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  • 1
    Language: English
    In: Transport in Porous Media, 11/2012, Vol.95(2), pp.425-446
    Description: In this article, we extend the analysis of Diaz and Brevdo (J. Fluid Mech. 681:567-596, 2011) of the absolute/convective instability dichotomy at the onset of convection in a saturated porous layer with either horizontal or vertical salinity and inclined temperature gradients to studying the influence of the Soret effect on the dichotomy in a similar model. Only longitudinal modes are considered. We treat first normal modes and analyze the influence of the Soret effect on the critical values of the vertical thermal Rayleigh number, R (sub v) , wavenumber, l, and frequency, omega , for a variety of values of the horizontal thermal Rayleigh number R (sub h) , and the vertical salinity Rayleigh number, S (sub v) . Our results for normal modes agree well with relevant results of Narayana et al. (J. Fluid Mech. 612:1-19, 2008) obtained for a similar model in a different context. In the computations, we use a high-precision pseudo-spectral Chebyshev-collocation method. Further, we apply the formalism of absolute and convective instabilities and compute the group velocity of the unstable wavepacket emerging in a marginally unstable state to determine the nature of the instability at the onset of convection. The influence of the Soret effect on the absolute/convective instability dichotomy present in the model is treated by considering the destabilization for seven values of the Soret number: S (sub r) = -1, -0.5, -0.1, 0, 0.1, 0.5, 1, for all the parameter cases in the treatment of normal modes. Copyright 2012 Springer Science+Business Media Dordrecht and Springer Science+Business Media B.V.
    Keywords: General Geochemistry ; Hydrogeology ; Convection ; Fluid Flow ; Hydrology ; Models ; Numerical Models ; Porous Materials ; Rayleigh Number ; Salinity ; Saturation ; Solutes ; Soret Effect ; Stability ; Temperature ; Thermal Gradient;
    ISSN: 0169-3913
    E-ISSN: 1573-1634
    Source: Springer (via CrossRef)
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  • 2
    Language: English
    In: Journal of Hydrology, May 2018, Vol.560, pp.97-108
    Description: Mobile-immobile transport models can be effective in reproducing heavily tailed breakthrough curves of concentration. However, such models may not adequately describe transport along multiple flow paths with intermediate velocity contrasts in connected fields. We propose using the mobile-mobile model for simulating subsurface flow and associated mixing-controlled reactive transport in connected fields. This model includes two local concentrations, one in the fast- and the other in the slow-flow domain, which predict both the concentration mean and variance. The normalized total concentration variance within the flux is found to be a non-monotonic function of the discharge ratio with a maximum concentration variance at intermediate values of the discharge ratio. We test the mobile-mobile model for mixing-controlled reactive transport with an instantaneous, irreversible bimolecular reaction in structured and connected random heterogeneous domains, and compare the performance of the mobile-mobile to the mobile-immobile model. The results indicate that the mobile-mobile model generally predicts the concentration breakthrough curves (BTCs) of the reactive compound better. Particularly, for cases of an elliptical inclusion with intermediate hydraulic-conductivity contrasts, where the travel-time distribution shows bimodal behavior, the prediction of both the BTCs and maximum product concentration is significantly improved. Our results exemplify that the conceptual model of two mobile domains with diffusive mass transfer in between is in general good for predicting mixing-controlled reactive transport, and particularly so in cases where the transfer in the low-conductivity zones is by slow advection rather than diffusion.
