Analytical solutions of the advection-dispersion equation for transient groundwater flow. A numerical validation

2008 ◽  
Vol 22 (17) ◽  
pp. 3500-3506 ◽  
Author(s):  
Erick Carlier
Keyword(s):  
Groundwater Flow ◽  
Dispersion Equation ◽  
Analytical Solutions ◽  
Numerical Validation ◽  
Advection Dispersion

scholarly journals Exact analytical solutions for contaminant transport in rivers 1. The equilibrium advection-dispersion equation

2013 ◽  
Vol 61 (2) ◽  
pp. 146-160 ◽  
Author(s):  
Martinus Th. van Genuchten ◽  
Feike J. Leij ◽  
Todd H. Skaggs ◽  
Nobuo Toride ◽  
Scott A. Bradford ◽  
...  
Keyword(s):  
Surface Water ◽  
Dispersion Equation ◽  
Contaminant Transport ◽  
Analytical Solutions ◽  
Decay Chain ◽  
Transport Processes ◽  
Dispersive Transport ◽  
Chain Reactions ◽  
Surface Water Hydrology ◽  
Advection Dispersion

Abstract Analytical solutions of the advection-dispersion equation and related models are indispensable for predicting or analyzing contaminant transport processes in streams and rivers, as well as in other surface water bodies. Many useful analytical solutions originated in disciplines other than surface-water hydrology, are scattered across the literature, and not always well known. In this two-part series we provide a discussion of the advection-dispersion equation and related models for predicting concentration distributions as a function of time and distance, and compile in one place a large number of analytical solutions. In the current part 1 we present a series of one- and multi-dimensional solutions of the standard equilibrium advection-dispersion equation with and without terms accounting for zero-order production and first-order decay. The solutions may prove useful for simplified analyses of contaminant transport in surface water, and for mathematical verification of more comprehensive numerical transport models. Part 2 provides solutions for advective- dispersive transport with mass exchange into dead zones, diffusion in hyporheic zones, and consecutive decay chain reactions.

scholarly journals Exact Analytical Solutions for Contaminant Transport in Rivers

2013 ◽  
Vol 61 (3) ◽  
pp. 250-259 ◽  
Author(s):  
Martinus Th. van Genuchten ◽  
Feike J. Leij ◽  
Todd H. Skaggs ◽  
Nobuo Toride ◽  
Scott A. Bradford ◽  
...  
Keyword(s):  
Dispersion Equation ◽  
Contaminant Transport ◽  
Analytical Solutions ◽  
Hyporheic Zone ◽  
Decay Chain ◽  
Transport Processes ◽  
Dispersive Transport ◽  
Chain Reactions ◽  
First Order ◽  
Advection Dispersion

Abstract Contaminant transport processes in streams, rivers, and other surface water bodies can be analyzed or predicted using the advection-dispersion equation and related transport models. In part 1 of this two-part series we presented a large number of one- and multi-dimensional analytical solutions of the standard equilibrium advection-dispersion equation (ADE) with and without terms accounting for zero-order production and first-order decay. The solutions are extended in the current part 2 to advective-dispersive transport with simultaneous first-order mass exchange between the stream or river and zones with dead water (transient storage models), and to problems involving longitudinal advectivedispersive transport with simultaneous diffusion in fluvial sediments or near-stream subsurface regions comprising a hyporheic zone. Part 2 also provides solutions for one-dimensional advective-dispersive transport of contaminants subject to consecutive decay chain reactions.

scholarly journals Generalized Analytical Solutions of The Advection-Dispersion Equation with Variable Flow and Transport Coefficients

2021 ◽  
Vol 13 (14) ◽  
pp. 7796
Author(s):  
Abhishek Sanskrityayn ◽  
Heejun Suk ◽  
Jui-Sheng Chen ◽  
Eungyu Park
Keyword(s):  
Dispersion Equation ◽  
Analytical Solutions ◽  
Numerical Solutions ◽  
Transient Flow ◽  
Dispersion Coefficient ◽  
Transport Coefficients ◽  
Variable Coefficients ◽  
Dispersion Coefficients ◽  
Transform Method ◽  
Advection Dispersion

