On the importance of diffusion and compound-specific mixing for groundwater transport: an investigation from pore to field scale

Evolution of plume geometry, dilution and reactive mixing in porous media under highly transient flow fields at the surface water-groundwater interface

Highly transient boundary conditions affect mixing of dissolved solutes in groundwater. An example of these transient boundary conditions occurs at the surface water-groundwater interface, where the water level in rivers can change rapidly due to the operation of hydropower plants, leading to a regime known as hydropeaking. Inspired by this phenomenon, this work studies at laboratory scale the effects of fluctuating surface water bodies on solute transport in aquifers. We performed flow-through experiments at two different flow velocities and under steady and transient flow conditions where a conservative tracer was injected in the system and its concentration measured with optical imaging methods. The experimental results were quantitatively interpreted with numerical simulations implementing a non-linear velocity-dependent dispersive transport model. We estimated plume dilution by computing the dilution index and its evolution as well as two key geometrical metrics of the transient plumes: the perimeter and the area. We further investigated reactive mixing and mixing enhancement considering mixing-controlled bimolecular reactions using different critical mixing ratios. In general, highly transient boundary conditions lead to a larger area, perimeter and plume dilution and the results show greater relative enhancement for the scenarios with low groundwater flow velocity. A linear relationship was observed between the evolution of the area and the dilution index of the plumes for the transient flow scenarios investigated. Considering reactive transport and mixing-limited reactions at the surface water-groundwater interface, we identified different dilution and reaction dominated regimes, characterized, respectively, by increasing and decreasing plume entropies at different mixing ratios of the reactants. Furthermore, reactive mixing was enhanced by transient flows leading to a faster degradation of contaminant plumes compared to corresponding steady flow conditions.

Numerical modeling of an abiotic hyporheic mixing-dependent reaction: Chemical evolution of mixing and reactant production zones

Mixing-dependent reactions occur where groundwater and surface water mix in shallow sediments (hyporheic zone) and can attenuate contaminants along upwelling flowpaths, thus reducing transport to surface water. Here we used MODFLOW/SEAM3D to numerically simulate prior laboratory observations of a mixing-dependent reaction between sodium sulfite (Na₂SO₃) and dissolved oxygen (DO) to produce sodium sulfate (Na₂SO₄). This reaction is not common in nature but is used as a surrogate for mixing-dependent DO consuming reactions of environmental significance. We evaluated how location and thickness of mixing zones and reaction product production zones dynamically respond to variations in hydraulic and chemical boundary conditions and reaction kinetic rate. Sensitivity analysis showed that location and thickness of mixing zones and reactant production zones were most sensitive to changes in the balance of hydrologic inflow from groundwater and surface water (inflow ratio). Mixing zone thickness for reactive DO calibrated to experimental data was thinner than that for the "DO tracer" (identical source location and concentration as DO but conservative tracer), indicating that as DO is consumed its mixing zone narrows. The SO₄ production zone was consistently thicker than the DO mixing zone. Small changes in mixing/production zone thicknesses were linked to large changes in mass consumed and produced, indicating the potential for simpler field metrics like thickness to act as surrogates for more challenging measurements such as contaminant flux or consumption in monitoring natural attenuation. This study improves understanding of the evolution of hyporheic mixing-dependent reaction zones that occur even under steady state hydraulics, emphasizing their complex controls.

Oxidative Dissolution of Arsenic-Bearing Sulfide Minerals in Groundwater: Impact of Hydrochemical and Hydrodynamic Conditions on Arsenic Release and Surface Evolution

The dissolution of sulfide minerals can lead to hazardous arsenic levels in groundwater. This study investigates the oxidative dissolution of natural As-bearing sulfide minerals and the related release of arsenic under flow-through conditions. Column experiments were performed using reactive As-bearing sulfide minerals (arsenopyrite and löllingite) embedded in a sandy matrix and injecting oxic solutions into the initially anoxic porous media to trigger the mineral dissolution. Noninvasive oxygen measurements, analyses of ionic species at the outlet, and scanning electron microscopy allowed tracking the propagation of the oxidative dissolution fronts, the mineral dissolution progress, and the change in mineral surface composition. Process-based reactive transport simulations were performed to quantitatively interpret the geochemical processes. The experimental and modeling outcomes show that pore-water acidity exerts a key control on the dissolution of sulfide minerals and arsenic release since it determines the precipitation of secondary mineral phases causing the sequestration of arsenic and the passivation of the reactive mineral surfaces. The impact of surface passivation strongly depends on the flow velocity and on the spatial distribution of the reactive minerals. These results highlight the fundamental interplay of reactive mineral distribution and hydrochemical and hydrodynamic conditions on the mobilization of arsenic from sulfide minerals in flow-through systems.

