Solution of the advection-dispersion equation in two dimensions by a finite-volume Eulerian-Lagrangian localized adjoint method

We extend the finite-volume Eulerian-Lagrangian localized adjoint method (FVELLAM) for solution of the advection-dispersion equation to two dimensions. The method can conserve mass globally and is not limited by restrictions on the size of the grid Peclet or Courant number. Therefore, it is well suited for solution of advection-dominated ground-water solute transport problems. In test problem comparisons with standard finite differences, FVELLAM is able to attain accurate solutions on much coarser space and time grids. On fine grids, the accuracy of the two methods is comparable. A critical aspect of FVELLAM (and all other ELLAMs) is evaluation of the mass storage integral from the preceding time level. In FVELLAM this may be accomplished with either a forward or backtracking approach. The forward tracking approach conserves mass globally and is the preferred approach. The backtracking approach is less computationally intensive, but not globally mass conservative. Boundary terms are systematically represented as integrals in space and time which are evaluated by a common integration scheme in conjunction with forward tracking through time. Unlike the one-dimensional case, local mass conservation cannot be guaranteed, so slight oscillations in concentration can develop, particularly in the vicinity of inflow or outflow boundaries.     

A novel platform to evaluate the dampening of water and solute transport in an experimental channel under unsteady flow conditions

This paper presents a novel platform to study the dampening of water and solute transport in an experimental channel under unsteady flow conditions, where literature data are scarce. We address the question about what could be the smallest size of experimental platform that is useful for research, project studies, and teaching activities and that allows to do rational experiments characterized by small space occupation, short experimental duration, high measurement precision, high quality and reproducible experimental curves, low water and energy consumption, and the possibility to test a large variety of hydrograph scenarios. Whereas large scale hydraulic laboratories have focused their studies on sediment transport, our platform deals with solute transport. The objectives of our study are (a) building a platform that allows to do rational experiments, (b) enriching the lack of experimental data concerning water and solute transport under unsteady state conditions, and (c) studying the dampening of water and solute transport. We studied solute transport in a channel with lateral gain and lateral loss under different experimental configurations, and we show how the same lateral loss flow event can lead to different lateral loss mass repartitions under different configurations. In order to characterize water and solute dampening between the input and the output of the channel, we calculate dampening ratios based on peak coordinates of time flow curves and time mass curves and that express the decrease of peak amplitude and the increase of peak occurrence time between the input and output curves. Finally, we use a solute transport model coupling the diffusive wave equation for water transfer and the advection–diffusion equation for solute transport in order to simulate the experimental data. The simulations are quite good with a Nash–Sutcliffe efficiency NSE > 0.98 for water transfer and 0.84 < NSE < 0.97 for solute transport. This platform could serve hydrological modellers because it offers a variety of measured parameters (flow, water height, and solute concentration), at a fine time step under unsteady flow conditions.     

Evaluation of volatilization as a natural attenuation pathway for MTBE

Volatilization and diffusion through the unsaturated zone can be an important pathway for natural attenuation remediation of methyl tert-butyl ether (MTBE) at gasoline spill sites. The significance of this pathway depends primarily on the distribution of immiscible product within the unsaturated zone and the relative magnitude of aqueous-phase advection (ground water recharge) to gaseous-phase diffusion. At a gasoline spill site in Laurel Bay, South Carolina, rates of MTBE volatilization from ground water downgradient from the source are estimated by analyzing the distribution of MTBE in the unsaturated zone above a solute plume. Volatilization rates of MTBE from ground water determined by transport modeling ranged from 0.0020 to 0.0042 g m(-2)/year, depending on the assumed rate of ground water recharge. Although diffusive conditions at the Laurel Bay site are favorable for volatilization, mass loss of MTBE is insignificant over the length (230 m) of the solute plume. Based on this analysis, significant volatilization of MTBE from ground water downgradient from source areas at other sites is not likely. In contrast, model results indicate that volatilization coupled with diffusion to the atmosphere could be a significant mass loss pathway for MTBE in source areas where residual product resides above the capillary zone. Although not documented, mass loss of MTBE at the Laurel Bay site due to volatilization and diffusion to the atmosphere are predicted to be two to three times greater than mass loading of MTBE to ground water due to dissolution and recharge. This result would imply that volatilization in the source zone may be the critical natural attenuation pathway for MTBE at gasoline spill sites, especially when considering capillary zone limitations on volatilization of MTBE from ground water and the relative recalcitrance of MTBE to biodegradation.     

