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  • 1
    In: Water Resources Research, December 2016, Vol.52(12), pp.9390-9411
    Description: We present a semianalytical model for the transport of solutes being subject to sorption in porous aquifers. We couple a travel time‐based model of advective transport with a spherical diffusion model of kinetic sorption in nonuniform material mixtures. The model is formulated in the Laplace domain and transformed to the time domain by numerical inversion. By this, three‐dimensional transport of solutes undergoing mass transfer between aqueous and solid phases can be simulated very efficiently. The model addresses both hydraulic and reactive heterogeneity of porous aquifers by means of hydrofacies, which function as homogeneous but nonuniform subunits. The total exposure time to each of these subunits controls the magnitude of sorption effects, whereas the particular sequence of facies through which the solute passes is irrelevant. We apply the model to simulate the transport of phenanthrene in a fluvio‐glacial aquifer, for which the hydrofacies distribution is known at high resolution, the lithological composition of each facies has been analyzed, and sorption properties of the lithological components are available. Taking the fully resolved hydrofacies model as reference, we evaluate different approximations referring to lower information levels, reflecting shortcomings in typical modeling projects. The most important feature for a good description of both the main breakthrough and tailing of phenanthrene is the nonuniformity of the porous medium. While spatial heterogeneity of chemical properties might be neglected without introducing a large error, an approximation of the facies' composition in terms of a uniform substitute material considerably compromises the quality of the modeling result. Efficient semianalytical transport model for sorbing solutes in heterogeneous porous media Hydraulic and reactive heterogeneity are considered by spatially distributed nonuniform hydrofacies Results show major significance of facies nonuniformity to accuracy of simulated solute breakthrough
    Keywords: Mathematical Model ; Solute Transport ; Kinetic Sorption ; Aquifer Heterogeneity
    ISSN: 0043-1397
    E-ISSN: 1944-7973
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  • 2
    Language: English
    In: Journal of Contaminant Hydrology, April 2015, Vol.175-176, pp.26-43
    Description: Travel-time based models simplify the description of reactive transport by replacing the spatial coordinates with the groundwater travel time, posing a quasi one-dimensional (1-D) problem and potentially rendering the determination of multidimensional parameter fields unnecessary. While the approach is exact for strictly advective transport in steady-state flow if the reactive properties of the porous medium are uniform, its validity is unclear when local-scale mixing affects the reactive behavior. We compare a two-dimensional (2-D), spatially explicit, bioreactive, advective–dispersive transport model, considered as “virtual truth”, with three 1-D travel-time based models which differ in the conceptualization of longitudinal dispersion: (i) neglecting dispersive mixing altogether, (ii) introducing a local-scale longitudinal dispersivity constant in time and space, and (iii) using an effective longitudinal dispersivity that increases linearly with distance. The reactive system considers biodegradation of dissolved organic carbon, which is introduced into a hydraulically heterogeneous domain together with oxygen and nitrate. Aerobic and denitrifying bacteria use the energy of the microbial transformations for growth. We analyze six scenarios differing in the variance of log-hydraulic conductivity and in the inflow boundary conditions (constant versus time-varying concentration). The concentrations of the 1-D models are mapped to the 2-D domain by means of the kinematic (for case i), and mean groundwater age (for cases ii & iii), respectively. The comparison between concentrations of the “virtual truth” and the 1-D approaches indicates extremely good agreement when using an effective, linearly increasing longitudinal dispersivity in the majority of the scenarios, while the other two 1-D approaches reproduce at least the concentration tendencies well. At late times, all 1-D models give valid approximations of two-dimensional transport. We conclude that the conceptualization of nonlinear bioreactive transport in complex multidimensional domains by quasi 1-D travel-time models is valid for steady-state flow fields if the reactants are introduced over a wide cross-section, flow is at quasi steady state, and dispersive mixing is adequately parametrized.
