Two-dimensional power series solution for non-axisymmetrical transport in a radially convergent tracer test with scale-dependent dispersion

It has been known for many years that dispersivity increases with solute travel distance in a subsurface environment. The increase of dispersivity with solute travel distance results from the significant variation of hydraulic properties of heterogeneous media and was identified in the literature as scale-dependent dispersion. This study presents an analytical solution for describing two-dimensional non-axisymmetrical solute transport in a radially convergent flow tracer test with scale-dependent dispersion. The power series technique coupling with the Laplace and finite Fourier cosine transform has been applied to yield the analytical solution to the two-dimensional, scale-dependent advection–dispersion equation in cylindrical coordinates with variable-dependent coefficients. Comparison between the breakthrough curves of the power series solution and the numerical solutions shows excellent agreement at different observation points and for various ranges of scale-related transport parameters of interest. The developed power series solution facilitates fast prediction of the breakthrough curves at any observation point.     

A 3D ERT study of solute transport in a large experimental tank

A high resolution, cross-borehole, 3D electrical resistivity tomography (ERT) study of solute transport was conducted in a large experimental tank. ERT voxels comprising the time sequence of electrical images were converted into a 3D array of ERT estimated fluid conductivity breakthrough curves and compared with direct measurements of fluid conductivity breakthrough made in wells. The 3D ERT images of solute transport behaviour were also compared with predictions based on a 3D finite-element, coupled flow and transport model, accounting for gravity induced flow caused by concentration differences.The tank (dimensions 185×245×186 cm) was filled with medium sand, with a gravel channel and a fine sand layer installed. This heterogeneous system was designed to complicate solute transport behaviour relative to a homogeneous sand tank, and to thus provide a challenging but insightful analysis of the ability of 3D ERT to resolve transport phenomena. Four ERT arrays and 20 piezometers were installed during filling. A NaCl tracer (conductivity 1.34 S/m) was injected and intensively monitored with 3D ERT and direct sampling of fluid chemistry in piezometers.We converted the bulk conductivity estimate for 250 voxels in the ERT imaged volume into ERT estimated voxel fluid conductivity by assuming that matrix conduction in the tank is negligible. In general, the ERT voxel response is in reasonable agreement with the shape of fluid conductivity breakthrough observed in six wells in which direct measurements of fluid conductivity were made. However, discrepancies occur, particularly at early times, which we attribute to differences between the scale of the image voxels and the fluid conductivity measurement, measurement errors mapped into the electrical inversion and artificial image roughness resulting from the inversion.ERT images revealed the 3D tracer distribution at 15 times after tracer injection. The general pattern and timing of solute breakthrough observed with ERT agreed with that predicted from the flow/transport modelling. However, the ERT images indicate a vertical component of tracer transport and preferential flow paths in the medium sand. We attribute this to transient vertical gradients established during tracer injection, and heterogeneity caused by sorting of the sand resulting from the filling procedure. In this study, ERT provided a unique dataset of 250 voxel breakthrough curves in 1.04 m³. The use of 3D ERT to generate an array of densely sampled estimated fluid conductivity breakthrough curves is a potentially powerful tool for quantifying solute transport processes.     

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.     

An effective scale-dependent dispersivity deduced from a purely convective flow field

Abstract

In the case of straight flow but with hydraulic conductivity varying in a transverse direction, the distribution of hydraulic conductivity has been determined for which the breakthrough curve due to convection only will have the same analytical form as the onedimensional convection/dispersion equation solution at the outlet end of a porous medium. That distribution is found exactly and it is very similar to the lognormal distribution. This result is significant since field evidence indicates that the logarithm of hydraulic conductivity is normally distributed. For the case considered, a simple relation between dispersivity and the coefficient of variation of hydraulic conductivity is found. One can thus determine very simply dispersivity in terms of the parameters of the distribution of hydraulic conductivity. This is particularly useful to estimate dispersivity in various cells of finite difference or finite element models when the distribution of hydraulic conductivity is not stationary, i.e. varies in space.     

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.     

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.     

Analysis of solute transport with a hyperbolic scale-dependent dispersion model

An empirical hyperbolic scale-dependent dispersion model, which predicts a linear growth of dispersivity close to the origin and the attainment of an asymptotic dispersivity at large distances, is presented for deterministic modelling of field-scale solute transport and the analysis of solute transport experiments. A simple relationship is derived between local dispersivity, which is used in numerical simulations of solute transport, and effective dispersivity, which is estimated from the analysis of tracer breakthrough curves. The scale-dependent dispersion model is used to interpret a field tracer experiment by nonlinear least-squares inversion of a numerical solution for unsaturated transport. Simultaneous inversion of concentration-time data from several sampling locations indicates a linear growth of the dispersion process over the scale of the experiment. These findings are consistent with the results of an earlier analysis based on the use of a constant dispersion coefficient model at each of the sampling depths.     