Surface complexation reactions in sandy porous media: Effects of incomplete mixing and mass-transfer limitations in flow-through systems

Although mixing and surface complexation reactions are key processes for solute transport in porous media, their coupling has not been extensively investigated. In this work, we study the impact of mass-transfer limitations on heterogeneous reactions taking place at the solid-solution interface of a natural sandy porous medium under advection-dominated flow-through conditions. A comprehensive set of 36 column experiments with different grain sizes (0.64, 1.3 and 2.3 mm), seepage velocities (1, 30 and 90 m/day), and hydrochemical conditions were performed. The injection of NaBr solutions of different concentrations (1-100 mM) led to the release of protons via deprotonation reactions of the quartz surface. pH and solute concentration breakthrough curves were measured at the outlet of the columns and the propagation of pH fronts in the column setups was tracked inside the porous medium with non-invasive optode sensors. The experimental results show that the deprotonation of the reactive surfaces, resulting from their interactions with the injected ionic species, strongly depends on the hydrodynamic conditions and differs among the tested porous media despite their apparent similar surface properties. Reactive transport modeling was used to quantitatively interpret the experimental results and to analyze the effects of mass-transfer limited physical processes on surface complexation reactions, propagation of pH fronts, transport of major ions and spatio-temporal evolution of surface composition. A dual domain mass transfer formulation (DDMT) combined with a surface complexation model (SCM) allowed capturing the effects of incomplete mixing on the surface reactions and to reproduce the experimental observations collected in the experiments with high flow velocities. The SCM was parameterized with a single set of surface complexation parameters, accounting for the similar surface properties of the porous media, and was capable of describing the surface complexation mechanisms and their impact on the hydrochemistry over the large range of tested ionic strengths.

Impact of solute charge and diffusion coefficient on electromigration and mixing in porous media

The application of electrokinetic techniques in porous media has great potential to enhance mass transfer rates and, thus, to mobilize contaminants and effectively deliver reactants and amendments. However, the transport mechanisms induced by the application of an external electric field are complex and entail the coupling of physical, chemical and electrostatic processes. In this study we focus on electromigration and we provide experimental evidence of the impact of compound-specific properties, such as the aqueous diffusivity and the valence of charged species, on the macroscopic electrokinetic transport. We performed a series of multidimensional experiments considering the displacement of three different tracer plumes (i.e., permanganate, allura red and new coccine) in different background electrolyte solutions. The outcomes of the experiments clearly show that both the compound-specific diffusivity and the charge of the injected and resident ions impact the transport of the selected color tracer plumes, whose evolution was monitored with image analysis. The investigated experimental scenarios led to distinct plume behavior characterized by different mass distribution, average displacement velocities, longitudinal and lateral plume spreading, shape of the invading and receding fronts, as well as dilution of the injected solutes. A numerical simulator, based on the Nernst-Planck-Poisson equations and on aqueous speciation reactions in the pore water, allowed us to quantitatively interpret the experimental results, to capture the observed patterns of plume evolution, and to illuminate the coupling between the governing physico-chemical mechanisms and the controlling role of small scale compound-specific and electrostatic properties. Finally, the model was also extended to a typical configuration of in situ electrokinetic remediation of contaminated groundwater to show the impact of such mechanisms at larger scale.

Hyporheic transverse mixing zones and dispersivity: Laboratory and numerical experiments of hydraulic controls

Mixing of surface water and groundwater in shallow sediments is important to biogeochemical cycling and contaminant migration, and is often used to define the hyporheic zone. Yet knowledge of mixing processes in hyporheic zones is supported by surprisingly few rigorous lab or field observations, and differ from those in deeper groundwater by presence of enhanced head gradients, sediment heterogeneity, and temporal fluctuations. In a laboratory sediment (sand) tank we photographed a conservative dye to analyze transverse mixing zones between upwelling groundwater and bidirectional hyporheic exchange flows. We then conducted numerical modeling to investigate processes behind observed phenomena and estimate dispersivities. We found that transverse mixing zones were thin (i.e. mixing thickness measured in direction of steepest concentration gradient, δ, less than 5 cm), consistent with a small calibrated transverse dispersivity (~0.1 mm) and prior lab studies conducted at similar scales. In steady-state experiments and simulations, δ and estimated dispersion coefficients increased with the surface water head drop driving exchange flows. Given relatively constant deeper groundwater heads, increased Δh led to increased mixing zone length for both steady-state and transient conditions, indicating larger bedforms or weaker gaining conditions enhance subsurface mixing. However, Peclet number and flux-related dilution index simultaneously increased and decreased, respectively, indicating that enhancement of subsurface advection outpaced that of dispersion. In transient experiments and simulations, δ was greater than for steady-state, probably from temporary addition of longitudinal dispersion. During transient experiments, δ exhibited temporal noise, perhaps due to the mixing zone moving past varying patterns of sediment packing. Our results provide basic knowledge of mixing zone behavior in hyporheic zones with implications for hyporheic zone definitions, solute transport, mixing-dependent reaction, and water quality.

