We present a theoretical investigation on the processes underpinning the reduced longitudinal spreading documented in stable variable density flows, as opposed to constant density settings, within heterogeneous porous media. We do so by decomposing velocity and pressure in terms of stationary and dynamic components. The former corresponds to the solution of the constant density flow problem, while the latter accounts for the effects induced by density variability. We focus on a stable flow configuration and analyze the longitudinal spread of saltwater injected from the bottom of a column formed by a heterogeneous porous medium initially fully saturated by freshwater. We adopt a perturbation expansion approach and derive the equations satisfied by section-averaged concentrations and their ensemble mean values. These formulations are respectively characterized by a single realization and an ensemble dispersive flux, which we determine through appropriate closure equations. The latter are solved via semi-analytical and numerical approaches. Our formulations and associated results enable us to discriminate the relative impact on the density-driven solute displacement of (a) covariance of the permeability of the porous medium, (b) cross-covariance between permeability and concentration, which is in turn linked to the coupling of flow and transport problems, and (c) cross-covariance between the dynamic and stationary velocities.
Estimating the statistical parameters (mean, variance, and integral scale) that define the spatial structure of the transmissivity or hydraulic conductivity fields is a fundamental step for the accurate prediction of subsurface flow and contaminant transport. In practice, the determination of the spatial structure is a challenge because of spatial heterogeneity and data scarcity. In this paper, we describe a novel approach that uses time drawdown data from multiple pumping tests to determine the transmissivity statistical spatial structure. The method builds on the pumping test interpretation procedure of Copty et al. (2011) (Continuous Derivation method, CD), which uses the time-drawdown data and its time derivative to estimate apparent transmissivity values as a function of radial distance from the pumping well. A Bayesian approach is then used to infer the statistical parameters of the transmissivity field by combining prior information about the parameters and the likelihood function expressed in terms of radially-dependent apparent transmissivities determined from pumping tests. A major advantage of the proposed Bayesian approach is that the likelihood function is readily determined from randomly generated multiple realizations of the transmissivity field, without the need to solve the groundwater flow equation. Applying the method to synthetically-generated pumping test data, we demonstrate that, through a relatively simple procedure, information on the spatial structure of the transmissivity may be inferred from pumping tests data. It is also shown that the prior parameter distribution has a significant influence on the estimation procedure, given the non-uniqueness of the estimation procedure. Results also indicate that the reliability of the estimated transmissivity statistical parameters increases with the number of available pumping tests.
Benson, D.; Aquino, T.; Bolster, D.; Engdahl, N.; Henri, C.V.; Fernandez, D. Advances in water resources Vol. 99, p. 15-37 DOI: 10.1016/j.advwatres.2016.11.003 Data de publicació: 2017-01 Article en revista
When laboratory-measured chemical reaction rates are used in simulations at the field-scale, the models typically overpredict the apparent reaction rates. The discrepancy is primarily due to poorer mixing of chemically distinct waters at the larger scale. As a result, realistic field-scale predictions require accurate simulation of the degree of mixing between fluids. The Lagrangian particle-tracking (PT) method is a now-standard way to simulate the transport of conservative or sorbing solutes. The method’s main advantage is the absence of numerical dispersion (and its artificial mixing) when simulating advection. New algorithms allow particles of different species to interact in nonlinear (e.g., bimolecular) reactions. Therefore, the PT methods hold a promise of more accurate field-scale simulation of reactive transport because they eliminate the masking effects of spurious mixing due to advection errors inherent in grid-based methods. A hypothetical field-scale reaction scenario is constructed and run in PT and Eulerian (finite-volume/finite-difference) simulators. Grid-based advection schemes considered here include 1st- to 3rd-order spatially accurate total-variation-diminishing flux-limiting schemes, both of which are widely used in current transport/reaction codes. A homogeneous velocity field in which the Courant number is everywhere unity, so that the chosen Eulerian methods incur no error when simulating advection, shows that both the Eulerian and PT methods can achieve convergence in the L1 (integrated concentration) norm, but neither shows stricter pointwise convergence. In