Constraining a Flow Model with Field Measurements to Assess Water Transit Time Through a Vadose Zone

The modeling of thick vadose zones is particularly challenging because of difficulties in collecting a variety of measured sediment properties, which are required for parameterizing the model. Some models rely on synthetic data, whereas others are simplified by running as homogeneous sediment domains and relying on a single set of sediment properties. Few studies have simulated flow processes through a thick vadose zone using real and comprehensive data sets comprising multiple measurements. Here, we develop a flow model for a 7-m-thick vadose zone. This model, combining the numerical codes CTRAN/W with SEEP/W, includes the measured sediment hydraulic properties of the investigated vadose zone and incorporates the actual climate and subsurface conditions of the study site (precipitations, water-table elevations, and stable isotope data). The model is calibrated by fitting the simulated and measured vertical profiles of water content. Our flow model calculates a transit time of 1 year for the travel of water through the 7-m vadose zone; this estimate matches stable isotope-based results obtained previously for this site. A homogeneous sediment domain flow model, which considers only a single set of sediment properties, produces a transit time that is approximately half the duration of that of the heterogeneous flow model. This difference highlights the importance of assuming heterogeneous material within models of thick vadose zones and testifies to the advantage gained when using real sediment hydraulic properties to parametrize a flow model.     

Gas tracer transport through a heterogeneous fracture zone under two phase flow conditions: Model development and parameter sensitivity

Large amounts of gas can result from anaerobic corrosion of metals and from chemical and biological degradation of organic substances in underground repositories for radioactive waste. Gas generation may lead to the formation of a gas phase bubble and to the migration of radioactive gaseous species. Transport occurs in, at least, in two forms: (1) gas bubble, migration is controlled by advection, dispersion and diffusion in the gas phase, and (2) within water pockets, the dissolved species migrate mainly by diffusion. We consider a two-dimensional system representing an isolated heterogeneous fractured zone. A dipole gas flow field is generated and gas tracers are injected. The delay in the breakthrough curves is studied. A simple method is used to solve the gas species transport equations in multiphase conditions. This method is based on a formal analogy between the equations of gas transport in a two phase system and the equations of solute tracer transport in water saturated systems. We perform a sensitivity analysis to quantify the relevance of the various transport mechanisms. We find that gas tracer migration is very sensitive to gas tracer solubility, which affects gas tracer transport of both mobile and immobile zones, and shows high sensitivity to diffusion in the gas phase, to heterogeneity and to gas pressure, but the largest sensitivity was observed with respect to injection borehole properties, i.e. borehole volume and water filled fraction.     

Stream water infiltration, bank storage, and storage zone changes due to stream-stage fluctuations

During a flood period, stream-stage increases induce infiltration of stream water into an aquifer; subsequent declines in stream stage cause a reverse motion of the infiltrated water. This paper presents the results of the water exchange rate between a stream and aquifer, the storage volume of the infiltrated stream water in the surrounding aquifer (bank storage), and the storage zone. The storage zone is the part of aquifer where groundwater is replaced by stream water during the flood. MODFLOW was used to simulate stream–aquifer interactions and to quantify rates of stream infiltration and return flow. MODPATH was used to trace the pathlines of the infiltrated stream water and to determine the size of the storage zone. Simulations were focused on the analyses of the effects of the stream-stage fluctuation, aquifer properties, the hydraulic conductivity of streambed sediments, regional hydraulic gradients, and recharge and evapotranspiration (ET) rates on stream–aquifer interactions. Generally, for a given stream–aquifer system, larger flow rates result from larger stream-stage fluctuations; larger storage volumes and storage zones are produced by larger and longer-lasting fluctuations. For a given stream-stage hydrograph, a lower-permeable streambed, an aquitard, or an anisotropic aquifer of low vertical hydraulic conductivity can significantly reduce the rate of infiltration and limit the size of the storage zone. The bank storage solely caused by the stage fluctuation differs slightly between gaining and losing streams. Short-term rainfall recharge and ET loss in the shallow groundwater slightly influence on the flow rate, but their effects on bank storage in a larger area for a longer period can be considerable.     

