Nonreactive Solute Transport Research Articles

An Improved Dual‐Permeability Model of Water Flow and Solute Transport in the Vadose Zone

We introduce an improved, one‐dimensional, non‐steady‐state dual‐permeability model (MACRO 5.1). The model simulates water flow and solute transport in the vadose zone of structured soils by coupling a high‐conductivity–low porosity macropore domain to a low‐conductivity–high porosity domain representing the soil matrix. Mass exchange between the domains is approximated by first‐order expressions. The numerical solutions are briefly described, focusing on the dual‐permeability formulation. The solution method for water flow in macropores was verified by comparing simulation results with analytical solutions for a “kinematic wave”. The model was tested against high time‐resolution measurements of water flow and nonreactive (Cl−) solute transport in transient microlysimeter experiments. The objective was to test the identifiability of four key model parameters determining the degree of preferential flow using the generalized likelihood uncertainty estimation (GLUE) procedure. The parameters were chosen either because they are difficult or impossible to measure directly or because they were considered sensitive on the basis of earlier experience with the model. The measurements, indicating strong preferential flow, were adequately reproduced by the model simulations (overall model efficiency = 0.62). The GLUE procedure conditioned the saturated matrix hydraulic conductivity, the macroporosity, and the mass exchange coefficient (diffusion pathlength), indicating that these parameters would be identifiable in inverse modeling approaches based on microlysimeter experiments. The conditioning of the kinematic exponent was poor, which was attributed primarily to correlation with the macroporosity.

Spatial Moment Analysis for Transport of Nonreactive Solutes in Fracture-Matrix System

This paper presents an analysis using spatial moments for transport of nonreactive solutes in a single fracture-matrix system using a dual porosity framework. The velocity and dispersion obtained using the first and second spatial moments are found to have two regimes. The effect of fracture velocity, fracture dispersivity, fracture spacing, matrix diffusion coefficient, and matrix porosity on both regimes are analyzed. The first regime is characterized by a behavior wherein both velocity and dispersion are functions of time and all of the above parameters of the fracture-matrix system are found to have an influence. In the second regime, they are independent of time similar to the behavior of conservative solutes in an ideal porous media. This regime is characterized by the influence of a few parameters of the fracture-matrix system. The empirical relationships for solute velocity, macrodispersion coefficient, and dispersivity in the asymptotic stage are presented.

Evaluation of MACRO model by short-term water and solute transport simulation in Maury silt loam soil

Modeling preferential flow has been a concern of many academic fields in the past 30 years all over the world and helps to prevent groundwater contamination. A dual-porosity model, MACRO, was evaluated for short-term (less than 2 days) simulation of water flow and non-reactive solute (chloride) transport through the profile of six plots in well-structured Maury silt loam soil. Water flow in micropores is calculated by the Richards’ equation while simple gravity flow is assumed in the macropores. Solute transport in the micropores is calculated by the convection-dispersion equation (CDE) while the dispersion and diffusion in the CDE is neglected for the solute transport in the macropores. The applied water and chloride reached the bottom of the profile during the 2 and 1-hour(s) application periods in studies 2 and 3, respectively. There is a strong indication of macropore flow in this soil. Based on the statistical criteria, the model accurately simulated water flow and solute transport with depth and time in all plots. The mean values of three statistical parameters (coefficient of residual mass, model efficiency, and correlation coefficient) for water and chloride transport were –0.0014, 0.791, 0.903 and 0.0333, 0.923, 0.956, respectively. Preliminary studies showed that the model could not simulate flow and transport well enough with the one-domain flow concept. In the two-domain flow, effective diffusion path-length, boundary hydraulic conductivity, and boundary soil water pressure were the three most important parameters that control flow and transport between the two domains. The effective diffusion path-length represented the structural development with depth in the Maury silt loam soil.

Transient transport of reactive and non-reactive solutes in groundwater

A numerical model capable of predicting the transient changes in concentration levels of a solute along a homogeneous aquifer system is presented. The advection-dispersion equation (ADE) is utilised in predicting the concentration levels for cases of continuous and instantaneous release modes. The Crank–Nicholson equation is employed in the presented finite difference model. The numerical calculations are carried out using the implicit Gauss–Seidel method with over- and under-relaxation coefficients depending on the state of convergence. The correction terms resulting from the removal of zero- and first-order truncation errors in the ADE with a reaction term have significantly improved the performance of the numerical scheme. Comparisons between the numerically predicted concentrations with analytical and measured values were carried out for cases of non-reactive (tracer) and reactive (organic) solutes with continuous injection in homogeneous isotropic soils. The overshooting problems experienced in the numerical calculations are minimised by refining the finite grid size. The analysis of results has shown that the model can produce reliable simulations for cases of non-reactive solutes. While for the case of solutes undergoing adsorption, accurate concentrations can be predicted by adjusting the influent pore water velocity through the use of a retardation factor, which is suitable for aquifers with low organic carbon content and undergoing hydrophobic partitioning.