    Keywords: Travel Time ; Groundwater Age ; Reactive Transport ; Streamtube Methods ; Biodegradation ; Mixing ; Engineering ; Environmental Sciences ; Geography
    ISSN: 0169-7722
    E-ISSN: 1873-6009
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  • 3
    Language: English
    In: Journal of Contaminant Hydrology, April 2016, Vol.187, pp.1-17
    Description: In travel-time models, the spatially explicit description of reactive transport is replaced by associating reactive-species concentrations with the travel time or groundwater age at all locations. These models have been shown adequate for reactive transport in river-bank filtration under steady-state flow conditions. Dynamic hydrological conditions, however, can lead to fluctuations of infiltration velocities, putting the validity of travel-time models into question. In transient flow, the local travel-time distributions change with time. We show that a modified version of travel-time based reactive transport models is valid if only the magnitude of the velocity fluctuates, whereas its spatial orientation remains constant. We simulate nonlinear, one-dimensional, bioreactive transport involving oxygen, nitrate, dissolved organic carbon, aerobic and denitrifying bacteria, considering periodic fluctuations of velocity. These fluctuations make the bioreactive system pulsate: The aerobic zone decreases at times of low velocity and increases at those of high velocity. For the case of diurnal fluctuations, the biomass concentrations cannot follow the hydrological fluctuations and a transition zone containing both aerobic and obligatory denitrifying bacteria is established, whereas a clear separation of the two types of bacteria prevails in the case of seasonal velocity fluctuations. We map the 1-D results to a heterogeneous, two-dimensional domain by means of the mean groundwater age for steady-state flow in both domains. The mapped results are compared to simulation results of spatially explicit, two-dimensional, advective-dispersive-bioreactive transport subject to the same relative fluctuations of velocity as in the one-dimensional model. The agreement between the mapped 1-D and the explicit 2-D results is excellent. We conclude that travel-time models of nonlinear bioreactive transport are adequate in systems of time-periodic flow if the flow direction does not change.
    Keywords: Bioreactive Transport ; Travel-Time Model ; Denitrification ; Transient Flow ; Engineering ; Environmental Sciences ; Geography
    ISSN: 0169-7722
    E-ISSN: 1873-6009
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  • 4
    Language: English
    In: Journal of Contaminant Hydrology, 2015, Vol.175-176, p.26(18)
    Description: To link to full-text access for this article, visit this link: http://dx.doi.org/10.1016/j.jconhyd.2015.02.003 Byline: Alicia Sanz-Prat, Chuanhe Lu, Michael Finkel, Olaf A. Cirpka Abstract: Travel-time based models simplify the description of reactive transport by replacing the spatial coordinates with the groundwater travel time, posing a quasi one-dimensional (1-D) problem and potentially rendering the determination of multidimensional parameter fields unnecessary. While the approach is exact for strictly advective transport in steady-state flow if the reactive properties of the porous medium are uniform, its validity is unclear when local-scale mixing affects the reactive behavior. We compare a two-dimensional (2-D), spatially explicit, bioreactive, advective-dispersive transport model, considered as "virtual truth", with three 1-D travel-time based models which differ in the conceptualization of longitudinal dispersion: (i) neglecting dispersive mixing altogether, (ii) introducing a local-scale longitudinal dispersivity constant in time and space, and (iii) using an effective longitudinal dispersivity that increases linearly with distance. The reactive system considers biodegradation of dissolved organic carbon, which is introduced into a hydraulically heterogeneous domain together with oxygen and nitrate. Aerobic and denitrifying bacteria use the energy of the microbial transformations for growth. We analyze six scenarios differing in the variance of log-hydraulic conductivity and in the inflow boundary conditions (constant versus time-varying concentration). The concentrations of the 1-D models are mapped to the 2-D domain by means of the kinematic (for case i), and mean groundwater age (for cases ii & iii), respectively. The comparison between concentrations of the "virtual truth" and the 1-D approaches indicates extremely good agreement when using an effective, linearly increasing longitudinal dispersivity in the majority of the scenarios, while the other two 1-D approaches reproduce at least the concentration tendencies well. At late times, all 1-D models give valid approximations of two-dimensional transport. We conclude that the conceptualization of nonlinear bioreactive transport in complex multidimensional domains by quasi 1-D travel-time models is valid for steady-state flow fields if the reactants are introduced over a wide cross-section, flow is at quasi steady state, and dispersive mixing is adequately parametrized. Article History: Received 26 August 2014; Revised 30 January 2015; Accepted 5 February 2015
    Keywords: Hydrogeology – Analysis ; Groundwater – Analysis ; Biodegradation – Analysis
    ISSN: 0169-7722
    Source: Cengage Learning, Inc.