this specific case with a constant dispersion coefficient and bimolecular reaction A+B¿P, the correct total amount of product is 0.221MA0, where MA0 is the original mass of reactant A. When the Courant number drops, the grid-based simulations can show remarkable errors due to spurious over- and under-mixing. In a heterogeneous velocity field (keeping the same constant and isotropic dispersion), the PT simulations show an increased reaction total from 0.221MA0 to 0.372MA0 due to fluid deformation, while the 1st-order Eulerian simulations using ˜ 106 cells (with a classical grid Peclet number ¿x/aL of 10) have total product of 0.53MA0, or approximately twice as much additional reaction due to advection error. The 3rd-order TVD algorithm fares better, with total product of 0.394MA0, or about 1.14 times the increased reaction total. A very strict requirement on grid Peclet numbers for Eulerian simulations will be required for realistic reactions because of their nonlinear nature. We analytically estimate the magnitude of the effect for the end-member cases of very fast and very slow reactions and show that in either case, the mass produced is proportional to View the MathML source where Pe is the Peclet number. Therefore, extra mass is produced according to View the MathML source where the dispersion includes any numerical dispersion error. We test two PT methods, one that kills particles upon reaction and another that decrements a particle’s mass. For the bimolecular reaction studied here, the computational demands of the particle-killing methods are much smaller than, and the particle-number-preserving algorithm are on par with, the fastest Eulerian methods.
CO2 that is injected into a geological storage reservoir can leak in dissolved form because of brine displacement from the reservoir, which is caused by large-scale groundwater motion. Simulations of the reactive transport of leaking CO2aq along a conducting fracture in a clay-rich caprock are conducted to analyze the effect of various physical and geochemical processes. Whilst several modeling transport studies along rock fractures have considered diffusion as the only transport process in the surrounding rock matrix (diffusive transport), this study analyzes the combined role of advection and dispersion in the rock matrix in addition to diffusion (advection-dominated transport) on the migration of CO2aq along a leakage pathway and its conversion in geochemical reactions. A sensitivity analysis is performed to quantify the effect of fluid velocity and dispersivity. Variations in the porosity and permeability of the medium are found in response to calcite dissolution and precipitation along the leakage pathway. We observe that advection and dispersion in the rock matrix play a significant role in the overall transport process. For the parameters that were used in this study, advection-dominated transport increased the leakage of CO2aq from the reservoir by nearly 305%, caused faster transport and increased the mass conversion of CO2aq in geochemical reactions along the transport pathway by approximately 12.20% compared to diffusive transport.
Water is collected from a drain situated at the centre of a concrete cell that stores radioactive waste at ‘El Cabril’, which is the low and intermediate level radioactive waste disposal facility of Spain. This indicates flow of water within the cell. 2D numerical models have been made in order to reproduce and understand the processes that take place inside the cell. Temperature and relative humidity measured by sensors in the cells and thermo-hydraulic parameters from laboratory test have been used. Results show that this phenomenon is caused by capillary rise from the phreatic level, evaporation and condensation within the cell produced by temperature gradients caused by seasonal temperature fluctuations outside. At the centre of the cell, flow of gas and convection also play a role. Three remedial actions have been studied that may avoid the leakage of water from the drain.
We describe the coupled biotic and abiotic dynamics in intertidal environments using a point model that includes suspended sediment deposition, wave-and current-driven erosion, biofilm sediment stabilization, and sediment production and stabilization by vegetation. We explore the effects of two widely different types of vegetation: salt-marsh vegetation and mangroves. These two types of vegetation, which colonize distinct geographical areas, are characterized by different biomass productivities and stabilization mechanisms. We show that changing vegetation and biofilm properties result in differing stable states, both in their type and number. The presence of the biofilm exerts a dominant control on the tidal flat (lower intertidal) equilibrium elevation and stability. Vegetation controls the elevation of the marsh platform (i.e., the upper intertidal equilibrium). The two types of vegetation considered lead to similar effects on the stability of the system despite their distinct biophysical interactions, they ultimately lead to similar e¿ects on the stability of the system.