Time-related capture zones for radial flow in two dimensional randomly heterogeneous media

We consider the effect of randomly heterogeneous hydraulic conductivity on the spatial location of time-related capture zones (isochrones) for a non-reactive tracer in the steady-state radial flow field due to a pumping well in a confined aquifer. A Monte Carlo (MC) procedure is used in conjunction with FFT-based spectral methods. The log hydraulic conductivity field is assumed to be Gaussian and stationary, with isotropic exponential correlation. Various degrees of domain heterogeneity are considered and stability and accuracy of the MC procedure is examined. The location of an isochrone becomes uncertain due to heterogeneity, and it is strongly influenced by hydraulic conductivity variance. The probability that a particle released at a point in the aquifer is pumped by the well within a given time is identified. We propose a new expression for the probabilistic spatial distribution of isochrones, which is formally similar to the analytical solution for a uniform medium and takes into account the effects of heterogeneity.     

Estimating longitudinal dispersion in rivers using Acoustic Doppler Current Profilers

The longitudinal dispersion coefficient (D) is an important parameter needed to describe the transport of solutes in rivers and streams. The dispersion coefficient is generally estimated from tracer studies but the method can be expensive and time consuming, especially for large rivers. A number of empirical relations are available to estimate the dispersion coefficient; however, these relations are known to produce estimates within an order of magnitude of the tracer value. The focus of this paper is on using the shear-flow dispersion theory to directly estimate the dispersion coefficient from velocity measurements obtained using an Acoustic Doppler Current Profiler (ADCP). Using tracer and hydrodynamic data collected within the same river reaches, we examined conditions under which the ADCP and tracer methods produced similar results. Since dead zones / transient storage (TS) are known to influence the dispersion coefficient, we assessed the relative importance of dead zones in different stream reaches using two tracer-based approaches: (1) TS modeling which explicitly accounts for dead zones and (2) the advection–dispersion equation (ADE) which does not have separate terms for dead zones. Dispersion coefficients based on the ADE tend to be relatively high as they describe some of the effects of dead zones as well. Results based on the ADCP method were found to be in good agreement with the ADE estimates indicating that storage zones play an important role in the estimated dispersion coefficients, especially at high flows. For the river sites examined in this paper, the tracer estimates of dispersion were close to the median values of the ADCP estimates obtained from multiple datasets within a reach. The ADCP method appears to be an excellent alternative to the traditional tracer-based method if care is taken to avoid spurious data and multiple datasets are used to compute a distance-weighted average or other appropriate measure that represents reach-averaged conditions.     

Dilution of non-reactive tracers in variably saturated sandy structures

Based on a dye tracer experiment in a sand tank we addressed the problem of local dispersion of conservative tracers in the unsaturated zone. The sand bedding was designed to have a defined spatial heterogeneity with a strong anisotropy. We estimated the parameters that characterize the local dispersion and dilution from concentration maps of a high spatial and temporal resolution obtained by image analysis. The plume spreading and mixing behavior was quantified on the basis of the coefficient of variation of the concentration and of the dilution index. The heterogeneous structure modified the flow pattern depending on water saturation. The shape of the tracer plumes revealed the structural signature of the sand bedding at low saturation only. In this case pronounced preferential flow was observed. At higher flow rates the structure remained hidden by a spatially almost homogeneous behavior of the plumes. In this context, we mainly discuss the mechanism of re-distributing a finite mass of inert solutes over a large volume, due to macro- and micro-heterogeneities of the structure.     

Delineation of three-dimensional well capture zones for complex multi-aquifer systems

The delineation of well capture zones is a basic component of ground water protection. The conventional methodology for capture zone delineation is backward advective particle tracking, often applied under the assumption of a two-dimensional aquifer. The suitability of the conventional approach for complex heterogeneous multi-aquifer systems was investigated, using the Waterloo Moraine aquifer system as an example. It was found that the conventional approach produces irregular particle tracks that require judgment to interpret in a meaningful way, and it can raise questions that may affect the credibility of the capture zone delineation. As an alternative, the potentially powerful but little-used backward-in-time advective-dispersive transport approach was investigated. A key advantage of this approach is its capability to represent local heterogeneities through the dispersion term. The dispersion process has a natural smoothing effect that results in unambiguous capture zones without the need for interpretation, thus enhancing credibility. The question of capture zone validation is also addressed. The meaning of a three-dimensional capture zone is considered, and it is shown that a fully three-dimensional representation of the system is crucial for valid results. The distinction between the maximum extent capture zone and the surface capture zone is also explained. In the case of complex heterogeneous systems, advective particle tracking can be used as an initial screening tool, whereas the more realistic backward-transport modeling approach can be used for final capture-zone delineation.     