Comparison of heat and bromide as ground water tracers near streams

Heat and bromide were compared as tracers for examining stream/ground water exchanges along the middle reaches of the Santa Clara River, California, during a 10-hour surface water sodium bromide injection test. Three cross sections that comprise six shallow (<1 m) piezometers were installed at the upper, middle, and lower sections of a 17 km long study reach, to monitor temperatures and bromide concentrations in the shallow ground water beneath the stream. A heat and ground water transport simulation model and a closely related solute and ground water transport simulation model were matched up for comparison of simulated and observed temperatures and bromide concentrations in the streambed. Vertical, one-dimensional simulations of sediment temperature were fitted to observed temperature results, to yield apparent streambed hydraulic conductivities in each cross section. The temperature-based hydraulic conductivities were assigned to a solute and ground water transport model to predict sediment bromide concentrations, during the sodium bromide injection test. Vertical, one-dimensional simulations of bromide concentrations in the sediments yielded a good match to the observed bromide concentrations, without adjustment of any model parameters except solute dispersivities. This indicates that, for the spatial and temporal scales examined on the Santa Clara River, the use of heat and bromide as tracers provide comparable information with respect to apparent hydraulic conductivities and fluxes for sediments near streams. In other settings, caution should be used due to differences in the nature of conservative (bromide) versus nonconservative (heat) tracers, particularly when preferential flowpaths are present.     

Coupling water flow and solute transport into a physically-based surface-subsurface hydrological model

A distributed-parameter physically-based solute transport model using a novel approach to describe surface-subsurface interactions is coupled to an existing flow model. In the integrated model the same surface routing and mass transport equations are used for both hillslope and channel processes, but with different parametrizations for these two cases. For the subsurface an advanced time-splitting procedure is used to solve the advection-dispersion equation for transport and a standard finite element scheme is used to solve Richards equation for flow. The surface-subsurface interactions are resolved using a mass balance-based surface boundary condition switching algorithm that partitions water and solute into actual fluxes across the land surface and changes in water and mass storage. The time stepping strategy allows the different time scales that characterize surface and subsurface water and solute dynamics to be efficiently and accurately captured. The model features and performance are demonstrated in a series of numerical experiments of hillslope drainage and runoff generation.     

Characterizing hyporheic transport processes — Interpretation of electrical geophysical data in coupled stream–hyporheic zone systems during solute tracer studies

Quantifying hyporheic solute dynamics has been limited by our ability to assess the magnitude and extent of stream interactions with multiple domains: mobile subsurface storage (MSS, e.g., freely flowing pore water) and immobile subsurface storage (ISS, e.g., poorly connected pore water). Stream-tracer experiments coupled with solute transport modeling are frequently used to characterize lumped MSS and ISS dynamics, but are limited by the ability to sample only “mobile” water and by window of detection issues. Here, we couple simulations of near-surface electrical resistivity (ER) methods with conservative solute transport to directly compare solute transport with ER interpretations, and to determine the ability of ER to predict spatial and temporal trends of solute distribution and transport in stream–hyporheic systems. Results show that temporal moments from both ER and solute transport data are well correlated for locations where advection is not the dominant solute transport process. Mean arrival time and variance are especially well-predicted by ER interpretation, providing the potential to estimate rate-limited mass transport (i.e. diffusive) parameters from these data in a distributed domain, substantially increasing our knowledge of the fate and transport of subsurface solutes.     