The release of industrial contaminants into the subsurface has led to a rapid degradation of groundwater resources. Contamination caused by Dense Non-Aqueous Phase Liquids (DNAPLs) is particularly severe owing to their limited solubility, slow dissolution and in many cases high toxicity. A greater insight into how the DNAPL source zone behavior and the contaminant release towards the aquifer impact human health risk is crucial for an appropriate risk management. Risk analysis is further complicated by the uncertainty in aquifer properties and contaminant conditions. This study focuses on the impact of the DNAPL release mode on the human health risk propagation along the aquifer under uncertain conditions. Contaminant concentrations released from the source zone are described using a screening approach with a set of parameters representing several scenarios of DNAPL architecture. The uncertainty in the hydraulic properties is systematically accounted for by high-resolution Monte Carlo simulations. We simulate the release and the transport of the chlorinated solvent perchloroethylene and its carcinogenic degradation products in randomly heterogeneous porous media. The human health risk posed by the chemical mixture of these contaminants is characterized by the low-order statistics and the probability density function of common risk metrics. We show that the zone of high risk (hot spot) is independent of the DNAPL mass release mode, and that the risk amplitude is mostly controlled by heterogeneities and by the source zone architecture. The risk is lower and less uncertain when the source zone is formed mostly by ganglia than by pools. We also illustrate how the source zone efficiency (intensity of the water flux crossing the source zone) affects the risk posed by an exposure to the chemical mixture. Results display that high source zone efficiencies are counter-intuitively beneficial, decreasing the risk because of a reduction in the time available for the production of the highly toxic subspecies.
The interplay between the spatial variability of the aquifer hydraulic properties, mass transfer due to sub-grid heterogeneity and chemical reactions often complicates reactive transport simulations. It is well documented that hydro-biochemical properties are ubiquitously heterogeneous and that diffusion and slow advection at the sub-grid scale typically leads to the conceptualization of an aquifer as a multi-porosity system. Within this context, chemical reactions taking place in mobile/immobile water regions can be substantially different between each other. This paper presents a particle-based method that can efficiently simulate heterogeneity, network reactions and multi-rate mass transfer. The approach is based on the development of transition probabilities that describe the likelihood that particles belonging to a given species and mobile/immobile domain at a given time will be transformed into another species and mobile/immobile domain afterwards. The joint effect of mass transfer and sequential degradation is shown to be non-trivial. A characteristic rebound of degradation products can be observed. This late rebound of concentrations is not driven by any change in the flow regime (e.g., pumping ceases in the pump-and-treat remediation strategy) but due to the natural interplay between mass transfer and chemical reactions. To illustrate that the method can simultaneously represent mass transfer, spatially varying properties and network reactions without numerical problems, we have simulated the degradation of tetrachloroethylene (PCE) in a three-dimensional fully heterogeneous aquifer subjected to rate-limited mass transfer. Two types of degradation modes were considered to compare the effect of an active biofilm with that of clay pods present in the aquifer. Results of the two scenarios display significantly differences. Biofilms that promote the degradation of compounds in an immobile region are shown to significantly enhance degradation, rapidly producing daughter products and less tailing.
García, L.; Barreiro, J.; Escobar, E.; Téllez, D.; Quijano, N.; Ocampo-Martinez, C.A. Advances in water resources Vol. 85, p. 120-132 DOI: 10.1016/j.advwatres.2015.08.007 Data de publicació: 2015 Article en revista
Urban drainage systems (UDS) may be considered large–scale systems given their large number of associated states and decision actions, making challenging their real–time control (RTC) design. Moreover, the complexity of the dynamics of the UDS makes necessary the development of strategies for the control design. This paper reviews and discusses several techniques and strategies commonly used for the control of UDS. Moreover, the models to describe, simulate, and control the transport of wastewater in UDS are also reviewed.