Arsenic release and transport during oxidative dissolution of spatially-distributed sulfide minerals

The oxidative dissolution of sulfide minerals, naturally present in the subsurface, is one of the major pathways of arsenic mobilization. This study investigates the release and fate of arsenic from arsenopyrite and löllingite oxidation under dynamic redox conditions. We performed multidimensional flow-through experiments focusing on the impact of chemical heterogeneity on arsenic mobilization and reactive transport. In the experimental setups the As-bearing sulfide minerals were embedded, with different concentrations and spatial distributions, into a sandy matrix under anoxic conditions. Oxic water flushed in the flow-through setups triggered the oxidative dissolution of the reactive minerals, the release of arsenic, as well as changes in pore water chemistry, surface-solution interactions and mineral precipitation. We developed a reactive transport model to quantitatively interpret the experimental results. The simulation outcomes showed that 40% of the arsenic released was reincorporated into a freshly precipitated iron-arsenate phase that created a coating on the mineral surface limiting the dissolution reactions. The faster dissolution rate of löllingite compared to arsenopyrite was responsible for sustaining the continuous release of As-contaminated plumes. The model also allowed shedding light on the spatial distribution, on the temporal dynamics, and on the interactions between arsenic sources (As-bearing minerals) and sinks (freshly formed secondary phases) in flow-through systems.

Reactive transport in porous media: a review of recent mathematical efforts in modeling geochemical reactions in petroleum subsurface reservoirs

The rapid advancements in the computational abilities of numerical simulations have attracted researchers to work on the area of reactive transport in porous media to improve the hydrocarbon production processes from mature reservoirs. In the hydrology community, reactive transport is well developed where the main research focuses on studying the movement of groundwater and contaminants in aquifers, and quantifying the effect of chemical reactions between the rocks and water. Recently, great efforts have been made to adapt similar models for petroleum applications where multiphase flow is experienced in the subsurface reservoirs. In such systems, thermodynamic and chemical equilibrium is key in establishing an accurate description of the states of the fluids existing in the reservoir. This paper presents a detailed and comprehensive review on the concepts of geochemical modeling, and how it can be mathematically adapted to petroleum multiphase flow problems in porous media. We introduce key physical concepts outlining the treatment of chemical reactions in experimental trials and then explain in detail how a network of chemical reactions can be modeled mathematically for numerical simulation applications. The steps of characterizing the physical behavior of the fluid flow—through a set of governing equations by either natural or molar variables formulations, and the methodology to simplify and incorporate the numerical algorithms into an existing reservoir simulation scheme are shown as well. We finally present two numerical cases from the literature to highlight the key variations between the different variable formulations and comment on the advantages and disadvantages of each approach.

Impact of diffuse layer processes on contaminant forward and back diffusion in heterogeneous sandy-clayey domains

Low-permeability aquitards can significantly affect the transport, distribution, and persistence of contaminant plumes in subsurface systems. Although such low-permeability materials are often charged, the key role of charge-induced electrostatic processes during contaminant transport has not been extensively studied. This work presents a detailed investigation exploring the coupled effects of heterogeneous distribution of physical, chemical and electrostatic properties on reactive contaminant transport in field-scale groundwater systems including spatially distributed clay zones. We performed an extensive series of numerical experiments in three distinct heterogeneous sandy-clayey domains with different levels of complexity. The flow and reactive transport simulations were performed by explicitly resolving the complex velocity fields, the small-scale electrostatic processes, the compound-specific diffusive/dispersive fluxes and the chemical processes utilizing a multi-continua based reactive transport code (MMIT-Clay). In each particular domain, numerical experiments were performed focusing on both the forward and back diffusion through the sandy-clayey interfaces. The results illuminate the control of microscopic electrostatic mechanisms on macroscopic mass transfer. Coulombic interactions in the clay's diffuse layer can significantly accelerate or retard a particular species depending on its charge. Furthermore, the chemical heterogeneity plays a major role in mass storage and release during reactive transport. Neglecting such processes can lead to substantial over- or underestimation of the overall transport behavior, which underlines the need for integrated physical, chemical and electrostatic approaches to accurately describe mass transfer processes in systems including low-permeability inclusions.

Electrokinetic Delivery of Reactants: Pore Water Chemistry Controls Transport, Mixing, and Degradation

Electrokinetics in porous media entails complex transport processes occurring upon the establishment of electric potential gradients, with a wide spectrum of environmental applications ranging from remediation of contaminated sites to biotechnology. The resulting electric forces cause the movement of pore water ions in opposite directions, leading to charge interactions that can affect the distribution of charged species in the domain. Here, we demonstrate that changes in chemical conditions, such as the concentration of a background electrolyte in the pore water of a saturated porous medium, exert a key control on the macroscopic transport of charged tracers and reactants. The difference in concentration between the background electrolyte and an injected solute can limit or enhance the reactant delivery, cause nonintuitive patterns of concentration distribution, and ultimately control mixing and degradation kinetics. With nonreactive and reactive electrokinetic transport experiments combined with process-based modeling, we show that microscopic charge interactions in the pore water play a crucial role on the transport of injected plumes and on the mechanisms and rate of both physical and chemical processes at larger, macroscopic scales. Our results have important implications on electrokinetic transport in porous media and may greatly impact injection and delivery strategies in a wide range of applications, including in situ remediation of soil and groundwater.