Eulerian-Lagrangian method for solving transport in aquifers

A Eulerian-Langrangian scheme is used to reformulate the equation of solute transport with ground water in saturated soils. The governing equation is decomposed into advection along characteristic path lines and propagation of the residue at a fixed grid.The method was employed to simulate transport of a conservative pollutant in a hypothetical aquifer, subject to the equivalence of real conditions. Implementation was based on data involving parameters of a heterogeneous aquifer, heavy flux stresses of densed pumpage/recharge wells, precipitation and seasonally changing flow regimes. Simulation, with coarse grid and high Peclet numbers yielded minute mass balance errors.     

Grid resolution study of ground water flow and transport

Three-dimensional grids representing a heterogeneous, ground water system are generated at 10 different resolutions in support of a site-scale flow and transport modeling effort. These grids represent hydrostratigraphy near Yucca Mountain, Nevada, consisting of 18 stratigraphic units with contrasting fluid flow and transport properties. The grid generation method allows the stratigraphy to be modeled by numerical grids of different resolution so that comparison studies can be performed to test for grid quality and determine the resolution required to resolve geologic structure and physical processes such as fluid flow and solute transport. The process of generating numerical grids with appropriate property distributions from geologic conceptual models is automated, thus making the entire process easy to implement with fewer user-induced errors. The series of grids of various resolutions are used to assess the level at which increasing resolution no longer influences the flow and solute transport results. Grid resolution is found to be a critical issue for ground water flow and solute transport. The resolution required in a particular instance is a function of the feature size of the model, the intrinsic properties of materials, the specific physics of the problem, and boundary conditions. The asymptotic nature of results related to flow and transport indicate that for a hydrologic model of the heterogeneous hydrostratigraphy under Yucca Mountain, a horizontal grid spacing of 600 m and vertical grid spacing of 40 m resolve the hydrostratigraphic model with sufficient precision to accurately model the hypothetical flow and solute transport to within 5% of the value that would be obtained with much higher resolution.     

The effect of non divergence-free velocity fields on field scale ground water solute transport

Solute plume subjected to field scale hydraulic conductivity heterogeneity shows a large dispersion/macrodispersion, which is the manifestation of existing fields scale heterogeneity on the solute plume. On the other hand, due to the scarcity of hydraulic conductivity measurements at field scale, hydraulic conductivity heterogeneity can only be defined statistically, which makes the hydraulic conductivity a random variable/function. Random hydraulic conductivity as a parameter in flow equation makes the pore flow velocity also random and the ground water solute transport equation is a stochastic differential equation now. In this study, the ensemble average of stochastic ground water solute transport equation is taken by the cumulant expansion method in order to upscale the laboratory scale transport equation to field scale by assuming pore flow velocity is a non stationary, non divergence-free and unsteady random function of space and time. Besides the stochastic explanation of macrodispersion and the velocity correction term obtained by Kavvas and Karakas (J Hydrol 179:321–351, 1996) before a new velocity correction term, which is a function of mean pore flow velocity divergence, is obtained in this study due to strict second order cumulant expansion (without omitting any term after the expansion) performed. The significance of the new velocity correction term is investigated on a one dimensional transport problem driven by a density dependent flow field.     

Modeling interaction of fluid and salt in an aquifer/lagoon system

To simulate the dynamic interaction between a saline lagoon and a ground water system, a numerical model for two-dimensional, variable-density, saturated-unsaturated, and coupled flow and solute transport (saltwater intrusion by finite elements and characteristics [SIFEC]) was modified to allow the volume of water and mass of salt in the lagoon to vary with each time step. The modified SIFEC allows the stage of a lagoon to vary in accordance with a functional relation between the stage and water volume of the lagoon, and also allows the salt concentration of the lagoon to vary in accordance with the salt budget of the lagoon including chemical precipitation and dissolution of salt. The updated stage and salt concentration of the lagoon are in turn used as transient boundary conditions for the coupled flow and solute transport model. The utility of the modified model was demonstrated by applying it to the eastern Mediterranean coastal region of Turkey for assessing impacts of climate change on the subsurface environment under scenarios of sea level rise, increased evaporation, and decreased precipitation.     

