Analytical solution of the solute transport equation for the binary homovalent ion exchange in groundwater

doi:10.1016/0022-1694(95)02901-X

Journal of Hydrology

Volume 180, Issues 1–4, 15 May 1996, Pages 139-153

https://doi.org/10.1016/0022-1694(95)02901-X Get rights and content

Abstract

A binary homovalent ion exchange transport model governed by local chemical equilibrium is considered for a one-dimensional, steady flow in a homogeneous soil column. An analytical solution of the aqueous concentration distribution for the convex exchange is obtained by applying nonlinear shock wave theory. The main nonlinear feature is the breaking of fronts into shock waves. The corresponding mathematical theory is the method of characteristics with a special treatment of shock waves. The wave velocity and front thickness are also obtained to illustrate the front propagation and structure. The derivation of the solution presented may offer a wide range of application opportunities and may also provide a good approach for solving the binary heterovalent exchange transport model.

References (18)

H. Rhee et al.
A study of the shock layer in equilibrium exchange systems
Chem. Eng. Sci.
(1971)
M.J. Ablowitz et al.
The evolution of multi-phase modes for nonlinear dispersive waves
Stud. Appl. Math.
(1970)
J. Bear
Dynamics of Fluids in Porous Media
(1972)
G.H. Bolt
Movement of solutes in soil: principles of adsorption/exchange chromatography
W.J. Bond et al.
Approximate solutions for cation transport during unsteady, unsaturated soil water flow
Water Resour. Res.
(1990)
R.J. Charbeneau
Groundwater contaminant transport with adsorption and ion exchange chemistry: method of characteristics for the case without dispersion
Water Resour. Res.
(1981)
R.J. Charbeneau
Multicomponent exchange and subsurface solute transport: characteristics, coherence, and the Riemann problem
Water Resour. Res.
(1988)
P.A. Domentico et al.
Physical and Chemical Hydrogeology
(1990)
W. Dou
Modeling of transport of ion exchange solutes in groundwater

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Cited by (4)

An analytical approach to transient homovalent cation exchange problems
2009, Journal of Hydrology
Cation exchange in groundwater is one of the dominant surface reactions that occurs in nature and it carries with it many important environmental implications. The mass transfer of cation exchanging pollutants in groundwater can be described by a series of coupled partial differential equations, involving both aqueous and adsorbed species. The resulting system is mathematically challenging due to the complex nonlinearities that arise, which in turn complicates analytical approaches. While some analytical solutions for simplified problems exist, these typically lack the mechanisms that allow the waters to change their global chemical signature (in terms of total cations present in aqueous form) over time. We propose a methodology to solve the problem of exchanging two homovalent cations by deriving the driving equation for one of the aqueous species. This equation incorporates explicitly a retardation factor and a decay term, both with parameters that can vary in space and time. While the full solution can only be obtained numerically, we provide a solution in terms of a perturbative approach, where the leading terms can be obtained explicitly. The resulting solution provides physical explanations for the possible existence of non-monotonic concentrations for a range of parameters governing cation exchange processes.
A semi-analytical solution for linearized multicomponent cation exchange reactive transport in groundwater
2007, Transport in Porous Media
Analytical solution for monovalent-divalent ion exchange transport in groundwater
1999, Canadian Geotechnical Journal
Analytical solution for monovalent-divalent ion exchange transport in groundwater
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Research paperAnalytical solution of the solute transport equation for the binary homovalent ion exchange in groundwater

Abstract

Chem. Eng. Sci.

The evolution of multi-phase modes for nonlinear dispersive waves

Stud. Appl. Math.

Dynamics of Fluids in Porous Media

Movement of solutes in soil: principles of adsorption/exchange chromatography

Approximate solutions for cation transport during unsteady, unsaturated soil water flow

Water Resour. Res.

Groundwater contaminant transport with adsorption and ion exchange chemistry: method of characteristics for the case without dispersion

Water Resour. Res.

Multicomponent exchange and subsurface solute transport: characteristics, coherence, and the Riemann problem

Water Resour. Res.

Physical and Chemical Hydrogeology

Modeling of transport of ion exchange solutes in groundwater

Research paper
Analytical solution of the solute transport equation for the binary homovalent ion exchange in groundwater