Conservative Solute Transport Research Articles

Elucidating temperature effects on seasonal variations of biogeochemical turnover rates during riverbank filtration

Summary Riverbank filtration (RBF) is a mechanism by which undesired substances contained in infiltrating surface waters are attenuated during their passage across the riverbed and its underlying aquifer towards production wells. In this study, multi-component reactive transport modeling was used to analyze the biogeochemical processes that occur during subsurface passage at an existing RBF system – the Flehe Waterworks located along the Rhine River in Dusseldorf, Germany. The reactive transport model was established on the base of a conservative solute transport model for which temperature and chloride data served as calibration constraints. The model results showed that seasonal temperature changes superimposed by changes in residence time strongly affected the extent of the redox reactions along the flow path. The observed temporal, especially seasonal, changes in the breakthrough of dissolved oxygen were found to be best reproduced by the model when the temperature dependency of the biogeochemical processes was explicitly considered. High floods in the Rhine drastically reduced the travel time to the RBF well from an average travel time of 25–40 days to less than 8 days. On the other hand, low flow conditions increased the subsurface residence times between the Rhine River and the RBF well to about 60 days. The model results revealed that short term changes in the terminal electron acceptor consumption (biodegrdation extent) were solely attributed to fluctuations in residence time, while more gradual changes in biodegradation extent were due to both seasonal variations of the river water temperature and gradual changes in residence time.

Semi‐analytical solutions for solute transport and exchange in fractured porous media

Fracture‐matrix interactions can significantly affect solute transport in fractured porous media and rocks, even when fractures are major (or sole) conduits of flow. We develop a semi‐analytical solution for transport of conservative solutes in a single fracture. Our solution accounts for two‐dimensional dispersion in the fracture, two‐dimensional diffusion in the ambient matrix, and fully coupled fracture‐matrix exchange, without resorting to simplifying assumptions regarding any of these transport mechanisms. It also enables one to deal with arbitrary initial and boundary conditions, as well as with distributed and point sources. We investigate the impact of transverse dispersion in a fracture and longitudinal diffusion in the ambient matrix on the fracture‐matrix exchange, both of which are neglected in standard models of transport in fractured media.

Transfer Function Model for Pollutant Breakthrough in Geomedia

Pollutant transport in soil and geologic materials has been evaluated to prevent contamination of groundwater reservoirs. The objective of this project was to use two transfer function models for predicting X-ray computed tomography-measured chemical breakthrough in columns. Breakthrough experiments were conducted using undisturbed cores taken from a field site. Application of the convection-dispersion model is more limited to homogeneous columns while the lognormal and convection-dispersion probability density function (pdf) transfer function models worked well for both heterogeneous as well as homogeneous columns. The parameters for travel time pdf were accurately estimated by the solute breakthrough time distributions when the resolution of the scan was 0.5 x 0.5mm. However, group-pixel averages of 2.0 x 2.0mm or 5.0 x 5.0mm worked best to reduce fluctuations of CT scan numbers. In this study, the application of the transfer function model was limited to conservative solute transport in undisturbed columns. Future studies can evaluate chemical adsorption and degradation processes.

Application of Kalman Filter with Time-Correlated Measurement Errors in Subsurface Contaminant Transport Modeling

AbstractPrediction of a conservative solute transport in the subsurface is investigated by applying a Kalman filter (KF) that uses time-correlated-error and a KF that uses Gaussian error. The observation data generated from an analytical solution of a two-dimensional advection-dispersion equation with additive time-correlated random errors were used as the measurement equation for the KF with time-correlated measurement errors and the KF with white Gaussian errors. A measurement-differencing algorithm was adopted in deriving a discrete time varying KF with time-correlated measurement errors for predicting contaminant transport in the subsurface in the case of observations with time-correlated errors. Simulation results indicated an improved root mean square error (RMSE) profile of KF with time-correlated errors over KF with white Gaussian error. The KF with time-correlated-error reduced the error in the prediction by 11.4% when compared to the KF with white Gaussian error. The stability analysis of the tw...