Modeling plume behavior for nonlinearly sorbing solutes in saturated homogeneous porous media

Transport of a sorbing solute in a two-dimensional steady and uniform flow field is modeled using a particle tracking random walk method. The solute is initially introduced from an instantaneous point source. Cases of linear and nonlinear sorption isotherms are considered. Local pore velocity and mechanical dispersion are used to describe the solute transport mechanisms at the local scale. The numerical simulation of solute particle transport yields the large scale behavior of the solute plume. Behavior of the plume is quantified in terms of the center-of-mass displacement distance, relative velocity of the center-of-mass, mass breakthrough curves, spread variance, and longitudinal skewness. The nonlinear sorption isotherm affects the plume behavior in the following way relative to the linear isotherm: (1) the plume velocity decreases exponentially with time; (2) the longitudinal variance increases nonlinearly with time; (3) the solute front is steepened and tailing is enhanced     

Convergent Radial Tracing of Viral and Solute Transport in Gneiss Saprolite

Deeply weathered crystalline rock aquifer systems comprising unconsolidated saprolite and underlying fractured bedrock (saprock) underlie 40% of sub-Saharan Africa. The vulnerability of this aquifer system to contamination, particularly in rapidly urbanizing areas, remains poorly understood. In order to assess solute and viral transport in saprolite derived from Precambrian gneiss, forced-gradient tracer experiments using chloride and Escherichia coli phage ΦX174 were conducted in southeastern Uganda. The bacteriophage tracer was largely unrecovered; adsorption to the weathered crystalline rock matrix is inferred and enabled by the low pH (5.7) of site ground water and the bacteriophage's relatively high isoelectric point (pI = 6.6). Detection of the applied ΦX174 phage in the pumping well discharge at early times during the experiment traces showed, however, that average ground water flow velocities exceed that of the inert solute tracer, chloride. This latter finding is consistent with observations in other hydrogeological environments where statistically extreme sets of microscopic flow velocities are considered to transport low numbers of fecal pathogens and their proxies along a selected range of linked ground water pathways. Application of a radial advection-dispersion model with an exponentially decaying source term to the recovered chloride tracer estimates a dispersivity (α) of 0.8 ± 0.1 m over a distance of 4.15 m. Specific yield (S_y) is estimated to be 0.02 from volume balance calculations based on tracer experiments. As single-site observations, our estimates of saprolite S_y and α are tentative but provide a starting point for assessing the vulnerability of saprolite aquifers in sub-Saharan Africa to contamination and estimating quantitatively the impact of climate and abstraction on ground water storage.     

An assessment of aquifer storage recovery using ground water flow models

Owing to increased demands on ground water accompanied by increased drawdowns, technologies that use recharge options, such as aquifer storage recovery (ASR), are being used to optimize available water resources and reduce adverse effects of pumping. In this paper, three representative ground water flow models were created to assess the impact of hydrogeologic and operational parameters/factors on recovery efficiency of ASR systems. Flow/particle tracking and solute transport models were used to track the movement of water during injection, storage, and recovery. Results from particle tracking models consistently produced higher recovery efficiency than the solute transport models for the parameters/properties examined because the particle tracking models neglected mixing of the injected and ambient water. Mixing between injected and ambient water affected recovery efficiency. Results from this study demonstrate the interactions between hydrogeologic and operational parameters on predictions of recovery efficiency. These interactions are best simulated using coupled numerical ground water flow and transport models that include the effects of mixing of injected water and ambient ground water.     

