A field study of the coupled effects of aquifer stratification,fluid density,and groundwater fluctuations on dispersivity assessments

A number of experimental studies have tackled the issue of solute transport parameter assessments either in the laboratory or in the field. But yet, the behavior of a plume in the field under density driven forces, is not well known due to possible development of instabilities. Some field tracer tests on the fate of plumes denser than native groundwater such as those encountered under waste disposal facilities, have pointed out the processes of sinking and splitting at the early stage of migration. The process of dispersion was widely investigated, but the range of dispersivity values obtained from either experimental tests, or numerical and theoretical calculations is still very large, even for the same type of aquifers. These discrepancies were considered to be essentially caused by soil heterogeneities and scale effects. In the meantime, studies on the influence of sinking and fingering have remained more scarce. The objective of the work is to analyze how transport parameters such as dispersivities can be affected by unstable conditions, which lead to plume sinking and fingering. A series of tracer tests were carried out to study under natural conditions, the transport of a dense chloride solution injected in a shallow two-layered aquifer. Two types of experiments were performed: in the first type, source injection was such that the plume could travel downward from one layer to the other of higher pore velocity, and in the second one, the migration took place only in the faster layer. The results suggest some new insights in the processes occurring at the early stages of a dense plume migration moving in a stratified aquifer under groundwater fluctuations, which can be summarized through the following points: (i) Above a stability criterion threshold, a fingering process and a multi modal plume transport take place, but local dispersivities can be cautiously derived, using breakthrough curves matching. (ii) When water table is subject to some cycling or rising, the plume can be significantly distorted in the transverse direction, leading to unusual values of the ratio between longitudinal and transverse dispersivities. (iii) Under stable conditions, for example in the case of straightforward injection in the faster aquifer layer, longitudinal dispersivity is greater than the transverse component as usually encountered, and the obtained transport parameters are closed to macro dispersivity values, which reach their asymptotic limit at very short distances. (iv) The classical scale effect about the varying dispersivity at short distances could be a process mainly due to the distance required for a plume stabilization.     

A Critical Analysis of Transverse Dispersivity Field Data

Transverse dispersion, or tracer spreading orthogonal to the mean flow direction, which is relevant e.g, for quantifying bio-degradation of contaminant plumes or mixing of reactive solutes, has been studied in the literature less than the longitudinal one. Inferring transverse dispersion coefficients from field experiments is a difficult and error-prone task, requiring a spatial resolution of solute plumes which is not easily achievable in applications. In absence of field data, it is a questionable common practice to set transverse dispersivities as a fraction of the longitudinal one, with the ratio 1/10 being the most prevalent. We collected estimates of field-scale transverse dispersivities from existing publications and explored possible scale relationships as guidance criteria for applications. Our investigation showed that a large number of estimates available in the literature are of low reliability and should be discarded from further analysis. The remaining reliable estimates are formation-specific, span three orders of magnitude and do not show any clear scale-dependence on the plume traveled distance. The ratios with the longitudinal dispersivity are also site specific and vary widely. The reliability of transverse dispersivities depends significantly on the type of field experiment and method of data analysis. In applications where transverse dispersion plays a significant role, inference of transverse dispersivities should be part of site characterization with the transverse dispersivity estimated as an independent parameter rather than related heuristically to longitudinal dispersivity.     

Determination of longitudinal dispersivity in an unconfined sandy aquifer

Study of the mobility of contaminants in an aquifer is an important issue for the proper remediation of contaminated groundwater. Determination of associated solute transport parameters therefore is essential for investigation of the extent to which groundwater can be contaminated. This study aimed at determining solute transport parameters for an unconfined sandy aquifer at a laboratory scale through various tracer tests using a conservative solute as a tracer. Tracer tests consisted of both well‐tracer tests (single and double wells) and an aquifer tracer test using a plume‐capturing device such as time domain reflectometry (TDR). The results showed that longitudinal dispersivities estimated from the single and double well‐tracer tests were 2·2 cm and 13·5 cm for a travel distance of 9·3 cm and 13·5 cm from the injection point respectively. These results agreed reasonably well with the results of the aquifer tracer test. The solute transport parameters obtained at multiple points in the aquifer through the aquifer tracer test revealed that the dispersivity length was proportional to the travel distance by a factor of 0·3, which was moderately higher than the value of 0·1 given in the literature. Copyright © 2002 John Wiley & Sons, Ltd.     