Transient transport of reactive and non-reactive solutes in groundwater*1

A numerical model capable of predicting the transient changes in concentration levels of a solute along a homogeneous aquifer system is presented. The advection-dispersion equation (ADE) is utilised in predicting the concentration levels for cases of continuous and instantaneous release modes. The Crank–Nicholson equation is employed in the presented finite difference model. The numerical calculations are carried out using the implicit Gauss–Seidel method with over- and under-relaxation coefficients depending on the state of convergence. The correction terms resulting from the removal of zero- and first-order truncation errors in the ADE with a reaction term have significantly improved the performance of the numerical scheme. Comparisons between the numerically predicted concentrations with analytical and measured values were carried out for cases of non-reactive (tracer) and reactive (organic) solutes with continuous injection in homogeneous isotropic soils. The overshooting problems experienced in the numerical calculations are minimised by refining the finite grid size. The analysis of results has shown that the model can produce reliable simulations for cases of non-reactive solutes. While for the case of solutes undergoing adsorption, accurate concentrations can be predicted by adjusting the influent pore water velocity through the use of a retardation factor, which is suitable for aquifers with low organic carbon content and undergoing hydrophobic partitioning.

Eulerian spatial moments for solute transport in three-dimensional heterogeneous, dual-permeability media

A Eulerian analytical method is developed for nonreactive solute transport in heterogeneous, dual-permeability media where the hydraulic conductivities in fracture and matrix domains are both assumed to be stochastic processes. The analytical solution for the mean concentration is given explicitly in Fourier and Laplace transforms. Instead of using the fast fourier transform method to numerically invert the solution to real space (Hu et al., 2002), we apply the general relationship between spatial moments and concentration (Naff, 1990; Hu et al., 1997) to obtain the analytical solutions for the spatial moments up to the second for a pulse input of the solute. Owing to its accuracy and efficiency, the analytical method can be used to check the semi-analytical and Monte Carlo numerical methods before they are applied to more complicated studies. The analytical method can be also used during screening studies to identify the most significant transport parameters for further analysis. In this study, the analytical results have been compared with those obtained from the semi-analytical method (Hu et al., 2002) and the comparison shows that the semi-analytical method is robust. It is clearly shown from the analytical solution that the three factors, local dispersion, conductivity variation in each domain and velocity convection flow difference in the two domains, play different roles on the solute plume spreading in longitudinal and transverse directions. The calculation results also indicate that when the log-conductivity variance in matrix is 10 times less than its counterpart in fractures, it will hardly influence the solute transport, whether the conductivity field is matrix is treated as a homogeneous or random field.

Modeling of non-reactive solute transport in fractured clayey till during variable flow rate and time

Fractures and biopores can act as preferential flow paths in clay aquitards and may rapidly transmit contaminants into underlying aquifers. Reliable numerical models for assessment of groundwater contamination from such aquitards are needed for planning, regulatory and remediation purposes. In this investigation, high resolution preferential water-saturated flow and bromide transport data were used to evaluate the suitability of equivalent porous medium (EPM), dual porosity (DP) and discrete fracture/matrix diffusion (DFMD) numerical modeling approaches for assessment of flow and non-reactive solute transport in clayey till. The experimental data were obtained from four large undisturbed soil columns (taken from 1.5 to 3.5 m depth) in which biopores and channels along fractures controlled 96–99% of water-saturated flow. Simulating the transport data with the EPM effective porosity model (FRACTRAN in EPM mode) was not successful because calibrated effective porosity for the same column had to be varied up to 1 order of magnitude in order to simulate solute breakthrough for the applied flow rates between 11 and 49 mm/day. Attempts to simulate the same data with the DP models CXTFIT and MODFLOW/MT3D were also unsuccessful because fitted values for dispersion, mobile zone porosity, and mass transfer coefficient between mobile and immobile zones varied several orders of magnitude for the different flow rates, and because dispersion values were furthermore not physically realistic. Only the DFMD modeling approach (FRACTRAN in DFMD mode) was capable to simulate the observed changes in solute transport behavior during alternating flow rate without changing values of calibrated fracture spacing and fracture aperture to represent the macropores.