Transport of nonsorbing solutes in a streambed with periodic bedforms

Previous studies of hyporheic zone focused largely on the net mass transfer of solutes between stream and streambed. Solute transport within the bed has attracted less attention. In this study, we combined flume experiments and numerical simulations to examine solute transport processes in a streambed with periodic bedforms. Solute originating from the stream was subjected to advective transport driven by pore water circulation due to current–bedform interactions as well as hydrodynamic dispersion in the porous bed. The experimental and numerical results showed that advection played a dominant role at the early stage of solute transport, which took place in the hyporheic zone. Downward solute transfer to the deep ambient flow zone was controlled by transverse dispersion at the later stage when the elapsed time exceeded the advective transport characteristic time t_c (= L/u_c with L being the bedform length and u_c the characteristic pore water velocity). The advection-based pumping exchange model was found to predict reasonably well solute transfer between the overlying water and streambed at the early stage but its performance deteriorated at the later stage. With dispersion neglected, the pumping exchange model underestimated the long-term rate and total mass of solute transfer from the overlying water to the bed. Therefore both advective and dispersive transport components are essential for quantification of hyporheic exchange processes.     

Experimental and analytical studies of solute transport during run‐off over vegetated surfaces

Solute transport in overland flow is considered as one of the main contributors to water pollution. Although many models of pollutant transport mechanism from soil to run‐off water have been proposed, the characteristics of solute transport accompanying the water run‐off over vegetated surface have not been well studied. In this study, a series of laboratory experiments were conducted to study the solute transport over vegetated surfaces. Based on the experimental results, an idea of the “stationary water layer” in run‐off was proposed. Applying the complete mixing theory in the stationary water layer, an analytical solute transport model was developed with the assumption that the upper run‐off completely mixes with the underlying water in the stationary water layer for each site. The results show that the predictions made by the present model are in good agreement with the measured experimental data. For the vegetated surfaces, the depth of stationary water layer is related to the rainfall intensity, bed slope, and vegetation density. The analytical solution shows that the maximum solute transport occurs at the time of concentration. This study advances our understanding of the mechanisms of solute transport over vegetated areas.     

Travel Time Distributions Derived from Particle Tracking in Models Containing Weak Sinks

A travel time distribution based on a particle-tracking analysis in a ground water model containing weak sinks is often uncertain because whether a particle is discharged or allowed to pass through a weak sink is unresolved by particle-tracking theory. We present a probability-based method to derive an objective travel time distribution in models containing weak sinks. The method discharges a fraction of the particle at the weak sink and allows the remaining fraction to pass through the weak sink. The weight of the discharged fraction depends on the ratio of the sink flux to the influx into the weak sink cell. We tested this approach on a coarse (100 × 100 m) and a fine (25 × 25 m) horizontal resolution regional scale ground water model (34.5 × 24 km). We compared the travel time distributions in a small subcatchment derived from particle-tracking analysis with one derived from a transport model. We found that the particle-tracking analysis with the coarse model underestimated the travel time distribution of the catchment compared to the transport solution or a particle-tracking analysis with the fine model. The underestimation of travel times with the coarse model was a result of a large area covered by sink cells in this model and the more accurate flow patterns simulated by the fine model. The probability-based method presented here compares favorably with a solute transport solution and provides an accurate travel time distribution when used with a fine-resolution ground water model.     

Laboratory and numerical investigation of flow and transport near a seepage-face boundary

Laboratory and numerical modeling investigations were completed to study the unconfined ground water flow and transport processes near a seepage-face boundary. The laboratory observations were made in a radial sand tank and included measurements of the height of the seepage face, flow velocity near the seepage face, travel time distribution of multiple tracer slugs, and streamlines. All the observations were reliably reproduced with a three-dimensional, axi-symmetric, variably saturated ground water flow model. Physical data presented in this work demonstrate and quantify the importance of three-dimensional transport patterns within a seepage-face zone. The results imply that vertically averaged flow models that employ Dupuit approximations might introduce error in the analysis of localized solute transport near a seepage-face boundary. The experimental dataset reported in this work will also be of interest for those who are attempting to validate a numerical algorithm for solving ground water and contaminant discharge patterns near a surface-water boundary.     