Determination of two‐dimensional laboratory‐scale dispersivities

A tracer test was conducted in a laboratory chamber representing a two‐dimensional aquifer to investigate the longitudinal dispersivity (α_L) and the ratio (α_T/α_L) of transverse to longitudinal dispersivity of sandy aquifer materials. Dispersive parameters were obtained by matching the observed chloride plumes at 9 hours and 16 hours after tracer injection with those simulated by a flow and transport model. The best match was found for α_L = 0·2 ? 0·25 cm and α_T/α_L = 0·2. The ratio of α_T/α_L = 0·2 was within the range of laboratory values reported in the literature. Sensitivity analysis revealed that the tracer plume concentration and shape were more sensitive to variations in longitudinal dispersivity than to the ratio of transverse to longitudinal dispersivity. This result contrasted with findings of others, showing that the dispersivity ratio greatly affects contaminant plume shape. However, our experimental boundary conditions restricted expansion of the plume normal to the direction of flow and thus affected the parameter estimation. Copyright © 2004 John Wiley & Sons, Ltd.     

Evaluation of longitudinal and transverse dispersivities/distance ratios for tracer test in a radially convergent flow field with scale-dependent dispersion

This study presents a novel mathematical model for analysis of non-axisymmetrical solute transport in a radially convergent flow field with scale-dependent dispersion. A two-dimensional, scale-dependent advection–dispersion equation in cylindrical coordinates is derived based on assuming that the longitudinal and transverse dispersivities increase linearly with the distance of the solute transported from its injected source. The Laplace transform finite difference technique is applied to solve the two-dimensional, scale-dependent advection–dispersion equation with variable-dependent coefficients. Concentration contours for different times, breakthrough curves of average concentration over concentric circles with a fixed radial distance, and breakthrough curves of concentration at a fixed observation point obtained using the scale-dependent dispersivity model are compared with those from the constant dispersivity model. The salient features of scale-dependent dispersion are illustrated during the non-axisymmetrical transport from the injection well into extraction well in a convergent flow field. Numerical tests show that the scale-dependent dispersivity model predicts smaller spreading than the constant-dispersivity model near the source. The results also show that the constant dispersivity model can produce breakthrough curves of averaged concentration over concentric circles with the same shape as those from the proposed scale-dependent dispersivity model at observation point near the extraction well. Far from the extracting well, the two models predict concentration contours with significantly different shapes. The breakthrough curves at observation point near the injection well from constant dispersivity model always produce lesser overall transverse dispersion than those from scale-dependent dispersivity model. Erroneous dimensionless transverse/longitudinal dispersivity ratio may result from parametric techniques which assume a constant dispersivity if the dispersion process is characterized by a distance-dependent dispersivity relationship. A curve-fitting method with an example is proposed to evaluate longitudinal and transverse scale-proportional factors of a field with scale-dependent dispersion.     

Transport and fate of nonaqueous phase liquid (NAPL) in variably saturated porous media with evolving scales of heterogeneity

 A stochastic simulation is performed to study multiphase flow and contaminant transport in fractal porous media with evolving scales of heterogeneity. Numerical simulations of residual NAPL mass transfer and subsequent transport of dissolved and/or volatilized NAPL mass in variably saturated media are carried out in conjunction with Monte Carlo techniques. The impact of fractal dimension, plume scale and anisotropy (stratification) of fractal media on relative dispersivities is investigated and discussed. The results indicate the significance of evolving scale of porous media heterogeneity to the NAPL transport in the subsurface. In general, the fractal porous media enhance the dispersivities of NAPL mass plume transport in both the water phase and the gas phase while the influence on the water phase is more significant. The porous media with larger fractal dimension have larger relative dispersivities. The aqueous horizontal dispersivity exhibits a most significant increase against the plume scale.     