    Keywords: Mobile-Mobile ; Mobile-Immobile ; Mixing ; Reactive Transport ; Geography
    ISSN: 0022-1694
    E-ISSN: 1879-2707
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  • 3
    In: Water Resources Research, May 2014, Vol.50(5), pp.4149-4162
    Description: Models of microbial dynamics coupled to solute transport in aquifers typically require the introduction of a bacterial capacity term to prevent excessive microbial growth close to substrate‐injection boundaries. The factors controlling this carrying capacity, however, are not fully understood. In this study, we propose that grazers or bacteriophages may control the density of bacterial biomass in continuously fed porous media. We conceptualize the flow‐through porous medium as a series of retentostats, in which the dissolved substrate is advected with water flow whereas the biomasses of bacteria and grazers are considered essentially immobile. We first model a single retentostat with Monod kinetics of bacterial growth and a second‐order grazing law, which shows that the system oscillates but approaches a stable steady state with nonzero concentrations of substrate, bacteria, and grazers. The steady state concentration of the bacteria biomass is independent of the substrate concentration in the inflow. When coupling several retentostats in a series to mimic a groundwater column, the steady state bacteria concentrations thus remain at a constant level over a significant travel distance. The one‐dimensional reactive transport model also accounts for substrate dispersion and a random walk of grazers influenced by the bacteria concentration. These dispersive‐diffusive terms affect the oscillations until steady state is reached, but hardly the steady state value itself. We conclude that grazing, or infection by bacteriophages, is a possible explanation of the maximum biomass concentration frequently needed in bioreactive transport models. Its value depends on parameters related to the grazers or bacteriophages and is independent of bacterial growth parameters or substrate concentration, provided that there is enough substrate to sustain bacteria and grazers. One‐dimensional transport model with substrate‐bacteria‐grazer interactions Steady state bacteria concentration is constant over a certain length Grazing may explain the carrying capacity of bacteria in groundwater ecosystems
    Keywords: Groundwater Ecology ; Grazer ; Retentostat ; Reactive Transport ; Microbial Dynamics ; Top‐Down Control ; Linearized Stability Analysis ; Carrying Capacity
    ISSN: 0043-1397
    E-ISSN: 1944-7973
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  • 4
    Language: English
    In: Journal of environmental quality, July 2014, Vol.43(4), pp.1392-403
    Description: The persistent insecticide lindane [(1α,2α,3β,4α,5α,6β)-1,2,3,4,5,6-hexachlorocyclohexane] is still in use in many tropical countries and remains a threat to soil and water quality. We studied the sorption and transport of lindane onto and through lateritic soils in both the absence and presence of lignite particles, onto which lindane may preferably sorb. We determined a linear distribution coefficient of lindane onto the soil matrix of 3.38 ± 0.16 L kg. Soil particles were not released from the porous medium on changing ionic strength, and also transport of lindane was not affected by changes in ionic strength. We fitted coupled transport models for lindane and the particles to the data, revealing that: (i) sorption kinetics of lindane onto the matrix is described best by intraparticle diffusion; (ii) 20% of the total porosity of the lateritic sample is intraparticle porosity; and (iii) only lignite particles with a median diameter 〈0.45 μm were not retained in the porous medium and thus facilitated the transport of lindane. We conclude that although lindane and similar pollutants may sorb on tropical lateritic porous media, their transport may be facilitated by particles with high organic-C content or dissolved organic C (DOC). This may be of relevance in farmlands and swamp groundwater systems where DOC, produced by leaching or slow biodegradation of surface organic matter, could cause rapid groundwater contamination by sorbing pollutants. Moreover, the results of this study can help to understand nanoparticle behavior in lateritic soils as the size of particles that facilitate lindane transport approaches the nanoparticle size range.
