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P Grathwohl - One of the best experts on this subject based on the ideXlab platform.
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Transverse vertical dispersion in groundwater and the Capillary Fringe.
Journal of contaminant hydrology, 2020Co-Authors: I D Klenk, P GrathwohlAbstract:Transverse dispersion is the most relevant process in mass transfer of contaminants across the Capillary Fringe (both directions), dilution of contaminants, and mixing of electron acceptors and electron donors in biodegrading groundwater plumes. This paper gives an overview on literature values of transverse vertical dispersivities alpha(tv) measured at different flow velocities and compares them to results from well-controlled laboratory-tank experiments on mass transfer of trichloroethene (TCE) across the Capillary Fringe. The measured values of transverse vertical dispersion in the Capillary Fringe region were larger than in fully saturated media, which is credited to enhanced tortuosity of the flow paths due to entrapped air within the Capillary Fringe. In all cases, the values observed for alpha(tv) were
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oxygen transfer in a fluctuating Capillary Fringe impact of microbial respiratory activity
Vadose Zone Journal, 2015Co-Authors: Daniel Jost, P Grathwohl, Christina M Haberer, Josef Winter, Claudia GallertAbstract:Laboratory-scale flow-through experiments in a sand-filled chamber were performed to investigate the impact of aerobically growing Escherichia coli HB101-K12 on oxygen transfer across the Capillary Fringe (CF) to oxygen-depleted groundwater. In the experiments, both the effects of different nutrient concentrations and transient flow conditions were tested. The results of biotic experiments under oligotrophic and eutrophic conditions (6.8 g organic C L −1 ) were compared with those of an abiotic experiment. Moreover, in each experiment steady-state and transient conditions were considered, the latter induced by changing the water-table height. Growth of E. coli was quantified by cell counting in effluent samples and could be monitored due to intracellular production of the green fluorescent protein (GFP). Under eutrophic conditions, highest cell densities and strongest cell attachment were observed in the transition region of the CF. In this region, intensive bacterial respiration decreased oxygen concentrations relatively quickly, causing a steep oxygen gradient that resulted in a higher oxygen flux across the unsaturated–saturated interface. Under oligotrophic conditions, this effect was considerably reduced, but was still detectable. Due to oxygen supply from entrapped air, bacterial growth was slightly enhanced within the upper, newly formed CF region, directly after raising the water table. After lowering the water table to the initial height only a minor microbial impact on oxygen transfer was noticed, even under eutrophic conditions, because of the fast diffusion of oxygen in the (partially) air-filled pore spaces. Bacteria that remained in the transition region of the CF grew to higher densities due to better oxygen supply.
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impact of heterogeneity on oxygen transfer in a fluctuating Capillary Fringe
Ground Water, 2015Co-Authors: Christina M Haberer, Massimo Rolle, Olaf A Cirpka, P GrathwohlAbstract: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.
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experimental sensitivity analysis of oxygen transfer in the Capillary Fringe
Ground Water, 2014Co-Authors: Christina M Haberer, Massimo Rolle, Olaf A Cirpka, P GrathwohlAbstract:Oxygen transfer in the Capillary Fringe (CF) is of primary importance for a wide variety of biogeochemical processes occurring in shallow groundwater systems. In case of a fluctuating groundwater table two distinct mechanisms of oxygen transfer within the Capillary zone can be identified: vertical predominantly diffusive mass flux of oxygen, and mass transfer between entrapped gas and groundwater. In this study, we perform a systematic experimental sensitivity analysis in order to assess the influence of different parameters on oxygen transfer from entrapped air within the CF to underlying anoxic groundwater. We carry out quasi two-dimensional flow-through experiments focusing on the transient phase following imbibition to investigate the influence of the horizontal flow velocity, the average grain diameter of the porous medium, as well as the magnitude and the speed of the water table rise. We present a numerical flow and transport model that quantitatively represents the main mechanisms governing oxygen transfer. Assuming local equilibrium between the aqueous and the gaseous phase, the partitioning process from entrapped air can be satisfactorily simulated. The different experiments are monitored by measuring vertical oxygen concentration profiles at high spatial resolution with a noninvasive optode technique as well as by determining oxygen fluxes at the outlet of the flow-through chamber. The results show that all parameters investigated have a significant effect and determine different amounts of oxygen transferred to the oxygen-depleted groundwater. Particularly relevant are the magnitude of the water table rise and the grain size of the porous medium.
