Reactive Solute Transport Research Articles

Reactive solute transport in physically and chemically heterogeneous porous media with multimodal reactive mineral facies: The Lagrangian approach

Physical and chemical heterogeneities have a large impact on reactive transport in porous media. Examples of heterogeneous attributes affecting reactive mass transport are the hydraulic conductivity (K), and the equilibrium sorption distribution coefficient (Kd). This paper uses the Deng et al. (2013) conceptual model for multimodal reactive mineral facies and a Lagrangian-based stochastic theory in order to analyze the reactive solute dispersion in three-dimensional anisotropic heterogeneous porous media with hierarchical organization of reactive minerals. An example based on real field data is used to illustrate the time evolution trends of reactive solute dispersion. The results show that the correlation between the hydraulic conductivity and the equilibrium sorption distribution coefficient does have a significant effect on reactive solute dispersion. The anisotropy ratio does not have a significant effect on reactive solute dispersion. Furthermore, through a sensitivity analysis we investigate the impact of changing the mean, variance, and integral scale of K and Kd on reactive solute dispersion.

Back diffusion from thin low permeability zones.

Aquitards can serve as long-term contaminant sources to aquifers when contaminant mass diffuses from the aquitard following aquifer source mass depletion. This study describes analytical and experimental approaches to understand reactive and nonreactive solute transport in a thin aquitard bounded by an adjacent aquifer. A series of well-controlled laboratory experiments were conducted in a two-dimensional flow chamber to quantify solute diffusion from a high-permeability sand into and subsequently out of kaolinite clay layers of vertical thickness 15 mm, 20 mm, and 60 mm. One-dimensional analytical solutions were developed for diffusion in a finite aquitard with mass exchange with an adjacent aquifer using the method of images. The analytical solutions showed very good agreement with measured breakthrough curves and aquitard concentration distributions measured in situ by light reflection visualization. Solutes with low retardation accumulated more stored mass with greater penetration distance in the aquitard compared to high-retardation solutes. However, because the duration of aquitard mass release was much longer, high-retardation solutes have a greater long-term back diffusion risk. The error associated with applying a semi-infinite domain analytical solution to a finite diffusion domain increases as a function of the system relative diffusion length scale, suggesting that the solutions using image sources should be applied in cases with rapid solute diffusion and/or thin clay layers. The solutions presented here can be extended to multilayer aquifer/low-permeability systems to assess the significance of back diffusion from thin layers.

Numerical modeling of reactive solute transport in a single fracture with matrix diffusion under complex boundary condition

A numerical model using finite volume QUICK scheme has been developed for simulating the transport behavior of solutes in a coupled fracture–matrix system for pulse-type boundary condition as against the conventional constant continuous source-type boundary condition, which essentially reflects the reality better, as it is practically not feasible for any source type to discharge it continuously with the same magnitude for a very long period. The sensitivity of fracture and rock matrix parameters, namely fracture aperture thickness, matrix porosity, and matrix diffusion coefficient have been analyzed under this complex boundary condition. In addition, the role of nonlinear sorption as well as decay has also been investigated. Numerical results suggest that the reduction in relative concentration within the fracture resulting from pulse-type boundary condition should always not be mistaken for matrix diffusion. It has been concluded from the present numerical study that segregating and quantifying the role on individual components, namely (a) source exhaustion (pulse-type boundary condition); (b) matrix diffusion; (c) sorption; and (d) decay in characterizing the resultant transport behavior of solutes in a single fracture with matrix diffusion under a pulse-type boundary condition remains challenging and needs further research.

Simulation of experimental breakthrough curves using multiprocess non-equilibrium model for reactive solute transport in stratified porous media

In this paper, we have studied the behaviour of reactive solute transport through stratified porous medium under the influence of multi-process non-equilibrium transport model. Various experiments were carried out in the laboratory and the experimental breakthrough curves were observed at spatially placed sampling points for stratified porous medium. Batch sorption studies were also performed to estimate the sorption parameters of the material used in stratified aquifer system. The effects of distance dependent dispersion and tailing are visible in the experimental breakthrough curves. The presence of physical and chemical non-equilibrium are observed from the pattern of breakthrough curves. Multi-process non-equilibrium model represents the combined effect of physical and chemical non-ideality in the stratified aquifer system. The results show that the incorporation of distance dependent dispersivity in multi-process non-equilibrium model provides best fit of observed data through stratified porous media. Also, the exponential distance dependent dispersivity is more suitable for large distances and at small distances, linear or constant dispersivity function can be considered for simulating reactive solute in stratified porous medium.