Analysis of solute transport in a divergent flow tracer test with scale‐dependent dispersion

It has been known for many years that dispersivities increase with solute displacement distance in a subsurface. The increase of dispersivities with solute travel distance results from significant variation in hydraulic properties of porous media and was identified in the literature as scale‐dependent dispersion. In this study, Laplace‐transformed analytical solutions to advection‐dispersion equations in cylindrical coordinates are derived for interpreting a divergent flow tracer test with a constant dispersivity and with a linear scale‐dependent dispersivity. Breakthrough curves obtained using the scale‐dependent dispersivity model are compared to breakthrough curves obtained from the constant dispersivity model to illustrate the salient features of scale‐dependent dispersion in a divergent flow tracer test. The analytical results reveal that the breakthrough curves at the specific location for the constant dispersivity model can produce the same shape as those from the scale‐dependent dispersivity model. This correspondence in curve shape between these two models occurs when the local dispersivity at an observation well in the scale‐dependent dispersivity model is 1·3 times greater than the constant dispersivity in the constant dispersivity model. To confirm this finding, a set of previously reported data is interpreted using both the scale‐dependent dispersivity model and the constant dispersivity model to distinguish the differences in scale dependence of estimated dispersivity from these two models. The analytical result reveals that previously reported dispersivity/distance ratios from the constant dispersivity model should be revised by multiplying these values by a factor of 1·3 for the scale‐dependent dispersion model if the dispersion process is more accurately characterized by scale‐dependent dispersion. Copyright © 2007 John Wiley & Sons, Ltd.     

Key features of artificial aquifers for use in modeling contaminant transport

Two large-scale (9.5 m long, 4.7 m wide, 2.6 m deep), three-dimensional artificial aquifers were constructed to investigate the influence of spatial variations in aquifer properties on contaminant transport. One aquifer was uniformly filled with coarse sand media (0.6 to 2.0 mm) and the other was constructed as a heterogeneous aquifer using blocks of fine, medium, and coarse sands. The key features of these artificial aquifers are described. An innovative deaeration tower was constructed to overcome a problem of the aquifers becoming blocked with excess air from the ground water source. A series of tracer injection experiments were conducted to test the homogeneity of the first aquifer that was purposely built as a homogeneous aquifer and to calculate values of aquifer parameters. Experimental data show that the aquifer is slightly heterogeneous, and hydraulic conductivity values are significantly higher down one side of the aquifer compared to the mean value. There was very good agreement in estimated dispersivity values between the plume area ratio methods and the curve fitting of tracer breakthrough curves. Dispersivity estimates from a full areal source injection (12.2 m2) experiment using a 1D analytical model were higher than estimates from a limited source injection (0.2 m2) experiment using a 3D model, possibly because the 1D model does not take account of the heterogeneity of hydraulic conductivity in the aquifer, thus overestimating dispersivity. Transverse and vertical dispersivity values were about five times less than the longitudinal dispersivity. There was slight sorption of Rhodamine WT onto the aquifer media.     

Anisotropic dispersive Henry problem

The Henry problem has played a key role in our understanding of seawater intrusion into coastal aquifers and in benchmarking density dependent flow codes. This paper seeks to modify Henry’s problem to ensure sensitivity to density variations and vertical salinity profiles that resemble field observations. In the proposed problem, the “dispersive Henry problem”, mixing is represented by means of the traditional Scheidegger dispersion tensor (dispersivity times water flux). Anisotropy in the hydraulic conductivity is acknowledged and Henry’s seaside boundary condition of prescribed salt concentration is replaced by a flux dependent boundary condition, which represents more realistically salt transport across the seaside boundary. This problem turns out to be very sensitive to density variations and its solution gets closer to reality. However, an improvement in the traditional Henry problem (gain in sensitivity and realism) can be also achieved if the value of the Peclet number is significantly reduced.Although the dispersive problem lacks an analytical solution, it can shed light on flow in coastal aquifers. It provides significant information about the factors controlling seawater penetration, width of the mixing zone and influx of seawater. The width of the mixing zone depends basically on dispersion with longitudinal and transverse dispersion controlling different parts of the mixing zone but displaying similar overall effects. Toe penetration is mainly controlled by the horizontal permeability and by the geometric mean of the dispersivities. Finally, transverse dispersivity and the geometric mean of the hydraulic conductivity are the leading parameters controlling the amount of saltwater that enters the aquifer.     

