Impact of mineral fouling on hydraulic behavior of permeable reactive barriers

This paper describes reactive transport simulations conducted to assess the impact of mineral fouling on the hydraulic behavior of continuous-wall permeable reactive barriers (PRBs) employing granular zero-valent iron (ZVI) in carbonate-rich alluvial aquifers. The reactive transport model included a geochemical algorithm for simulating corrosion and mineral precipitation reactions that have been observed in ZVI PRBs. Results of simulations show that porosity and hydraulic conductivity of the ZVI decrease over time and that flows are redistributed throughout the PRB in response to fouling of the pore space. Under typical conditions, only subtle changes occur within the first 10 years (i.e., duration of the current field experience record with PRBs), and the most significant changes do not occur until the PRB has operated for at least 30 years. However, changes can occur sooner (or later) if the rate at which mineral-forming ions are delivered to the PRB is higher (or lower) than that expected under typical conditions (i.e., due to higher/lower flow rate or inflowing ground water that has higher/lower ionic strength). When the PRB is more permeable than the aquifer, the median Darcy flux in the PRB does not change appreciably over time because the aquifer controls the rate of flow through the PRB. However, seepage velocities in the PRB increase, and residence times decrease, due to porosity reductions caused by accumulation of minerals in the pore space. When fouling becomes extensive, bypassing and reductions in flow rate in the PRB occur.     

Analytical Solutions for Flow Fields near Drain-and-Gate Reactive Barriers

Permeable reactive barriers (PRBs) are a popular technology for passive contaminant remediation in aquifers through installation of reactive materials in the pathway of a plume. Of fundamental importance are the degree of remediation inside the reactor (residence time) and the portion of groundwater intercepted by a PRB (capture width). Based on a two-dimensional conformal mapping approach (previously used in related work), the latter is studied in the present work for drain-and-gate (DG) PRBs, which may possess a collector and a distributor drain (“full” configuration) or a collector drain only (“simple” configuration). Inherent assumptions are a homogeneous unbounded aquifer with a uniform far field, in which highly permeable drains establish constant head boundaries. Solutions for aquifer flow fields in terms of the complex potential are derived, illustrated, and analyzed for doubly symmetric DG configurations and arbitrary reactor hydraulic resistance as well as ambient groundwater flow direction. A series of practitioner-friendly charts for capture width is given to assist in PRB design and optimization without requiring complex mathematics. DG PRBs are identified as more susceptible to flow divergence around the reactor than configurations using impermeable side structures (e.g., funnel-and-gate), and deployment of impermeable walls on drains is seen to mitigate this problem under certain circumstances.     

Metal Retention Experiments for the Design of Soil‐Mix Technology Permeable Reactive Barriers

Soil‐mix technology is effective for the construction of permeable reactive barriers (PRBs) for in situ groundwater treatment. The objective of this study was to perform initial experiments for the design of soil‐mix technology PRBs according to (i) sorption isotherm, (ii) reaction kinetics and (iii) mass balance of the contaminants. The four tested reactive systems were: (i) a granular zeolite (clinoptilolite–GZ), (ii) a granular organoclay (GO), (iii) a 1:1‐mixture GZ and model sandy clayey soil and (iv) a 1:1:1‐mixture of GZ, GO and model soil. The laboratory experiments consisted of batch tests (volume 900 mL and sorbent mass 18 g) with a multimetal solution of Pb, Cu, Zn, Cd and Ni. For the adsorption experiment, the initial concentrations ranged from 0.01 to 0.5 mM (2.5 to 30 mg/L). The maximum metal retention was measured in a batch test (300 mg/L for each metal, volume 900 mL, sorbent mass 90–4.5 g). The reactive material efficiency order was found to be GZ > GZ‐soil mix > GZ‐soil‐GO mix > GO. Langmuir isotherms modelled the adsorption, even in presence of a mixed cations solution. Adsorption was energetically favourable and spontaneous in all cases. Metals were removed according to the second order reaction kinetics; GZ and the 1:1‐mix were very similar. The maximum retention capacity was 0.1–0.2 mmol/g for Pb in the presence of clinoptilolite; for Cu, Zn, Cd and Ni, it was below 0.05 mmol/g for the four reactive systems. Mixing granular zeolite, organoclay and model soil increased the chemisorption. Providing that GZ is reactive enough for the specific conditions, GZ can be mixed to obtain the required sorption. Granular clinoptilolite addition to soil is recommended for PRBs for metal contaminated groundwater.     