Field Test of Enhanced Remedial Amendment Delivery Using a Shear‐Thinning Fluid

Heterogeneity of hydraulic properties in aquifers may lead to contaminants residing in lower‐permeability zones where it is difficult to deliver remediation amendments using conventional injection processes. The focus of this study is to examine use of a shear‐thinning fluid (STF) to improve the uniformity of remedial amendment distribution within a heterogeneous aquifer. Previous studies have demonstrated the significant potential of STFs for improving remedial amendment delivery in heterogeneous aquifers, but quantitative evaluation of these improvements from field applications is lacking. A field‐scale test was conducted that compares data from successive injection of a tracer in water followed by injection of a tracer in an STF to evaluate the impact of the STF on tracer distribution uniformity in the presence of permeability contrasts within the targeted injection zone. Data from tracer breakthrough at multiple depth‐discrete monitoring intervals and electrical resistivity tomography (ERT) showed that inclusion of STF in the injection solution improved the distribution of the injected fluid within the targeted treatment zone. One improvement was a reduction in the movement of injected fluids through high‐permeability pathways, as evidenced by slower breakthrough of tracer at monitoring locations where breakthrough in baseline tracer‐only injection data was faster. In addition, STF‐amended injection solutions arrived faster and to a greater extent in monitoring locations within low‐permeability zones. ERT data showed that the STF injection covered a higher percentage of a two‐dimensional cross section within the injection interval between the injection well and a monitoring well about 3 m away.     

On the Performance of Pilot-Point Based Hydraulic Tomography with a Geophysical a Priori Model

We present a novel method to estimate the hydraulic and storage properties of a heterogeneous aquifer system using pilot-point-based hydraulic tomography (HT) inversion in conjunction with a geophysical a priori model. The a priori model involved a soil stratification obtained by combining electrical resistivity tomography inversion and field data from hydrogeological experiments. Pilot-point densities were assigned according to the stratification, which also constrained aquifer parameters during HT inversion. The forward groundwater flow model, HydroGeoSphere, was supplied to the parameter-estimation tool, PEST, to perform HT inversion. The performance of our method was evaluated on a hypothetical, two-dimensional, multi-layered, granitic aquifer system representative of those commonly occurring in the Kandi region in Telangana. Inversion results were compared using two commonly adopted methods of modeling parameter-heterogeneity: (1) using piece-wise zones of property values obtained from geostatistical interpolation of local-scale estimates; and (2) HT inversion starting from a homogeneous parameter field with a uniform distribution of pilot-points. Performances of the inverted models were evaluated by conducting independent pumping tests and statistical analyses (using a Taylor diagram) of the model-to-measurement discrepancies in drawdowns. Our results showed that using the aforementioned geophysical a priori model could improve the parameter-estimation process.     

Hydraulic head applications of flow logs in the study of heterogeneous aquifers

Permeability profiles derived from high-resolution flow logs in heterogeneous aquifers provide a limited sample of the most permeable beds or fractures determining the hydraulic properties of those aquifers. This paper demonstrates that flow logs can also be used to infer the large-scale properties of aquifers surrounding boreholes. The analysis is based on the interpretation of the hydraulic head values estimated from the flow log analysis. Pairs of quasi-steady flow profiles obtained under ambient conditions and while either pumping or injecting are used to estimate the hydraulic head in each water-producing zone. Although the analysis yields localized estimates of transmissivity for a few water-producing zones, the hydraulic head estimates apply to the far-field aquifers to which these zones are connected. The hydraulic head data are combined with information from other sources to identify the large-scale structure of heterogeneous aquifers. More complicated cross-borehole flow experiments are used to characterize the pattern of connection between large-scale aquifer units inferred from the hydraulic head estimates. The interpretation of hydraulic heads in situ under steady and transient conditions is illustrated by several case studies, including an example with heterogeneous permeable beds in an unconsolidated aquifer, and four examples with heterogeneous distributions of bedding planes and/or fractures in bedrock aquifers.     

