An analytical solution of the convection–dispersion–reaction equation for a finite region with a pulse boundary condition

Ziskind, G.; Shmueli, H.; Gitis, Vitaly

doi:10.1016/j.cej.2010.11.047

Cited by 24 publications

(9 citation statements)

References 17 publications

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“…The advection–dispersion equation (e.g. Chen et al ., , , ; Ziskind et al ., ) is commonly used to describe the physical process governing advective, molecular diffusive and hydrodynamic dispersive transport in unsaturated zone (e.g. Fretwell et al ., ; Van den Daele et al ., ; Rivett et al ., ) and saturated zone (e.g.…”

Section: Introductionmentioning

confidence: 99%

Modelling of the groundwater flow and of tracer movement in the porous and fissured media: Chalk Aquifer (Northern part of Paris Basin, France)

et al. 2016

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A groundwater flow model has been developed in order to study the chalk aquifer of Paris Basin, based on most of the geological and hydrological available data. The numerical processes are intended to modelling the groundwater flow in the Senonian (Late Cretaceous) formations and to visualize the tracer movement in groundwater resources in the experimental site of LaSalle Beauvais (northern part Paris Basin). Both objectives were achieved as follows: (i) the comprehension of the spatial distribution of the hydraulic conductivity in the chalk aquifer taking into account the characteristics of the hydrogeological system and (ii) the use of the analytical solution for describing one‐dimensional to two‐dimensional solute transport in a unidirectional steady‐state flow tracer with scale‐dependent dispersion. Advection and diffusion mechanisms are taken into account. Comparison between the breakthrough curves of the analytical and the numerical solutions provided an excellent agreement for various ranges of scale‐related transport parameters of interest. The developed power series solution facilitates fast prediction of the breakthrough curves at each observation point. Thus, the derived new solutions are widely applicable and are very useful for the validation of numerical transport. The numerical approach is carried out by MT3DMS, a Modular 3‐D Multi‐Species Transport Model for Simulation of Advection, Dispersion, and Chemical Reactions of Contaminants in Groundwater Systems, and based on total variation‐diminishing method using the ULTIMATE algorithm. The estimation of the infected surface could constitute an approach in water management and allows to prevent the risks of pollution and to manage the groundwater resource from a durable development perspective. Copyright © 2016 John Wiley & Sons, Ltd.

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Section: Introductionmentioning

confidence: 99%

Modelling of the groundwater flow and of tracer movement in the porous and fissured media: Chalk Aquifer (Northern part of Paris Basin, France)

et al. 2016

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“…For t>t 0 , we have the following boundary conditions: c(0,t)= f (t) and, at the outflow, we assume continuous concentration, forcing an homogeneous Neumann exit, which is also referred to as Danckwerts condition in finite transport domains [2,5,7]. Assuming that f (t) is time periodic and has a Fourier representation, we may consider that Eq.…”

Section: Analytic Solution For the 1d Transient Problemmentioning

confidence: 99%

“…Among them, it can be found in the works by van Genuchten and Alves [6], Logan and Zlotnik [4], Logan [3], Goltz and Dorroh [2], Ziskind et al [7], Chen and Liu [1] and Pérez Guerrero et al [5], analytical solutions pertaining to time varying boundary conditions, which is of practical interest to many fields as hydrogeology, pollution dispersion and process industry.…”

Section: Introductionmentioning

confidence: 99%

Multidimensional Unsteady Solutions to the Convection-Diffusion-Reaction Equation with a Time Dependent Boundary Condition

Filho¹,

Mangiavacchi²

2017

Proceeding Series of the Brazilian Society of Computational and Applied Mathematics

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Abstract. This paper provides analytical solutions to one, two and three-dimensional convection-diffusion equation with decay term, subjected to a time dependent and periodic boundary condition. These solutions are suitable benchmarks to asses the correctness of computational codes implemented for the problems of multidimensional reactive flows, which are of considerable interest to many fields of science and engineering. Tests are illustrated through computational codes and is remarked the feature of representing periodic oscillations in all dimensions considered.

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“…Up to the present, as in the works cited above, this indeterminacy is treated either by considering that the outlet concentration gradients are zero, which may be physically unrealistic (Ziskind et al, 2011), or by using Robin type BCs, best suited to represent inlet conditions.…”

Section: Scopementioning

confidence: 99%

“…These solutions assume either prescribed or Neumann's outlet BCs mostly at semi-infinite domains. Moreover, even the solutions for finite domains that accept one or other of those BC are subjected to criticism (Ziskind, 2011).…”

Section: Mathematical Formulationmentioning

confidence: 99%

Simulation of species concentration distribution in reactive flows with unsteady boundary conditions

Filho

Mangiavacchi

Pontes

2017

Braz. J. Chem. Eng.

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-The determination of species concentration profiles in reactive flows with variable inlets is a problem of practical interest to many fields such as in flow reactor transient operation and in cyclic degradable pollutants disposals in watercourses. In these cases, the inflow condition often consists of a time-dependent function, which may imply unsteady outflows, not always well represented by the usual boundary conditions (BC) used so far. A new approach, using an outlet condition in the form of a material derivative, termed Material Derivative Boundary Condition (MDBC), is introduced and a numerical model to solve convection-diffusion-reaction equations in twodimensional (2-D) incompressible flows is developed. Upon reviewing the literature, it is noted that the Finite Element Method (FEM) is rarely used in the simulation of reactive flows, in spite of its ability of consistently coping with variable BCs. The above facts are reasons to explore its use along with a semi-discrete formulation with the Galerkin Method in our simulations. Results are obtained for various conditions, in order to show features of the code, and are compared to existing solutions. Use of the MDBC is shown to provide a better approximation of the exit concentrations and use of FEM in reactive flows is further enhanced.

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An analytical solution of the convection–dispersion–reaction equation for a finite region with a pulse boundary condition

Cited by 24 publications

References 17 publications

Modelling of the groundwater flow and of tracer movement in the porous and fissured media: Chalk Aquifer (Northern part of Paris Basin, France)

Modelling of the groundwater flow and of tracer movement in the porous and fissured media: Chalk Aquifer (Northern part of Paris Basin, France)

Multidimensional Unsteady Solutions to the Convection-Diffusion-Reaction Equation with a Time Dependent Boundary Condition

Simulation of species concentration distribution in reactive flows with unsteady boundary conditions

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