Lagrangian models of reactive transport in heterogeneous porous media with uncertain properties

Severino, Gerardo; Tartakovsky, Daniel M.; Srinivasan, G.; Viswanathan, Hari

doi:10.1098/rspa.2011.0375

Cited by 25 publications

(10 citation statements)

References 32 publications

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“…A useful characterization of transport in aquifers can be formulated in terms of average flux concentration [e.g., Dagan et al , 1992; Cvetkovic and Dagan , 1994] since it is consistent with common procedures for measuring concentrations [e.g., Andricevic and Cvetkovic , 1997]. The average flux concentration was considered in numerous studies dealing with MU flows [e.g., Cvetkovic and Dagan , 1994; Cvetkovic et al , 1998; Severino et al , 2012]. Current regulatory standards for the subsurface environment, especially those set in terms of the travel time approach , make the solute flux approach an appealing framework for predicting/analyzing subsurface contaminant transport.…”

Section: Introductionmentioning

confidence: 99%

Travel time approach to kinetically sorbing solute by diverging radial flows through heterogeneous porous formations

Severino

Bartolo

Toraldo

et al. 2012

Water Resources Research

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[1] Diverging radial flow takes place in a heterogeneous porous medium where the log conductivity Y ¼ ln K is modeled as a stationary random space function (RSF). The flow is steady, and is generated by a fully penetrating well. A linearly sorbing solute is injected through the well envelope, and we aim at computing the average flux concentration (breakthrough curve). A relatively simple solution for this difficult problem is achieved by adopting, similar to Indelman and Dagan (1999), a few simplifying assumptions: (i) a thick aquifer of large horizontal extent, (ii) mildly heterogeneous medium, (iii) strongly anisotropic formation, and (iv) large Peclet number. By introducing an appropriate Lagrangian framework, three-dimensional transport is mapped onto a one-dimensional domain ( , t) where and t represent the fluid travel and current time, respectively. Central for this approach is the probability density function of the RSF that is derived consistently with the adopted assumptions stated above. Based on this, it is shown that the travel time can be regarded as a Gaussian random variable only in the far field. The breakthrough curves are analyzed to assess the impact of the hydraulic as well as reactive parameters. Finally, the travel time approach is tested against a forced-gradient transport experiment and shows good agreement.

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Section: Introductionmentioning

confidence: 99%

Travel time approach to kinetically sorbing solute by diverging radial flows through heterogeneous porous formations

Severino

Bartolo

Toraldo

et al. 2012

Water Resources Research

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“…In fact, it is well known that in this case the larger scales impact the dispersion of the migrating plume(s) (see e.g. Severino et al, , , ), whereas the smaller scales affect mixing and/or reactions to which solutes may undergo (Bellin et al, ). Thus, the knowledge of the existence of more than one scale provides fundamental insights about: (i) how to set up proper remediation strategies and (ii) to design sampling networks.…”

Section: Discussionmentioning

confidence: 99%

On the dependence of the saturated hydraulic conductivity upon the effective porosity through a power law model at different scales

Fallico

Bartolo

Veltri

et al. 2016

Hydrological Processes

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Abstract:We study the scale dependence of the saturated hydraulic conductivity K s through the effective porosity n e by means of a newly developed power-law model (PLM) which allows to use simultaneously measurements at different scales. The model is expressed as product between a single PLM (capturing the impact of the dominating scale) and a characteristic function κ ⋆ accounting for the correction because of the other scale(s). The simple (closed form) expression of the κ ⋆ -function enables one to easily identify the scales which are relevant for K s . The proposed model is then applied to a set of real data taken at the experimental site of Montalto Uffugo (Italy), and we show that in this case two (i.e. laboratory and field) scales appear to be the main ones. The implications toward an important application (solute transport) in Hydrology are finally discussed.

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“…In this study, we focus on characterizing the solute transport process at the field scale through the Lagrangian perspective of travel time statistics (e.g., Cvetkovic, Cheng, & Wen, ; Cvetkovic, Shapiro, & Dagan, ; Dagan & Nguyen, ; Dentz, Kang, & Borgne, ; Destouni et al, ; Severino, Tartakovsky, Srinivasan, & Viswanathan, ; Shapiro & Cvetkovic, ; Simmons, ; Zhang, Andricevic, Sun, Hu, & He, ). The statistics of the solute travel time are useful for assessing the risk to environmentally sensitive locations, which are often needed in the context of environmental risk assessment (Maxwell, Kastenberg, & Rubin, ; Zimmerman et al, ).…”

Section: Introductionmentioning

confidence: 99%

Quantification of Lagrangian travel time statistics under nonstationary random groundwater flow conditions

Chang

Yeh

2018

Hydrological Processes

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This study presents a Lagrangian description of advection dominated field-scale transport of inert solutes, namely, the statistics of advective solute travel time and trajectory, in nonstationary random groundwater flow fields. The vertical flow field is generated by the effects of changes in total stress applied in fluid-saturated heterogeneous deformable porous media. The Lagrangian statistics are developed directly from the velocity statistics based on the application of stochastic methodology such as the representation theorem and Fourier-Stieltjes integral representation. The focus of our numerical evaluation is placed on the influence of the soil compressibility on the Lagrangian statistics. The prediction on the statistics of solute travel time and trajectory may serve as the basic input to the environmental risk assessment. KEYWORDS heterogeneous deformable porous media, nonstationary groundwater flow fields, soil compressibility, statistics of the solute travel time

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Lagrangian models of reactive transport in heterogeneous porous media with uncertain properties

Cited by 25 publications

References 32 publications

Travel time approach to kinetically sorbing solute by diverging radial flows through heterogeneous porous formations

Travel time approach to kinetically sorbing solute by diverging radial flows through heterogeneous porous formations

On the dependence of the saturated hydraulic conductivity upon the effective porosity through a power law model at different scales

Quantification of Lagrangian travel time statistics under nonstationary random groundwater flow conditions

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