variance and aspect ratio. The results confirmed that both tide- and wave-forcing produce an upper saline plume beneath the beach face in addition to the classical saltwater wedge. For the no-forcing and tide-only cases (during rising tides), an additional small circulation cell below the beach face was observed. Oceanic forcing affects strongly the solute plume’s flow path, residence time and discharge rate across the beach face, as well as its spreading. For the same oceanic forcing, solute plumes with different densities follow different trajectories from the source to the discharge location (beach face). The residence time and plume spreading increased with plume density. It was concluded that simulations that neglect the effect of waves or tides cannot reproduce accurately solute plume dispersion and also, in the case of coasts with small waves or tides, the solute residence time in the aquifer.     

Relationship between dual-domain parameters and practical characterization data

Dual-domain solute transport models produce significantly improved agreement to observations compared to single-domain (advection-dispersion) models when used in an a posteriori data fitting mode. However, the use of dual-domain models in a general predictive manner has been a difficult and persistent challenge, particularly at field-scale where characterization of permeability and flow is inherently limited. Numerical experiments were conducted in this study to better understand how single-rate mass transfer parameters vary with aquifer attributes and contaminant exposure. High-resolution reference simulations considered 30 different scenarios involving variations in permeability distribution, flow field, mass transfer timescale, and contaminant exposure time. Optimal dual-domain transport parameters were empirically determined by matching to breakthrough curves from the high-resolution simulations. Numerical results show that mobile porosity increases with lower permeability contrast/variance, smaller spatial correlation length, lower connectivity of high-permeability zones, and flow transverse to strata. A nonzero non-participating porosity improves empirical fitting, and becomes larger for flow aligned with strata, smaller diffusion coefficient, and larger spatial correlation length. The non-dimensional mass transfer coefficient or Damkohler number tends to be close to 1.0 and decrease with contaminant exposure time, in agreement with prior studies. The best empirical fit is generally achieved with a combination of macrodispersion and first-order mass transfer. Quantitative prediction of ensemble-average dual-domain parameters as a function of measurable aquifer attributes proved only marginally successful.