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oxygen transfer in a fluctuating Capillary Fringe
Vadose Zone Journal, 2012Co-Authors: Christina M Haberer, Massimo Rolle, Olaf A Cirpka, P GrathwohlAbstract:Dynamic fluctuations in water table elevation cause the entrapment of air, which affects the hydraulic properties of the porous medium in the Capillary Fringe as well as the biogeochemical status of the underlying, potentially O 2 –depleted groundwater. In this study, we conducted quasi two-dimensional flow-through experiments at the laboratory bench scale to investigate in detail the mass transfer of O 2 in a fluctuating Capillary Fringe. We evaluated the effects of different boundary conditions such as single drainage and imbibition events as well as periodic fast and slow water table fluctuations. High-resolution vertical profiles of O 2 concentration, measured at two distances in the horizontal groundwater flow direction, and mass fluxes, determined in the effluent of the flow-through chamber, were used to quantify O 2 transfer under the different boundary conditions applied. The results show that the partitioning between the aqueous and the gaseous phases plays a significant role in the supply of O 2 to groundwater at medium time scales. In the case of fast water table fluctuations, the specific yield has to be considered. The experiments with a periodically changing boundary condition demonstrate that highly dynamic fluctuations of the water table enhance the mass transfer of O 2 from the atmosphere into the groundwater when compared with steady-state conditions. Moreover, the characteristics of the water table fluctuations determine a specific dynamic response of the system: we observed an approximately double amount of O 2 transferred to the groundwater when applying slow fluctuations compared with the case of cyclic, abrupt changes in the water table elevation.
E G Youngs - One of the best experts on this subject based on the ideXlab platform.
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effect of the Capillary Fringe on steady state water tables in drained lands ii effect of an underlying impermeable bed
Journal of Irrigation and Drainage Engineering-asce, 2013Co-Authors: E G YoungsAbstract:AbstractA tension-saturated Capillary Fringe above the water table in drained lands gives rise to lower water tables than would occur in its absence. Results of a conformal mapping solution for the flow from uniform steady rainfall rates on the soil surface to deep drains installed above an impermeable bed when the soil above the drains is wholly tension-saturated show that the effect on the water table is greater the nearer the drain is to the impermeable floor. The effect becomes less with increasing rainfall rate. For the very deep tension-saturated soils assumed in the analysis (that implies a very large negative value for the air-entry pressure for the soil), the results obtained give lower bounds for the water-table heights in real soils with finite air-entry values that lie between the calculated ones and those obtained by theory neglecting a Capillary Fringe.
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Environmental Mechanics - The seepage exclusion problem for tunnel cavities in the saturated Capillary Fringe
Geophysical monograph, 2013Co-Authors: E G YoungsAbstract:Vertical downward flow of water through the tension-saturated Capillary Fringe above a water table is perturbed by the presence of cavities that may exclude or allow water entry over different parts of their surface, with some critical shape that just excludes water entry over their whole surface. The analysis by Philip and his colleagues of the seepage exclusion problem was for a soil with an exponential hydraulic conductivity function that does not show a tension-saturated Capillary Fringe and was for an infinite flow field. The analysis given here is for the critical condition of water exclusion from two-dimensional tunnel cavities located above a water table in the saturated Capillary Fringe with a horizontal upper boundary where the soil-water pressure is the air-entry value for the soil. Conformal mapping, used to solve Laplace's equation with these boundary conditions, gives the critical shape of the tunnel cavity and also the flux density distribution through the upper boundary of given height. The shape of the cavity near its top can be approximated by a parabola that over-estimates the width of the cavity at depth below the apex. This is in contrast to the exact parabolic shape obtained for soils with an exponential hydraulic conductivity. Upper and lower bounds for a uniform flux density that raises the top of the saturated region in the vicinity above the cavity are obtained for the calculated critical shape.
