Semianalytical solutions for contaminant transport under variable velocity field in a coastal aquifer

Koohbor, Behshad; Fahs, Marwan; Ataie-Ashtiani, Behzad; Simmons, Craig T.; Younès, Anis

doi:10.1016/j.jhydrol.2018.03.048

Cited by 6 publications

(9 citation statements)

References 68 publications

(91 reference statements)

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“…Similar to other existing 2‐D semianalytical solutions, we take the dispersion tensor as isotropic and constant. Kalejaiye and Cardoso () and Koohbor et al () showed that this assumption is valid when gravity is the main driving force and Rayleigh number is less than 1,000. Both conditions hold in our study.…”

Section: Problem and Model Statementmentioning

confidence: 99%

A 3‐D Semianalytical Solution for Density‐Driven Flow in Porous Media

Shao

Fahs

Hoteit

et al. 2018

Water Resources Research

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Existing analytical and semianalytical solutions for density-driven flow (DDF) in porous media are limited to 2-D domains. In this work, we develop a semianalytical solution using the Fourier Galerkin method to describe DDF induced by salinity gradients in a 3-D porous enclosure. The solution is constructed by deriving the vector potential form of the governing equations and changing variables to obtain periodic boundary conditions. Solving the 3-D spectral system of equations can be computationally challenging. To alleviate computations, we develop an efficient approach, based on reducing the number of primary unknowns and simplifying the nonlinear terms, which allows us to simplify and solve the problem using only salt concentration as primary unknown. Test cases dealing with different Rayleigh numbers are solved to analyze the solution and gain physical insight into 3-D DDF processes. In fact, the solution displays a 3-D convective cell (actually a vortex) that resembles the quarter of a torus, which would not be possible in 2-D. Results also show that 3-D effects become more important at high Rayleigh number. We compare the semianalytical solution to research (Transport of RadioACtive Elements in Subsurface) and industrial (COMSOL Multiphysics®) codes. We show cases (high Raleigh number) where the numerical solution suffers from numerical artifacts, which highlight the worthiness of our semianalytical solution for code verification and benchmarking. In this context, we propose quantitative indicators based on several metrics characterizing the fluid flow and mass transfer processes and we provide open access to the source code of the semianalytical solution and to the corresponding numerical models. SHAO ET AL.10,094

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Section: Problem and Model Statementmentioning

confidence: 99%

A 3‐D Semianalytical Solution for Density‐Driven Flow in Porous Media

Shao

Fahs

Hoteit

et al. 2018

Water Resources Research

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“…The 3‐D semianalytical solution is developed using the FS method also called Fourier‐Galerkin method (Peyret, 2013). This method has been used to obtain semianalytical solutions for several 2‐D density‐driven flow problems (Fahs et al, 2014, 2015, 2016; Henry, 1964; Koohbor et al, 2018; Segol, 1994; Shao, Fahs, Younes, & Makradi, 2016; Shao, Fahs, Younes, Makradi, et al, 2016; Simpson & Clement, 2003, 2004; van Reeuwijk et al, 2009; Younes & Fahs, 2014, 2015; Zidane et al, 2012). Shao et al (2018) extended the FS method to solve a three‐dimensional solute density‐driven flow problem.…”

Section: The Fs Solutionmentioning

confidence: 99%

A Fourier Series Solution for Transient Three‐Dimensional Thermohaline Convection in Porous Enclosures

Tabrizinejadas

Fahs

Ataie-Ashtiani³

et al. 2020

Water Resources Research

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Thermohaline convection (THC) in porous media is frequently investigated using the problem of porous enclosure. Most of the existing modeling-based studies are limited to 2-D simulations, because 2-D assumption is widely used to deal with computational requirement of 3-D numerical solutions. Analytical solutions serve as an alternative to deal with computational requirement of numerical solutions. Existing analytical solutions of THC are mostly limited to 2-D and also under steady-state regime. In this work, we develop a meshless 3-D semianalytical solution for the problem of THC in a porous box under crossed thermal and solute gradients, for both steady state and transient regimes. The semianalytical solution is developed using the Fourier series (FS) method applied to the vector potential form of the governing equations. The extension to transient solutions represents an important technical feature of this work, as the applications of the FS method to density-driven problems have been limited to steady-state conditions. The FS solution is validated against a finite element solution obtained using COMSOL Multiphysics. Numerical experiments show the worthiness of the developed FS solution as a benchmark because it clearly allows making distinction between different numerical techniques. The effects of governing parameters on three-dimensional THC have not been investigated previously. We perform a detailed parameter sensitivity analysis to address this gap. A vortex convective flow is observed and the orientation and intensity of the flow is sensitive to the gravity number. The increase in the temperature gradient reduces the salinity flux.