Process-based modeling of electrokinetic-enhanced bioremediation of chlorinated ethenes

This study presents a process-based modeling analysis of electrokinetic-enhanced bioremediation (EK-Bio) to illuminate the complex interactions between physical, electrostatic and biogeochemical processes occurring during the application of this remediation technique. The features of the proposed model include: (i) multidimensional electrokinetic transport in saturated porous media by electromigration and electroosmosis, (ii) charge interactions, (iii) degradation kinetics, (iv) microbial populations dynamics of indigenous and specialized exogenous degraders, (v) mass transfer limitations, and (vi) geochemical reactions. A scenario modeling investigation is presented, which was inspired by an EK-Bio pilot application conducted in a clayey aquitard at the Skuldelev site (Denmark) contaminated by chlorinated ethenes. Lactate and specialized degraders are delivered under conservative and reactive transport conditions. In the considered setup, transport of lactate using electrokinetics results in more than fourfold increase in the distribution efficiency with respect to a diffusion-only scenario. Moreover, EK transport by electromigration and electroosmosis yields fluxes at least two orders of magnitude larger than diffusive fluxes. Quantitative metrics are also defined and used to assess the amendment distribution and the enhanced contaminant biodegradation in the different conservative and reactive transport scenarios.

Charge interactions, reaction kinetics and dimensionality effects on electrokinetic remediation: A model-based analysis

The potential of electrokinetic remediation technologies (EKR) for the removal of different contaminants from subsurface porous media has been increasingly recognized. Despite electrokinetic applications have shown promising results, quantitative understanding of such systems is still challenging due to the complex interplay between physical transport processes, electrostatic interactions, and geochemical reactions. In this study, we perform a model-based analysis of electrokinetic transport in saturated porous media. We investigate the effects of: (i) Coulombic interactions between ions in the system mobilized by electromigration, (ii) reaction kinetics on the overall removal efficiency of a non-charged organic contaminant, and (iii) dimensionality and different electrode configurations. The results show that such effects play a major role on the performance of electrokinetic systems. The simulations illuminate the importance of microscopic processes, such as electrostatic interactions and ion-specific diffusivities, and their non-intuitive macroscopic impact on the delivery of charged amendments and on the efficiency of contaminant removal. The insights of this study are valuable to improve and optimize the design and the operational strategies of electrokinetic remediation systems.

A Large Undisturbed Column Method to Study Flow and Transport in Macropores and Fractured Media

Intact soil columns can bridge the gap between field studies and idealized laboratory investigations of flow and transport in macropores and fractured media. However, the value of intact column studies is often hampered by shortcomings such as lack of column intactness, small column size, and column rim flow, which can cause serious artifacts and hamper system understanding. The flexible-wall pressurized large undisturbed column (LUC) method overcomes these limitations and is a valuable approach to analyze fluid flow and solute transport in macroporous and fractured geological formations. The method investigates subsurface processes in complex media, mimicking in situ conditions and facilitating the control of system boundary conditions including effective stress. In recent years, considerable experience has been gained through different applications of the LUC approach. Modeling tools have also been developed for a detailed interpretation of flow and transport processes in LUC systems. This paper describes the steps of the LUC method from column excavation in the field to experimental setup in the laboratory. The description encompasses the key features of the sampling of LUCs in field excavations, the laboratory setup, the procedure for hydraulic and transport experiments, as well as practical challenges and potential issues during operation of an LUC system. Application examples with a fully three-dimensional numerical model of LUC tracer experiments are also presented to illustrate the quantitative interpretation of transport processes in macroporous clayey tills.

The effects of denitrification parameterization and potential benefits of spatially targeted regulation for the reduction of N-discharges from agriculture

Diffuse nitrate leaching from agricultural areas is a major environmental problem in many parts of the world. Understanding where in a catchment nitrate is removed is key for designing effective land use management strategies that protect water quality, while minimizing the impact on economic development. In this study we assess the effects of spatially targeted nitrate leaching regulation in a basin with limited knowledge of the complexity of chemical heterogeneity. Three alternative nitrate reactivity spatial parameterizations were incorporated in a catchment-scale flow and transport model and used to evaluate the effectiveness of four possible spatially targeted regulation options. Our findings confirm that denitrification parameterization cannot be numerically determined based on model inversion alone. Detailed field based characterization using physical and geochemical methods should be considered and incorporated in the numerical inversion scheme. We also demonstrate that there are potential benefits of implementing spatially targeted regulation compared to spatially uniform regulation. Focusing regulation in areas where nitrate residence time is short, such as riparian zones or areas with low natural N-reduction, results in greater reduction of N-discharges through groundwater. Significantly improved efficiencies can be expected when delineation of management zones considers the chemical heterogeneity and groundwater flow paths. These improved efficiencies are achieved by adopting management rules that regulate land use in discharge sensitive areas, where leaching changes contribute the most to the catchment nitrate discharges. In our case study, regulation in discharge sensitive zones was twice as efficient compared to other management options.