Analytical power series solutions to the two-dimensional advection–dispersion equation with distance-dependent dispersivities

As is frequently cited, dispersivity increases with solute travel distance in the subsurface. This behaviour has been attributed to the inherent spatial variation of the pore water velocity in geological porous media. Analytically solving the advection–dispersion equation with distance-dependent dispersivity is extremely difficult because the governing equation coefficients are dependent upon the distance variable. This study presents an analytical technique to solve a two-dimensional (2D) advection–dispersion equation with linear distance-dependent longitudinal and transverse dispersivities for describing solute transport in a uniform flow field. The analytical approach is developed by applying the extended power series method coupled with the Laplace and finite Fourier cosine transforms. The developed solution is then compared to the corresponding numerical solution to assess its accuracy and robustness. The results demonstrate that the breakthrough curves at different spatial locations obtained from the power series solution show good agreement with those obtained from the numerical solution. However, owing to the limited numerical operation for large values of the power series functions, the developed analytical solution can only be numerically evaluated when the values of longitudinal dispersivity/distance ratio e_L exceed 0·075. Moreover, breakthrough curves obtained from the distance-dependent solution are compared with those from the constant dispersivity solution to investigate the relationship between the transport parameters. Our numerical experiments demonstrate that a previously derived relationship is invalid for large e_L values. The analytical power series solution derived in this study is efficient and can be a useful tool for future studies in the field of 2D and distance-dependent dispersive transport. Copyright © 2008 John Wiley & Sons, Ltd.     

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     

Can Contaminant Transport Models Predict Breakthrough?

A solute breakthrough curve measured during a two-well tracer test was successfully predicted in 1986 using specialized contaminant transport models. Water was injected into a confined, unconsolidated sand aquifer and pumped out 125 feet (38.3 m) away at the same steady rate. The injected water was spiked with bromide for over three days; the outflow concentration was monitored for a month. Based on previous tests, the horizontal hydraulic conductivity of the thick aquifer varied by a factor of seven among 12 layers. Assuming stratified flow with small dispersivities, two research groups accurately predicted breakthrough with three-dimensional (12-layer) models using curvilinear elements following the arc-shaped flowlines in this test.
Can contaminant transport models commonly used in industry, that use rectangular blocks, also reproduce this breakthrough curve? The two-well test was simulated with four MODFLOW-based models, MT3D (FD and HMOC options), MODFLOWT, MOC3D, and MODFLOW-SURFACT.
Using the same 12 layers and small dispersivity used in the successful 1986 simulations, these models fit almost as accurately as the models using curvilinear blocks. Subtle variations in the curves illustrate differences among the codes. Sensitivities of the results to number and size of grid blocks, number of layers, boundary conditions, and values of dispersivity and porosity are briefly presented. The fit between calculated and measured breakthrough curves degenerated as the number of layers and/or grid blocks decreased, reflecting a loss of model predictive power as the level of characterization lessened. Therefore, the breakthrough curve for most field sites can be predicted only qualitatively due to limited characterization of the hydrogeology and contaminant source strength.     