    Keywords: Environmental Geology ; Africa ; Biodegradation ; Breakthrough Curves ; Cameroon ; Chlorinated Hydrocarbons ; Clay Minerals ; Concentration ; Douala Cameroon ; Experimental Studies ; Halogenated Hydrocarbons ; Hexachlorocyclohexane ; Hydrophobic Materials ; Insecticides ; Isotherms ; Kinetics ; Land Use ; Leaching ; Organic Compounds ; Organochlorine Pesticides ; Pesticides ; Pollution ; Porous Materials ; Sheet Silicates ; Silicates ; Sodium Chloride ; Soil Pollution ; Soil Profiles ; Solutes ; Sorption ; Toxic Materials ; Transport ; Water Quality ; West Africa ; Yaounde Cameroon;
    ISSN: 0047-2425
    E-ISSN: 15372537
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  • 5
    In: Water Resources Research, January 2015, Vol.51(1), pp.261-280
    Description: Characterizing the topology of three‐dimensional steady‐state flow fields is useful to describe the physical processes controlling the deformation of solute plumes and, consequently, obtain helpful information on mixing processes without solving the transport equation. In this work, we study the topology of flow in three‐dimensional nonstationary anisotropic heterogeneous porous media. In particular, we apply a topological metric, i.e., the helicity density, and two complementary kinematic descriptors of mixing, i.e., stretching and folding, to investigate: (i) the flow field resulting from applying a uniform‐in‐the‐average hydraulic gradient within a fully resolved heterogeneous three‐dimensional porous medium with a nonstationary anisotropic covariance function of the locally isotropic hydraulic log conductivity; (ii) the flow field obtained by averaging a set of Monte Carlo realizations of the former field; (iii) the flow field obtained considering the blockwise uniform anisotropic effective conductivity tensor computed for the fully resolved case. While in the fully resolved case, the local helicity density is zero as a consequence of the local isotropy of hydraulic conductivity, it differs from zero in the other two cases. We show, therefore, that this topological metric is scale dependent and should be computed at the appropriate scale to be informative about the leading patterns of plume deformation. Indeed, streamlines are helical in all three cases at scales larger than the characteristic scale of spatial variability. We apply stretching and folding metrics to investigate the scales at which plume deformation is more influenced by helical motion than by the effect of small‐scale spatial heterogeneity in the hydraulic‐conductivity field. Under steady‐state flow conditions, stretching, which quantifies the increasing length of an interface, dominates at short distances from a given starting plane, while folding, which describes how this interface is bent to fill a finite volume of space, dominates further downstream and can be correlated with the appearance of large‐scale secondary motion. We conclude that three‐dimensional flows in porous media may show a complex topology whose analysis is relevant for the description of plume deformation. These results have important implications for the understanding of mixing processes, as shown in detail in the companion paper focusing on solute transport. Macroscopic helical flow occurs in 3‐D nonstationary isotropic media Helicity density is scale dependent and is used to describe flow topology Stretching and folding metrics are used to describe plume deformation
    Keywords: Topology ; Helicity ; Stretching ; Folding ; Nonstationarity ; Anisotropic Correlation Structure
    ISSN: 0043-1397
    E-ISSN: 1944-7973
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  • 6
    In: Water Resources Research, June 2017, Vol.53(6), pp.4984-5001
    Description: The complexity of hyporheic flow paths requires reach‐scale models of solute transport in streams that are flexible in their representation of the hyporheic passage. We use a model that couples advective‐dispersive in‐stream transport to hyporheic exchange with a shape‐free distribution of hyporheic travel times. The model also accounts for two‐site sorption and transformation of reactive solutes. The coefficients of the model are determined by fitting concurrent stream‐tracer tests of conservative (fluorescein) and reactive (resazurin/resorufin) compounds. The flexibility of the shape‐free models give rise to multiple local minima of the objective function in parameter estimation, thus requiring global‐search algorithms, which is hindered by the large number of parameter values to be estimated. We present a local‐in‐global optimization approach, in which we use a Markov‐Chain Monte Carlo method as global‐search method to estimate a set of in‐stream and hyporheic parameters. Nested therein, we infer the shape‐free distribution of hyporheic travel times by a local Gauss‐Newton method. The overall approach is independent of the initial guess and provides the joint posterior distribution of all parameters. We apply the described local‐in‐global optimization method to recorded tracer breakthrough curves of three consecutive stream sections, and infer section‐wise hydraulic parameter distributions to analyze how hyporheic exchange processes differ between the stream sections. Compounds, dissolved in river water, are transported along the river, but also to some extent into the sediments and back into the river. While being in the sediments, they may react. In reactive stream‐tracer tests, we add easy‐to‐detect reactive compounds into a stream and measure time‐series of concentration in the river further downstream. We present an approach of analyzing such tracer tests in a flexible, yet reliable manner, which also provides the uncertainty of our interpretation. This can be useful in the assessment of river‐water quality The estimation of transport parameters is coupled with the inference of a continuous travel time distribution The nested local‐in‐global approach provides the joint posterior distribution of all parameters The presented approach is applied to reactive stream‐tracer data to determine hyporheic exchange processes
    Keywords: Hyporheic Travel Time Distribution ; Local‐In‐Global Estimation ; Reactive Tracer Test ; Markov‐Chain Monte Carlo
    ISSN: 0043-1397
    E-ISSN: 1944-7973
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  • 7
    Language: English
    In: Transport in Porous Media, 2016, Vol.111(3), pp.591-603
    Description: Helical flow can occur in porous media if the hydraulic conductivity tensor is anisotropic. We study the structure of steady-state flow fields in three-dimensional anisotropic porous media formed by two homogeneous layers, one of which is anisotropic. We simulate transient transport of a conservative scalar in such flow fields by a hybrid streamline/smoothed particle hydrodynamics method and analyze dilution. We use stretching and folding metrics to characterize the flow field and the dilution index of a conservative scalar divided by the volume of the domain to quantify plume dilution. Based on the results of detailed numerical simulations, we conclude that nonlinear deformation triggers dilution and that plume dilution is controlled by two parameters: the contrast between the principal directions of the anisotropic layer, and the orientation of the hydraulic conductivity tensor with respect to the main flow direction. Furthermore, we show that in this kind of flow fields transverse dispersion is responsible for an increase in plume dilution, while the effect of longitudinal dispersion is negligible.
