scholarly journals Subordinated advection-dispersion equation for contaminant transport

2001 ◽  
Vol 37 (6) ◽  
pp. 1543-1550 ◽  
Author(s):  
Boris Baeumer ◽  
David A. Benson ◽  
Mark M. Meerschaert ◽  
Stephen W. Wheatcraft
Keyword(s):  
Dispersion Equation ◽  
Contaminant Transport ◽  
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.

Using the Fractional Advection Dispersion Equation to Improve the Scale Effect in the Sampling Process of Column Tests with Lateritic Soils

2015 ◽  
Vol 365 ◽  
pp. 188-193 ◽  
Author(s):  
Ricardo Mendonça de Moraes ◽  
André Luís Brasil Cavalcante
Keyword(s):  
Dispersion Equation ◽  
Contaminant Transport ◽  
Dispersion Coefficient ◽  
Breakthrough Curves ◽  
Column Tests ◽  
Lateritic Soils ◽  
Advection Dispersion ◽  
Sampling Process ◽  
Heterogeneous Soil ◽  
Heavy Tailed

Breakthrough curves (BTCs) obtained from column tests in heterogeneous soils are not satisfactorily simulated with the advection-dispersion equation (ADE) for some heavy tailed cases. Furthermore, the dispersion coefficient calculated with the ADE for heavy tailed BTCs are scale dependent when simulating columns of soil larger than the original test depth. In this paper we compare the usage of a fractional ADE (FADE) and the classical ADE to fit column tests BTCs made with Brazilian lateritic soils, discussing both contaminant transport theories and underlying stochastic models. The FADE can more accurately simulate heavy tailed BTCs, and when applying the adjusted FADE parameters to longer depths of soil, the FADE also predicts a more realistic scenario of contaminant transport through heterogeneous soil. The addition of fractional calculus in the advection-dispersion equation proves to improve contaminant transport predictions based on column tests over the classical ADE, with the use of a constant fractional dispersion coefficient that is scale independent.

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