Characterizing solute transport with transient storage across a range of flow rates: The evidence of repeated tracer experiments in Austrian and Italian streams

Solute transport in rivers and streams with hyporheic zone exchange and/or in-stream storage is typically affected by the prevailing flow rate. The research reported here focuses on stream tracer experiments repeated many times along the same Austrian (Mödlingbach) and Italian (Torrente Lura) channel reaches to characterize parameter dependency on flow rate. Both groups of data sets showed an increase of storage zone area and main stream area with discharge. In either case, a strong negative correlation was obtained between storage zone residence time and flow rate. From the Mödlingbach data, no clear relationship with Q emerged for the dispersion coefficient and the dead zone ratio, whereas Torrente Lura showed a clear positive correlation of the dispersion coefficient with the flow rate and a slightly negative Q-dependency for the dead zone ratio. Mödlingbach and Torrente Lura results are presented against the background of other repeat experiments reported in literature.     

Analytic solutions to transient groundwater flow under time-dependent sources in a heterogeneous aquifer bounded by fluctuating river stage

Analytical solutions for the water table and lateral discharge in a heterogeneous unconfined aquifer with time-dependent source and fluctuating river stage were derived and compared with those in an equivalent homogeneous aquifer. The heterogeneous aquifer considered consists of a number of sections of different hydraulic conductivity values. The source term and river stage were assumed to be time-dependent but spatially uniform. The solutions derived is useful in studying various groundwater flow problems in a horizontally heterogeneous aquifer since the spatially piecewise-constant hydraulic conductivity and temporally piecewise-constant recharge and lateral discharge can be used to quantify variations in these processes commonly observed in reality. Applying the solutions derived to an aquifer of three sections of different hydraulic conductivity values shown that (1) the aquifer heterogeneity significantly increases the spatial variation of the water table and thus its gradient but it has little effect on lateral discharge in the case of temporally and spatially uniform recharge, (2) the time-dependent but spatially uniform recharge increases the temporal variation of groundwater table over the entire aquifer but its effect on lateral discharge is limited in the zone near the river, and (3) the effect of river stage fluctuation on the water table and lateral discharge is limited in the zone near the river and the effect of the heterogeneity is to increase lateral discharge to or recharge from the river.     

Funnel-and-Gate Performance in a Moderately Heterogeneous Flow Domain

The funnel-and-gate ground water remediation technology (Starr and Cherry 1994) has received increased attention and application as an in situ alternative to the typical pump-and-treat system. Understanding the effects of heterogeneity on system performance can mean the difference between a successful remediation project and one that fails to meet its cleanup goals.
In an attempt to characterize and quantify the effects of heterogeneity on funnel-and-gate system performance, a numerical modeling study of 15 simulated heterogeneous flow domains was conducted. Each realization was tested to determine if the predicted capture width met the capture width expected for a homogeneous flow domain with the same hulk properties. This study revealed that the capture width of the funnel-and-gate system varied significantly with the level of heterogeneity of the aquifer.
Two possible remedies were investigated for bringing systems with less than acceptable capture widths to acceptable levels of performance. First, it was determined that enlarging the funnel and gate via a factor of safety applied to the design capture width could compensate for the capture width variation in the heterogeneous flow domains. In addition, it was shown that the use of a pumping well downstream of the funnel and gate could compensate for the effects of aquifer heterogeneity on the funnel-and-gate capture width. However, if a pumping well is placed downstream of the funnel and gate to control the hydraulic gradient through the gate, consideration should be given to the gate residence time in relation to the geochemistry of the contaminant removal or destruction process in the gate.     

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.     

