Abstract:Abstract:In this study, analytical models for predicting groundwater contamination in isotropic and homogeneous porous formations are derived. The impact of dispersion and diffusion coefficients is included in the solution of the advection-dispersion equation (ADE), subjected to transient (time-dependent) boundary conditions at the origin. A retardation factor and zero-order production terms are included in the ADE. Analytical solutions are obtained using the Laplace Integral Transform Technique (LITT) and the… Show more
“…At the initial moment it is assumed that the aquifer is contaminated, a certain initial background concentration exists in the aquifer and it is represented by a linear combination of an initial concentration and the term of zero order production with rapid infiltration given by equation (11) : Where is the initial background concentration, is flow velocity, and γ is the zero order production rate coefficient for liquid phase solute production. A contaminant in radioactive waste decaying exponentially with time is imposed upon entering the aquifer as a linear combination of a source concentration with an initial background concentration at the origin, to describe the transport of solutes in a natural or artificial system as expressed by equation (12) ( Das et al, 2017 ; Singh et al, 2021 ): λ is the decay rate constant and is the flow velocity of fluids in the porous medium. Figure 4 Geometry of the problem.…”
Section: Methodsmentioning
confidence: 99%
“…An unconditionally stable Crank-Nicolson finite difference scheme was used by Ravi et al (2014) to analyze the constant and longitudinal dispersion profile of contaminants. In his studies, Ravi et al (2014) did not take into account the time-dependent dispersions coefficients, the decay rate constant and the zero-order production rate coefficient of solute in the liquid phase as done by Das et al (2017) , Guleria et al (2020) with a linear dispersion advection equation model. Our objective is to exploit the more stable fourth-order Runge-Kutta method (RK4) to evaluate the profile of C (X, T) contaminants through a porous medium and to conduct a comparative study between the profiles of the contaminants obtained from an asymptotic and linear dispersion coefficient, and on the other hand, from the initial and boundary conditions used in the work of Das et al (2017) .…”
“…At the initial moment it is assumed that the aquifer is contaminated, a certain initial background concentration exists in the aquifer and it is represented by a linear combination of an initial concentration and the term of zero order production with rapid infiltration given by equation (11) : Where is the initial background concentration, is flow velocity, and γ is the zero order production rate coefficient for liquid phase solute production. A contaminant in radioactive waste decaying exponentially with time is imposed upon entering the aquifer as a linear combination of a source concentration with an initial background concentration at the origin, to describe the transport of solutes in a natural or artificial system as expressed by equation (12) ( Das et al, 2017 ; Singh et al, 2021 ): λ is the decay rate constant and is the flow velocity of fluids in the porous medium. Figure 4 Geometry of the problem.…”
Section: Methodsmentioning
confidence: 99%
“…An unconditionally stable Crank-Nicolson finite difference scheme was used by Ravi et al (2014) to analyze the constant and longitudinal dispersion profile of contaminants. In his studies, Ravi et al (2014) did not take into account the time-dependent dispersions coefficients, the decay rate constant and the zero-order production rate coefficient of solute in the liquid phase as done by Das et al (2017) , Guleria et al (2020) with a linear dispersion advection equation model. Our objective is to exploit the more stable fourth-order Runge-Kutta method (RK4) to evaluate the profile of C (X, T) contaminants through a porous medium and to conduct a comparative study between the profiles of the contaminants obtained from an asymptotic and linear dispersion coefficient, and on the other hand, from the initial and boundary conditions used in the work of Das et al (2017) .…”
“…Second, the sorption related to concentration shock fronts and rarefactions is avoided (Sheng and Smith 1999;Malaguerra et al 2013). This simplification of calculation is a common assumption in reactive transport modeling (Henderson et al 2009;Malaguerra et al 2013;Das et al 2017 as follows (Hunt 1999):…”
Analytical studies for well design adjacent to river banks are the most significant practical task in cases involving the efficiency of riverbank filtration systems. In times when high pollution of river water is joined with increasing water demand, it is necessary to design pumping wells near the river that provide acceptable amounts of river water with minimum contaminant concentrations. This will guarantee the quality and safety of drinking water supplies. This article develops an analytical solution based on the Green's function approach to solve an inverse problem: based on the required level of contaminant concentration and planned pumping time period, the shortest distance to the riverbank that has the maximum percentage of river water is determined. This model is developed in a confined and homogenous aquifer that is partially penetrated by the stream due to the existence of clogging layers. Initially, the analytical results obtained at different pumping times, rates and with different values of initial concentration are checked numerically using the MODFLOW software. Generally, the distance results obtained from the proposed model are acceptable. Then, the model is validated by data related to two pumping wells located at the first riverbank filtration pilot project conducted in Malaysia.
“…7 In 2017, Das et al had performed modeling of ground water contamination by solving advection diffusion equation using robin boundary conditions. 8 A considerable dedication has been imparted towards the bulk transport of solutes, modeling with the mathematical phenomenon of advection diffusion equation. The bulk transport of pollutants is carried by advective moving aqueous chemical particles with the fluid flow.…”
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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