Analytical Solution for One-Dimensional Solute Dispersion with Time-Dependent Source Concentration along Uniform Groundwater Flow in a Homogeneous Porous Formation

Singh, Mritunjay Kumar; Ahamad, Shafique; Singh, Vijay P.

doi:10.1061/(asce)em.1943-7889.0000384

Cited by 23 publications

(10 citation statements)

References 2 publications

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“…Numerically, finite difference and finite element methods are the common approaches implemented by researchers (Doussan et al, 1998;Kim, 2006;Kim et al, 2003;Malaguerra et al, 2013). Alternately, Laplace and Fourier transforms are normally used to analytically estimate solute transport in aquifers (Chen, 2010;Chen et al, 2012;Connell, 2007;Singh et al, 2012;Singh, 2013). Bessel function expansion and the Hankel transform have been found to be the most appropriate analytical techniques for problems formulated with equations expressed in polar and cylindrical coordinates (Massab o et al, 2006;Singh et al, 2010a).…”

Section: Introductionmentioning

confidence: 99%

Modelling contaminant transport for pumping wells in riverbank filtration systems

Mustafa¹,

Bahar

Aziz

et al. 2016

Journal of Environmental Management

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Section: Introductionmentioning

confidence: 99%

Modelling contaminant transport for pumping wells in riverbank filtration systems

Mustafa¹,

Bahar

Aziz

et al. 2016

Journal of Environmental Management

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“…Numerous analytical solutions have been developed for modeling solute transport through fully-saturated aquifers [5][6][7][8][9][10][11][12][13][14][15][16][17]. However, there are some shortcomings associated with them.…”

Section: Introductionmentioning

confidence: 99%

Modeling Transport and Adsorption of Arsenic Ions in Iron-Oxide Laden Porous Media. Part I: Theoretical Developments

Pillai

Raizada

2021

Water

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The process of transport and trapping of arsenic ions in porous water filters is treated as a classic mass transport problem which, at the pore scale, is modeled using the traditional convection-diffusion equation, representing the migration of species present in very small (tracer) amounts in water. The upscaling, conducted using the volume averaging method, reveals the presence of two possible forms of the macroscopic equations for predicting arsenic concentrations in the filters. One is the classic convection-dispersion equation with the total dispersion tensor as its main transport coefficient, and which is obtained from a closure formulation similar to that of the passive diffusion problem. The other equation form includes an additional transport coefficient, hitherto ignored in the literature and identified here as the adsorption-induced vector. These two coefficients in the latter form are determined from a system of two closure problems that include the effects of both the passive diffusion as well as the adsorption of arsenic by the solid phase of the filter. This theoretical effort represents the first serious effort to introduce a detailed micro–macro coupling while modeling the transport of arsenic species in water filters representing homogeneous porous media.

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“…1 Chen et al in 2012 analytically solved advective-dispersive, multispecies, coupled transport equations. 2 Singh et al had demonstrated one-dimensional contaminant transport equation having time-dependent dispersive coefficient in a semi-infinite homogeneous porous medium in Singh et al 3 Francisca et al studied the hydraulic conductivity of porous medium in soils. 4 Later in 2013, Guerrero et al proposed the solution for the diffusive concentration transport problems by employing transient boundary conditions and using Duhamel's principle.…”

Section: Introductionmentioning

confidence: 99%

Study of one‐dimensional contaminant transport in soils using fractional calculus

Mirza

Akram

Akhtar

et al. 2021

Math Methods in App Sciences

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In this communication, the soil contamination transport phenomenon is studied using fractional calculus. Specifically, a variant of non‐integer fractional derivative known as Antangana–Baleanu fractional derivative is applied on one‐dimensional advection diffusion equation to obtain a fractional model for the contaminant transport in soils. This fractional model is examined under the hypothesis of initial and generalized Robin type boundary conditions. The analytical expression of solution for contaminant transport in soil is derived for the fractional initial‐boundary value problem for partial differential equation (PDE) of mixed type using integral transforms, namely, Laplace and finite sine–cosine Fourier transforms. The solution of the ordinary advection diffusion equation arises as a case of the obtained solution. The numerical results are obtained for initial concentrated loading and Heaviside unit step function as a boundary conditions, from the analytical solution for various parameters of interest, and the corresponding graphs are plotted with the help of software MATHCAD. The graphs illustrate that the memory effects are remarkable for small values of time and ordinary for large values of the time.

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Analytical Solution for One-Dimensional Solute Dispersion with Time-Dependent Source Concentration along Uniform Groundwater Flow in a Homogeneous Porous Formation

Cited by 23 publications

References 2 publications

Modelling contaminant transport for pumping wells in riverbank filtration systems

Modelling contaminant transport for pumping wells in riverbank filtration systems

Modeling Transport and Adsorption of Arsenic Ions in Iron-Oxide Laden Porous Media. Part I: Theoretical Developments

Study of one‐dimensional contaminant transport in soils using fractional calculus

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