Field Tracer Test for the Design of LNAPL Source Zone Surfactant Flushing

A field tracer test was carried out in a light nonaqueous phase liquid (LNAPL) source zone using a well pattern consisting of one injection well surrounded by four extraction wells (5‐spot well pattern). Multilevel sampling was carried out in two observation wells located inside the test cell characterized by heterogeneous lithology. Tracer breakthrough curves showed relatively uniform flow within soil layers. A numerical flow and solute transport model was calibrated on hydraulic heads and tracer breakthrough curves. The model was used to estimate an average accessible porosity of 0.115 for the swept zone and an average longitudinal dispersivity of 0.55 m. The model was further used to optimize the relative effects of viscous forces versus capillary forces under realistic imposed hydraulic gradients and to establish optimal surfactant solution properties. Maximum capillary number (N_Ca) values between injection and extraction wells were obtained for an injection flow rate of 16 L/min, a total extraction flow rate of 20 L/min, and a surfactant solution with a viscosity of 0.005 Pa?s. The unconfined nature of the aquifer limited further flow rate or viscosity increases that would have led to unrealistic hydraulic gradients. An N_Ca range of 3.8 × 10^?4 to 7.6 × 10^?3 was obtained depending on the magnitude of the simulated LNAPL‐water interfacial tension reduction. Finally, surfactant and chase water slug sizing was optimized with a radial form of the simplified Ogata‐Banks analytical solution (Ogata and Banks 1961) so that injected concentrations could be maintained in the entire 5‐spot cell.     

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.     

Investigating peat hydrological properties using field and laboratory methods: application to the Lanoraie peatland complex (southern Quebec,Canada)

Flow dynamics within a peatland are governed by hydraulic parameters such as hydraulic conductivity, dispersivity and specific yield, as well as by anisotropy and heterogeneity. The aim of this study is to investigate hydraulic parameters variability in peat through the use of different field and laboratory methods. An experimental site located in the Lanoraie peatland complex (southern Quebec, Canada) was used to test the different approaches. Slug and bail tests were performed in piezometer standpipes to investigate catotelm hydraulic conductivity. Combined Darcy tests and tracer experiments were conducted on cubic samples using the modified cube method (MCM) to assess catotelm hydraulic conductivity, anisotropy and dispersivity. A new laboratory method is proposed for assessing acrotelm hydraulic conductivity and gravity drainage using a laboratory experimental tank. Most of slug tests' recovery curves were characteristic of compressible media, and important variability was observed depending on the initial head difference. The Darcy experiments on cubic samples provided reproducible results, and anisotropy (K_h > K_v) was observed for most of samples. All tracer experiments displayed asymmetrical breakthrough curves, suggesting the presence of retardation and/or dual porosity. Hydraulic conductivity estimates performed using the experimental tank showed K variations over a factor of 44 within the upper 40 cm of the acrotelm. The results demonstrate that the intrinsic variability associated with the different field and laboratory methods is small compared with the spatial variability of hydraulic parameters. It is suggested that a comprehensive assessment of peat hydrological properties can be obtained through the combined use of complementary field and laboratory investigations. Copyright © 2007 John Wiley & Sons, Ltd.     

Development and application of a coupled-process parameter inversion model based on the maximum likelihood estimation method

The coupled flow-mass transport inverse problem is formulated using the maximum likelihood estimation concept. An evolutionary computational algorithm, the genetic algorithm, is applied to search for a global or near-global solution. The resulting inverse model allows for flow and transport parameter estimation, based on inversion of spatial and temporal distributions of head and concentration measurements. Numerical experiments using a subset of the three-dimensional tracer tests conducted at the Columbus, Mississippi site are presented to test the model's ability to identify a wide range of parameters and parametrization schemes. The results indicate that the model can be applied to identify zoned parameters of hydraulic conductivity, geostatistical parameters of the hydraulic conductivity field, angle of hydraulic conductivity anisotropy, solute hydrodynamic dispersivity, and sorption parameters. The identification criterion, or objective function residual, is shown to decrease significantly as the complexity of the hydraulic conductivity parametrization is increased. Predictive modeling using the estimated parameters indicated that the geostatistical hydraulic conductivity distribution scheme produced good agreement between simulated and observed heads and concentrations. The genetic algorithm, while providing apparently robust solutions, is found to be considerably less efficient computationally than a quasi-Newton algorithm.     