Reactive Transport in Fractured Permeable Porous Media

AbstractThe transport of reactive solutes can be influenced by transport-related and sorption-related nonequilibrium processes. The reactive contaminant transport model for fracture and the multiprocess nonequilibrium (MPNE) model for porous formation is considered. Two coupled transport equations, one for the porous formation and the other for the fracture, were solved numerically using a hybrid finite-volume method. The numerical model employs a globally second-order accurate explicit finite-volume method for the advective transport and a finite-difference method for the dispersive transport and coupled reaction terms. An attempt is made to investigate the effects of various MPNE model parameters on the concentration profile in the fracture. It was found that the higher values of mass transfer coefficient, sorption coefficient, matrix diffusion coefficient, fracture retardation coefficient, and matrix porosity in the advective and nonadvective regions of the porous matrix leads to a decrease in the solu...

A nonlinear ALE‐FCT scheme for non‐equilibrium reactive solute transport in moving domains

SUMMARYIn this paper, we present a conservative, positivity‐preserving, high‐resolution nonlinear ALE‐flux‐corrected transport (FCT) scheme for reactive transport models in moving domains. The mathematical model is a convection–diffusion equation with a nonlinear flux equation on the moving channel wall. The reactive transport is assumed to have dominant Péclet and Damköhler numbers, a phenomenon that often results in non‐physical negative solutions. The scheme presented here is proven to be mass conservative in time and positive at all times for a small enough Δt. Reactive transport examples are simulated using this scheme for its validation, to show its convergence, and to compare it against the linear ALE‐FCT scheme. The nonlinear ALE‐FCT is shown to perform better than the linear ALE‐FCT schemes for large time steps. Copyright © 2014 John Wiley & Sons, Ltd.

On the mechanism of field‐scale solute transport: Insights from numerical simulations and field observations

AbstractField‐scale transport of conservative and reactive solutes through a deep vadose zone was analyzed by means of two different model processes for the local description of the transport. The first is the advection‐dispersion equation (ADE) model, and the second is the mobile‐immobile (MIM) model. The analyses were performed by means of three‐dimensional (3‐D), numerical simulations of flow and transport considering realistic features of the flow system, pertinent to a turf field irrigated with treated sewage effluents (TSE). Simulated water content and concentration profiles were compared with available measurements of their counterparts. Results of the analyses suggest that the behavior of both solutes in the deep vadose zone of the Glil Yam site is better quantified by the MIM model than by the ADE model. Reconstruction of the shape of the measured solute concentration profiles using the MIM model required relatively small mass transfer coefficient, γ, and relatively large volume fraction of the immobile water θim. This implies that for an initially nonzero solute concentration profile, as compared with the MIM model, the ADE model may significantly overestimate the rate at which solutes are loaded in the groundwater. On the contrary, for an initially zero solute concentration profile, as compared with the MIM model, the ADE model may significantly underestimate solute velocities and early arrival times to the water table. These findings stem from the combination of relatively small γ and relatively large θim taken into account in the MIM model. In the first case, this combination forces a considerable portion of the solute mass to reside in the immobile region of the water‐filled pore space, while the opposite is true in the second case.

Impact of microforms on nitrate transport at the groundwater–surface water interface in gaining streams

Small streambed structures (or microforms, 0.01–1m in length) exist ubiquitously in riverbed systems. Small-scale topography is potentially important in controlling hyporheic exchange flow and transport of conservative and reactive solutes at the groundwater–surface water interface. The role of microforms on NO3- transfer in a riffle-scale (macroforms of >1m length) hyporheic zone within a gaining river setting is investigated using a 2-D flow and transport model which accounts for both nitrification and denitrification. Results show that the short pathlines caused by microforms lead to more NO3- discharge to the river compared with a macroform-only condition due to shortened residence times of both surface water and groundwater in mixing zones. Short hyporheic exchange flow pathways caused by microforms could remain oxic along their entire length or switch from nitrate producing to nitrate consuming as oxygen concentrations decline. Microforms affect net NO3- flux by the combined effect of introducing more stream mass flux and reducing their residence time in mixing zones under different hydrological and biogeochemical conditions. Our findings underscore that ignoring microforms in river beds may underestimate NO3- load to the river and have practical implications for pore water sampling strategies in groundwater–surface water studies.