A two-grid method for coupled free flow with porous media flow

This paper presents a two-grid method for solving systems of partial differential equations modelling incompressible free flow coupled with porous media flow. This work considers both the coupled Stokes and Darcy as well as the coupled Navier-Stokes and Darcy problems. The numerical schemes proposed are based on combinations of the continuous finite element method and the discontinuous Galerkin method. Numerical errors and convergence rates for solutions obtained from the two-grid method are presented. CPU times for the two-grid algorithm are shown to be significantly less than those obtained by solving the fully coupled problem.     

Numerically quantifying energy loss caused by squirt flow

In interconnected microcracks, or in microcracks connected to spherical pores, the deformation associated with the passage of mechanical waves can induce fluid flow parallel to the crack walls, which is known as squirt flow. This phenomenon can also occur at larger scales in hydraulically interconnected mesoscopic cracks or fractures. The associated viscous friction causes the waves to experience attenuation and velocity dispersion. We present a simple hydromechanical numerical scheme, based on the interface-coupled Lamé–Navier and Navier–Stokes equations, to simulate squirt flow in the frequency domain. The linearized, quasi-static Navier–Stokes equations describe the laminar flow of a compressible viscous fluid in conduits embedded in a linear elastic solid background described by the quasi-static Lamé–Navier equations. Assuming that the heterogeneous model behaves effectively like a homogeneous viscoelastic medium at a larger spatial scale, the resulting attenuation and stiffness modulus dispersion are computed from spatial averages of the complex-valued, frequency-dependent stress and strain fields. An energy-based approach is implemented to calculate the local contributions to attenuation that, when integrated over the entire model, yield results that are identical to those based on the viscoelastic assumption. In addition to thus validating this assumption, the energy-based approach allows for analyses of the spatial dissipation patterns in squirt flow models. We perform simulations for a series of numerical models to illustrate the viability and versatility of the proposed method. For a 3D model consisting of a spherical crack embedded in a solid background, the characteristic frequency of the resulting P-wave attenuation agrees with that of a corresponding analytical solution, indicating that the dissipative viscous flow problem is appropriately handled in our numerical solution of the linearized, quasi-static Navier–Stokes equations. For 2D models containing either interconnected cracks or cracks connected to a circular pore, the results are compared with those based on Biot's poroelastic equations of consolidation, which are solved through an equivalent approach. Overall, our numerical simulations and the associated analyses demonstrate the suitability of the coupled Lamé–Navier and Navier–Stokes equations and of Biot's equations for quantifying attenuation and dispersion for a range of squirt flow scenarios. These analyses also allow for delineating numerical and physical limitations associated with each set of equations.     

Analysis of hydrodynamic conditions in adjacent free and heterogeneous porous flow domains

The existence of a free‐flow domain (e.g. a liquid layer) adjacent to a porous medium is a common occurrence in many environmental and petroleum engineering problems. The porous media may often contain various forms of heterogeneity, e.g. layers, fractures, micro‐scale lenses, etc. These heterogeneities affect the pressure distribution within the porous domain. This may influence the hydrodynamic conditions at the free–porous domain interface and, hence, the combined flow behaviour. Under steady‐state conditions, the heterogeneities are known to have negligible effects on the coupled flow behaviour. However, the significance of the heterogeneity effects on coupled free and porous flow under transient conditions is not certain. In this study, numerical simulations have been carried out to investigate the effects of heterogeneous (layered) porous media on the hydrodynamics conditions in determining the behaviour of combined free and porous regimes. Heterogeneity in the porous media is introduced by defining a domain composed of two layers of porous media with different values of intrinsic permeability. The coupling of the governing equations of motion in free and porous domains has been achieved through the well‐known Beavers and Joseph interfacial condition. Of special interest in this work are porous domains with flow‐through ends. They represent the general class of problems where large physical domains are truncated to smaller sections for ease of mathematical analysis. However, this causes a practical difficulty in modelling such systems. This is because the information on flow behaviour, i.e. boundary conditions at the truncated sections, is usually not available. Use of artificial boundary conditions to solve these problems effectively implies the imposition of conditions that do not necessarily match with the solutions required for the interior of the domain. This difficulty is resolved in this study by employing ‘stress‐free boundary conditions’ at the open ends of the domains, which have been shown to provide accurate results by a number of previous workers. Copyright © 2005 John Wiley & Sons, Ltd.     