A spreadsheet program for two-well tracer test data analysis

Two-well tracer tests are often conducted to investigate subsurface solute transport in the field. Analyzing breakthrough curves in extraction and monitoring wells using numerical methods is nontrivial due to highly nonuniform flow conditions. We extended approximate analytical solutions for the advection-dispersion equation for an injection-extraction well doublet in a homogeneous confined aquifer under steady-state flow conditions for equal injection and extraction rates with no transverse dispersion and negligible ambient flow, and implemented the solutions in Microsoft Excel using Visual Basic for Application (VBA). Functions were implemented to calculate concentrations in extraction and monitoring wells at any location due to a step or pulse injection. Type curves for a step injection were compared with those calculated by numerically integrating the solution for a pulse injection. The results from the two approaches are similar when the dispersivity is small. As the dispersivity increases, the latter was found to be more accurate but requires more computing time. The code was verified by comparing the results with published-type curves and applied to analyze data from the literature. The method can be used as a first approximation for two-well tracer test design and data analysis, and to check accuracy of numerical solutions. The code and example files are publicly available.     

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.     

Saltwater intrusion modeling in heterogeneous confined aquifers using two-relaxation-time lattice Boltzmann method

This study develops a lattice Boltzmann method (LBM) with a two-relaxation-time collision operator (LTRT) to solve saltwater intrusion problems. A directional-speed-of-sound (DSS) technique is introduced to take into account the hydraulic conductivity heterogeneity and discontinuity, as well as the velocity-dependent dispersion coefficient. The forcing terms in the LTRT model are customized in order to recover the density-dependent groundwater flow and mass transport equations. Using the LTRT with the squared DSS achieves at least second-order accuracy. The LTRT results are verified with Henry’s analytical solution as well as compared with several numerical examples and modified Henry problems that consider heterogeneous hydraulic conductivity and velocity-dependent dispersion. The numerical results show good agreement with the Henry analytical solution and with the numerical solutions obtained by other numerical methods.     

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.     

Stochastic analysis of unsaturated transport in soils with fractal log-conductivity distribution

Within the framework of stochastic theory and the spectral perturbation techniques, three-dimensional dispersion in partially saturated soils with fractal log hydraulic conductivity distribution is analyzed. Our analysis is focused on the impact of fractal dimension of log hydraulic conductivity distribution, local dispersivity, and unsaturated flow parameters, such as the soil poresize distribution parameter and the moisture distribution parameter, on the spreading behavior of solute plume and the concentration variance. Approximate analytical solutions to the stochastic partial differential equations are derived for the variance of asymptotic solute concentration and asymptotic macrodispersivities.     

Scaling of flow and transport behavior in heterogeneous groundwater systems

Three-dimensional numerical simulations using a detailed synthetic hydraulic conductivity field developed from geological considerations provide insight into the scaling of subsurface flow and transport processes. Flow and advective transport in the highly resolved heterogeneous field were modeled using massively parallel computers, providing a realistic baseline for evaluation of the impacts of parameter scaling. Upscaling of hydraulic conductivity was performed at a variety of scales using a flexible power law averaging technique. A series of tests were performed to determine the effects of varying the scaling exponent on a number of metrics of flow and transport behavior. Flow and transport simulation on high-performance computers and three-dimensional scientific visualization combine to form a powerful tool for gaining insight into the behavior of complex heterogeneous systems.Many quantitative groundwater models utilize upscaled hydraulic conductivity parameters, either implicitly or explicitly. These parameters are designed to reproduce the bulk flow characteristics at the grid or field scale while not requiring detailed quantification of local-scale conductivity variations. An example from applied groundwater modeling is the common practice of calibrating grid-scale model hydraulic conductivity or transmissivity parameters so as to approximate observed hydraulic head and boundary flux values. Such parameterizations, perhaps with a bulk dispersivity imposed, are then sometimes used to predict transport of reactive or non-reactive solutes. However, this work demonstrates that those parameters that lead to the best upscaling for hydraulic conductivity and head do not necessarily correspond to the best upscaling for prediction of a variety of transport behaviors. This result reflects the fact that transport is strongly impacted by the existence and connectedness of extreme-valued hydraulic conductivities, in contrast to bulk flow which depends more strongly on mean values. It provides motivation for continued research into upscaling methods for transport that directly address advection in heterogeneous porous media.An electronic version of this article is available online at the journal's homepage at http://www.elsevier.nl/locate/advwatres or http://www.elsevier.com/locate/advwatres (see “Special section on vizualization”. The online version contains additional supporting information, graphics, and a 3D animation of simulated particle movement.©1998 Elsevier Science Limited. All rights reserved     

Modelling of the groundwater flow and of tracer movement in the porous and fissured media: Chalk Aquifer (Northern part of Paris Basin,France)