A conservative, positivity preserving scheme for reactive solute transport problems in moving domains

We study the mathematical models and numerical schemes for reactive transport of a soluble substance in deformable media. The medium is a channel with compliant adsorbing walls. The solutes are dissolved in the fluid flowing through the channel. The fluid, which carries the solutes, is viscous and incompressible. The reactive process is described as a general physico-chemical process taking place on the compliant channel wall. The problem is modeled by a convection–diffusion adsorption–desorption equation in moving domains. We present a conservative, positivity preserving, high resolution ALE-FCT scheme for this problem in the presence of dominant transport processes and wall reactions on the moving wall. A Patankar type time discretization is presented, which provides conservative treatment of nonlinear reactive terms. We establish CFL-type constraints on the time step, and show the mass conservation of the time discretization scheme. Numerical simulations are performed to show validity of the schemes against effective models under various scenarios including linear adsorption–desorption, irreversible wall reaction, infinite adsorption kinetics, and nonlinear Langmuir kinetics. The grid convergence of the numerical scheme is studied for the case of fixed meshes and moving meshes in fixed domains. Finally, we simulate reactive transport in moving domains under linear and nonlinear chemical reactions at the wall, and show that the motion of the compliant channel wall enhances adsorption of the solute from the fluid to the channel wall. Consequences of this result are significant in the area of, e.g., nano-particle cancer drug delivery. Our result shows that periodic excitation of the cancerous tissue using, e.g., ultrasound, may enhance adsorption of cancer drugs carried by nano-particles via the human vasculature.

Groundwater flow dynamics and arsenic source characterization in an aquifer system of West Bengal, India

AbstractNumerical groundwater flow modeling, reverse particle tracking, and environmental tracers are used to locate the source of geogenic As affecting an aquifer in West Bengal. The aquifer is hosted by point‐bar sands deposited in a meandering fluvial environment. Wells tapping the aquifer exhibit As concentrations up to 531 μg/L. High‐As groundwaters are recharged in ponds marking an abandoned river channel. The source of As is traced to the underlying fine‐grained channel‐fill sediments. Arsenic release within these sediments is accompanied by a concomitant release of Br and DOC indicating that these species may be decay products of natural organobromines codeposited along with As. Mass transfer of As to the dissolved phase and its flushing from source sediments are described using a simplified reactive solute transport model. Based on this model, a characteristic reaction time for mass transfer is estimated at 6.7 years. Average groundwater residence times in the source are estimated to have declined from 16.6 to 6.6 years with the advent of intensive irrigation pumping. The ratio of residence and reaction times, a Damköhler number, has declined correspondingly from 2.49 to 0.99, indicating a shift from transport to reaction rate limited As mobilization. Greater insight into the As problem in SE Asia may be achieved by shifting the focus of field investigations from aquifers to potential contamination sources in aquitards.

A new method to quantify how water repellency compromises soils' filtering function

SummarySoil water repellency (SWR) is known to lead to preferential flow and to degrade the soil's filtering efficiency. However, no method is available to quantify directly how SWR affects the transport of reactive solutes. We propose a new method for conducting solute transport experiments in water‐repellent soils. It involves sequentially applying two liquids, one water, the other a reference fully wetting liquid, namely aqueous ethanol, to the same intact soil core with air‐drying between liquids. We applied this approach to quantify the impact of SWR on the filtering of the herbicide 2,4‐Dichlorophenoxyacetic acid (2,4‐D) in two Andosols. In batch experiments conducted prior to the transport experiments, 2,4‐D sorption was not influenced by aqueous ethanol for one soil. However, sorption in the second soil followed the co‐solvency theory, which predicts decreasing sorption with increasing solvent fractions. Thus, sorption experiments are necessary to complement our new method. Breakthrough curves were characterized by preferential flow with large initial concentrations, tailing and a long prevalence of solutes remaining in the soil. In the soil in which 2,4‐D sorption was unaffected by aqueous ethanol, SWR increased 2,4‐D losses by four and 50 times in the first 5‐mm outflow compared with the 2,4‐D losses with water. After 50‐mm outflow, the 2,4‐D losses were similar for one core, but in the other core they were still about four times greater with water than with aqueous ethanol. This method to quantify the reduction of the soil's filtering efficiency by SWR is needed for assessing the increased risk of groundwater contamination by solutes exogenously applied to water‐repellent soils.

Study on Simulation of Heavy Metal Transport in Soil Using PHREEQC

This paper looked back on the current situation about simulation using PHREEQC of heavy metal transport in soil and the current situation of coupling with other value simulation software. On such a base, the feasibility, advantages and problems of heavy metal reactive solute transport in soil using PHREEQC were discussed.