90Sr migration to the geo-sphere from a waste burial in the Chernobyl exclusion zone

Results are presented from an ongoing field-scale experimental study (namely the Chernobyl Pilot Site project) aimed at characterization of processes controlling 90Sr releases from a shallow trench containing nuclear fuel particles, and subsequent radionuclide transport in the underlying sandy aquifer at the Chernobyl nuclear power plant site. Microscopic analyses of waste material and leaching experiments have shown that 10–30% of the radioactive inventory is associated with chemically extra-stable Zr–U–O particles. The largest fraction of 90Sr activity in the trench (≈30–60%) is currently associated with relatively slowly dissolving non-oxidized UO 2 matrix fuel particles. The 90Sr migration velocity in the eolian sand aquifer is retarded by sorption to ≈9% of groundwater flow velocity ( K d ≈ 2 ml/g). The dispersivity values for non-reactive solute transport in the aquifer predicted by geostatistics (i.e. 0.8 6 cm) were confirmed by a natural gradient tracer test using 36Cl. The observed negative correlation between hydraulic conductivity and K d of aquifer sediments suggests that 90Sr could be subjected to larger dispersion in the subsurface compared with 36Cl.

Flow and transport in highly heterogeneous formations: 2. Semianalytical results for isotropic media

Flow and transport of nonreactive solutes in heterogeneous porous media is studied by adopting a multi‐indicator model of permeability structure. The porous formation is modeled as a collection of blocks of uniform permeability K implanted at random in a matrix of constant conductivity K0. The multi‐indicator model leads to simple semianalytical solutions based on the self‐consistent argument, which are valid for a high degree of heterogeneity. The methodology is applied to isotropic formations to derive a few statistical moments of the velocity field and of the solute particles trajectory as functions of time and of the log conductivity variance σY2. Along the common models of aquifer permeability distribution the distribution of Y = ln K is assumed to be normal. All the semianalytical results degenerate in the well‐known first‐order results when σY2 ≪ 1. In particular, it is shown that the first‐order longitudinal dispersivity αL seems to hold for values of the log conductivity variance much larger than expected, up to σY2 ≈ 4. This results from a compensation of errors associated with the first‐order approximation. In contrast, for σY2 ≫ 1, the asymptotic αL grows exponentially with σY2. The effect of molecular diffusion is considered in a simple manner by introducing a cutoff κC for the conductivity contrast κ. The time to reach the asymptotic αL grows with the log conductivity variance. It is thus observed that transport in highly heterogeneous formations can be characterized by a very prolonged, non‐Fickian stage, with dispersivity αL growing continuously with time. Further analysis of third‐order moment of trajectory indicates that for growing values of σY2 the time needed for the plume to become Gaussian can be quite large.

Macropore transport of bromide as influenced by soil structure differences

Macropore transport of chemicals in soil often causes unexpected contamination of groundwater. The effect of soil structure on the functions of various sized macropores was assessed, investigating transport of nonreactive bromide (Br) under matric heads of 0, −2, −5 and −10 cm using undisturbed soil columns from A, B w and E horizons of a Thatuna silt loam soil (fine-silty, mixed, mesic Xeric Argialbolls). The experimental breakthrough curves (BTC) for Br were described with a two-region physical nonequilibrium model. Greatest macroporosity occurred in the A horizon and lowest in the E horizon. The measured pore water velocity ν under saturated conditions ranged from 18.92 cm day −1 in the E horizon to 64.28 cm day −1 in the A horizon. While the greatest dispersivity λ occurred in the B w horizon due to medium subangular blocky and prizmatic aggregates, the lowest dispersivity occurred in the E horizon due to its low macroporosity and massive structure. The fitted mobile water partitioning coefficient β ranged from 0.30 in the A horizon under 0 cm matric head to 0.93 in the E horizon under 0 cm matric head. The calculated values of rate of diffusive mass exchange α decreased with decreasing matric head in A and B w horizons, and slightly increased and then decreased in the E horizon. The difference among each of the values of the parameters ν, β, α and λ for the A, B w and E horizons was greatest under saturated conditions. However, gradually decreasing matric head until about −3 cm decreased the difference among the values for a particular parameter for different horizons, sharply. The difference remained fairly unchanged with further decreases in the matric head, suggesting that most of the variability in macropore transport of bromide for these horizons caused by pores with radii larger than about 0.5 mm. In A and B w horizons, there was a sudden change in soil solution movement between −2 and −5 cm matric head, indicating that macropore flow generally occurred at matric heads greater than −5 cm in the A and B w horizons. However, decreasing matric head had no effect on mobile water content of the columns from the E horizon. It was concluded that macropore transport of nonreactive solutes generated in the A and B w horizons may be hampered in the E horizon. Therefore, the depth, thickness and position of the E horizon should be considered in studies targeted to modeling macropore transport of nonreactive chemicals in the soils of Thatuna Series.