A groundwater flow model has been developed in order to study the chalk aquifer of Paris Basin, based on most of the geological and hydrological available data. The numerical processes are intended to modelling the groundwater flow in the Senonian (Late Cretaceous) formations and to visualize the tracer movement in groundwater resources in the experimental site of LaSalle Beauvais (northern part Paris Basin). Both objectives were achieved as follows: (i) the comprehension of the spatial distribution of the hydraulic conductivity in the chalk aquifer taking into account the characteristics of the hydrogeological system and (ii) the use of the analytical solution for describing one‐dimensional to two‐dimensional solute transport in a unidirectional steady‐state flow tracer with scale‐dependent dispersion. Advection and diffusion mechanisms are taken into account. Comparison between the breakthrough curves of the analytical and the numerical solutions provided an excellent agreement for various ranges of scale‐related transport parameters of interest. The developed power series solution facilitates fast prediction of the breakthrough curves at each observation point. Thus, the derived new solutions are widely applicable and are very useful for the validation of numerical transport. The numerical approach is carried out by MT3DMS, a Modular 3‐D Multi‐Species Transport Model for Simulation of Advection, Dispersion, and Chemical Reactions of Contaminants in Groundwater Systems, and based on total variation‐diminishing method using the ULTIMATE algorithm. The estimation of the infected surface could constitute an approach in water management and allows to prevent the risks of pollution and to manage the groundwater resource from a durable development perspective. Copyright © 2016 John Wiley & Sons, Ltd.     

Incorporation of conceptual and parametric uncertainty into radionuclide flux estimates from a fractured granite rock mass

Detailed numerical flow and radionuclide simulations are used to predict the flux of radionuclides from three underground nuclear tests located in the Climax granite stock on the Nevada Test Site. The numerical modeling approach consists of both a regional-scale and local-scale flow model. The regional-scale model incorporates conceptual model uncertainty through the inclusion of five models of hydrostratigraphy and five models describing recharge processes for a total of 25 hydrostratigraphic–recharge combinations. Uncertainty from each of the 25 models is propagated to the local-scale model through constant head boundary conditions that transfer hydraulic gradients and flow patterns from each of the model alternatives in the vicinity of the Climax stock, a fluid flux calibration target, and model weights that describe the plausibility of each conceptual model. The local-scale model utilizes an upscaled discrete fracture network methodology where fluid flow and radionuclides are restricted to an interconnected network of fracture zones mapped onto a continuum grid. Standard Monte Carlo techniques are used to generate 200 random fracture zone networks for each of the 25 conceptual models for a total of 5,000 local-scale flow and transport realizations. Parameters of the fracture zone networks are based on statistical analysis of site-specific fracture data, with the exclusion of fracture density, which was calibrated to match the amount of fluid flux simulated through the Climax stock by the regional-scale models. Radionuclide transport is simulated according to a random walk particle method that tracks particle trajectories through the fracture continuum flow fields according to advection, dispersion and diffusional mass exchange between fractures and matrix. The breakthrough of a conservative radionuclide with a long half-life is used to evaluate the influence of conceptual and parametric uncertainty on radionuclide mass flux estimates. The fluid flux calibration target was found to correlate with fracture density, and particle breakthroughs were generally found to increase with increases in fracture density. Boundary conditions extrapolated from the regional-scale model exerted a secondary influence on radionuclide breakthrough for models with equal fracture density. The incorporation of weights into radionuclide flux estimates resulted in both noise about the original (unweighted) mass flux curves and decreases in the variance and expected value of radionuclide mass flux.     

Matching solute breakthrough with deterministic and stochastic aquifer models

Two different deterministic and two alternative stochastic (i.e., geostatistical) approaches to modeling the distribution of hydraulic conductivity (K) in a nonuniform (sigma2ln(K)) = 0.29) glacial sand aquifer were used to explore the influence of conceptual model selection on simulations of three-dimensional tracer movement. The deterministic K models employed included a homogeneous effective K and a perfectly stratified 14 layer model. Stochastic K models were constructed using sequential Gaussian simulation and sequential i ndicator simulation conditioned to available K values estimated from measured grain size distributions. Standard simulation software packages MODFLOW, MT3DMS, and MODPATH were used to model three-dimensional ground water flow and transport in a field tracer test, where a pulse of bromide was injected through an array of three fully screened wells and extracted through a single fully screened well approximately 8 m away. Agreement between observed and simulated transport behavior was assessed through direct comparison of breakthrough curves (BTCs) and selected breakthrough metrics at the extraction well and at 26 individual multilevel sample ports distributed irregularly between the injection and extraction wells. Results indicate that conceptual models incorporating formation variability are better able to capture observed breakthrough behavior. Root mean square (RMS) error of the deterministic models bracketed the ensemble mean RMS error of stochastic models for simulated concentration vs. time series, but not for individual BTC characteristic metrics. The spatial variability models evaluated here may be better suited to simulating breakthrough behavior measured in wells screened over large intervals than at arbitrarily distributed observation points within a nonuniform aquifer domain.