Injection-extraction treatment well pairs: an alternative to permeable reactive barriers

Two of the biggest drawbacks of using permeable reactive barriers (PRBs) to treat contaminated ground water are the high capital cost of installation, particularly when the contaminated ground water is deep below ground surface, and the uncertainty of whether or not PRBs remain effective for the long time scales (e.g., decades) needed for many contaminant plumes. The use of an injection-extraction treatment well pair (IETWP) for capture and treatment of contaminated ground water can circumvent these difficulties, while still providing many of the same advantages offered by PRBs. In this paper, the hydraulics of IETWPs and PRBs are compared, focusing primarily on the width of the captured plume. It is demonstrated that IETWPs act as hydraulic barriers in a manner similar to PRBs, and that IETWPs provide excellent plume capture. A mathematical expression is presented for the plume capture width of an IETWP oriented perpendicular to the ground water flow direction in a homogeneous aquifer. Also discussed are other practical considerations that might determine whether an IETWP is better suited than a PRB for a particular contaminated site; these considerations include operating and maintenance costs, and the conditions under which an IETWP system can be used for in situ remediation.     

A novel semi-analytical approach for non-uniform vegetated flows

In this paper a semi-analytical approach is proposed to understand the mechanism by which a non-uniform vegetated flowpasses over a finite thick soil layer covered with grass. The flow region is divided into three layers: a homogenous water layer, a mixed water-grass layer, and a finite thick soil layer (hereafter referred to as the water layer, the grass layer, and the soil layer). The flow of the water layer is governed by the Navier–Stokes equations. Both the grass and soil layers are regarded as porous media and the Biot’s theory of poroelasticity is applied to the porous medium flow. The semi-closed solutions are then obtained by the Runge–Kutta method. The drag force induced by the flow through the grass layer and the flow profiles of three patterns: submerged grass, emergent grass and mixed type are also discussed.     

A transient phreatic surface mound,evidenced by a strip of vegetation on an earth dam

Abstract

On the slopes of the embankment of the Al-Khod groundwater recharge–flood protection dam (Oman), a band of scrub vegetation community emerged after torrential rains and temporary filling of the dam reservoir. Species composition differs markedly on both sides of the embankment, with many exotics found on the reservoir side and more typical gravel-desert species on the outside. Hydro-ecologically, the vegetation is interpreted as the footprint of a temporary storage of water, which is a small-sized groundwater mound within the permeable shoulder of the levee. The levee, as an anthropogenic landform, induces a U-turn (gravitational slumping–lateral seepage–transpirational moisture ascent) topology of seepage. The Lembke method of successive variations of steady states is used in modelling the water table dynamics. In the early stage of the mound decay, outflow through a seepage face of the shoulder is modelled by the Barenblatt slumping parabola of the phreatic-zone part of the flow domain, which is perfectly matched with the Youngs exact solution for a purely horizontal flow through a porous wedge. At the stitching cross-section, the flow rates and saturated depths in the two zones coincide. The late stage of mound evolution is characterized by transpiration by the plant roots projected onto a shrinking free surface, with the Barenblatt and Youngs solutions conjugated but without the outcrop of the saturated mound on the levee slope. Ordinary differential equations for the sliding or descending locus of the intersection of the parabola and the triangle hypotenuse are integrated in a closed form or by the Runge-Kutta method. The dwindling saturated volume and the rate of drainage are obtained. They can be used in assessments of the hydro-ecological sustainability of slope-rooted shrubs (vegetation survival between rare rainfall episodes).