Understanding the changes in multiphase flow parameters caused by mineral dissolution-precipitation is required for multiple applications ranging from geological storage of CO2, enhanced geothermal energy production or ground water pollution. We present a physically-based theoretical model for describing the temporal evolution of porosity, saturated and relative permeabilities, retention curve and diffusion coefficient during rock dissolution by reactive fluids. The derivation of the model is based on the assumption that the pore structure of the rock can be represented by an ensemble of capillary tubes with fractal tortuosity and cumulative pore size distribution. Therefore, the model depends only on the minimum and maximum pore radii, the size of the representative elementary volume and the fractal dimensions of pore size and tortuosity, but do not need any other fitting parameters. Using this fractal description and known physical properties, we obtain analytical expressions for the hydrodynamic properties required by continuum (i.e., Darcy scale) multiphase flow models. Further, assuming periodic fluctuations in the radius of the pores, it is also possible to represent constrictivity and hysteresis. Finally, assuming a constant rate dissolution reaction it is possible to derive closed-form analytical expressions for the time evolution of porosity, retention curve, saturated and relative permeabilities and diffusion coefficient. (C) 2014 Elsevier Ltd. All rights reserved.
Saaltink, M.; Vilarrasa, V.; De Gaspari, F.; Silva, O.E.; Carrera, J.; Rötting, T. Advances in water resources Vol. 62, num. Part C, p. 431-441 DOI: 10.1016/j.advwatres.2013.09.013 Data de publicació: 2013-12 Article en revista
CO2 injection and storage in deep saline aquifers involves many coupled processes, including multiphase flow, heat and mass transport, rock deformation and mineral precipitation and dissolution. Coupling is especially critical in carbonate aquifers, where minerals will tend to dissolve in response to the dissolution of CO2 into the brine. The resulting neutralization will drive further dissolution of both CO2 and calcite. This suggests that large cavities may be formed and that proper simulation may require full coupling of reactive transport and multiphase flow. We show that solving the latter may suffice whenever two requirements are met: (1) all reactions can be assumed to occur in equilibrium and (2) the chemical system can be calculated as a function of the state variables of the multiphase flow model (i.e., liquid and gas pressure, and temperature). We redefine the components of multiphase flow codes (traditionally, water and CO2), so that they are conservative for all reactions of the chemical system. This requires modifying the traditional constitutive relationships of the multiphase flow codes, but yields the concentrations of all species and all reaction rates by simply performing speciation and mass balance calculations at the end of each time step. We applied this method to the H2O-CO2-Na-Cl-CaCO3 system, so as to model CO2 injection into a carbonate aquifer containing brine. Results were very similar to those obtained with traditional formulations, which implies that full coupling of reactive transport and multi-phase flow is not really needed for this kind of systems, but the resulting simplifications may make it advisable even for cases where the above requirements are not met. Regarding the behavior of carbonate rocks, we find that porosity development near the injection well is small because of the low solubility of calcite. Moreover, dissolution concentrates at the front of the advancing CO2 plume because the brine below the plume tends to reach high CO2 concentrations quite rapidly...
We analyze conservative solute transport under convergent flow to a well in perfectly stratified porous media, in which the hydraulic conductivity is treated as a random spatial function along the vertical direction (K(z)). The stratified model provides a rare exception of an exact analytical solution of travel time distributions in the proximity of pumping wells, and it is used here to obtain insights about ergodic and nonergodic transport conditions under nonuniform flow conditions. In addition, it provides a benchmark for numerical models aiming to correctly reproduce convergent flow transport in heterogeneous media, such as indicating the minimum number of layers required to obtain ergodic travel time distributions using only one model realization. The model provides important insights about the shape of the depth-integrated concentrations over time measured at the well (breakthrough curves, BTCs), which are usually applied to obtain transport parameters of the subsurface. It can be applied to any degree of system's heterogeneity and using either resident or flux-weighted injection modes. It can be built using different probabilistic distributions of K. In our analysis, we consider a log-normal K distribution, and the results indicate that, especially for highly heterogeneous systems, described by the log-K variance (sY2), the minimum number of layers required for from one model simulation to reproduce ergodic travel time distributions can be prohibitively high, e.g., above 106 for sY2=8 considering flux-weighted injections. This issue poses serious concerns for numerical applications aiming to simulate transport in the proximity of pumping wells. In addition, this simple solution confirms that stratification can lead BTCs to display strong preferential flow and persistent, power-law-like late-time tailing. ..