Effects of Cemented Porous Media on Temporal Mixing Behavior of Conservative Solute Transport

The cementation of porous media leads to the variation of the pore space and heterogeneity of the porous media. In this study, four porous media (PM1, PM2, PM3, and PM4) with the different radii of solid grains were generated to represent the different cementation degrees of the porous media. The direct simulations of flow and conservative solute transport in PM1–4 were conducted to investigate the influence of the cemented porous media and Peclet number (Pe) on the temporal mixing behavior. Two metrics, scalar dissipation rates (SDR) and dilution index, were employed to quantify the temporal mixing behavior. It was found that the spatial velocity variability of the flow field was enhanced as cementation degree increased. The results of the coefficient of velocity variation ( C V U ) increased from 0.943 to 2.319 for PM1–4. A network consisted of several preferential flow paths was observed in PM1–4. The preferential flow enhanced the mixing of the conservative solute but had a negative influence on the mixing of the solute plume when the cemented solid grains formed several groups, and there were some stagnant regions where the flow was almost immobile. As the Pe increased, for PM1–3, the exponent of the best-fitting power law of the global SDR decreased. At the case of Pe = 400, the slope of the global SDR reduced to around −1.9. In PM4 where the preferential flow was enhanced by the cemented solid grains, the slope of the global SDR increased as the Pe increased. The global SDR results indicated that the temporal mixing behavior followed a Fickian scaling ( S D R ∝ p v − 1.5 ) in the early stage (Pv < 0.05), while the mixing behavior turned to be non-Fickian in the late stage. The transition time from the Fickian scaling to the non-Fickian scaling was found to be sensitive to the cementation degree of the porous media.

Experimental and numerical evaluation of Groundwater Circulation Wells as a remediation technology for persistent, low permeability contaminant source zones

Contaminants removal stoked inside low permeability zones of aquifers is one of the most important challenge of groundwater remediation process today. Low permeability layers can be considered persistent secondary sources of contamination because they release pollutants by molecular diffusion after primary source of contamination is reduced, causing long plum tails (Back-Diffusion). In this study, the Groundwater Circulation Well (GCW) system was investigated as an alternative remediation technology to the low efficient traditional pumping technologies to restore contaminated low permeability layers of aquifers. The GCW system creates vertical groundwater circulation cells by drawing groundwater through a screen of a multi-screen well and discharging it through another screen. The suitability of this technology to remediate contaminated low permeability zones was investigated by laboratory test and numerical simulations. The collected data were used to calibrate a model created to simulate the Back-Diffusion process and to evaluate the effect of different pumping technologies on the depletion time of that process. Results show that the efficiency of the GCW is dependent on the position and on the geometry of the low permeability zones, however the GCW system appears more suitable to restore contaminated low permeability layers of aquifers than the traditional pumping technology.

Recent Advances in Experimental Studies of Steady-State Dilution and Reactive Mixing in Saturated Porous Media

Transverse dispersive mixing plays an important role in controlling natural attenuation of contaminant plumes and the performance of engineered remediation strategies. The extent of transverse mixing can be significantly affected by porous media heterogeneity and anisotropy. For instance, flow focusing in the high-permeability inclusions leads to an enhancement of dilution and reactive mixing in steady-state solute transport. Numerous modeling studies have been performed to understand the mechanism of conservative and reactive transport in homogeneous and complex heterogeneous porous media. However, experimental investigations are necessary to show an intuitive phenomenon and to validate the modeling results. This paper briefly reviews recent laboratory experimental studies on dilution and reactive mixing of steady-state transport in saturated homogeneous and heterogeneous porous media. In this context, setups and measuring techniques are described in pore-scale and Darcy-scale experiments. Parameters quantifying dilution and reactive mixing in the experiments are also introduced. Finally, we discuss the further experimental works necessary to deepen our understanding of dilution and reactive mixing in natural aquifers.