Upscaled flow and transport properties for heterogeneous unsaturated media

To represent a heterogeneous unsaturated medium by its homogeneous equivalent, stochastic theory‐based analytical formulas and numerical Monte Carlo simulations are used to obtain upscaled (effective) flow and transport properties. The Monte Carlo experiments simulate steady state flow and transient transport of nonreactive solute in two‐dimensional heterogeneous media. Constitutive relations for unsaturated media at the mesh‐size scale are based on the van Genuchten‐Mualem relationships. A unit‐mean‐gradient approach is used to derive upscaled properties for flow parallel and perpendicular to bedding. Upscaled moisture retention and unsaturated conductivities (K) and longitudinal dispersivities are obtained by simulating steady gravity drainage conditions for a series of applied infiltration rates, characteristic of relatively dry conditions in coarse‐textured sediments. Macrodispersivities are calculated on the basis of spatial moments of the ensemble‐mean plume. Results show that the calculated effective unsaturated K based on the analytical formulas compare well with those based on Monte Carlo simulations. The macroscopic anisotropy (ratio of K parallel to bedding to K perpendicular to bedding) increases with increasing tension, although the increase is rather mild. The longitudinal macrodispersivity for the equivalent homogeneous medium also increases with increasing tension. A comparison of numerical results with stochastic solutions suggests that the computed dispersivities are of the same order of magnitude at low tensions. At higher tensions the dispersivity estimates deviate significantly. Nonetheless, both numerical and analytical results show that the longitudinal dispersivities for flow parallel to bedding are higher than those for flow perpendicular to bedding. In addition, our results suggest that the Fickian regime is reached much earlier for cases with flow perpendicular to bedding than for those with flow parallel to bedding.

Solute Concentration Statistics in Heterogeneous Aquifers for Finite Péclet Values

A Lagrangian framework is used for analysing the concentration fields associated with transport of nonreactive solutes in heterogeneous aquifers. This is related to two components: advection by the random velocity field v(x) and pore-scale dispersion, characterized by the dispersion tensor Dd; the relative effect of the two components is quantified by the Peclet number. The principal aim of this paper is to define the probability density function (pdf) of a nonreactive solute concentration and its relevant moments >C< and σ2c as sampled on finite detection volumes. This problem could be relevant in technical applications such as risk analysis, field monitoring and pollution control. A method to compute the concentration statistical moments and pdf is developed in the paper on the basis of the reverse formulation widely adopted to study solute dispersion in turbulent flows. The main advantages of this approach are: (i) a closed form solution for concentration mean and variance is attained, in case of small size of the sampling volume; (ii) a numerically efficient estimate of the concentration pdf can be derived. The relative effects of injection and sampling volume size and Peclet number on concentration statistics are assessed. The analysis points out that the concentration pdf can be reasonably fitted by the beta function. These results are suitable to be employed in practical applications, when the estimate of probability related to concentration thresholds is required.

The Lagrangian concentration approach for determining dilution in aquifer transport: Theoretical analysis and comparison with field experiments

Transport of nonreactive solutes in aquifers of random permeability is considered. The local concentration C, which is a random function of space and time, can be modeled through 〈C〉, the ensemble mean, and σC2, the variance. Because of the irregular spatial distribution of the concentration, which is a consequence of the spreading and dilution of the solute plume, the uncertainty in the local concentration prediction can be very large, and the mean concentration 〈C〉 may not accurately predict the concentration distribution in the field, in particular, the peak concentration. The aim of the present paper is to quantify dilution through the peak concentration by introducing a quantity denoted as Lagrangian concentration (CL). According to the proposed methodology the combined effects of dispersion, which is ruled by large‐scale advection, and dilution, which is a consequence of pore‐scale dispersion, are analyzed by following each Darcy‐scale solute particle constituting the initial plume by focusing on the mass exchanges between the examined particle and the surrounding ones. After definition and derivation of CL and its statistical moments, illustrative examples are shown for a small solute injection. Then the comparison of the theoretical results with the Borden and Cape Cod experimental findings shows that the Lagrangian concentration gives a reasonable prediction of the peak concentration: conversely, the often employed mean concentration 〈C〉 underestimates the maximum concentration. Furthermore, the fluctuations of CL are also smaller than those for C, as indicated by the analysis of the variance. The results are of some importance for applications in which the environmental regulations are formulated in terms of maximal admissible local concentrations.