    Keywords: Anisotropic porous media ; Helical flow ; Flow topology ; Solute dilution
    ISSN: 0169-3913
    E-ISSN: 1573-1634
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  • 8
    In: Water Resources Research, April 2017, Vol.53(4), pp.2813-2832
    Description: The spatial variability of hydraulic conductivity is known to have a strong impact on solute spreading and mixing. In most investigations, its local anisotropy has been neglected. Recent studies have shown that spatially varying orientation in sedimentary anisotropy can lead to twisting flow enhancing transverse mixing, but most of these studies used geologically implausible geometries. We use an object‐based approach to generate stacked scour‐pool structures with either isotropic or anisotropic filling which are typically reported in glacial outwash deposits. We analyze how spatially variable isotropic conductivity and variation of internal anisotropy in these features impacts transverse plume deformation and both longitudinal and transverse spreading and mixing. In five test cases, either the scalar values of conductivity or the spatial orientation of its anisotropy is varied between the scour‐pool structures. Based on 100 random configurations, we compare the variability of velocity components, stretching and folding metrics, advective travel‐time distributions, one and two‐particle statistics in advective‐dispersive transport, and the flux‐related dilution indices for steady state advective‐dispersive transport among the five test cases. Variation in the orientation of internal anisotropy causes strong variability in the lateral velocity components, which leads to deformation in transverse directions and enhances transverse mixing, whereas it hardly affects the variability of the longitudinal velocity component and thus longitudinal spreading and mixing. The latter is controlled by the spatial variability in the scalar values of hydraulic conductivity. Our results demonstrate that sedimentary anisotropy is important for transverse mixing, whereas it may be neglected when considering longitudinal spreading and mixing. When sediments are deposited in stream channels they retain the “imprint” of the stream flow that deposited them. Groundwater flows more easily along the path of this streamflow imprint than against it—this is called anisotropy. Many groundwater systems are made up of deposits from many different streams and so will have many different imprints, even when the deposits are close to each other. We found that this can cause groundwater to flow along complicated and tangled paths. These tangled groundwater paths can change the way that compounds move through the system, especially at right angles to the main groundwater flow direction. This is important because groundwater scientists often do not think about the imprint, or anisotropy, of the sediments in their studies, and perhaps they should. Internal anisotropy in realistic glacial outwash deposits causes complex three‐dimensional groundwater flow patterns Dilution of steady state plumes in anisotropic test cases is not adequately characterized by two‐particle statistics Sedimentary anisotropy is of critical importance when considering contaminant plumes controlled by transverse mixing
    Keywords: Sedimentary Anisotropy ; Transverse Mixing ; Glacial Outwash Deposits ; Dilution ; Two‐Particle Moments ; Flow Topology
    ISSN: 0043-1397
    E-ISSN: 1944-7973
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  • 9
    In: Water Resources Research, January 2015, Vol.51(1), pp.241-260
    Description: Groundwater plumes originating from continuously emitting sources are typically controlled by transverse mixing between the plume and reactants in the ambient solution. In two‐dimensional domains, heterogeneity causes only weak enhancement of transverse mixing in steady‐state flows. In three‐dimensional domains, more complex flow patterns are possible because streamlines can twist. In particular, spatially varying orientation of anisotropy can cause steady‐state groundwater whirls. We analyze steady‐state solute transport in three‐dimensional locally isotropic heterogeneous porous media with blockwise anisotropic correlation structure, in which the principal directions of anisotropy differ from block to block. For this purpose, we propose a transport scheme that relies on advective transport along streamlines