Effective retardation factor for transport of reactive solutes in highly heterogeneous porous formations

[1] The effective retardation factor of highly heterogeneous porous formations is investigated using an analytical derivation and numerical simulations based on the self-consistent approximation and the multi-indicator conductivity model, used in the past for the effective hydraulic conductivity estimation. Both positive and negative correlation between the logarithm of hydraulic conductivity K and the logarithm of sorption distribution coefficient Kd are investigated, including the effects of random noise. The arithmetic average of the random retardation factor is found to represent accurately the effective retardation factor of isotropic and anisotropic formations regardless of correlation between ln Kd and ln K, and for variance of ln K as large as 8.

Hybrid modeling of heterogeneous geochemical reactions in fractured porous media

[1] Quantitative modeling of geochemical reactions at the Darcy scale is challenging due to their dependence on pore-scale characteristics that often cannot be averaged out. We propose a hybrid pore-scale/continuum-scale algorithm to bridge the gap between the pore-scale mechanisms of reactive transport and the Darcy-scale observations of their impact. These two scales are coupled by introducing extra nodes at the pore/continuum interfaces, in which the continuity of both concentrations and mass fluxes is enforced. Our algorithm is applicable to highly localized transport phenomena that can be adequately described by Darcy-scale equations in most of a computational domain except for small regions (e.g., reaction fronts) wherein pore-scale simulations are necessary. We employ the proposed hybrid algorithm to model transient reactive solute transport involving fracture cementation.

PoreFlow: A complex pore-network model for simulation of reactive transport in variably saturated porous media

This study introduces PoreFlow, a pore-network modeling tool capable of simulating fluid flow and multi-component reactive and adsorptive transport under saturated and variably saturated conditions. PoreFlow includes a variety of modules, such as: pore network generator, drainage simulator, calculation of pressure and velocity distributions, and modeling of reactive solute transport accounting for advection and diffusion. The pore space is represented using a multi-directional pore-network capable of capturing the random structure of a given porous media with user-defined directional connectivities for anisotropic pore structures. The chemical reactions can occur within the liquid phase, as well as between the liquid and solid phases which may result in an evolution of porosity and permeability. Under variably saturated conditions the area of interfaces changes with degree of the fluid saturation.PoreFlow uses complex formulations for more accurate modeling of transport problems in presence of the nonwetting phase. This is done by refining the discretization within drained pores. An implicit numerical scheme is used to solve the governing equations, and an efficient substitution method is applied to considerably minimize computational times. Several examples are provided, under saturated and variably saturated conditions, to demonstrate the model applicability in hydrogeology problems and petroleum fields. We show that PoreFlow is a powerful tool for upscaling of flow and transport in porous media, utilizing different pore scale information such as various interfaces, phase distributions and local fluxes and concentrations to determine macro scale properties such as average saturation, relative permeability, solute dispersivity, adsorption coefficients, effective diffusion and tortuosity. Such information can be used as constitutive relations within continuum scale governing equations to model physical and chemical processes more accurately at the larger scales.

Radial reactive solute transport in an aquifer–aquitard system

Radial reactive transport is investigated in an aquifer–aquitard system considering the important processes such as advection, radial and vertical dispersions for the aquifer, vertical advection and dispersion for the aquitards, and first-order biodegradation or radioactive decay. We solved the coupled governing equations of transport in the aquifer and the aquitards by honoring the continuity of concentration and mass flux across the aquifer–aquitard interfaces and recognizing the concentration variation along the aquifer thickness. This effort improved the averaged-approximation (AA) model, which dealt with radial dispersion in an aquifer–aquitard system by excluding the aquitard advection. To compare with our new solution, we expanded the AA model by including the aquitard advection. The expanded AA model considerably overestimated the mass in the upper aquitard when an upward advection existed there. The rates of mass change in the upper aquitard from the new solution and the AA model solution increased with time following sub-linear fashions. The times corresponding to the peak values of the residence time distributions for the AA model, the expanded AA model, and the new model were almost the same. The residence time distributions seemed to follow the Maxwell–Boltzmann distribution closely when plotting the time in logarithmic scale. In addition, we developed a finite-element COMSOL Multiphysics simulation of the problem, and found that the COMSOL solution agreed with the new solution well.

Application of a data assimilation method via an ensemble Kalman filter to reactive urea hydrolysis transport modeling

With growing importance of water resources in the world, remediations of anthropogenic contaminations due to reactive solute transport become even more important. A good understanding of reactive rate parameters such as kinetic parameters is the key to accurately predicting reactive solute transport processes and designing corresponding remediation schemes. For modeling reactive solute transport, it is very difficult to estimate chemical reaction rate parameters due to complex processes of chemical reactions and limited available data. To find a method to get the reactive rate parameters for the reactive urea hydrolysis transport modeling and obtain more accurate prediction for the chemical concentrations, we developed a data assimilation method based on an ensemble Kalman filter (EnKF) method to calibrate reactive rate parameters for modeling urea hydrolysis transport in a synthetic one-dimensional column at laboratory scale and to update modeling prediction. We applied a constrained EnKF method to pose constraints to the updated reactive rate parameters and the predicted solute concentrations based on their physical meanings after the data assimilation calibration. From the study results we concluded that we could efficiently improve the chemical reactive rate parameters with the data assimilation method via the EnKF, and at the same time we could improve solute concentration prediction. The more data we assimilated, the more accurate the reactive rate parameters and concentration prediction. The filter divergence problem was also solved in this study.