We analyze conservative solute transport under convergent flow to a well in perfectly stratified porous media, in which the hydraulic conductivity is treated as a random spatial function along the vertical direction (K(z)). The stratified model provides a rare exception of an exact analytical solution of travel time distributions in the proximity of pumping wells, and it is used here to obtain insights about ergodic and nonergodic transport conditions under nonuniform flow conditions. In addition, it provides a benchmark for numerical models aiming to correctly reproduce convergent flow transport in heterogeneous media, such as indicating the minimum number of layers required to obtain ergodic travel time distributions using only one model realization. The model provides important insights about the shape of the depth-integrated concentrations over time measured at the well (breakthrough curves, BTCs), which are usually applied to obtain transport parameters of the subsurface. It can be applied to any degree of system’s heterogeneity and using either resident or flux-weighted injection modes. It can be built using different probabilistic distributions of K. In our analysis, we consider a log-normal K distribution, and the results indicate that, especially for highly heterogeneous systems, described by the log-K variance (View the MathML source), the minimum number of layers required for from one model simulation to reproduce ergodic travel time distributions can be prohibitively high, e.g., above 106 for View the MathML source considering flux-weighted injections. This issue poses serious concerns for numerical applications aiming to simulate transport in the proximity of pumping wells. In addition, this simple solution confirms that stratification can lead BTCs to display strong preferential flow and persistent, power-law-like late-time tailing. Since the latter are common phenomenological macroscale evidences of other microscale hydrodynamic processes than pure advection (e.g., mass-transfer), caution must be taken when inferring aquifer properties controlling the anomalous transport dynamics in heterogeneous media from BTCs fitting.
Particle tracking methods to simulate solute transport deal with the issue of having to reconstruct smooth concentrations from a limited number of particles. This is an error-prone process that typically leads to large fluctuations in the determined late-time behavior of breakthrough curves (BTCs). Kernel density estimators (KDE) can be used to automatically reconstruct smooth BTCs from a small number of particles. The kernel approach incorporates the uncertainty associated with subsampling a large population by equipping each particle with a probability density function. Two broad classes of KDE methods can be distinguished depending on the parametrization of this function: global and adaptive methods. This paper shows that each method is likely to estimate a specific portion of the BTCs. Although global methods offer a valid approach to estimate early-time behavior and peak of BTCs, they exhibit important fluctuations at the tails where fewer particles exist. In contrast, locally adaptive methods improve tail estimation while oversmoothing both early-time and peak concentrations. Therefore a new method is proposed combining the strength of both KDE approaches. The proposed approach is universal and only needs one parameter (a) which slightly depends on the shape of the BTCs. Results show that, for the tested cases, heavily-tailed BTCs are properly reconstructed with a˜0.5.
We provide an approximate analytical solution for the substrate-microbial dynamics of the organic carbon cycle in natural soils under hydro-climatic variable forcing conditions. The model involves mass balance in two carbon pools: substrate and biomass. The analytical solution is based on a perturbative solution of concentrations, and can properly reproduce the numerical solutions for the full non-linear problem in a system evolving towards a steady state regime governed by the amount of labile carbon supplied to the system. The substrate and the biomass pools exhibit two distinct behaviors depending on whether the amount of carbon supplied is below or above a given threshold. In the latter case, the concentration versus time curves are always monotonic. Contrarily, in the former case the C-pool concentrations present oscillations, allowing the reproduction of non-monotonic small-scale biomass concentration data in a natural soil, observed so far only in short-term experiments in the rhizosphere. Our results illustrate the theoretical dependence of oscillations from soil moisture and temperature and how they may be masked at intermediate scales due to the superposition of solutions with spatially variable parameters.