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“…With the development of economy of human society, a myriad of coastal hydrogeological, engineering, biochemical, ecological and environmental problems arise. The problems include, for instance, seawater invasion, land subsidence, engineering structures stability and marine environment deterioration [ 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 ]. Among them, the environmental pollution caused by aquaculture is more serious, which is related to the formation of red tide [ 13 ].…”

Section: Introductionmentioning

confidence: 99%

“…In recent years, the laboratory experiment, analytical solution and numerical simulation were used to solve the problem of contamination migration in coastal zones [ 8 , 35 , 36 , 37 , 38 , 39 , 40 , 41 , 42 , 43 , 44 , 45 , 46 ]. The experimental method has been applied earlier to resolve the problem of pollutant migration in coastal aquifer.…”

Section: Introductionmentioning

confidence: 99%

“…In addition, an analytical solution was developed to explain directly the physical process in the ideal situation, in order to verify the model. Koohbor et al [ 8 ] derived semi-analytical solutions describing the pollutant transport in the confined coastal aquifer under the condition of variable velocity field recently. Nevertheless, because of the complexity of boundary conditions, analytical approach can only be used to solve the contaminant transport under simple conditions.…”

Section: Introductionmentioning

confidence: 99%

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Contamination Transport in the Coastal Unconfined Aquifer under the Influences of Seawater Intrusion and Inland Freshwater Recharge—Laboratory Experiments and Numerical Simulations

Guo

Zhao

et al. 2021

IJERPH

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The coupled effect of seawater intrusion and inland freshwater recharge plays an important role in contamination transport in coastal heterogeneous aquifer. In this study, the effects of seawater intrusion and inland recharge on contamination transport were investigated by conducting laboratory experiments and numerical simulations. The laboratory tests were conducted in a sand tank considering two scenarios, namely the conditions of landward and seaward hydraulic gradients. The SEAWAT software was applied for validating the contaminant transport in coastal heterogeneous aquifer. The results indicated that the simulated seawater wedge and contours of the saltwater contaminant matched the observed ones well. The length of the seawater wedge in the scenario of seaward hydraulic gradient was smaller than that in the scenario of landward hydraulic gradient, which reflected that the large quantity of inland recharge have a negative effect on the invasion process of seawater. The plume moved mainly downward in the heterogeneous unconfined aquifer for both scenarios. The pollution plume became concave at the interface between each two layers, which was because the velocity of contaminant plume migration increased gradually from the upper layer to lower layer. The migration direction of the front of the plume was consistent with the direction of hydraulic gradient, which indicated that it was influenced by the water flowing. The maximum area of plume in the scenario of seaward hydraulic gradient was slightly smaller than that in the scenario of landward hydraulic gradient. The maximum area and vertical depth of the pollutant plume were sensitive to the hydraulic conductivity, dispersivity and contamination concentration. This study was of great significance to the controlling of pollution and utilization of freshwater resources in coastal areas.

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Semianalytical solutions for contaminant transport under variable velocity field in a coastal aquifer

Cited by 6 publications

References 68 publications

A 3‐D Semianalytical Solution for Density‐Driven Flow in Porous Media

A 3‐D Semianalytical Solution for Density‐Driven Flow in Porous Media

A Fourier Series Solution for Transient Three‐Dimensional Thermohaline Convection in Porous Enclosures

Contamination Transport in the Coastal Unconfined Aquifer under the Influences of Seawater Intrusion and Inland Freshwater Recharge—Laboratory Experiments and Numerical Simulations

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