Temporal Mixing Behavior of Conservative Solute Transport through 2D Self-Affine Fractures

In this work, the influence of the Hurst exponent and Peclet number (Pe) on the temporal mixing behavior of a conservative solute in the self-affine fractures with variable-aperture fracture and constant-aperture distributions were investigated. The mixing was quantified by the scalar dissipation rate (SDR) in fractures. The investigation shows that the variable-aperture distribution leads to local fluctuation of the temporal evolution of the SDR, whereas the temporal evolution of the SDR in the constant-aperture fractures is smoothly decreasing as a power-law function of time. The Peclet number plays a dominant role in the temporal evolution of mixing in both variable-aperture and constant-aperture fractures. In the constant-aperture fracture, the influence of Hurst exponent on the temporal evolution of the SDR becomes negligible when the Peclet number is relatively small. The longitudinal SDR can be related to the global SDR in the constant-aperture fracture when the Peclet number is relatively small. As the Peclet number increases the longitudinal SDR overpredicts the global SDR. In the variable-aperture fractures, predicting the global SDR from the longitudinal SDR is inappropriate due to the non-monotonic increase of the longitudinal concentration second moment, which results in a physically meaningless SDR.

Longitudinal dispersion coefficients for numerical modeling of groundwater solute transport in heterogeneous formations

Most recent research on hydrodynamic dispersion in porous media has focused on whole-domain dispersion while other research is largely on laboratory-scale dispersion. This work focuses on the contribution of a single block in a numerical model to dispersion. Variability of fluid velocity and concentration within a block is not resolved and the combined spreading effect is approximated using resolved quantities and macroscopic parameters. This applies whether the formation is modeled as homogeneous or discretized into homogeneous blocks but the emphasis here being on the latter. The process of dispersion is typically described through the Fickian model, i.e., the dispersive flux is proportional to the gradient of the resolved concentration, commonly with the Scheidegger parameterization, which is a particular way to compute the dispersion coefficients utilizing dispersivity coefficients. Although such parameterization is by far the most commonly used in solute transport applications, its validity has been questioned. Here, our goal is to investigate the effects of heterogeneity and mass transfer limitations on block-scale longitudinal dispersion and to evaluate under which conditions the Scheidegger parameterization is valid. We compute the relaxation time or memory of the system; changes in time with periods larger than the relaxation time are gradually leading to a condition of local equilibrium under which dispersion is Fickian. The method we use requires the solution of a steady-state advection-dispersion equation, and thus is computationally efficient, and applicable to any heterogeneous hydraulic conductivity K field without requiring statistical or structural assumptions. The method was validated by comparing with other approaches such as the moment analysis and the first order perturbation method. We investigate the impact of heterogeneity, both in degree and structure, on the longitudinal dispersion coefficient and then discuss the role of local dispersion and mass transfer limitations, i.e., the exchange of mass between the permeable matrix and the low permeability inclusions. We illustrate the physical meaning of the method and we show how the block longitudinal dispersivity approaches, under certain conditions, the Scheidegger limit at large Péclet numbers. Lastly, we discuss the potential and limitations of the method to accurately describe dispersion in solute transport applications in heterogeneous aquifers.

Pore-scale simulations of concentration tails in heterogeneous porous media

The retention of contaminants in the finest and less-conductive regions of natural aquifer is known to strongly affect the decontamination of polluted aquifers. In fact, contaminant transfer from low to high mobility regions at the back end of a contaminant plume (i.e. back diffusion) is responsible for the long-term release of contaminants during remediation operation. In this paper, we perform pore-scale calculations for the transport of contaminant through heterogeneous porous media composed of low and high mobility regions with two objectives: (i) study the effect of permeability contrast and solute transport conditions on the exchange of solutes between mobile and immobile regions and (ii) estimate the mass of contaminants sequestered in low mobility regions based on concentration breakthrough curves.

Recirculation zones induce non-Fickian transport in three-dimensional periodic porous media

In this work, the influence of pore space geometry on solute transport in porous media is investigated performing computational fluid dynamics pore-scale simulations of fluid flow and solute transport. The three-dimensional periodic domains are obtained from three different pore structure configurations, namely, face-centered-cubic (fcc), body-centered-cubic (bcc), and sphere-in-cube (sic) arrangements of spherical grains. Although transport simulations are performed with media having the same grain size and the same porosity (in fcc and bcc configurations), the resulting breakthrough curves present noteworthy differences, such as enhanced tailing. The cause of such differences is ascribed to the presence of recirculation zones, even at low Reynolds numbers. Various methods to readily identify recirculation zones and quantify their magnitude using pore-scale data are proposed. The information gained from this analysis is then used to define macroscale models able to provide an appropriate description of the observed anomalous transport. A mass transfer model is applied to estimate relevant macroscale parameters (hydrodynamic dispersion above all) and their spatial variation in the medium; a functional relation describing the spatial variation of such macroscale parameters is then proposed.