Fluorescent dye imaging of the volume sampled by single well forced-gradient tracer tests evaluated in a laboratory-scale aquifer physical model

This study presents a new method to visualise forced-gradient tracer tests in 2-D using a laboratory-scale aquifer physical model. Experiments were designed to investigate the volume of aquifer sampled in vertical dipole flow tracer tests (DFTT) and push–pull tests (PPT), using a miniature monitoring well and straddle packer arrangement equipped with solute injection and recovery chambers. These tests have previously been used to estimate bulk aquifer hydraulic and transport properties for the evaluation of natural attenuation and other remediation approaches. Experiments were performed in a silica glass bead-filled box, using a fluorescent tracer (fluorescein) to deduce conservative solute transport paths. Digital images of fluorescein transport were captured under ultraviolet light and processed to analyse tracer plume geometry and obtain point-concentration breakthrough histories. Inorganic anion mixtures were also used to obtain conventional tracer breakthrough histories. Concentration data from the conservative tracer breakthrough curves was compared with the digital images and a well characterised numerical model. The results show that the peak tracer breakthrough response in dipole flow tracer tests samples a zone of aquifer close to the well screen, while the sampling volume of push–pull tests is limited by the length of the straddle packers used. The effective sampling volume of these single well forced-gradient tests in isotropic conditions can be estimated with simple equations. The experimental approach offers the opportunity to evaluate under controlled conditions the theoretical basis, design and performance of DFTTs and PPTs in porous media in relation to measured flow and transport properties. 2 2 DFTT = Dipole Flow Tracer Test, PPT = Push Pull Tracer Test.

Comparative Study of Analytical Solutions for Time-Dependent Solute Transport Along Unsteady Groundwater Flow in Semi-infinite Aquifer

A comparative study is made among Laplace Transform Technique (LTT) and Fourier Transform Technique (FTT) to obtain one-dimensional analytical solution for conservative solute transport along unsteady groundwater flow in semi-infinite aquifer. The time-dependent source of contaminant concentration is considered at the origin and at the other end of the aquifer is supposed to be zero. Initially, aquifer is not solute free which means that the solute concentration exits in groundwater system and it is assumed as a uniform concentration. The aquifer is considered homogeneous and semi-infinite. The time-dependent velocity expressions are considered. The result may be used as preliminary predictive tools in groundwater management and benchmark the numerical code and solutions.

Single and Dual-Domain Models to Evaluate the Effects of Preferential Flow Paths in Alluvial Sediments

Typical features of preferential flow paths were evidenced by numerical tests of convective transport of conservative solutes performed in three blocks of alluvial sediments at the scale of depositional elements. The numerical experiments are analysed with standard single-domain models (SDMs) and with dual-domain models (DDMs): the model parameters are identified by minimisation of the misfit between the “experimental” and the modelled cumulative breakthrough curves (BTCs) and between the “experimental” and the modelled temporal moments of the BTCs. The results for the SDMs show different behaviours for the three model blocks and for the different flow directions, in good agreement with their hydrostratigraphic characteristics. The results for the DDMs sometimes correspond to cases for which one of the two domains is dominant and its values of diffusivity and average velocity are close to those obtained for the SDM; in some cases the DDM performs much better than the SDM and correctly represents the effects of preferential flow paths. Finally the relevance of the DDM is analysed in the framework of multi-objective optimisation: a proper choice of the objective-functions yields Pareto sets whose geometries are different for single- and dual-domain media.