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  • 5
    Language: English
    In: Journal of Contaminant Hydrology, September 2016, Vol.192, pp.35-49
    Description: Transport of reactive solutes in groundwater is affected by physical and chemical heterogeneity of the porous medium, leading to complex spatio-temporal patterns of concentrations and reaction rates. For certain cases of bioreactive transport, it could be shown that the concentrations of reactive constituents in multi-dimensional domains are approximately aligned with isochrones, that is, lines of identical travel time, provided that the chemical properties of the matrix are uniform. We extend this concept to combined physical and chemical heterogeneity by additionally considering the time that a water parcel has been exposed to reactive materials, the so-called exposure time. We simulate bioreactive transport in a one-dimensional domain as function of time and exposure time, rather than space. Subsequently, we map the concentrations to multi-dimensional heterogeneous domains by means of the mean exposure time at each location in the multi-dimensional domain. Differences in travel and exposure time at a given location are accounted for as time difference. This approximation simplifies reactive-transport simulations significantly under conditions of steady-state flow when reactions are restricted to specific locations. It is not expected to be exact in realistic applications because the underlying assumption, such as neglecting transverse mixing altogether, may not hold. We quantify the error introduced by the approximation for the hypothetical case of a two-dimensional, binary aquifer made of highly-permeable, non-reactive and low-permeable, reactive materials releasing dissolved organic matter acting as electron donor for aerobic respiration and denitrification. The kinetically controlled reactions are catalyzed by two non-competitive bacteria populations, enabling microbial growth. Even though the initial biomass concentrations were uniform, the interplay between transport, non-uniform electron-donor supply, and bio-reactions led to distinct spatial patterns of the two types of biomass at late times. Results obtained by mapping the exposure-time based results to the two-dimensional domain are compared with simulations based on the two-dimensional, spatially explicit advection-dispersion-reaction equation. Once quasi-steady state has been reached, we find a good agreement in terms of the chemical-compound concentrations between the two approaches inside the reactive zones, whereas the exposure-time based model is not able to capture reactions occurring in the zones with zero electron-donor release. We conclude that exposure-time models provide good approximations of nonlinear bio-reactive transport when transverse mixing is not the overall controlling process and all reactions are essentially restricted to distinct reactive zones.
    Keywords: Exposure Time ; Travel Time ; Denitrification ; Bioreactive Transport ; Engineering ; Environmental Sciences ; Geography
    ISSN: 0169-7722
    E-ISSN: 1873-6009
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  • 6
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  • 7
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  • 8
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  • 9
    In: Water Resources Research, November 2004, Vol.40(11), pp.n/a-n/a
    Description: Hydraulic failure of a funnel‐and‐gate system may occur when the contaminant plume bypasses the funnels rather than being captured by the gate. We analyze the uncertainty of capturing the plumes by funnel‐and‐gate systems in heterogeneous aquifers. Restricting the analysis to two‐dimensional, steady state flow, we characterize plume capture by the values of the stream function at the boundaries of the plume and the funnels. On the basis of the covariance of the log conductivity distribution we compute the covariance matrix of the relevant stream function values by a matrix‐based first‐order second‐moment method, making use of efficient matrix‐multiplication techniques. From the covariance matrix of stream function values, we can approximate the probability that the plume is bypassing the funnels. We condition the log conductivity field to measurements of the log conductivity and the hydraulic head. Prior to performing additional measurements, we estimate their worth by the expected reduction in the variance of stream function differences. In an application to a hypothetical aquifer, we demonstrate that our method of uncertainty propagation and our sampling strategy enable us to discriminate between cases of success and failure of funnel‐and‐gate systems with a small number of additional samples.
    Keywords: Conditioning ; Data Worth ; Funnel‐And‐Gate Systems ; Heterogeneous Aquifers ; Stream Function ; Uncertainty Propagation
    ISSN: 0043-1397
    E-ISSN: 1944-7973
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