A spectral modelling approach for fluid flow into a line sink in a confined aquifer

Al-Ali, Suha Ibrahim Salih; Hocking, Graeme C.; Farrow, Duncan E.; Zhang, Hong

doi:10.1017/s0956792521000310

Cited by 4 publications

(5 citation statements)

References 15 publications

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“…The steady-state profile gave useful insights into the aquifer's behaviour and allowed for estimating the surface profile under steady-state flow conditions. The alignment between this work and other works [20] on similar systems validates the current findings. For the steadystate flow analysis, it was assumed that the effect of the function ζ(x) on the water surface y=z was negligible.…”

Section: Outcomes and Discussionsupporting

confidence: 90%

Linear Free Surface of Steady and Unsteady Flow Theoretical Study

AL-Ali,

AL-Awsi

2024

Tikrit J. Pure Sci.

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This study investigates the relationship between the crucial cone point in limiting steady and unsteady simulation flows inside a simple two-dimensional, vertical sand column subjected to water withdrawal. The analysis employs a versatile technique applicable to both linear steady and linear unsteady problems. By utilizing Fourier series techniques, the method finds the solution for a line sink in a vertical duct and extends the steady technique to achieve unsteady solutions. The evolution of the beneath-the-water table surface towards steady states is monitored when they exist. The key findings highlight that as the impermeable base moves further away, the distance between the interface and the sink increases. With increasing flow rates, the critical depth elevates; however, a minor decrease in the critical flow rate is observed when the sink approaches the base. The prior behaviour of the flow impacts the critical flow rate value for each interface height. The study provides steady and unsteady solutions, employing linearized formulations, which demonstrate good agreement with observed phenomena. The length scale of the spatial separation between the interface and the sink emerges as a critical factor in determining cone. These findings contribute to a better understanding of cone phenomena and emphasize the significance of considering specific dimensions in the analysis of flow dynamics within porous media.

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Section: Outcomes and Discussionsupporting

confidence: 90%

Linear Free Surface of Steady and Unsteady Flow Theoretical Study

AL-Ali,

AL-Awsi

2024

Tikrit J. Pure Sci.

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“…In the present study, the problem is investigated numerically using a finite-element modelling package, COMSOL Multiphysics [11], which has been employed to solve various partial differential equations in engineering fields [1, 5, 12, 24, 31]. The impacts of the dimensions of the apparatus and the soil properties on the dispersion of density-dependent solute transport in porous media are analysed numerically.…”

Section: Introductionmentioning

confidence: 99%

Numerical Analysis of Apparatus-Induced Dispersion for Density-Dependent Solute Transport in Porous Media

ZHANG,

BARRY,

SEYMOUR

et al. 2023

ANZIAM J.

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The effects of apparatus-induced dispersion on nonuniform, density-dependent flow in a cylindrical soil column were investigated using a finite-element model. To validate the model, the results with an analytical solution and laboratory column test data were analysed. The model simulations confirmed that flow nonuniformities induced by the apparatus are dissipated within the column when the distance to the apparatus outlet exceeds $3R/2$ , where R represents the radius of the cylindrical column. Furthermore, the simulations revealed that convergent flow in the vicinity of the outlet introduces additional hydrodynamic dispersion in the soil column apparatus. However, this effect is minimal in the region where the column height exceeds $3R/2$ . Additionally, it is found that an increase in the solution density gradient during the solute breakthrough period led to a decrease in flow velocity, which stabilized the flow and ultimately reduced dispersive mixing. Overall, this study provides insights into the behaviour of apparatus-induced dispersion in nonuniform, density-dependent flow within a cylindrical soil column, shedding light on the dynamics and mitigation of flow nonuniformities and dispersive mixing phenomena.

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“…Henry [17] developed steady-state solutions for a 2D seawater intrusion model that subsequently served as a benchmark for the evaluation of seawater intrusion models. Various modelling packages have been developed using different numerical techniques, including the finite element method (FEM) [13,18], finite difference method (FDM) [19,20], and spectral method [21]. The vulnerability and sustainability of groundwater facing saltwater intrusion can be predicted via the models [22], and numerical models have therefore become an increasingly important decision support tool for sustainable coastal planning and management [4,23].…”

Section: Introductionmentioning

confidence: 99%

“…The FEM cannot reach the accuracy of analytical solutions or the BEM, but it offers the widest application. COMSOL Multiphysics [38] is one of the finite-element modelling packages that is widely utilized for solving various partial differential equations in engineering fields [21,36,37]. It features high flexibility in combining different physics as required in complex problems like saltwater intrusion.…”

Section: Introductionmentioning

confidence: 99%

Comparing Darcy’s Law and the Brinkman Equation for Numerical Simulations of Saltwater Intrusion

Yao,

Zhang

2023

Sustainability

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Saltwater intrusion into coastal aquifers presents a significant global challenge to fresh groundwater resources. Numerical modelling represents a valuable tool to study this phenomenon. Darcy’s Law is widely applied to groundwater studies and is extended into the Brinkman Equation to account for kinetic dissipations due to viscous shear. However, their comparative performance and accuracy in density-driven flows remain unclear. To determine the circumstances where the Brinkman Equation is required, numerical simulations with both models were implemented in hypothetical coastal aquifer scenarios. The results revealed that the largest discrepancies between the two models occur inside the dispersion zone during the break-through period, with concentration differences of up to 2.5%. The mixing of freshwater and saltwater induces rapid density and velocity variations. Brinkman’s viscous term moderates the rate of change and decreases the intrusion length by up to 6.1 m in a 180 m intrusion case. Furthermore, higher permeability and a lower recharge rate both strengthen the viscous effects in most sandy coastal aquifers. The Brinkman Equation excels at capturing intricate flow patterns with large variations. Therefore, it is necessary to be employed for studies on freshwater–saltwater interfaces and other similar conditions including groundwater–surface water interfaces, non-isothermal flows, and complex geological conditions.

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A spectral modelling approach for fluid flow into a line sink in a confined aquifer

Cited by 4 publications

References 15 publications

Linear Free Surface of Steady and Unsteady Flow Theoretical Study

Linear Free Surface of Steady and Unsteady Flow Theoretical Study

Numerical Analysis of Apparatus-Induced Dispersion for Density-Dependent Solute Transport in Porous Media

Comparing Darcy’s Law and the Brinkman Equation for Numerical Simulations of Saltwater Intrusion

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