Blade, E.; Gomez, M.; Dolz, J.; Aragon, J.; Corestein, G.; Sanchez-Juny, M. Advances in water resources Vol. 42, p. 17-29 DOI: 10.1016/j.advwatres.2012.03.021 Data de publicació: 2012-06 Article en revista
Pedretti, D.; Barahona-Palomo, M.; Bolster, D.; Fernandez, D.; Sanchez-Vila, X.; Tartakovsky, D. Advances in water resources Vol. 36, p. 23-35 DOI: 10.1016/j.advwatres.2011.07.008 Data de publicació: 2012-02 Article en revista
Guadagnini, A.; Sanchez-Vila, X.; Saaltink, M.; Bussini, M.; Berkowitz, B. Advances in water resources Vol. 32, num. 5, p. 756-766 DOI: 10.1016/j.advwatres.2008.07.005 Data de publicació: 2009-05 Article en revista
Connectivity of high/low-permeability areas has been recognized to significantly impact groundwater flow and solute transport. The task of defining a rigorous quantitative measure of connectivity for continuous variables has failed so far, and thus there exist a suite of connectivity indicators which are dependent on the specific hydrodynamic processes and the interpretation method. Amongst the many existing indicators, we concentrate on those characterizing connectivity between the points involved in a hydraulic or tracer test. The flow connectivity indicator used here is based on the time elapsed for hydraulic response in a pumping test (e.g., the storage coefficient estimated by the Cooper–Jacob method, ). Regarding transport, we select the estimated porosity from the breakthrough curve . According to Knudby and Carrera [Knudby C, Carrera J. On the relationship between indicators of geostatistical, flow and transport connectivity. Adv Water Resour 2005;28(4):405–21] these two indicators measure connectivity differently, and are poorly correlated. Here, we use perturbation theory to analytically investigate the intrinsic relationship between and . We find that can be expressed as a weighted line integral along the particle trajectory involving two parameters: the transmissivity point values, T, and the estimated values of along the particle path. The weighting function is linear with the distance from the pumping well, thus the influence of the weighting function is maximum at the injection area, whereas the hydraulic information close to the pumping well becomes redundant (null weight). The relative importance of these two factors is explored using numerical simulations in a given synthetic aquifer and tested against intermediate-scale laboratory tracer experiments. We conclude that the degree of connectivity between two points of an aquifer (point-to-point connectivity) is a key issue for risk assessment studies aimed at predicting the travel time of a potential contaminant.
Chemical species are advected by water and undergo mixing processes due to effects of local diffusion and/or dispersion. In turn, mixing causes reactions to take place so that the system can locally equilibrate. In general, a multicomponent reactive transport problem is described through a system of coupled non-linear partial differential equations. Under instantaneous chemical equilibrium, a complex geochemical problem can be highly simplified by fully defining the system in terms of conservative quantities, termed master species or components, and the space–time distribution of reaction rates. We investigate the parameters controlling reaction rates in a heterogeneous aquifer at short distances from the source. Hydraulic conductivity at this scale is modeled as a random process with highly anisotropic correlation structure. In the limit for very large horizontal integral scales, the medium can be considered as stratified. Upon modeling transport by means of an ADE (Advection Dispersion Equation), we derive closed-form analytical solutions for statistical moments of reaction rates for the particular case of negligible transverse dispersion. This allows obtaining an expression for an effective hydraulic conductivity, , as a representative parameter describing the mean behavior of the reactive system. The resulting is significantly smaller than the effective conductivity representative of the flow problem. Finally, we analyze numerically the effect of accounting for transverse local dispersion. We show that transverse dispersion causes no variation in the distribution of (ensemble) moments of local reaction rates at very short travel times, while it becomes the dominant effect for intermediate to large travel times.
