Analytical solution for one-dimensional advection–dispersion transport equation with distance-dependent coefficients

Based on the one-dimensional Biot consolidation equations, this paper developed an advection-diffusion equation that incorporates saturation, compressibility of the pore fluid and longitudinal dispersivity of the solute transport in an unsaturated, deforming porous medium. A simplified model was proposed for the case of a landfill liner. Numerical results demonstrated that the longitudinal dispersivity and compressibility of the pore fluid can be significant. Furthermore, the degree of soil saturation and loading rate of the waste surcharge affect significantly the contamination advective emission, namely the cumulative contaminant mass outflow per unit area from compacted clay liner (CCL) due to advective flow.

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“…Some analytical solutions for solute transport in porous media without a geomembrane are available [26,27,28].…”

Section: Application To a Landfill Profilementioning

confidence: 99%

Solute transport in partially-saturated deformable porous media: Application to a landfill clay liner

Zhang

Jeng

Seymour

et al. 2012

Advances in Water Resources

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“…Huang et al (2006) employed a parabolic distance-dependent dispersivity in a finite column. Guerrero and Skaggs (2010) analysed the analytical solution for the advection-dispersion equation with the distance-dependent coefficient using the generalised integral transform technique (GITT). Chen et al (2012) presented a novel method for solving analytically multi-species advectivedispersive transport equations sequentially coupled with firstorder decay reactions.…”

Section: Introductionmentioning

confidence: 99%

Mathematical modeling of groundwater contamination with varying velocity field

Das

Begam

Singh

2017

Journal of Hydrology and Hydromechanics

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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 concept of linear isotherm. For illustration, analytical solutions for linearly space-and time-dependent hydrodynamic dispersion coefficients along with molecular diffusion coefficients are presented. Analytical solutions are explored for the Peclet number. Numerical solutions are obtained by explicit finite difference methods and are compared with analytical solutions. Numerical results are analysed for different types of geological porous formations i.e., aquifer and aquitard. The accuracy of results is evaluated by the root mean square error (RMSE).

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“…Fox and Lee (2008) discussed the problem of large strain consolidation and solute coupled migration process, which analyzed the movement of fluid particles and solid particle in the Lagrangian coordinate system. Based on one-dimensional linear convection-diffusion equation of contaminants, Guerrero and Skaggs (2010) established analytical solutions with variable coefficients in heterogeneous porous media. Li and Cleall (2010) also presented analytical solutions for conservative solute diffusion in one-dimensional double-layered porous media, which are suitable for various combinations of fixed solute concentration and zero-flux boundary conditions.…”

Section: Introductionmentioning

confidence: 99%

The transport processes of soluble contaminant in unsaturated soils under pond infiltration

Nie

Bai

et al. 2016

JGS Special Publication

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A convection-diffusion transport model of soluble contaminant suitable for one-dimensional homogeneous unsaturated three-layered soils is established. The transport processes of soluble contaminant are analyzed by a semi-analytical method, which takes into account the boundary conditions of pond infiltration. Various combined soil layers and various absorption models (e.g. linear or nonlinear adsorption) are discussed. Studies show that, under pond infiltration, the immigration velocity in coarse grained soil will be greater than that in fine grained soil; furthermore the diffusion ratio of the former will also be higher than the latter. Besides, the influence of initial pressure head on immigration velocity can be neglected; however the concentration peaks of contaminant will increase with the decrease of initial pressure head.

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Analytical solution for one-dimensional advection–dispersion transport equation with distance-dependent coefficients

Cited by 98 publications

References 26 publications

Solute transport in partially-saturated deformable porous media: Application to a landfill clay liner

Solute transport in partially-saturated deformable porous media: Application to a landfill clay liner

Mathematical modeling of groundwater contamination with varying velocity field

The transport processes of soluble contaminant in unsaturated soils under pond infiltration

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