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the seepage exclusion problem for tunnel cavities in the saturated Capillary Fringe
Geophysical monograph, 2013Co-Authors: E G YoungsAbstract:Vertical downward flow of water through the tension-saturated Capillary Fringe above a water table is perturbed by the presence of cavities that may exclude or allow water entry over different parts of their surface, with some critical shape that just excludes water entry over their whole surface. The analysis by Philip and his colleagues of the seepage exclusion problem was for a soil with an exponential hydraulic conductivity function that does not show a tension-saturated Capillary Fringe and was for an infinite flow field. The analysis given here is for the critical condition of water exclusion from two-dimensional tunnel cavities located above a water table in the saturated Capillary Fringe with a horizontal upper boundary where the soil-water pressure is the air-entry value for the soil. Conformal mapping, used to solve Laplace's equation with these boundary conditions, gives the critical shape of the tunnel cavity and also the flux density distribution through the upper boundary of given height. The shape of the cavity near its top can be approximated by a parabola that over-estimates the width of the cavity at depth below the apex. This is in contrast to the exact parabolic shape obtained for soils with an exponential hydraulic conductivity. Upper and lower bounds for a uniform flux density that raises the top of the saturated region in the vicinity above the cavity are obtained for the calculated critical shape.
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effect of the Capillary Fringe on steady state water tables in drained lands
Journal of Irrigation and Drainage Engineering-asce, 2012Co-Authors: E G YoungsAbstract:AbstractWhen the flow in the Capillary Fringe above the water table is taken into account in land-drainage theory, water-table heights are lower than those predicted when incident rainfall on the surface is assumed to travel vertically through the vadose zone. An analytical solution is given here to the steady-state drainage problem of the flow of surface-incident rainfall to cylindrical drain channels for the situation of a completely tension-saturated soil above the water table. This gives the maximum effect that the unsaturated soil region above the water table can have on the water-table height for the given drainage system. Calculated results show that the water-table height above drain level is smaller for deeper drains below the soil surface and for larger drain radii than is the case when the effect of the Capillary Fringe is ignored. It follows that drainage design based on customary land-drainage theory ignoring the effect of a Capillary Fringe gives an overestimate for the drain spacing.
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water exclusion from tunnel cavities in the saturated Capillary Fringe
Advances in Water Resources, 2004Co-Authors: E G Youngs, A R Kacimov, Yu V ObnosovAbstract:Abstract The problem of water flow around a tunnel cavity located in the saturated Capillary Fringe on top of a very permeable, freely draining substratum is considered for the critical non-leakage condition when there is uniform vertical downward flow through the upper surface of the saturated region. In this critical condition the soil–water pressure is equal to zero everywhere on the cavity wall that is also a streamline. The conditions at the upper Fringe boundary are that the soil–water pressure is equal to the air-entry value of the soil and the flux through this surface is the uniform infiltration rate. The cavity surface and the Fringe boundary which is elevated above the cavity position, are found through conformal mapping and the use of integral representations of non-standard mixed boundary-value problems. They are calculated for a range of infiltration rates and compared with those obtained by assuming the upper Fringe boundary to be horizontal. The exact analysis given here gives larger tunnel cavities than those given by the approximate treatment of the problem. The results have application in the design of underground repositories against entry of seepage water, the construction of protective Capillary barriers and in the design of interceptor drainage systems.
Christopher P Niewoehner - One of the best experts on this subject based on the ideXlab platform.