Demand has increased for analytical solutions to determine the velocities and dispersion coefficients that describe solute transport with spatial, temporal, or spatiotemporal variations encountered in the field. However, few analytical solutions have considered spatially, temporally, or spatiotemporally dependent dispersion coefficients and velocities. The proposed solutions consider eight cases of dispersion coefficients and velocities: both spatially dependent, both spatiotemporally dependent, both temporally dependent, spatiotemporally dependent dispersion coefficient with spatially dependent velocity, temporally dependent dispersion coefficient with constant velocity, both constant, spatially dependent dispersion coefficient with spatiotemporally dependent velocity, and constant dispersion coefficient with temporally dependent velocity. The spatial dependence is linear, while the temporal dependence may be exponential, asymptotical, or sinusoidal. An advection–dispersion equation with these variable coefficients was reduced to a non-homogeneous diffusion equation using the pertinent coordinate transform method. Then, solutions were obtained in an infinite medium using Green’s function. The proposed analytical solutions were validated against existing analytical solutions or against numerical solutions when analytical solutions were unavailable. In this study, we showed that the proposed analytical solutions could be applied for various spatiotemporal patterns of both velocity and the dispersion coefficient, shedding light on feasibility of the proposed solution under highly transient flow in heterogeneous porous medium.

scholarly journals How to use solutions of Advection-Dispersion Equation to describe reactive solute transport through porous media

2021 ◽  
Vol 60 (3) ◽  
pp. 229-240
Author(s):  
Jetzabeth Ramírez Sabag ◽  
Dennys Armando López Falcón
Keyword(s):  
Boundary Condition ◽  
Porous Media ◽  
Solute Transport ◽  
Dispersion Equation ◽  
Analytical Solutions ◽  
Peclet Number ◽  
Reactive Solute Transport ◽  
Péclet Number ◽  
Advection Dispersion ◽  
Outlet Boundary Condition

ResumenLas soluciones de la Ecuación de Advección-Dispersión son usadas frecuentemente para describir el transporte de solutos a través de medios porosos, considerando adsorción en equilibrio, de tipo lineal y reversible. Para indicar algunas sugerencias acerca de este tema, se hizo una revisión de las soluciones analíticas disponibles. Hay soluciones para Problemas con Condiciones de Frontera, de primer y tercer-tipo en la entrada así como de primer y segundo-tipo a la salida. Se analiza el comportamiento de las soluciones equivalentes, para sistemas finitos y semi-infinitos, observando que las soluciones de los sistemas semi-infinitos se aproximan a las correspondientes de los sistemas finitos conforme la condición de frontera de salida en el infinito se aproxima a la ubicación de medición del sistema finito. Solamente se presentan las soluciones analíticas con condiciones de frontera de segundo-tipo a la salida, ya que son iguales a las correspondientes soluciones analíticas con frontera de primer-tipo a la salida, para ambos tipos de condiciones de frontera de entrada usadas. Un análisis paramétrico, basado en el número de Peclet, muestra que todas las soluciones convergen cuando el número de Peclet es mayor que veinte. Los sistemas investigados deben tener un número de Peclet mayor que cinco para usar con confianza las soluciones de la Ecuación de Advección-Dispersión para describir el transporte de soluto en medios porosos.Palabras Clave: Ecuación de Advección-Difusión, Soluciones Analíticas, Transporte de Solutos Reactivos, Medios Porosos.AbstractThe solutions of Advection-Dispersion Equation are frequently used to describe solute transport through porous media when considering lineal and reversible equilibrium adsorption. To notice some warnings about this item, a review of analytical solutions available was done. There are solutions for Boundary Value Problems with first and third-type inlet boundary conditions as well as first and second-type outlet boundary condition. The behavior of equivalent solutions for finite and semi-infinite systems are analyzed, observing that semi-infinite system solutions approximates to the corresponding finite ones as the “infinite” outlet boundary condition approach to the finite measurement location. Because the analytical solutions with a first-type outlet boundary condition are equal to the corresponding analytical solutions with a second-type one, for both inlet boundary condition type used, only the latter is presented. A parametric analysis based on Peclet number shows that all solutions converge for Peclet number greater than twenty. Systems under research must have Peclet number greater than five to use confidently the solutions of Advection-Dispersion Equation to describe reactive solute transport through porous media.Keywords: Advection-Diffusion Equation, Analytical solutions, Reactive Solute Transport, Porous Media.

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