The structure of the coastal density front at the outflow of Long Island Sound during spring 2002

South of the eastern end of Long Island (Montauk Point) along the Eastern U.S. coast, a coastal density front forms between the buoyant outflow plume of the Long Island Sound (LIS) and the denser shelf waters offshore. During a 2-day cruise in April 2002, measurements of the density and velocity structure of this front were obtained from high-resolution CTD and ADCP data. Transects show the front intersecting the bottom inshore of the 30 m isobath and shoaling offshore. Variability in the location of the front is small offshore of the 40 m isobath, yet tidal excursions of the front along the bottom are significant (5 km) inshore of this depth.The frontal structure of the LIS plume was similar to observations of bottom-trapped coastal density fronts and shelf break fronts. A coastal jet in the along front direction was the main feature of the mean velocity field and was found to be in thermal wind balance with the mean density field. Stronger than expected offshore velocities near the surface, most likely a result of wind forcing, were the only exception to these similarities. In addition, analysis of temperature and salinity gradients along isopycnals gives evidence of secondary cross-frontal circulation and detachment of the bottom boundary layer. Characteristics of the LIS plume are used to evaluate recent analytical models of bottom-trapped coastal density fronts and bottom-advected plume theory, finding good agreement.     

Analysis of the impact of injection mode in transport through strongly heterogeneous aquifers

Large-scale advective transport through highly heterogeneous 3D formations is investigated using highly resolved numerical simulations and simple analytic models. Investigations are focused on impacts of two types of contaminant injection on transport through isotropic formations where flow conditions are uniform in the average. Transport is quantified by analyzing breakthrough curves for control planes at various distances from the injection zone. In flux-proportional injection mode local mass in injection zone is proportional to local groundwater flux; this setup models many practical cases such as contaminant injection through wells. In resident concentration mode local concentration in injection zone is constant. Results show that impacts of injection mode on breakthrough curves and their moments are strong and they persist for hundreds of correlation scales. The resident concentration mode leads to a fatter tails of the breakthrough curves, while the peaks are generally underpredicted. For a synthetic porous medium with logconductivity variance of 8, dispersivity computed using resident concentration mode at control plane 100 integral scales away from the injection zone was about 10 times larger than corresponding one for flux-proportional mode. Hence, injection mode impacts on transport through highly heterogeneous formations are strong and they persist for large distances from the injection zone.     

Thermal Impact of Residential Ground-Water Heat Pumps

A computer simulation study was conducted to quantify the potential thermal impact of residential water-source heat pump usage on ground-water aquifers. In a first phase of the study, weather data for nine locations throughout the country were used to estimate the energy requirements for heating and air conditioning a typical residence. These energy requirements were then translated into the volumetric water demands for a selected heat pump at each location. A representative model aquifer was then defined and its characteristics used, along with the heat pump water requirements and design ΔT's (difference between inlet and outlet water temperature) to identify the important parameters that contribute to heat transfer and to model the movement of the thermal front resulting from injection of heat pump discharge water at the nine locations. The major factor that determines the heat pump thermal impact was found to be the net amount of heat injected into, or removed from an aquifer. Other significant factors included well design, heat pump design ΔT, and physical properties of the aquifer such as thickness, porosity and dispersivity. The study showed that, in climates where winter heating demand is very nearly equal to summer cooling demands, the injection of heat pump discharge water did not cause any significant modification of the ambient model aquifer temperature. However, in hot or cold climates where air conditioning or heating demand dominates, measurable thermal changes occurred in the model aquifer. In most cases, the maximum temperature     

A simple method for calculating growth rates of petroleum hydrocarbon plumes

Consumption of aquifer Fe(III) during biodegradation of ground water contaminants may result in expansion of a contaminant plume, changing the outlook for monitored natural attenuation. Data from two research sites contaminated with petroleum hydrocarbons show that toluene and xylenes degrade under methanogenic conditions, but the benzene and ethylbenzene plumes grow as aquifer Fe(III) supplies are depleted. By considering a one-dimensional reaction front in a constant unidirectional flow field, it is possible to derive a simple expression for the growth rate of a benzene plume. The method balances the mass flux of benzene with the Fe(III) content of the aquifer, assuming that the biodegradation reaction is instantaneous. The resulting expression shows that the benzene front migration is retarded relative to the ground water velocity by a factor that depends on the concentrations of hydrocarbon and bioavailable Fe(III). The method provides good agreement with benzene plumes at a crude oil study site in Minnesota and a gasoline site in South Carolina. Compared to the South Carolina site, the Minnesota site has 25% higher benzene flux but eight times the Fe(III), leading to about one-sixth the expansion rate. Although it was developed for benzene, toluene, ethylbenzene, and xylenes, the growth-rate estimation method may have applications to contaminant plumes from other persistent contaminant sources.     