Implications of the change in confinement status of a heterogeneous aquifer for scale-dependent dispersion and mass-transfer processes

A series of experimental tracer tests were performed to explore the implications of the change in the pressure status of a heterogeneous bimodal aquifer for scale-dependent dispersion and mass-transfer processes. The sandbox was filled with sands and gravel channels and patches to form an alluvial-like bimodal aquifer. We performed multiple injections of a conservative tracer from 26 different locations of the sandbox and interpreted the resulting depth-integrated breakthrough curves (BTCs) at the central pumping well to obtain a scale-dependent distribution of local and field-integrated apparent longitudinal dispersivity (respectively, α_L^loc and α_L^app). We repeated the experiments under confined (CS) and unconfined (UNS) pressure status, keeping the same heterogeneous configuration. Results showed that α_L^loc(associated with transport through gravel zones) was poorly influenced by the change in aquifer pressure and the presence of channels. Instead, α_L^app(i.e. macrodispersion) strongly increased when changing from CS to UNS. In specific, we found α_L^app≈0.03r for the CS and α_L^app≈0.15r for the UNS (being r the distance from the well). Second-to-fourth-order temporal moments showed strong spatial dependence in the UNS and no spatial dependence in the CS. These results seem consistent with a "vadose-zone-driven" kinetic mass-transfer process occurring in the UNS but not in the CS. The vadose zone enhances vertical flow due to the presence of free surface and large contrasts in hydraulic conductivity triggered by the desaturation of gravel channels nearby the pumping well. The vadose zone enhances vertical mixing between gravel and sands and generates BTC tailing. In the CS vertical mixing is negligible and anomalous transport is not observed.

Image analysis procedure for studying Back-Diffusion phenomena from low-permeability layers in laboratory tests

In this study, the long-term tailing derived from the storage process of contaminants in low-permeability zones is investigated. The release from these areas in the groundwater can be considered a long-term source that often undermines remediation efforts. An Image Analysis technique is used to analyze the process and evaluate the concentrations of a tracer at different points of the test section. Furthermore, the diffusive flux from the low-permeability lenses is determined. To validate the proposed technique, the results are compared with samples, and the diffusive fluxes resulting from the low-permeability zones of the reconstructed aquifer are compared with a theoretical approach.

Experimental investigation of transverse mixing in porous media under helical flow conditions

Plume dilution and transverse mixing can be considerably enhanced by helical flow occurring in three-dimensional heterogeneous anisotropic porous media. In this study, we perform tracer experiments in a fully three-dimensional flow-through chamber to investigate the effects of helical flow on plume spiraling and deformation, as well as on its dilution. Porous media were packed in angled stripes of materials with different grain sizes to create blocks with macroscopically anisotropic hydraulic conductivity, which caused helical flows. Steady-state transport experiments were carried out by continuously injecting dye tracers at different inlet ports. High-resolution measurements of concentration and flow rates were performed at 49 outlet ports. These measurements allowed quantifying the spreading and dilution of the solute plumes at the outlet cross section. Direct evidence of plume spiraling and visual proof of helical flow was obtained by freezing and slicing the porous media at different cross sections and observing the dye-tracer distribution. We simulated flow and transport to interpret our experimental observations and investigate the effects of helical flow on mixing-controlled reactive transport. The simulation results were evaluated using metrics of reactive mixing such as the critical dilution index and the length of continuously injected steady-state plumes. The results show considerable reaction enhancement, quantified by the remarkable decrease of reactive plume lengths (up to four times) in helical flows compared to analogous scenarios in uniform flows.

Experimental Evidence of Helical Flow in Porous Media

Helical flow leads to deformation of solute plumes and enhances transverse mixing in porous media. We present experiments in which macroscopic helical flow is created by arranging different materials to obtain an anisotropic macroscopic permeability tensor with spatially variable orientation. The resulting helical flow entails twisting streamlines which cause a significant increase in lateral mass exchange and thus a large enhancement of plume dilution (up to 235%) compared to transport in homogenous media. The setup may be used to effectively mix solutes in parallel streams similarly to static mixers, but in porous media.

Evolution of carbon isotope signatures during reactive transport of hydrocarbons in heterogeneous aquifers