The Henry problem has played a key role in our understanding of seawater intrusion into coastal aquifers and in benchmarking density dependent flow codes. This paper seeks to modify Henry’s problem to ensure sensitivity to density variations and vertical salinity profiles that resemble field observations. In the proposed problem, the “dispersive Henry problem”, mixing is represented by means of the traditional Scheidegger dispersion tensor (dispersivity times water flux). Anisotropy in the hydraulic conductivity is acknowledged and Henry’s seaside boundary condition of prescribed salt concentration is replaced by a flux dependent boundary condition, which represents more realistically salt transport across the seaside boundary. This problem turns out to be very sensitive to density variations and its solution gets closer to reality. However, an improvement in the traditional Henry problem (gain in sensitivity and realism) can be also achieved if the value of the Peclet number is significantly reduced.
Although the dispersive problem lacks an analytical solution, it can shed light on flow in coastal aquifers. It provides significant information about the factors controlling seawater penetration, width of the mixing zone and influx of seawater. The width of the mixing zone depends basically on dispersion with longitudinal and transverse dispersion controlling different parts of the mixing zone but displaying similar overall effects. Toe penetration is mainly controlled by the horizontal permeability and by the geometric mean of the dispersivities. Finally, transverse dispersivity and the geometric mean of the hydraulic conductivity are the leading parameters controlling the amount of saltwater that enters the aquifer.
We investigate effective solute transport in a chemically heterogeneous medium subject to temporal fluctuations of the flow conditions. Focusing on spatial variations in the equilibrium adsorption properties, the corresponding fluctuating retardation factor is modeled as a stationary random space function. The temporal variability of the flow is represented by a stationary temporal random process. Solute spreading is quantified by effective dispersion coefficients, which are derived from the ensemble average of the second centered moments of the normalized solute distribution in a single disorder realization. Using first-order expansions in the variances of the respective random fields, we derive explicit compact expressions for the time behavior of the disorder induced contributions to the effective dispersion coefficients. Focusing on the contributions due to chemical heterogeneity and temporal fluctuations, we find enhanced transverse spreading characterized by a transverse effective dispersion coefficient that, in contrast to transport in steady flow fields, evolves to a disorder-induced macroscopic value (i.e., independent of local dispersion). At the same time, the asymptotic longitudinal dispersion coefficient can decrease. Under certain conditions the contribution to the longitudinal effective dispersion coefficient shows superdiffusive behavior, similar to that observed for transport in s stratified porous medium, before it decreases to its asymptotic value. The presented compact and easy to use expressions for the longitudinal and transverse effective dispersion coefficients can be used for the quantification of effective spreading and mixing in the context of the groundwater remediation based on hydraulic manipulation and for the effective modeling of reactive transport in heterogeneous media in general.
Tracer tests designed to estimate field-scale dispersivities are commonly based upon the interpretation of breakthrough curves. Implicitly, no distinction is made between these dispersivity values and those inferred by analyzing the evolution of tracer plumes. Although this assumption is reasonable in ideal homogeneous media, its applicability to complex geologic formations is unclear. Recent laboratory tracer tests in a heterogeneous test aquifer have suggested that some differences may exist. This work provides computational investigations aimed to study the meaning and differences of these two types of dispersivity estimates in three-dimensional chemically and physically heterogeneous porous media. Specifically, the scale-dependence of longitudinal dispersivities for conservative and linearly sorbing tracers estimated from temporal moments of breakthrough curves are compared with those obtained from spatial moments of tracer plumes in uniform flow systems. The scale-dependence of dispersivity from spatial and temporal moments was found to be identical for small and . For larger values of and , however, the dispersivities estimated from temporal moments approach a constant value at smaller distances than estimates obtained from spatial moments. Yet, both dispersivities asymptotically approach the same constant value at large travel distances. From a practical standpoint, it is also shown that accurate field dispersivity coefficients can be obtained from uniform flow tracer test by simply using few fully-penetrating observation wells, bypassing the need for more expensive tracer techniques based upon the spatial description of concentrations.