and transverse‐dispersive mass exchange between them based on Voronoi tessellation. We compare flow and transport results obtained for a nonstationary anisotropic log‐hydraulic conductivity field to an equivalent stationary field with identical mean, variance, and two‐point correlation function disregarding the nonstationarity. The nonstationary anisotropic field is affected by mean secondary motion and causes neighboring streamlines to strongly diverge, which can be quantified by the two‐particle semivariogram of lateral advective displacements. An equivalent kinematic descriptor of the flow field is the advective folding of plumes, which is more relevant as precursor of mixing than stretching. The separation of neighboring streamlines enhances transverse mixing when considering local dispersion. We quantify mixing by the flux‐related dilution index, which is substantially larger for the nonstationary anisotropic conductivity field than for the stationary one. We conclude that nonstationary anisotropy in the correlation structure has a significant impact on transverse plume deformation and mixing. In natural sediments, contaminant plumes most likely mix more effectively in the transverse directions than predicted by models that neglect the nonstationarity of anisotropy. Natural sediments exhibit nonstationary anisotropic structures Nonstationary anisotropy causes secondary groundwater motion Secondary motion enhances transverse mixing and dilution
    Keywords: Nonstationarity ; Anisotropic Correlation Structure ; Secondary Motion ; Mixing ; Dilution
    ISSN: 0043-1397
    E-ISSN: 1944-7973
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  • 10
    In: Water Resources Research, July 2011, Vol.47(7), pp.n/a-n/a
    Description: Different measures of dilution have been proposed to describe solute mixing in heterogeneous porous media. Most of these approaches lead to the definition of effective dispersion coefficients. In order to quantify mixing, these up‐scaled parameters should account for both local‐scale dispersion and effects of flow variability in heterogeneous formations (e.g., flow focusing in high‐conductivity and defocusing in low‐conductivity inclusions). The correct quantification of mixing is particularly important for transport of compounds undergoing reactions. Recent results of multitracer laboratory experiments showed a dependency of local transverse dispersion on molecular diffusion over a wide range of flow velocities, implying compound‐specific transverse mixing even at intermediate and high Péclet numbers. The goal of this study is to assess the relevance of a compound‐specific local‐scale transverse dispersion on conservative and reactive mixing in heterogeneous domains at the field scale. We restrict our analysis to steady state two‐dimensional flow and transport with continuous injection from a line source. We present numerical simulations in heterogeneous domains with different characteristics of variability in the conductivity field, and apply as measures of solute mixing: (1) the effective transverse dispersion coefficient derived from second central spatial moments, (2) a dispersion coefficient derived from flux‐related second central spatial moments, (3) the scalar dissipation rate, and (4) a dispersion coefficient derived from the flux‐related dilution index. The results indicate compound‐specific transverse mixing behavior also at the field scale which is particularly significant in case of low to moderately heterogeneous porous media. Moreover, we show that measures of dilution calculated in a flux‐related framework result in an improved quantification of mixing processes and allow to define up‐scaled parameters (i.e., effective transverse dispersion coefficients) affected by a low degree of uncertainty. For mixing‐controlled reactive transport we illustrate the importance of compound‐dependent local effects on the length of reactive solute plumes. Relevance of local compound‐specific transverse dispersion at the field scale Effective parameters from flux‐related measures of dilution show low uncertainty Reactive mixing: critical flux‐related dilution index and scalar dissipation rate
    Keywords: Mixing ; Compound‐Specific Transverse Dispersion ; Dilution ; Reactive Transport ; Effective Dispersion Coefficient
    ISSN: 0043-1397
    E-ISSN: 1944-7973
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