Solute transport through a heterogeneous coupled vadose‐saturated zone system with temporally random rainfall

The transport of nonreactive solutes through a coupled, two‐dimensional, randomly heterogeneous vadose‐saturated zone system subject to temporally random rainfall is predicted by Monte Carlo simulation and compared with previously published analytic results for three different rainfall patterns. The relative contributions of the uncertain inputs (i.e., rainfall and saturated conductivity) to the prediction uncertainty of solute transport are quantified in terms of the statistical moments of the pore water velocity, the plume spatial moments, and solute flux breakthrough curves at downstream control planes. Results show that the mean and variance of the saturated zone pore water velocity were approximately equivalent for the cases of uniform and random rainfall and were well predicted by the analytical relationships developed by Rubin and Bellin [1994]. As a result, the mean plume displacement, estimated by the trajectory of the mean plume center of mass, was found to be nearly identical for these cases. In the temporally random rainfall case, the saturated zone mean plume experienced more spread in the direction of mean flow at early times. However, the asymptotic rates of spatial spreading of the mean solute plumes were found to be approximately equivalent for the uniform and random rainfall cases and well predicted by the approximate expressions for longitudinal macrodispersivity in nonuniform flow proposed by Destouni and Graham [1995]. Random rainfall and random soil properties increased prediction uncertainty of the solute plume behavior in the vadose zone by an order of magnitude when compared with the uniform rain and random soil case. This effect was reduced considerably when the solute entered the saturated zone, where random rainfall produced only slightly larger prediction uncertainty than the uniform rainfall case. The analytic model developed by Destouni and Graham [1995] accurately predicted the temporal breakthrough of the mean solute plume at saturated zone control planes for all cases, if transport through the unsaturated zone accounted for the effects of temporally random rainfall using the methodology developed by Foussereau et al. [2000a, 2000b]. Results of this work indicate that for the humid climates studied here, uncertain rainfall patterns dominate transport prediction uncertainty in the shallow unsaturated zone, while uncertain solute breakthrough to the saturated zone and uncertain hydraulic conductivity dominate prediction uncertainty in the saturated zone.

Sources of error in model predictions of pesticide leaching: a case study using the MACRO model

Uncalibrated predictions of soil water balance, water content, non-reactive solute transport (bromide) and pesticide leaching (bentazone) made by three users of a comprehensive mechanistic model (MACRO) are compared to measured data obtained for a sandy soil at Vredepeel in the Netherlands. The objective was to assess the significance of different sources of error for making predictions of pesticide leaching. Objective statistical indices were used to compare the simulations made by different users and to evaluate overall model performance. All three users predicted very similar water balances. Soil water contents were in good agreement with the measurements, with the simulation based on measured hydraulic functions giving somewhat better predictions than those based on automatic estimation procedures (pedo-transfer functions). Bromide movement was also satisfactorily predicted by all three users despite an inability to reproduce the strong retention near the soil surface caused by finger flow. Bentazone dissipation in the field was severely underpredicted by all three users based on laboratory measurements of degradation. This error overshadowed the effects of differences in parameterisation between users.

Characterizing multiple timescales of stream and storage zone interaction that affect solute fate and transport in streams

