Data completion problem for the advection‐diffusion equation with aquifer point sources

Hassin, Anis Bel Hadj; Hariga, Nejla T.; Khayat, Faten

doi:10.1002/mma.6868

Cited by 3 publications

(7 citation statements)

References 26 publications

(42 reference statements)

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“…We identify the positions concentrations by using the reciprocity principle respectively with the darcean equations and the advectiondiffusion. As shown on table (6), positions as well as concentrations are identified with a satisfying errors which don't exceed 8%.…”

Section: Multiply Point-source Pollution Identificationmentioning

confidence: 89%

“…Whereas, the required large amount of data, including the full knowledge of concentration and fluxes at the boundaries and interfaces (generally not available), constitutes its main drawback. However, using incomplete data sets remains possible as shown in [6]. These simplified direct identification methods can be used in conjunction with other advanced parameter identification methods.…”

Section: Discussionmentioning

confidence: 99%

“…with N f the number of flow point-source (N f > N p ); T (x, y) the transmissivity field, Q s j the fluid volume flux rate at the j th point-source [T −1 ], h D the prescribed heads at the flow Dirichlet boundary Γ ′ D , Q N the prescribed flux at the remaining flow Neuman boundary Γ ′ N . Note that systems (3) and ( 7) are coupled via the Darcy velocity (6) and that the pollutant point-sources form a sub-set of the pumping point-sources.…”

Section: The Transport and Flow Equations In Porous Mediamentioning

confidence: 99%

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Identification of aquifer pollution’s point sources with the Reciprocity Principle

Hariga¹,

Bouhlila²

2021

Preprint

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The principle of reciprocity, called Maxwell-Bettitheorem, initially used in mechanics in an elastic structure, establishes a relation of equality between two distinct strains under different loads. In this paper, we extend and apply this principle to flow and solute transport equations in porous media, in order to perform the pollution sources identification in aquifers. We developed general 2D expressions of the reciprocity principle for transient transport problems. This model leads to a linear equations set, with point sources coordinates, concentrations and associated water fluxes as unknowns. The proposed model is then applied to the Rocky Mountain Arsenal aquifer, where polluted water is injected into a well in the domain. The proposed inverse technique successfully recovered the position and the pollutant concentration in addition to the associated water flux. Moreover, we developed and implemented the inverse method for different knowledge levels of the degrees of the aquifer contamination, i.e. more or less data available in the field. Multiple pollution point sources and noisy data situations are also developed and tested with high efficiency. The proposed method would be easy and useful to be implemented in the modeling software now widely used by researchers and groundwater managers. It can thus be applied in real case studies, to help authorities and regulators to efficiently identify the polluters and the contamination process i.e. its location, onset, duration and the associated mass and water fluxes.

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Section: Multiply Point-source Pollution Identificationmentioning

confidence: 89%

Section: Discussionmentioning

confidence: 99%

Section: The Transport and Flow Equations In Porous Mediamentioning

confidence: 99%

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Identification of aquifer pollution’s point sources with the Reciprocity Principle

Hariga¹,

Bouhlila²

2021

Preprint

Self Cite

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“…Since not all boundary conditions of this aquifer are known a priori, the data completion method is used to solve the problem. This method has been applied in several fields, including medical diagnosis, remote sensing, traffic studies, and groundwater flow 15 . The data completion method has also been used for marine intrusion problems in 6 , 15 , 16 .…”

Section: Introductionmentioning

confidence: 99%

“…This method has been applied in several fields, including medical diagnosis, remote sensing, traffic studies, and groundwater flow 15 . The data completion method has also been used for marine intrusion problems in 6 , 15 , 16 . In 6 , the authors applied this technique to locate the land-sea interface in a coastal aquifer.…”

Section: Introductionmentioning

confidence: 99%

A data completion method for identifying pollution intrusion in aquifers

Guellouz

Khayat

2022

Sci Rep

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The data completion method combined with the modeling of water flow and solute transport in saturated porous media is used twice to identify the extent of polluted water intrusion from the downstream boundary of an aquifer. The aim of this work is to solve the problem even though data are missing on some of the boundaries, by exploiting the fact that there are over specified data on the other boundaries. Indeed, it is assumed that the flow and the water head are known on the upstream boundary while the pollutant concentrations are known on the downstream boundary. The method developed in this work allows to determine the flows, water heads and pollutant concentrations in the whole domain. The method is applied in different aquifer configurations with pumping wells, the results are satisfactory. The model developed has shown its effectiveness in detecting the intrusion of polluted water and can be used in real cases.

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Identification of aquifer pollution’s point sources with the reciprocity principle

Bouhlila

Hariga²

2022

Sci Rep

Self Cite

View full text Add to dashboard Cite

The principle of reciprocity, called Maxwell–Betti theorem, initially used in mechanics in an elastic structure, establishes a relation of equality between two distinct strains under different loads. In this paper, we extend and apply this principle to flow and solute transport equations in porous media, in order to perform the pollution sources identification in aquifers. We developed general 2D expressions of the reciprocity principle for transient transport problems. This model leads to a linear equations set, with point sources coordinates, concentrations and associated water fluxes as unknowns The proposed model is then applied to the Rocky Mountain Arsenal aquifer (Konikow in Modeling Chloride Movement in the Alluvial Aquifer at the Rocky Mountain Arsenal, Colorado. Technical Report Water-Supply Paper 2044, USGS, 1979), where polluted water is injected into a well in the domain. The used inverse technique successfully recovered the position and the pollutant concentration in addition to the associated water flux. In addition, we developed and implemented the inverse method for different knowledge levels of the degrees of the aquifer contamination, i.e. more or less data available in the field. Multiple pollution point sources and noisy data situations are also developed and tested with high efficiency. The proposed method would be easy and useful to be implemented in the modeling software now widely used by researchers and groundwater managers. It can thus be applied in real case studies, to help authorities and regulators to efficiently identify the polluters and the contamination process, i.e. its location, onset, duration and the associated mass and water fluxes.

show abstract

Data completion problem for the advection‐diffusion equation with aquifer point sources

Cited by 3 publications

References 26 publications

Identification of aquifer pollution’s point sources with the Reciprocity Principle

Identification of aquifer pollution’s point sources with the Reciprocity Principle

A data completion method for identifying pollution intrusion in aquifers

Identification of aquifer pollution’s point sources with the reciprocity principle

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