Editor D. Koutsoyiannis; Associate editor A. Porporato     

Review of Abiotic Degradation of Chlorinated Solvents by Reactive Iron Minerals in Aquifers

Abiotic degradation of chlorinated solvents by reactive iron minerals such as iron sulfides, magnetite, green rust, and other Fe(II)‐containing minerals has been observed in both laboratory and field studies. These reactive iron minerals form under iron‐ and sulfate‐reducing conditions which are commonly found in permeable reactive barriers (PRBs), enhanced reductive dechlorination (ERD) treatment locations, landfills, and aquifers that are chemically reducing. The objective of this review is to synthesize current understanding of abiotic degradation of chlorinated solvents by reactive iron minerals, with special focus on how abiotic processes relate to groundwater remediation. Degradation of chlorinated solvents by reactive minerals can proceed through reductive elimination, hydrogenolysis, dehydrohalogenation, and hydrolysis reactions. Degradation products of abiotic reactions depend on degradation pathways and parent compounds. Some degradation products (e.g., acetylene) have the potential to serve as a signature product for demonstrating abiotic reactions. Laboratory and field studies show that various minerals have a range of reactivity toward chlorinated solvents. A general trend of mineral reactivity for degradation of chlorinated solvents can be approximated as follows: disordered FeS > FeS > Fe(0) > FeS₂ > sorbed Fe²⁺ > green rust = magnetite > biotite = vermiculite. Reaction kinetics are also influenced by factors such as pH, natural organic matter (NOM), coexisting metal ions, and sulfide concentration in the system. In practice, abiotic reactions can be engineered to stimulate reactive mineral formation for groundwater remediation. Under appropriate site geochemical conditions, abiotic reactions can occur naturally, and can be incorporated into remedial strategies such as monitored natural attenuation.     

Hierarchical simulator of biofilm growth and dynamics in granular porous materials

A new simulator is developed for the prediction of the rate and pattern of growth of biofilms in granular porous media. The biofilm is considered as a heterogeneous porous material that exhibits a hierarchy of length scales. An effective-medium model is used to calculate the local hydraulic permeability and diffusion coefficient in the biofilm, as functions of the local geometric and physicochemical properties. The Navier–Stokes equations and the Brinkman equation are solved numerically to determine the velocity and pressure fields within the pore space and the biofilm, respectively. Biofilm fragments become detached if they are exposed to shear stress higher than a critical value. The detached fragments re-enter into the fluid stream and move within the pore space until they exit from the system or become reattached to downstream grain or biofilm surfaces. A Lagrangian-type simulation is used to determine the trajectories of detached fragments. The spatiotemporal distributions of a carbon source, an electron acceptor and a cell-to-cell signaling molecule are determined from the numerical solution of the governing convection–diffusion–reaction equations. The simulator incorporates growth and apoptosis kinetics for the bacterial cells and production and lysis kinetics for the EPS. The specific growth rate of active bacterial cells depends on the local concentrations of nutrients, mechanical stresses, and a quorum sensing mechanism. Growth-induced deformation of the biofilms is implemented with a cellular automaton approach. In this work, the spatiotemporal evolution of biofilms in the pore space of a 2D granular medium is simulated under high flow rate and nutrient-rich conditions. Transient changes in the pore geometry caused by biofilm growth lead to the formation of preferential flowpaths within the granular porous medium. The decrease of permeability caused by clogging of the porous medium is calculated and is found to be in qualitative agreement with published experimental results.     

An improved gray lattice Boltzmann model for simulating fluid flow in multi-scale porous media

A lattice Boltzmann (LB) model is proposed for simulating fluid flow in porous media by allowing the aggregates of finer-scale pores and solids to be treated as ‘equivalent media’. This model employs a partially bouncing-back scheme to mimic the resistance of each aggregate, represented as a gray node in the model, to the fluid flow. Like several other lattice Boltzmann models that take the same approach, which are collectively referred to as gray lattice Boltzmann (GLB) models in this paper, it introduces an extra model parameter, n_s, which represents a volume fraction of fluid particles to be bounced back by the solid phase rather than the volume fraction of the solid phase at each gray node. The proposed model is shown to conserve the mass even for heterogeneous media, while this model and that model of Walsh et al. (2009) [1], referred to the WBS model thereafter, are shown analytically to recover Darcy–Brinkman’s equations for homogenous and isotropic porous media where the effective viscosity and the permeability are related to n_s and the relaxation parameter of LB model. The key differences between these two models along with others are analyzed while their implications are highlighted. An attempt is made to rectify the misconception about the model parameter n_s being the volume fraction of the solid phase. Both models are then numerically verified against the analytical solutions for a set of homogenous porous models and compared each other for another two sets of heterogeneous porous models of practical importance. It is shown that the proposed model allows true no-slip boundary conditions to be incorporated with a significant effect on reducing errors that would otherwise heavily skew flow fields near solid walls. The proposed model is shown to be numerically more stable than the WBS model at solid walls and interfaces between two porous media. The causes to the instability in the latter case are examined. The link between these two GLB models and a generalized Navier–Stokes model [2] for heterogeneous but isotropic porous media are explored qualitatively. A procedure for estimating model parameter n_s is proposed.     