The fate of contaminants in streams and rivers is affected by exchange and biogeochemical transformation in slowly moving or stagnant flow zones that interact with rapid flow in the main channel. In a typical stream, there are multiple types of slowly moving flow zones in which exchange and transformation occur, such as stagnant or recirculating surface water as well as subsurface hyporheic zones. However, most investigators use transport models with just a single storage zone in their modeling studies, which assumes that the effects of multiple storage zones can be lumped together. Our study addressed the following question: Can a single‐storage zone model reliably characterize the effects of physical retention and biogeochemical reactions in multiple storage zones? We extended an existing stream transport model with a single storage zone to include a second storage zone. With the extended model we generated 500 data sets representing transport of nonreactive and reactive solutes in stream systems that have two different types of storage zones with variable hydrologic conditions. The one storage zone model was tested by optimizing the lumped storage parameters to achieve a best fit for each of the generated data sets. Multiple storage processes were categorized as possessing I, additive; II, competitive; or III, dominant storage zone characteristics. The classification was based on the goodness of fit of generated data sets, the degree of similarity in mean retention time of the two storage zones, and the relative distributions of exchange flux and storage capacity between the two storage zones. For most cases (&gt;90%) the one storage zone model described either the effect of the sum of multiple storage processes (category I) or the dominant storage process (category III). Failure of the one storage zone model occurred mainly for category II, that is, when one of the storage zones had a much longer mean retention time (ts ratio &gt; 5.0) and when the dominance of storage capacity and exchange flux occurred in different storage zones. We also used the one storage zone model to estimate a “single” lumped rate constant representing the net removal of a solute by biogeochemical reactions in multiple storage zones. For most cases the lumped rate constant that was optimized by one storage zone modeling estimated the flux‐weighted rate constant for multiple storage zones. Our results explain how the relative hydrologic properties of multiple storage zones (retention time, storage capacity, exchange flux, and biogeochemical reaction rate constant) affect the reliability of lumped parameters determined by a one storage zone transport model. We conclude that stream transport models with a single storage compartment will in most cases reliably characterize the dominant physical processes of solute retention and biogeochemical reactions in streams with multiple storage zones.

Nonreactive solute transport in variously structured soil materials as determined by laboratory-based time domain reflectometry (TDR)

The possibility of using the time domain reflectometry technique (TDR) is tested for estimating transport parameters of an inert solute (KCl) in the soil. Undisturbed soil samples underwent steady flow processes in the laboratory in near-saturation conditions. Space/time distributions of the chloride ion concentration were analysed with the two-parameter convection–dispersion model (CD). Conventional nonlinear optimisation algorithm was used for the derivation of the parameter values. Applied to soil samples of different textures and structures, the method supplied satisfactory results, which indicates that the straightforward use of TDR may permit the method to be more widely applied, both in the laboratory and in the field. Research is currently going on to study the spatial variability of characteristic parameters of solute transport.

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

Model for Nonreactive Solute Transport in Structured Soils with Continuous Preferential Flow Paths

AbstractA mathematical model for solute movement in a structured soil with well‐defined and continuous preferential paths was developed. The model divides the soil profile into one mobile and one “stagnant” pore group. For well‐structured soils, the mobile pore group consists of a few well‐connected pores that conduct the nonreactive solute downward very rapidly. Only a narrow matrix layer of stagnant solute along the interface between the two pore groups takes part in solute exchange with the preferential paths. Due to differences in time scales between convection and chemical transfer, the rate of chemical exchange between the preferential path and the active matrix layer for short and moderate times after chemical application is controlled mainly by the preferential flow concentration and, to a lesser extent, by the concentration in the matrix active layer. This is expressed mathematically by multiplying the concentration in the active matrix layer in the mass balance equation by a small dimensionless parameter, ɛ ≪ 1. A regular small perturbations problem is then obtained whose solution is expressed as the sum of the zeroth‐ and first‐order approximations. The simulated breakthrough curve (BTC) is made up of piecewise linear lines and shows a good fit to the measured solute concentration in the outflow of undisturbed columns that have significant preferential flow. Due to the model's simplicity, the transport parameters are estimated directly by fitting the model output to the measured BTCs.

Prediction of local concentration statistics in variably saturated soils: Influence of observation scale and comparison with field data

The methodology developed in Destouni and Graham [Destouni, G., Graham, W.D., 1997. The influence of observation method on local concentration statistics in the subsurface. Water Resour. Res. 33 (4) 663–676.] for predicting locally measured concentration statistics for solute transport in heterogeneous porous media under saturated flow conditions is applied to the prediction of conservative nonreactive solute transport in the vadose zone where observations are obtained by soil coring. Exact analytical solutions are developed for both the mean and variance of solute concentrations measured in discrete soil cores using a simplified physical model for vadose-zone flow and solute transport. Theoretical results show that while the ensemble mean concentration is relatively insensitive to the length-scale of the measurement, predictions of the concentration variance are significantly impacted by the sampling interval. Results also show that accounting for vertical heterogeneity in the soil profile results in significantly less spreading in the mean and variance of the measured solute breakthrough curves, indicating that it is important to account for vertical heterogeneity even for relatively small travel distances. Model predictions for both the mean and variance of locally measured solute concentration, based on independently estimated model parameters, agree well with data from a field tracer test conducted in Manatee County, Florida.