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Soil and hydrologic effects on fate and horizontal transport in the Capillary Fringe of surface-applied nitrate
Geoderma, 2012Co-Authors: Sergio M Abit, Aziz Amoozegar, Michael J Vepraskas, Christopher P NiewoehnerAbstract:Substantial horizontal solute transport has been demonstrated to occur in the Capillary Fringe (CF) above a flowing ground water, yet the importance of the CF for solute movement has generally been ignored. This study was conducted to evaluate the fate and horizontal transport of surface-applied nitrate (NO3−) in the CF under simulated hydrologic conditions that varied flow rates. Two soils of different organic carbon content were packed in separate 240-cm long, 60-cm high and 25-cm thick flow cells. A simulated water table (WT) was established at 20 cm above the bottom of each flow cell and different pore-water velocities across the flow cell were simulated while a solution containing NO3− and bromide (Br−) was continuously applied over a small area on the surface of the soil in the flow cell. Soil solution samples were collected from two depths below the WT and two depths within the CF above the WT at four locations along the flow cell. Subsurface horizontal transport of surface-applied NO3− tended to occur exclusively in the CF as the pore-water velocity was increased. In the flow cell with soil having a small amount of organic carbon (0.3 g kg− 1), normalized concentration of NO3− and Br− remained very comparable at all monitoring locations above and below the WT. Nitrate loss via denitrification in this case was not observed as conditions were oxidizing. In flow cells with soils having an organic carbon content of 35 g kg− 1, some Br− was detected below the WT while NO3− was essentially absent. Conditions below the WT favored NO3− loss via denitrification as reflected by very low redox potentials (
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soil and hydrologic effects on fate and horizontal transport in the Capillary Fringe of surface applied nitrate
Geoderma, 2012Co-Authors: Sergio M Abit, Aziz Amoozegar, Michael J Vepraskas, Christopher P NiewoehnerAbstract:Substantial horizontal solute transport has been demonstrated to occur in the Capillary Fringe (CF) above a flowing ground water, yet the importance of the CF for solute movement has generally been ignored. This study was conducted to evaluate the fate and horizontal transport of surface-applied nitrate (NO3−) in the CF under simulated hydrologic conditions that varied flow rates. Two soils of different organic carbon content were packed in separate 240-cm long, 60-cm high and 25-cm thick flow cells. A simulated water table (WT) was established at 20 cm above the bottom of each flow cell and different pore-water velocities across the flow cell were simulated while a solution containing NO3− and bromide (Br−) was continuously applied over a small area on the surface of the soil in the flow cell. Soil solution samples were collected from two depths below the WT and two depths within the CF above the WT at four locations along the flow cell. Subsurface horizontal transport of surface-applied NO3− tended to occur exclusively in the CF as the pore-water velocity was increased. In the flow cell with soil having a small amount of organic carbon (0.3 g kg− 1), normalized concentration of NO3− and Br− remained very comparable at all monitoring locations above and below the WT. Nitrate loss via denitrification in this case was not observed as conditions were oxidizing. In flow cells with soils having an organic carbon content of 35 g kg− 1, some Br− was detected below the WT while NO3− was essentially absent. Conditions below the WT favored NO3− loss via denitrification as reflected by very low redox potentials (< 250 mV). These results suggest that collection of samples from the CF should be considered when monitoring subsurface fate and transport of surface-applied NO3− in locations with laterally moving shallow ground water.
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solute transport in the Capillary Fringe and shallow groundwater field evaluation
Vadose Zone Journal, 2008Co-Authors: Sergio M Abit, Aziz Amoozegar, Michael J Vepraskas, Christopher P NiewoehnerAbstract:Lateral transport of waterborne contaminants is generally assumed to occur below the water table (WT), but recent laboratory studies have suggested that subsurface lateral solute transport could occur above the WT through the Capillary Fringe (CF). The objective of this study was to evaluate the horizontal transport of solutes in the CF and shallow groundwater (SGW). Two consecutive field experiments were conducted in a Leon sand (Aeric Alaquod) at a site with a shallow WT. In both experiments, a bromide (Br − ) solution was applied to the bottom of an auger hole dug to within 10 cm above the projected CF. Movement of Br − in the subsurface was monitored by collecting CF and SGW samples using nests of tension samplers installed at radial distances of 60, 120, 220, and 320 cm from the application spot. Each nest of samplers contained a tension sampler at 45, 60, 75, 90, and 105 cm depth. Bromide transport was monitored for 58 d in the first experiment while the more detailed second experiment was conducted for 84 d. Peak Br − concentration generally occurred in the upper 60 cm of the soil where the CF was located for most of the experiment. The Br − plume that entered the CF moved horizontally in it until Br − was partially moved into the SGW by the fluctuating WT. In the second experiment, approximately 48% of the Br − detected in the CF at a distance of 320 cm from the application spot was still in the CF after 15 cm of rain through 59 d.