New combined log and tracer test interpretation method for identifying transfers in fissured aquifers

Tracer tests represent the most appropriate approach for assessing hydrodispersive parameters such as transversal and longitudinal dispersivities or kinematic porosity on an aquifer scale. They are generally carried out by injecting a tracer in a borehole and measuring its concentration over time in neighboring boreholes by extracted volume sampling or downhole measurements. Logging is one of the most suitable methods for evaluating fissured reservoirs. But short circuits between fractures with different hydraulic potential through boreholes induce mixing phenomena that cannot be avoided without packers. This mixing can shift the breakthrough curves deduced from the logs for each producing fracture and distort determination of their location.
The method proposed in this paper aims at measuring the flow rate and the solute breakthrough for hydraulically active fractures, in open boreholes. It involves estimating a velocity profile along the borehole column by the analysis of two successive logs: a shift function according to depth is thus determined by comparison between log portions on each successive one. The velocity gradients reflect the inward or outward flow rates produced by each fracture. On the basis of these flow rates, it is possible to determine the mixing effects inside the borehole and then to plot unbiased breakthrough curves for each producing fracture.
This method was applied at a granitic site in the eastern Pyrenees. In spite of some questionable limitations, the results showed that the method seems adapted to situations with many fractures. The precise hydraulic pattern which is obtained at the borehole scale is discussed in terms of a dual porosity model. Furthermore, interpretation of the breakthrough curves for fractures corrected for mixing effects revealed that Peclet numbers are strongly underestimated if this phenomenon is not considered.     

Upstream Dispersion in Solute Transport Models: A Simple Evaluation and Reduction Methodology

This article outlines analytical solutions to quantify the length scale associated with “upstream dispersion,” the artificial movement of solutes in the opposite direction to groundwater flow, in solute transport models. Upstream dispersion is an unwanted artifact in common applications of the advection-dispersion equation (ADE) in problems involving groundwater flow in the direction of increasing solute concentrations. Simple formulae for estimating the one-dimensional distance of upstream dispersion are provided. These show that under idealized conditions (i.e., steady-state flow and transport, and a homogeneous aquifer), upstream dispersion may be a function of only longitudinal dispersivity. The scale of upstream dispersion in a selection of previously presented situations is approximated to highlight the utility of the presented formulae and the relevance of this ADE anomaly in common transport problems. Additionally, the analytical solution is applied in a hypothetical scenario to guide the modification of dispersion parameters to minimize upstream dispersion.     

Fluid dispersion effects on density-driven thermohaline flow and transport in porous media

This study introduces the dispersive fluid flux of total fluid mass to the density-driven flow equation to improve thermohaline modeling of salt and heat transports in porous media. The dispersive fluid flux in the flow equation is derived to account for an additional fluid flux driven by the density gradient and mechanical dispersion. The coupled flow, salt transport and heat transport governing equations are numerically solved by a fully implicit finite difference method to investigate solution changes due to the dispersive fluid flux. The numerical solutions are verified by the Henry problem and the thermal Elder problem under a moderate density effect and by the brine Elder problem under a strong density effect. It is found that increment of the maximum ratio of the dispersive fluid flux to the advective fluid flux results in increasing dispersivity for the Henry problem and the brine Elder problem. The effects of the dispersive fluid flux on salt and heat transports under high density differences and high dispersivities are more noticeable than under low density differences and low dispersivities. Values of quantitative indicators such as the Nusselt number, mass flux, salt mass stored and maximum penetration depth in the brine Elder problem show noticeable changes by the dispersive fluid flux. In the thermohaline Elder problem, the dispersive fluid flux shows a considerable effect on the shape and the number of developed fingers and makes either an upwelling or a downwelling flow in the center of the domain. In conclusion, for the general case that involves strong density-driven flow and transport modeling in porous media, the dispersive fluid flux should be considered in the flow equation.