Solute and Heat Transport Model of the Henry and Hilleke Laboratory Experiment

SEAWAT is a coupled version of MODFLOW and MT3DMS designed to simulate variable-density ground water flow and solute transport. The most recent version of SEAWAT, called SEAWAT Version 4, includes new capabilities to represent simultaneous multispecies solute and heat transport. To test the new features in SEAWAT, the laboratory experiment of Henry and Hilleke (1972) was simulated. Henry and Hilleke used warm fresh water to recharge a large sand-filled glass tank. A cold salt water boundary was represented on one side. Adjustable heating pads were used to heat the bottom and left sides of the tank. In the laboratory experiment, Henry and Hilleke observed both salt water and fresh water flow systems separated by a narrow transition zone. After minor tuning of several input parameters with a parameter estimation program, results from the SEAWAT simulation show good agreement with the experiment. SEAWAT results suggest that heat loss to the room was more than expected by Henry and Hilleke, and that multiple thermal convection cells are the likely cause of the widened transition zone near the hot end of the tank. Other computer programs with similar capabilities may benefit from benchmark testing with the Henry and Hilleke laboratory experiment.     

Comparison of Stainless Steel vs. PTFE Miniwells for Monitoring Halogenated Organic Solute Transport

Field tests of organic solute transport behavior have often been monitored using small-diameter wells (miniwells). To determine if experimental results could be significantly biased by sorption to, desorption from, or diffusion through sampling lines, dissolved concentrations of tetrachloroethene and carbon tetrachloride were measured in ground water samples collected simultaneously from the same spatial location during a forced-gradient test in the Borden aquifer using polytetrafluoroethene (PTFE) and stainless steel miniwells (1/8-inch O.D.).
A semiautomated organic analytical system was used on-site to obtain real-time results, which avoided sample holding problems and permitted optimizing sampling times. The breakthrough curves (plots of concentration vs. time) for both organic compounds indicate that under the conditions of this experiment (low organic solute concentrations, short exposure time of sampling lines to the plume, adequate flushing of sampling lines) there is no significant difference between concentration histories (breakthrough curves) collected using a polytetrafluoroethene sampling line and those collected using a stainless steel sampling line. This suggests that organic solute tailing seen in this and also in a similar transport experiment previously conducted at the site is the result of transport processes in the aquifer rather than an artifact introduced by the PTFE miniwells.     

Pharmaceuticals and Other Organic Waste Water Contaminants Within a Leachate Plume Downgradient of a Municipal Landfill

Ground water samples collected from the Norman Landfill research site in central Oklahoma were analyzed as part of the U.S. Geological Survey (USGS) Toxic Substances Hydrology Program's national reconnaissance of pharmaceuticals and other organic waste water contaminants (OWCs) in ground water. Five sites, four of which are located downgradient of the landfill, were sampled in 2000 and analyzed for 76 OWCs using four research methods developed by the USGS. OWCs were detected in water samples from all of the sites sampled, with 22 of the 76 OWCs being detected at least once. Cholesterol (a plant and animal steroid), was detected at all five sites and was the only compound detected in a well upgradient of the landfill. N,N-diethyltoluamide (DEBT used in insect repellent) and tri(2-chloroethyl) phosphate (fire-retardant) were detected in water samples from all four sites located within the landfill-derived leachate plume. The sites closest to the landfill had more detections and greater concentrations of each of the detected compounds than sites located farther away. Detection of multiple OWCs occurred in the four sites located within the leachate plume, with a minimum of four and a maximum of 17 OWCs detected. Because the landfill was established in the 1920s and closed in 1985, many compounds detected in the leachate plume were likely disposed of decades ago. These results indicate the potential for long-term persistence and transport of some OWCs in ground water.