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fate of nitrate in the Capillary Fringe and shallow groundwater in a drained sandy soil
Geoderma, 2008Co-Authors: Sergio M Abit, Aziz Amoozegar, Michael J Vepraskas, Christopher P NiewoehnerAbstract:Abstract It is commonly assumed that nitrate (NO 3 − ) and other anions entering the soil move downward through the vadose zone, and then move horizontally in the groundwater. Recent laboratory studies, however, indicate that water movement and transport of pollutants can also take place in the Capillary Fringe (CF) above the water table (WT). This field study evaluated the fate of NO 3 − in the CF and shallow groundwater (SGW) for a sandy soil (Aeric Alaquod) with shallow water table. Ten L of a solution containing approximately 18 mmol L − 1 nitrate [2.66 g L − 1 Mg(NO 3 ) 2 ] and 77 mmol L − 1 bromide (9.12 g L − 1 KBr) were applied to the soil above the CF. The movement of both NO 3 − and Br − was monitored for 84 days by using tension lysimeters installed at depths between 45 and 105 cm at radial distances of 20, 60, 120, 220 and 320 cm from the application point. Nitrate and Br − plumes that entered the CF from the unsaturated zone moved horizontally in the CF until both species were partially carried into the groundwater by the fluctuating WT following rain events. Normalized concentrations of NO 3 − N and Br − remained comparable as they moved horizontally in the CF up to 320 cm from the tracer application spot. However, below the WT the detected normalized concentration of Br − was higher than that for NO 3 − indicating nitrate loss, perhaps due to denitrification. When monitoring subsurface NO 3 − , solely relying on collection of groundwater samples may lead to an underestimation of the extent of NO 3 − contamination and transport in the subsurface.
James E Smith - One of the best experts on this subject based on the ideXlab platform.
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The effect of surface-active solutes on water flow and contaminant transport in variably saturated porous media with Capillary Fringe effects.
Journal of contaminant hydrology, 2020Co-Authors: E J Henry, James E SmithAbstract:Organic contaminants that decrease the surface tension of water (surfactants) can have an effect on unsaturated flow through porous media due to the dependence of Capillary pressure on surface tension. We used an intermediate-scale 2D flow cell (2.44 x 1.53 x 0.108 m) packed with a fine silica sand to investigate surfactant-induced flow perturbations. Surfactant solution (7% 1-butanol and dye tracer) was applied at a constant rate at a point source located on the soil surface above an unconfined synthetic aquifer with ambient groundwater flow and a Capillary Fringe of approximately 55 cm. A glass plate allowed for visual flow and transport observations. Thirty instrumentation stations consist of time domain reflectometry probes and tensiometers measured in-situ moisture content and pressure head, respectively. As surfactant solution was applied at the point source, a transient flow perturbation associated with the advance of the surfactant solution was observed. Above the top of the Capillary Fringe the advance of the surfactant solution caused a visible drainage front that radiated from the point source. Upon reaching the Capillary Fringe, the drainage front caused a localized depression of the Capillary Fringe below the point source because the air-entry pressure decreased in proportion to the decrease in surface tension caused by the surfactant. Eventually, a new Capillary Fringe height was established. The height of the depressed Capillary Fringe was proportional to height of the initial Capillary Fringe multiplied by the relative surface tension of the surfactant solution. The horizontal transport of surfactant in the depressed Capillary Fringe, driven primarily by the ambient groundwater flow, caused the propagation of a wedge-shaped drying front in the downgradient direction. Comparison of dye transport during the surfactant experiment to dye transport in an experiment without surfactant indicated that because surfactant-induced drainage decreased the storage capacity of the vadose zone, the dye breakthrough time to the water table was more than twice as fast when the contaminant solution contained surfactant. The extensive propagation of the drying front and the effect of vadose zone drainage on contaminant breakthrough time suggest the importance of considering surface tension effects on unsaturated flow and transport in systems containing surface-active organic contaminants or systems, where surfactants are used for remediation of the vadose zone or unconfined aquifers.