Characteristics and controlling factors of dispersion in bounded heterogeneous porous media

In this study, we present first‐order (in terms of the log conductivity variance) analytical solutions to displacement covariances Xij and macrodispersion coefficients Dij for transport of conservative solutes in two‐dimensional, bounded heterogeneous porous media. These solutions are presented as infinity series and are explicit functions of the statistics of the log hydraulic conductivity. Using numerical examples, the convergence of these solutions in terms of the number of terms in truncated finite summations is first investigated, and the accuracy of these solutions is examined by comparing them with results from Monte Carlo simulations and the semianalytical solutions of Osnes (1998). Through several examples, the general features of time‐dependent Xij and Dij are discussed. Unlike in unbounded domains, the longitudinal macrodispersivity D11 for bounded domains does not approach an asymptotic value at large dimensionless time but instead increases quickly near the downstream constant head boundary. In addition, D11 for bounded domains is always larger than that in unbounded domains, and accordingly, the transverse macrodispersivity D22 in bounded domains is smaller than that in unbounded domains. These differences stem from the lateral no‐flow boundaries in our bounded domain models. We also investigated the effect of domain sizes on Xij and Dij. Our study shows that both Xij and Dij depend not only on the dimensionless size of the domain but also on its aspect ratio. The dependence of Xij and Dij on the particles' initial location has also been investigated at detail. Our results indicate that while this dependence is very small for X11 and D11, the release location has a significant impact on both X22 and D22. Our solutions to both displacement covariances and macrodispersivity are compared against those derived from tracer test data at the Borden site. The comparison shows that our solutions are quite close to observed data, indicating that they may be applicable to predict solute transport at the field scale.

Estimation of Degradation Rates by Satisfying Mass Balance at the Inlet

Using a steady-state mass conservative solute transport analytical solution that is based on the third-type (or flux-type or Cauchy) source condition, a method is developed to estimate the degradation parameters of solutes in groundwater. Then, the inadequacy of the methods based on the first-type source-based analytical solute transport solution is presented both theoretically and through an example. It is shown that the third-type source analytical solution exactly satisfies the mass balance constraint at the inlet location. It is also shown that the first-type source (or constant source concentration or Dirichlet) solution fails to satisfy the mass balance constraint at the inlet location and the degree of the failure depends on the value of the degradation as well as the flow and solute transport parameters. The error in the first-type source solution is determined with dimensionless parameters by comparing its results with the third-type source solution. Methods for estimating the degradation parameter values that are based on the first-type steady-state solute transport solution may significantly overestimate the degradation parameter values depending on the values of flow and solute transport parameters. It is recommended that the third-type source solution be used in estimating degradation parameters using measured concentrations instead of the first-type source solution.

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

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

Influences of seasonal flow regime on the fate and transport of fine particles and a dissolved solute in a New England stream

Fine particles are necessary for biogeochemical cycling but pose a risk to water quality if they are present in excess or carry sorbed contaminants. The objective of this work is to elucidate the effects of flow on the transport and retention of fine particles within a mountain stream and to compare particulate matter transport processes to those of a conservative solute tracer. We measured the migration of bromide (a conservative solute tracer) and micrometer‐sized titanium‐dioxide particles under three seasonal flow regimes in second‐order stream in Connecticut. A one‐dimensional transport model based upon the transient storage model was applied in inverse mode to the measured data to quantify solute and particle transport processes. Rates of particle movement by advection and longitudinal dispersion matched those of bromide. Transient, or temporary, storage influenced conservative solute transport, while particle storage was irreversible on the time scale of our experiments and likely dominated by deposition within the sediments of the hyporheic zone. Both solute transient storage and particle deposition increased with decreasing discharge.

