Adjoint Modeling of Contaminant Fate and Transport in Riverbank Filtration Systems

Larbkich, W.; Neupauer, R. M.; Colvin, David; Bauer, Jan; Herman, Janet S.

doi:10.1061/9780784413548.026

Cited by 2 publications

(2 citation statements)

References 9 publications

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“…In hydrogeology, the adjoint state method has been employed in many applications including interpretation of interference tests using geostastistical techniques (de Marsily et al, 1984), steady-state groundwater flow (Sykes et al, 1985;Wilson & Metcalfe, 1985), groundwater travel time uncertainty analysis (LaVenue et al, 1989), automated calibration of transmissivity fields (LaVenue et al, 1995;RamaRao et al, 1995), coupled nonlinear multiphase multicomponent flow (RamaRao & Mishra, 1996), modeling multidimensional groundwater flow (Clemo, 2007), adaptive multiscale parameterization of flow in unsaturated porous media (Hayek et al, 2008), transient groundwater flow in a bounded model domain (Lu & Vesselinov, 2015), fractured dual-porosity media (Delay et al, 2017;Fahs et al, 2014), and coupled surface water-groundwater modeling (RamaRao et al, 2017). However, few applications of the adjoint state method have been devoted to solute transport (e.g., Larbkich et al, 2014;Michalak & Kitanidis, 2004;Neupauer & Wilson, 1999, 2001Piasecki & Katopodes, 1997).…”

Section: Introductionmentioning

confidence: 99%

An Adjoint Sensitivity Model for Steady‐State Sequentially Coupled Radionuclide Transport in Porous Media

Hayek¹,

RamaRao

Lavenue

2019

Water Resources Research

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This work presents an efficient mathematical/numerical model to compute the sensitivity coefficients of a predefined performance measure to model parameters for one‐dimensional steady‐state sequentially coupled radionuclide transport in a finite heterogeneous porous medium. The model is based on the adjoint sensitivity approach that offers an elegant and computationally efficient alternative way to compute the sensitivity coefficients. The transport parameters include the radionuclide retardation factors due to sorption, the Darcy velocity, and the effective diffusion/dispersion coefficients. Both continuous and discrete adjoint approaches are considered. The partial differential equations associated with the adjoint system are derived based on the adjoint state theory for coupled problems. Physical interpretations of the adjoint states are given in analogy to results obtained in the theory of groundwater flow. For the homogeneous case, analytical solutions for primary and adjoint systems are derived and presented in closed forms. Numerically calculated solutions are compared to the analytical results and show excellent agreements. Insights from sensitivity analysis are discussed to get a better understanding of the values of sensitivity coefficients. The sensitivity coefficients are also computed numerically by finite differences. The numerical sensitivity coefficients successfully reproduce the analytically derived sensitivities based on adjoint states. A derivative‐based global sensitivity method coupled with the adjoint state method is presented and applied to a real field case represented by a site currently being considered for underground nuclear storage in Northern Switzerland, “Zürich Nordost”, to demonstrate the proposed method. The results show the advantage of the adjoint state method compared to other methods in term of computational effort.

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Section: Introductionmentioning

confidence: 99%

An Adjoint Sensitivity Model for Steady‐State Sequentially Coupled Radionuclide Transport in Porous Media

Hayek¹,

RamaRao

Lavenue

2019

Water Resources Research

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“…The adjoint method has been employed to calculate the sensitivity of the head or drawdown to hydraulic parameters (conductivity/transmissivity, storage coefficient/storativity) for steady state flow [ Neuman , ; Sykes et al ., ; Mazzilli et al ., ], transient flow [ Carrera and Medina , ; Zhu and Yeh , ; Sun et al ., ; Mao et al ., ], variably saturated flow [ Li and Yeh , ; Hughson and Yeh , ; Li and Yeh , ], and multilayer aquifer systems [ Lu et al ., ]. Applications of the adjoint method in solute transport include determining the sensitivity of the solute concentration to the source intensity [ Piasecki and Katopodes , ], the contamination source location and travel time probability and distribution [ Neupauer and Wilson , ; Larbkich et al ., ], and estimates of the historical groundwater contamination distribution [ Michalak and Kitanidis , ]. Other applications of the method in groundwater hydrology include combining the adjoint method with the level set method to identify heterogeneity in porous media [ Lu and Robinson , ] and selection of well locations for minimizing stream depletion [ Neupauer and Cronin , ], among others.…”

Section: Introductionmentioning

confidence: 99%

Analytical sensitivity analysis of transient groundwater flow in a bounded model domain using the adjoint method

Lü

Vesselinov

2015

Water Resources Research

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Sensitivity analyses are an important component of any modeling exercise. We have developed an analytical methodology based on the adjoint method to compute sensitivities of a state variable (hydraulic head) to model parameters (hydraulic conductivity and storage coefficient) for transient groundwater flow in a confined and randomly heterogeneous aquifer under ambient and pumping conditions. For a special case of two-dimensional rectangular domains, these sensitivities are represented in terms of the problem configuration (the domain size, boundary configuration, medium properties, pumping schedules and rates, and observation locations and times), and there is no need to actually solve the adjoint equations. As an example, we present analyses of the obtained solution for typical groundwater flow conditions. Analytical solutions allow us to calculate sensitivities efficiently, which can be useful for model-based analyses such as parameter estimation, data-worth evaluation, and optimal experimental design related to sampling frequency and locations of observation wells. The analytical approach is not limited to groundwater applications but can be extended to any other mathematical problem with similar governing equations and under similar conceptual conditions.

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Adjoint Modeling of Contaminant Fate and Transport in Riverbank Filtration Systems

Cited by 2 publications

References 9 publications

An Adjoint Sensitivity Model for Steady‐State Sequentially Coupled Radionuclide Transport in Porous Media

An Adjoint Sensitivity Model for Steady‐State Sequentially Coupled Radionuclide Transport in Porous Media

Analytical sensitivity analysis of transient groundwater flow in a bounded model domain using the adjoint method

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