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the effect of surface active solutes on water flow and contaminant transport in variably saturated porous media with Capillary Fringe effects
Journal of Contaminant Hydrology, 2002Co-Authors: E J Henry, James E SmithAbstract:Abstract Organic contaminants that decrease the surface tension of water (surfactants) can have an effect on unsaturated flow through porous media due to the dependence of Capillary pressure on surface tension. We used an intermediate-scale 2D flow cell (2.44×1.53×0.108 m) packed with a fine silica sand to investigate surfactant-induced flow perturbations. Surfactant solution (7% 1-butanol and dye tracer) was applied at a constant rate at a point source located on the soil surface above an unconfined synthetic aquifer with ambient groundwater flow and a Capillary Fringe of ∼55 cm. A glass plate allowed for visual flow and transport observations. Thirty instrumentation stations consist of time domain reflectometry probes and tensiometers measured in-situ moisture content and pressure head, respectively. As surfactant solution was applied at the point source, a transient flow perturbation associated with the advance of the surfactant solution was observed. Above the top of the Capillary Fringe the advance of the surfactant solution caused a visible drainage front that radiated from the point source. Upon reaching the Capillary Fringe, the drainage front caused a localized depression of the Capillary Fringe below the point source because the air-entry pressure decreased in proportion to the decrease in surface tension caused by the surfactant. Eventually, a new Capillary Fringe height was established. The height of the depressed Capillary Fringe was proportional to height of the initial Capillary Fringe multiplied by the relative surface tension of the surfactant solution. The horizontal transport of surfactant in the depressed Capillary Fringe, driven primarily by the ambient groundwater flow, caused the propagation of a wedge-shaped drying front in the downgradient direction. Comparison of dye transport during the surfactant experiment to dye transport in an experiment without surfactant indicated that because surfactant-induced drainage decreased the storage capacity of the vadose zone, the dye breakthrough time to the water table was more than twice as fast when the contaminant solution contained surfactant. The extensive propagation of the drying front and the effect of vadose zone drainage on contaminant breakthrough time suggest the importance of considering surface tension effects on unsaturated flow and transport in systems containing surface-active organic contaminants or systems, where surfactants are used for remediation of the vadose zone or unconfined aquifers.
I D Klenk - One of the best experts on this subject based on the ideXlab platform.
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Transverse vertical dispersion in groundwater and the Capillary Fringe.
Journal of contaminant hydrology, 2020Co-Authors: I D Klenk, P GrathwohlAbstract:Transverse dispersion is the most relevant process in mass transfer of contaminants across the Capillary Fringe (both directions), dilution of contaminants, and mixing of electron acceptors and electron donors in biodegrading groundwater plumes. This paper gives an overview on literature values of transverse vertical dispersivities alpha(tv) measured at different flow velocities and compares them to results from well-controlled laboratory-tank experiments on mass transfer of trichloroethene (TCE) across the Capillary Fringe. The measured values of transverse vertical dispersion in the Capillary Fringe region were larger than in fully saturated media, which is credited to enhanced tortuosity of the flow paths due to entrapped air within the Capillary Fringe. In all cases, the values observed for alpha(tv) were
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transverse vertical dispersion in groundwater and the Capillary Fringe
Journal of Contaminant Hydrology, 2002Co-Authors: I D Klenk, P GrathwohlAbstract:Transverse dispersion is the most relevant process in mass transfer of contaminants across the Capillary Fringe (both directions), dilution of contaminants, and mixing of electron acceptors and electron donors in biodegrading groundwater plumes. This paper gives an overview on literature values of transverse vertical dispersivities αtv measured at different flow velocities and compares them to results from well-controlled laboratory-tank experiments on mass transfer of trichloroethene (TCE) across the Capillary Fringe. The measured values of transverse vertical dispersion in the Capillary Fringe region were larger than in fully saturated media, which is credited to enhanced tortuosity of the flow paths due to entrapped air within the Capillary Fringe. In all cases, the values observed for αtv were ≪1 mm. The new measurements and the literature values indicate that αtv apparently declines with increasing flow velocity. The latter is attributed to incomplete diffusive mixing at the pore scale (pore throats). A simple conceptual model, based on the mean square displacement and the pore size accounting for only partial diffusive mixing at increasing flow velocities, shows very good agreement with measured and published data.