Compound-specific isotope analysis (CSIA) of organic pollutants has become a well-established tool for assessing the occurrence and extent of biodegradation processes in contaminated aquifers. However, the precision of CSIA is influenced by the degree to which assumptions underlying CSIA data interpretation hold under realistic field-scale conditions. For the first time this study demonstrates how aquifer analogs combined with reactive transport models offer an underexplored way to develop generic process understanding, evaluate monitoring and quantification strategies in highly heterogeneous subsurface settings. Data from high-resolution aquifer analogs were used in numerical experiments to track the propagation of a representative oxidizable organic compound (toluene) within a variety of realistic heterogeneous aquifers and to investigate its detailed fate. The simulations were used to analyze (1) the effects of physical aquifer heterogeneities on spatiotemporal patterns of contaminant concentrations and isotope signatures, (2) the performance of the commonly applied Rayleigh equation and (3) the applicability of an extension of the Rayleigh equation for complex hydrogeological conditions. The results indicate that if field-derived enrichment factors are applied without corrections for dilution, the conventional Rayleigh equation is inaccurate and estimates for biodegradation are typically overestimated and unreliable in heterogeneous aquifers. Underestimations can occur due to the partial source zone depletion. In contrast, if dilution can be accurately accounted for, field-derived enrichment factors comprise a suitable alternative to laboratory-derived and redox-specific enrichment factors. The study also examines to what extent variations in monitoring/sampling strategies influence the obtained results. Especially measurements from long-screened wells (>1 m) reveal to be inappropriate for the application of the Rayleigh equation in the investigated aquifer analogs, as low resolution data sampled from the simulated scenarios only enable a qualitative assessment of biodegradation. Measurements from both long- and short-screened wells employing the Rayleigh equation streamline approach are only partly viable for in situ biodegradation measurements in heterogeneous systems.

Impact of heterogeneity on oxygen transfer in a fluctuating capillary fringe

We performed quasi-two-dimensional flow through laboratory experiments to study the effect of a coarse-material inclusion, located in the proximity of the water table, on flow and oxygen transfer in the capillary fringe. The experiments investigate different phases of mass transfer from the unsaturated zone to anoxic groundwater under both steady-state and transient flow conditions, the latter obtained by fluctuating the water table. Monitoring of flow and transport in the different experimental phases was performed by visual inspection of the complex flow field using a dye tracer solution, measurement of oxygen profiles across the capillary fringe, and determination of oxygen fluxes in the effluent of the flow-through chamber. Our results show significant effects of the coarse-material inclusion on oxygen transfer during the different phases of the experiments. At steady state, the oxygen flux across the unsaturated/saturated interface was considerably enhanced due to flow focusing in the fully water-saturated coarse-material inclusion. During drainage, a zone of higher water saturation formed in the fine material overlying the coarse lens. The entrapped oxygen-rich aqueous phase contributed to the total amount of oxygen supplied to the system when the water table was raised back to its initial level. In case of imbibition, pronounced air entrapment occurred in the coarse lens, causing oxygen to partition between the aqueous and gaseous phases. The oxygen mass supplied to the anoxic groundwater following the imbibition event was found to be remarkably higher (approximately seven times) in the heterogeneous system compared with a similar experiment performed in a homogeneous porous medium.

Experimental investigation of compound-specific dilution of solute plumes in saturated porous media: 2-D vs. 3-D flow-through systems

Dilution of solute plumes in groundwater strongly depends on transverse mixing. Thus, the correct parameterization of transverse dispersion is of critical importance for the quantitative description of solute transport. In this study we perform flow-through laboratory experiments to investigate the influence of transport dimensionality on transverse mixing. We present a high-resolution experimental setup to study solute dilution and transverse dispersion in three-dimensional porous media. We conduct multi-tracer experiments in the new 3-D setup and compare the results with the outcomes of analogous tracer experiments performed in a quasi 2-D system. We work under steady-state flow and transport conditions and consider a range of velocities relevant for groundwater flow (0.5-8 m/day). Transverse dispersion coefficients are determined from high-resolution concentration profiles at the outlet of the flow-through chambers (7×7 ports in the 3-D setup and 7 ports in the quasi 2-D system), considering conservative tracers with significantly different aqueous diffusion coefficients, namely fluorescein and dissolved oxygen. To quantify dilution in the 2-D and 3-D systems, we experimentally determine the flux-related dilution index using the flow rates and the concentrations measured at the inlet and outlet ports, and we propose semi-analytical expressions to predict its evolution with travel distance in uniform groundwater flow. The experimental results in the quasi 2-D and 3-D flow-through systems are consistent and show a compound-specific behavior of the transverse dispersion coefficient and its non-linear dependence on the seepage velocity in both setups. The degree of dilution and the compound-specific effects of transverse dispersion are considerably more pronounced in 3-D than in quasi 2-D transport systems.

Pore-scale simulation of fluid flow and solute dispersion in three-dimensional porous media

In the present work fluid flow and solute transport through porous media are described by solving the governing equations at the pore scale with finite-volume discretization. Instead of solving the simplified Stokes equation (very often employed in this context) the full Navier-Stokes equation is used here. The realistic three-dimensional porous medium is created in this work by packing together, with standard ballistic physics, irregular and polydisperse objects. Emphasis is placed on numerical issues related to mesh generation and spatial discretization, which play an important role in determining the final accuracy of the finite-volume scheme and are often overlooked. The simulations performed are then analyzed in terms of velocity distributions and dispersion rates in a wider range of operating conditions, when compared with other works carried out by solving the Stokes equation. Results show that dispersion within the analyzed porous medium is adequately described by classical power laws obtained by analytic homogenization. Eventually the validity of Fickian diffusion to treat dispersion in porous media is also assessed.