Deterministic Analysis and Upscaling of Bromide Transport in a Heterogeneous Vadose Zone

Conservative solute transport experiments were conducted at a field plot and on an undisturbed soil core from the same site. The hydraulic and solute transport properties were extensively characterized so that the data could be analyzed from a deterministic perspective. To investigate the influence of scale and conceptual model on solute transport in the relatively homogeneous upper soil profile of the field site, breakthrough curves that were collected at different depths in the undisturbed column and in the field experiments were compared and analyzed. The mobile‐immobile model provided a physically realistic description of the column data that was largely independent of the transport distance, and upscaling from the undisturbed core to the field plot was relatively successful. Mean and variance of the Br− travel times were controlled by plot‐scale variability in soil water content and heterogeneity, which was overcome by averaging the concentration values from four locations at the same depth and time, and analyzing the Br− transport behavior as a one‐dimensional process. Differences between the measured and simulated mass balances, average concentration, and the variations in concentration were predicted reasonably well across depth and time. Although prediction of the exact concentration information at a given point was not achieved, this study demonstrates that area‐average Br− transport in a heterogeneous vadose zone can be deterministically quantified.

Examining the influence of heterogeneous porosity fields on conservative solute transport

It is widely recognized that groundwater flow and solute transport in natural media are largely controlled by heterogeneities. In the last three decades, many studies have examined the effects of heterogeneous hydraulic conductivity fields on flow and transport processes, but there has been much less attention to the influence of heterogeneous porosity fields. In this study, we use porosity and particle size measurements from boreholes at the Boise Hydrogeophysical Research Site (BHRS) to evaluate the importance of characterizing the spatial structure of porosity and grain size data for solute transport modeling. Then we develop synthetic hydraulic conductivity fields based on relatively simple measurements of porosity from borehole logs and grain size distributions from core samples to examine and compare the characteristics of tracer transport through these fields with and without inclusion of porosity heterogeneity. In particular, we develop horizontal 2D realizations based on data from one of the less heterogeneous units at the BHRS to examine effects where spatial variations in hydraulic parameters are not large. The results indicate that the distributions of porosity and the derived hydraulic conductivity in the study unit resemble fractal normal and lognormal fields respectively. We numerically simulate solute transport in stochastic fields and find that spatial variations in porosity have significant effects on the spread of an injected tracer plume including a significant delay in simulated tracer concentration histories.

Analytical Solution for Conservative Solute Transport in One-Dimensional Homogeneous Porous Formations with Time-Dependent Velocity

The space-time variation in contaminant concentration in unsteady flow in a homogeneous finite aquifer subjected to point source contamination is analytically derived under two conditions: (1) the flow velocity in the aquifer is of sinusoidal form; and (2) the flow velocity is an exponentially decreasing function. The analytical solution is illustrated using an example. Analytical solutions are perhaps most useful for benchmarking numerical codes and solutions.

A meshless method to simulate solute transport in heterogeneous porous media

We derive a meshless numerical method based on smoothed particle hydrodynamics (SPH) for the simulation of conservative solute transport in heterogeneous geological formations. We demonstrate that the new proposed scheme is stable, accurate, and conserves global mass. We evaluate the performance of the proposed method versus other popular numerical methods for the simulation of one- and two-dimensional dispersion and two-dimensional advective–dispersive solute transport in heterogeneous porous media under different Pèclet numbers. The results of those benchmarks demonstrate that the proposed scheme has important advantages over other standard methods because of its natural ability to control numerical dispersion and other numerical artifacts. More importantly, while the numerical dispersion affecting traditional numerical methods creates artificial mixing and dilution, the new scheme provides numerical solutions that are “physically correct”, greatly reducing these artifacts.

Longitudinal dispersion in a horizontal subsurface flow constructed wetland: a numerical solution