A Tracer Test to Characterize Treatment of TCE in a Permeable Reactive Barrier

A tracer test was conducted to characterize the flow of groundwater across a permeable reactive barrier constructed with plant mulch (a biowall) at the OU‐1 site on Altus Air Force Base, Oklahoma. This biowall is intended to intercept and treat groundwater contaminated by trichloroethylene (TCE) in a shallow aquifer. The biowall is 139‐m long, 7.3‐m deep, and 0.5‐m wide. Bromide was injected from an upgradient well into the groundwater as a conservative tracer, and was subsequently observed breaking through in monitoring wells within and downgradient of the biowall. The bromide breakthrough data demonstrate that groundwater entering the biowall migrated across it, following the slope of the local groundwater surface. The average seepage velocity of groundwater was approximately 0.06 m/d. On the basis of the Darcy velocity of groundwater and geometry of the biowall, the average residence time of groundwater in the biowall was estimated at 10 d. Assuming all TCE removal occurred in the biowall, the reduction in TCE concentrations in groundwater across the biowall corresponds to a first‐order attenuation rate constant in the range of 0.38 to 0.15 per d. As an independent estimate of the degradation rate constant, STANMOD software was used to fit curves through data on the breakthrough of bromide and TCE in selected wells downgradient of the injection wells. Best fits to the data required a first‐order degradation rate constant for TCE removal in the range of 0.13 to 0.17 per d. The approach used in this study provides an objective evaluation of the remedial performance of the biowall that can provide a basis for design of other biowalls that are intended to remediate TCE‐contaminated groundwater.     

Flow modelling in gravel‐bed rivers: rethinking the bottom boundary condition

A key problem in computational fluid dynamics (CFD) modelling of gravel‐bed rivers is the representation of multi‐scale roughness, which spans the range from grain size, through bedforms, to channel topography. These different elements of roughness do not clearly map onto a model mesh and use of simple grain‐scale roughness parameters may create numerical problems. This paper presents CFD simulations for three cases: a plane bed of fine gravel, a plane bed of fine gravel including large, widely‐spaced pebble clusters, and a plane gravel bed with smaller, more frequent, protruding elements. The plane bed of fine gravel is modelled using the conventional wall function approach. The plane bed of fine gravel including large, widely‐spaced pebble clusters is modelled using the wall function coupled with an explicit high‐resolution topographic representation of the pebble clusters. In these cases, the three‐dimensional Reynolds‐averaged continuity and Navier–Stokes equations are solved using the standard k ? ε turbulence model, and model performance is assessed by comparing predicted results with experimental data. For gravel‐bed rivers in the field, it is generally impractical to map the bed topography in sufficient detail to enable the use of an explicit high‐resolution topography. Accordingly, an alternative model based on double‐averaging is developed. Here, the flow calculations are performed by solving the three‐dimensional double‐averaged continuity and Navier‐Stokes equations with the spatially‐averaged 〈k ? ε〉 turbulence model. For the plane bed of fine gravel including large, widely‐spaced pebble clusters, the model performance is assessed by comparing the spatially‐averaged velocity with the experimental data. The case of a plane gravel bed with smaller, more frequent, protruding elements is represented by a series of idealized hypothetical cases. Here, the spatially‐averaged velocity and eddy viscosity are used to investigate the applicability of the model, compared with using the explicit high‐resolution topography. The results show the ability of the model to capture the spatially‐averaged flow field and, thus, illustrate its potential for representing flow processes in natural gravel‐bed rivers. Finally, practical data requirements for implementing such a model for a field example are given. Copyright © 2011 John Wiley & Sons, Ltd.     