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

Mixing processes significantly affect and limit contaminant transport and transformation rates in the subsurface. The correct quantification of mixing in groundwater systems must account for diffusion, local-scale dispersion and the flow variability in heterogeneous flow fields (e.g., flow-focusing in high-conductivity and de-focusing in low-conductivity zones). Recent results of multitracer laboratory experiments revealed the significant effect of compound-specific diffusive properties on the physical displacement of dissolved species across a representative range of groundwater flow velocities. The goal of this study is to investigate the role of diffusion and compound-specific mixing for solute transport across a range of scales including: (i) pore-scale (~10⁻² m), (ii) laboratory bench-scale (~10⁰ m) and (iii) field-scale (~10² m). We investigate both conservative and mixing-controlled reactive transport using pore-scale modeling, flow-through laboratory experiments and simulations, and field-scale numerical modeling of complex heterogeneous hydraulic conductivity fields with statistical properties similar to the ones reported for the extensively investigated Borden aquifer (Ontario, Canada) and Columbus aquifer (Mississippi, USA, also known as MADE site). We consider different steady-state and transient transport scenarios. For the conservative cases we use as a metric of mixing the exponential of the Shannon entropy to quantify solute dilution either in a given volume (dilution index) or in a given solute flux (flux-related dilution index). The decrease in the mass and the mass-flux of the contaminant plumes is evaluated to quantify reactive mixing. The results show that diffusive processes, occurring at the small-scale of a pore channel, strongly affect conservative and reactive solute transport at larger macroscopic scales. The outcomes of our study illustrate the need to consider and properly account for compound-specific diffusion and mixing limitations in order to accurately describe and predict conservative and reactive transport in porous media.

Reliability of the Multiple-Rate Adsorptive Model for Simulating Adsorptive Solute Transport in Soil Demonstrated by Pore-Scale Simulations

Minerals and organic matters in soils and sediments are chemically different and their ability to adsorb solute varies. Since individual minerals cannot be resolved in macroscopic models, these heterogeneous adsorption rates are often modelled as a random number with a pre-defined distribution function. Such an approach is also known as multiple-rate adsorption (MRA) models in reactive solute transport modelling. The MRA models have shown some improvement, but it is unclear that this improvement is due to their improved description of the statistics of the variable adsorption rates, or because of the extra parameters they introduced, which give them more freedom in curve-fitting. In this paper, we investigated this using pore-scale modelling. The pore-scale simulations were based on an idealised column packed with different minerals; solute concentration in the column was assumed to be low in comparison with the adsorptive capacity of the minerals. Hence, the adsorption of each mineral particle was assumed to be linear first-order kinetic. Both batch and column-displacement experiments at the pore scale were simulated using the lattice Boltzmann model. The simulated solute distributions were then volume-averaged to yield macroscopic concentration by treating the column as a continuum medium. The parameters in the MRA model were obtained from batch experiments and the dispersion coefficient was derived from displacement of an inert tracer. These parameters were then used to simulate the displacement of adsorptive solute under different water flow rates. The results showed that even though the MRA model accurately described the statistics of the heterogeneous adsorption rates, it failed to describe the macroscopic adsorption when the Pe number is high. We also found that the only way to improve the fitting is to increase the dispersion coefficient measured from the inert tracer. This yields a dispersion coefficient for adsorptive solute, which nonlinearly increases with the Pe number. To investigate whether this is a general phenomenon for adsorptive solute or only for solute under heterogeneous adsorption, we simulated solute displacement in the column filled by the same mineral. The results show that when the adsorption is homogeneous, the dispersion coefficients for adsorptive solute and inert tracer are the same. These findings imply that the MRA models should be used with care as the dispersion coefficient derived using inert tracers might not apply to adsorptive solute.

Analytical solution for reactive solute transport considering incomplete mixing within a reference elementary volume

Key Points Incomplete mixing at sub‐Darcy scale is relevant for reactive solute transport Incomplete mixing at sub‐Darcy scale can be modeled using a Beta distribution We propose a reactive transport model which considers incomplete mixing