A coupled vertically integrated model to describe lateral exchanges between surface and subsurface in large alluvial floodplains with a fully penetrating river

This paper presents a vertically averaged model for studying water and solute exchanges between a large river and its adjacent alluvial aquifer. The hydraulic model couples horizontal 2D Saint Venant equations for river flow and a 2D Dupuit equation for aquifer flow. The dynamic coupling between river and aquifer is provided by continuity of fluxes and water level elevation between the two domains. Equations are solved simultaneously by linking the two hydrological system matrices in a single global matrix in order to ensure the continuity conditions between river and aquifer and to accurately model two‐way coupling between these two domains. The model is applied to a large reach (about 36 km²) of the Garonne River (south‐western France) and its floodplain, including an instrumented site in a meander. Simulated hydraulic heads are compared with experimental measurements on the Garonne River and aquifer in the floodplain. Model verification includes comparisons for one point sampling date (27 piezometers, 30 March 2000) and for hydraulic heads variations measured continuously over 5 months (5 piezometers, 1 January to 1 June 2000). The model accurately reproduces the strong hydraulic connections between the Garonne River and its aquifer, which are confirmed by the simultaneous variation of the water level in the river and in piezometers located near the river bank. The simulations also confirmed that the model is able to reproduce groundwater flow dynamics during flood events. Given these results, the hydraulic model was coupled with a solute‐transport component, based on advection‐dispersion equations, to investigate the theoretical dynamics of a conservative tracer over 5 years throughout the 36 km² reach studied. Meanders were shown to favour exchanges between river and aquifer, and although the tracer was diluted in the river, the contamination moved downstream from the injection plots and affected both river banks. Copyright © 2008 John Wiley & Sons, Ltd.     

Semi-analytical solutions of groundwater flow in multi-zone (patchy) wedge-shaped aquifers

Alluvial fans are potential sites of potable groundwater in many parts of the world. Characteristics of alluvial fans sediments are changed radially from high energy coarse-grained deposition near the apex to low energy fine-grained deposition downstream so that patchy wedge-shaped aquifers with radial heterogeneity are formed. The hydraulic parameters of the aquifers (e.g. hydraulic conductivity and specific storage) change in the same fashion. Analytical or semi-analytical solutions of the flow in wedge-shaped aquifers are available for homogeneous cases. In this paper we derive semi-analytical solutions of groundwater flow to a well in multi-zone wedge-shaped aquifers. Solutions are provided for three wedge boundary configurations namely: constant head–constant head wedge, constant head–barrier wedge and barrier–barrier wedge. Derivation involves the use of integral transforms methods. The effect of heterogeneity ratios of zones on the response of the aquifer is examined. The results are presented in form of drawdown and drawdown derivative type curves. Heterogeneity has a significant effect on over all response of the pumped aquifer. Solutions help understanding the behavior of heterogeneous multi-zone aquifers for sustainable development of the groundwater resources in alluvial fans.     

Natural Gradient Tracer Test to Evaluate Natural Attenuation of MTBE Under Anaerobic Conditions

A natural gradient tracer test using perdeuterated MTBE was conducted in an anaerobic aquifer to determine the relative importance of dispersion and degradation in reducing MTBE concentrations in ground water. Preliminary ground water chemistry and hydraulic conductivity data were used to place the tracer within an existing dissolved MTBE plume at Port Hueneme, California. Following one year of transport, the tracer plume was characterized in detail.
Longitudinal dispersion was identified as the dominant mechanism for lowering the perdeuterated MTBE concentrations. The method of moments was used to determine the longitudinal and lateral dispersion coefficients (0.85 m²/day and 0.08 m²/day, respectively). A mass-balance analysis, carried out after one year of transport, accounted for 110% of the injected mass and indicated that no significant mass loss occurred. The plume structure created by zones of higher and lower hydraulic conductivity at the site was complex, consisting of several localized areas of high tracer concentration in a lower concentration plume. This is important because the aquifer has generally been characterized as exhibiting fairly minor heterogeneity. In addition, the tracer plume followed a curved flowpath that deviated from the more macroscopic direction of ground water flow inferred from local ground water elevation measurements and the behavior of the existing plume. Understanding the mass balance, plume structure, curvature of the tracer plume, and consequently natural attenuation behavior required the detailed sampling approach employed in this study. These data imply that a detailed understanding of site hydrogeology and an extensive sampling network may be critical for the correct interpretation of monitored natural attenuation of MTBE.     

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.