We present a numerical solution for the dead zone model which describes the solute transport in a subsurface and horizontal flow constructed wetland. This model is a system of two mass balance equations for two conceptual areas: the main channel and the storage zone. We use finite difference schemes to determine the numerical solution of the system and we study its convergence by presenting properties related to the stability and accuracy of the schemes. Concerning the experimental results, the magnitude of the longitudinal dispersion and the extension of dead volumes is estimated for clean conditions and after a certain operating period under organic loading conditions. The results showed a considerable amount of longitudinal dispersion through the bed, which was very strong near the feeding point, indicating the occurrence of mixing and significant presence of dead zones and short-circuiting. This approach is expected to be useful to determine operating conditions, such as, the control of the incoming organic loading, and also to avoid the increase of dead zones as a means to improve treatment performance. References J. M. Bahr and J. Rubin. Direct comparison of kinetic and local equilibrium formulations for solute transport affected by surface reactions. Water Resource Res. 23(3):438--452, 1987. doi:10.1029/WR023i003p00438 k: E. Bencala and R. A. Walters. Simulation of solute transport in a mountain pool-and-riffle stream: a transient storage model. Water Resour Res, 19(3):718--724, 1983. doi:10.1029/WR019i003p00718 K. Dekker and J. G. Verwer. Stability of Runge-Kutta Methods for Nonlinear Stiff Differential Equations. cwi Monograph 2, Elsevier, Amsterdam, 1984. S. H. Keefe, L. B. Barber, R. L. Runkel, J. N. Ryan, D. M. McKnight and R. D. Wass. Conservative and reactive solute transport in constructed wetlands. Water Resource Res., 40: W01201, 2004. doi:10.1029/2003WR002130 C. J. Martinez and W. R. Wise. Analysis of constructed treatment wetland hydraulics with the transient storage model otis. Ecological Engineering, 20(3):211, 2003. doi:10.1016/S0925-8574(03)00029-6 C. F. Nordin and B. M. Troutman. Longitudinal dispersion in rivers: the persistence of skewness in observed data. Water Resour Res, 16(1):123--128, 1980. doi:10.1029/WR016i001p00123 R. L. Runkel and S. C. Chapra. An efficient numerical solution of the transient storage equations for solute transport in small streams. Water Resour Res, 29(1):211--215, 1993. doi:10.1029/92WR02217 J. G. Verwer and J. M. Sanz-Serna. Convergence of Method of Lines Approximations to Partial Differential Equations. Computing, 33(3-4):297--313, 1984. doi:10.1007/BF02242274 B. J. Wagner and J. W Harvey. Experimental design for estimating parameters of rate-limited mass transfer: analysis of stream tracer studies. Water Resource Res., 33(7): 1731--1741, 1997. doi:10.1029/97WR01067

A Subgrid-Scale Stabilized Finite Element Method for Multicomponent Reactive Transport through Porous Media

Standard Galerkin finite element methods (GFEM) lack stability in solving advection-dominated solute transport in porous media. They usually require prohibitively fine grids and extremely small time steps to solve for advection-dominated problems. The algebraic subgrid-scale stabilized (ASGS) finite element method has been proved to overcome such problems for single-species reactive transport. Its potential for dealing with multicomponent reactive transport has not yet been explored. Here we present a numerical formulation of ASGS for steady and transient multicomponent reactive transport. Subgrid-scale transport equations are solved first by using an ASGS approximation and their solutions are substituted back into the grid-scale equations. A sequential iteration approach (SIA) is used to solve for coupled transport and chemical equations. Coupling of ASGS and SIA, ASGS+SIA, has been implemented in a reactive transport code, CORE2D V4, and verified for conservative solute transport. ASGS+SIA has been tested for a wide range of 1-D transient multicomponent reactive transport problems involving different types of chemical reactions such as: (1) Kinetically controlled aqueous species degradation, (2) Kinetic mineral dissolution, (3) Serial-parallel decay networks, and (4) Cation exchange and pyrite oxidation at local equilibrium. ASGS+SIA always provides accurate solutions and therefore offers an efficient option to solve for advection-dominated multicomponent reactive transport problems.