Characteristics of preferential flow and groundwater discharge to Shingobee Lake,Minnesota, USA

Small‐scale heterogeneities and large changes in hydraulic gradient over short distances can create preferential groundwater flow paths that discharge to lakes. A 170 m² grid within an area of springs and seeps along the shore of Shingobee Lake, Minnesota, was intensively instrumented to characterize groundwater‐lake interaction within underlying organic‐rich soil and sandy glacial sediments. Seepage meters in the lake and piezometer nests, installed at depths of 0·5 and 1·0 m below the ground surface and lakebed, were used to estimate groundwater flow. Statistical analysis of hydraulic conductivity estimated from slug tests indicated a range from 21 to 4·8 × 10^?3 m day^?1 and small spatial correlation. Although hydraulic gradients are overall upward and toward the lake, surface water that flows onto an area about 2 m onshore results in downward flow and localized recharge. Most flow occurred within 3 m of the shore through more permeable pathways. Seepage meter and Darcy law estimates of groundwater discharge agreed well within error limits. In the small area examined, discharge decreases irregularly with distance into the lake, indicating that sediment heterogeneity plays an important role in the distribution of groundwater discharge. Temperature gradients showed some relationship to discharge, but neither temperature profiles nor specific electrical conductance could provide a more convenient method to map groundwater–lake interaction. These results suggest that site‐specific data may be needed to evaluate local water budget and to protect the water quality and quantity of discharge‐dominated lakes. Copyright © 2002 John Wiley & Sons, Ltd.     

Bench‐Scaled Nano‐Fe0 Permeable Reactive Barrier for Nitrate Removal

There are many fundamental problems with the injection of nano‐zero‐valent iron (NZVI) particles to create permeable reactive barrier (PRB) treatment zone. Among them the loss of medium porosity or pore blocking over time can be considered which leads to reduction of permeability and bypass of the flow and contaminant plume up‐gradient of the PRB. Present study provides a solution for such problems by confining the target zone for injection to the gate in a funnel‐and‐gate configuration. A laboratory‐scale experimental setup is used in this work. In the designed PRB gate, no additional material from porous media exists. NZVI (d₅₀ = 52 ± 5 nm) particles are synthesized in water mixed with ethanol solvent system. A steady‐state condition is considered for the design of PRB size based on the concept of required contact time to obtain optimum width of PRB gate. Batch experiment is carried out and the results are used in the design of PRB gate width (~50 mm). Effect of high initial NO₃^–‐N concentration, NZVI concentration, and pore velocity of water in the range of laminar groundwater flow through porous media are evaluated on nitrate‐N reduction in PRB system. Results of PRB indicate that increasing the initial NO₃^–‐N concentration and pore velocity has inhibitor effect—against the effect of NZVI concentration—on the process of NO₃^–‐N removal. Settlement velocity (S.V.) of injected NZVI with different concentrations in the PRB is also investigated. Results indicate that the proposed PRB can solve the low permeability of medium in down‐gradient but increasing of the S.V. especially at higher concentration is one of the problems with this system that needs further investigations.     

Groundwater behaviour in Tenerife,volcanic island (Canary Islands,Spain)

Tenerife is the largest of the seven Canary Islands, encompassing an area of 2,058 km². It is situated in the Atlantic Ocean between 16–17°W longitude and 28–29°N latitude. The topography of the island is characterized by generally steep slopes. The Teide Volcano has an elevation of 3,718 m. Precipitation is caused mainly by invasions of maritime polar air. Maximum mean precipitation recorded for 25-year period (1940–1965) is 1,000 mm.The fractured volcanic aquifer of the Old Basaltic Series is the main supplier of groundwater in Tenerife. Smaller quantities of groundwater are supplied by the Cañadas Series and minor amounts by alluvial sediments. Groundwater compartments develop in areas of dikes and contacts between permeable and impermeable zones. These compartments are irregular in volume, shape, and structure. The groundwater system forms a tortuous chain of compartments. Water circulates from one groundwater compartment to another through secondary fractures and other permeable elements which branch and intersect. Fractures which extend to the surface play an important role in recharge.The hydrologic system at Tenerife is characterized by three zones: the upper vadose, the lower vadose, and the saturated zone. In both the upper and lower vadose zones the dominant direction of flow is vertical, while in the saturated zone flow is generally oblique toward the sea.     