Hyporheic flows in stratified beds

Surface‐subsurface exchange fluxes are receiving increasing interest because of their importance in the fate of contaminants, nutrients, and other ecologically relevant substances in a variety of aquatic systems. Solutions have previously been developed for pore water flows induced by geometrical irregularities such as bed forms for the cases of homogeneous sediment beds and idealized heterogeneous beds, but these solutions have not accounted for the fact that streambed sediments are subject to sorting processes that often produce well‐defined subsurface structures. Sediments at the streambed surface are often coarser than the underlying material because of size‐selective sediment transport, producing relatively thin armor layers. Episodic erosional and depositional processes also create thick layers of different composition within the porous medium, forming stratified beds. A series of experiments were conducted to observe conservative solute transport in armored and stratified beds. An analytical solution was developed for advective exchange with stratified beds and provides appropriate scaling of the physical variables that control exchange flows. The results show that armor layers are too thin to significantly alter the advective pumping process but provide significant solute storage at short time scales. Stratified beds with layers of significant thickness favor development of horizontal flow paths within the bed and change the rate of solute transfer across the stream‐subsurface interface compared to homogeneous beds.

Transport of conservative solutes in simulated fracture networks: 1. Synthetic data generation

This paper investigates whether particle ensembles in a fractured rock domain may be adequately modeled as an operator‐stable plume. If this statistical model applies to transport in fractured media, then an ensemble plume in a fractured rock domain may be modeled using the novel Fokker‐Planck evolution equation of the operator‐stable plume. These plumes (which include the classical multi‐Gaussian as a subset) are typically characterized by power law leading‐edge concentration profiles and super‐Fickian growth rates. To investigate the possible correspondence of ensemble plumes to operator‐stable densities, we use numerical simulations of fluid flow and solute transport through large‐scale (2.5 km by 2.5 km), randomly generated fracture networks. These two‐dimensional networks are generated according to fracture statistics obtained from field studies that describe fracture length, transmissivity, density, and orientation. A fracture continuum approach using MODFLOW is developed for the solution of fluid flow within the fracture network and low‐permeability rock matrix, while a particle‐tracking code, random walk particle method for simulating transport in heterogeneous permeable media (RWHet), is used to simulate the advective motion of conservative solutes through the model domain. By deterministically mapping individual fractures onto a highly discretized finite difference grid (1 m × 1 m × 1 m here), the MODFLOW “continuum” simulations can faithfully preserve details of the generated network and can approximate fluid flow in a discrete fracture network model. An advantage of the MODFLOW approach is that matrix permeability can be made nonzero to account for any degree of matrix flow and/or transport.

Transport of conservative solutes in simulated fracture networks: 2. Ensemble solute transport and the correspondence to operator‐stable limit distributions

In networks where individual fracture lengths follow a fractal distribution, ensemble transport of conservative solute particles at the leading plume edge exhibit characteristics of operator‐stable densities. These densities have, as their governing equations of transport, either fractional‐order or integer‐order advection‐dispersion equations. Model selection depends on the identification of either multi‐Gaussian or operator‐stable transport regimes, which in turn depends on the power law exponent of the fracture length distribution. Low to moderately fractured networks with power law fracture length exponents less than or equal to 1.9 produce solute plumes that exhibit power law leading‐edge concentration profiles and super‐Fickian plume growth rates. For these network types, a multiscaling fractional advection‐dispersion equation (MFADE) provides a model of multidimensional solute transport where different rates of power law particle motion are defined along multiple directions. The MFADE model is parameterized by a scaling matrix to describe the super‐Fickian growth process, in which the eigenvectors correspond to primary fracture group orientations and the eigenvalues code fracture length and transmissivity. The approximation of particle clouds by a multi‐Gaussian (a subset of the operator stable) for densely fractured networks with finite variance fracture length distributions can be ascribed to the classical ADE where Fickian scaling rates pertain along orthogonal plume growth directions. Fracture networks show long‐term particle retention in low‐velocity fractures so that coupling of the equations of motion with retention models such as continuous time random walk or multirate mobile/immobile will increase accuracy near the source. Particle arrival times at exit boundaries for multi‐Gaussian plumes vary with spatial density. Generally, arrival times are faster in sparsely fractured domains where transport is governed by a few very long fractures.