A coupled model for simulating surface water and groundwater interactions in coastal wetlands

Coastal wetlands are characterized by strong, dynamic interactions between surface water and groundwater. This paper presents a coupled model that simulates interacting surface water and groundwater flow and solute transport processes in these wetlands. The coupled model is based on two existing (sub) models for surface water and groundwater, respectively: ELCIRC (a three‐dimensional (3‐D) finite‐volume/finite‐difference model for simulating shallow water flow and solute transport in rivers, estuaries and coastal seas) and SUTRA (a 3‐D finite‐element/finite‐difference model for simulating variably saturated, variable‐density fluid flow and solute transport in porous media). Both submodels, using compatible unstructured meshes, are coupled spatially at the common interface between the surface water and groundwater bodies. The surface water level and solute concentrations computed by the ELCIRC model are used to determine the boundary conditions of the SUTRA‐based groundwater model at the interface. In turn, the groundwater model provides water and solute fluxes as inputs for the continuity equations of surface water flow and solute transport to account for the mass exchange across the interface. Additionally, flux from the seepage face was routed instantaneously to the nearest surface water cell according to the local sediment surface slope. With an external coupling approach, these two submodels run in parallel using time steps of different sizes. The time step (Δt_g) for the groundwater model is set to be larger than that (Δt_s) used by the surface water model for computational efficiency: Δt_g = M × Δt_s where M is an integer greater than 1. Data exchange takes place between the two submodels through a common database at synchronized times (e.g. end of each Δt_g). The coupled model was validated against two previously reported experiments on surface water and groundwater interactions in coastal lagoons. The results suggest that the model represents well the interacting surface water and groundwater flow and solute transport processes in the lagoons. Copyright © 2011 John Wiley & Sons, Ltd.     

Time–space fractional governing equations of transient groundwater flow in confined aquifers: Numerical investigation

In order to model non‐Fickian transport behaviour in groundwater aquifers, various forms of the time–space fractional advection–dispersion equation have been developed and used by several researchers in the last decade. The solute transport in groundwater aquifers in fractional time–space takes place by means of an underlying groundwater flow field. However, the governing equations for such groundwater flow in fractional time–space are yet to be developed in a comprehensive framework. In this study, a finite difference numerical scheme based on Caputo fractional derivative is proposed to investigate the properties of a newly developed time–space fractional governing equations of transient groundwater flow in confined aquifers in terms of the time–space fractional mass conservation equation and the time–space fractional water flux equation. Here, we apply these time–space fractional governing equations numerically to transient groundwater flow in a confined aquifer for different boundary conditions to explore their behaviour in modelling groundwater flow in fractional time–space. The numerical results demonstrate that the proposed time–space fractional governing equation for groundwater flow in confined aquifers may provide a new perspective on modelling groundwater flow and on interpreting the dynamics of groundwater level fluctuations. Additionally, the numerical results may imply that the newly derived fractional groundwater governing equation may help explain the observed heavy‐tailed solute transport behaviour in groundwater flow by incorporating nonlocal or long‐range dependence of the underlying groundwater flow field.     

Numerical modelling of downstream migrating antidunes

A numerical model is presented that compute the geometrical dimensions and movement of downstream migrating antidunes. The model solves the Navier–Stokes equations together with the k‐epsilon turbulence model to find the water flow field over the bedforms. A two‐dimensional width‐averaged grid is used. The bed elevation changes are computed by solving the convection–diffusion equation for suspended sediments and bedload, together with the Engelund–Hansen sediment transport formula. The free surface is computed with an algorithm based on water continuity in the surface cells. Non‐orthogonal adaptive grids were used, moving vertically with the computed location of the bed and the free water surface. The numerical model was tested on data from a physical model study where regular downstream migrating antidunes had been observed. The numerical model started out with a flat bed and the trains of antidunes formed over time. Many of the physical processes observed in earlier studies were replicated by the numerical model. Four dune parameters were computed in the current tests: The antidune wavelength, height and celerity, together with the average water depth. The antidune wavelengths were best predicted with an accuracy of 3 to 8% compared with the measurements. The antidune heights were computed with a deviation of 11 to 25% compared with an empirical formula. The water depths over the antidunes were predicted with an accuracy of 3 to 9% related to the measured values. The average antidune celerity was the parameter with largest deviation: For the coarsest grid it was overpredicted with 37%. Copyright © 2017 John Wiley & Sons, Ltd.