Equivalent diffusion coefficient and equivalent diffusion accessible porosity of a stratified porous medium

Huysmans, Marijke; Dassargues, Alain

doi:10.1007/s11242-006-0028-6

Cited by 14 publications

(8 citation statements)

References 44 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Eq (37) can be derived by using arguments presented for the continuum diffusion equation 31 that impose that the diffusive flux at x = L in the homogenized medium is equal to the diffusive flux at x = L in the heterogeneous medium.…”

Section: Homogenization Approachesmentioning

confidence: 99%

New homogenization approaches for stochastic transport through heterogeneous media

Carr

Simpson

2019

The Journal of Chemical Physics

View full text Add to dashboard Cite

The diffusion of molecules in complex intracellular environments can be strongly influenced by spatial heterogeneity and stochasticity. A key challenge when modelling such processes using stochastic random walk frameworks is that negative jump coefficients can arise when transport operators are discretized on heterogeneous domains. Often this is dealt with through homogenization approximations by replacing the heterogeneous medium with an effective homogeneous medium. In this work, we present a new class of homogenization approximations by considering a stochastic diffusive transport model on a one-dimensional domain containing an arbitrary number of layers with different jump rates. We derive closed form solutions for the kth moment of particle lifetime, carefully explaining how to deal with the internal interfaces between layers. These general tools allow us to derive simple formulae for the effective transport coefficients, leading to significant generalisations of previous homogenization approaches. Here, we find that different jump rates in the layers gives rise to a net bias, leading to a non-zero advection, for the entire homogenized system. Example calculations show that our generalized approach can lead to very different outcomes than traditional approaches, thereby having the potential to significantly affect simulation studies that use homogenization approximations.

show abstract

Section: Homogenization Approachesmentioning

confidence: 99%

New homogenization approaches for stochastic transport through heterogeneous media

Carr

Simpson

2019

The Journal of Chemical Physics

View full text Add to dashboard Cite

show abstract

“…Solute transport through a composite liner consisting of a multilayer system has been described by Foose et al (2001), Huysmans and Dassargues (2007), Haijian et al (2009), Li and Cleall (2010), and Rowe (2010, 2015). The equivalent diffusion coefficient for a composite liner can be derived based on the principle of mass conservation in a manner similar to the calculation of the equivalent hydraulic conductivity of a layered system (Liu et al 1998;Foose et al 2001;Guyonnet et al 2001;Huysmans and Dassargues 2007;Friedmann 2008;Li and Cleall 2010).…”

Section: Equivalent Diffusive Transport Through a Multilayer Geomembranementioning

confidence: 99%

Equivalent Transport Parameters for Volatile Organic Compounds in Coextruded Geomembrane–Containing Ethylene-Vinyl Alcohol

Eun

Tinjum

Benson

et al. 2018

J. Geotech. Geoenviron. Eng.

View full text Add to dashboard Cite

A method to estimate the equivalent diffusion coefficient and partition coefficient of a coextruded ethylene-vinyl alcohol (EVOH) geomembrane (GM) is presented. The method is based on the weighted harmonic mean of diffusion coefficients of each layer and the partition coefficient of the outer layers. The method was evaluated using experimental data obtained with five volatile organic compounds (VOCs) typically found in landfill leachate [methylene chloride (MC), methyl tertiary butyl ether (MTBE), trichloroethylene (TCE), toluene (TOL), and chlorobenzene (CB)] and a coextruded GM composed of outer layers of low-density polyethylene (LLDPE) or high-density polyethylene (HDPE), an adhesive tie layer (maleic anhydride), and a core of EVOH. Equivalent diffusion coefficients computed with the recommended equation were found to be no different statistically from equivalent diffusion coefficients measured using a modified double-compartment apparatus. VOC transport through a composite liner using a coextruded EVOH GM was predicted using a finite-difference model with the equivalent transport parameters as input. Good agreement was obtained between predictions from the model and measured concentrations from a column test simulating a composite liner.

show abstract

“…In we neglected advective fluxes which involve Darcy velocities. Indeed, in media with very low hydraulic conductivities, Darcy velocities are very small and diffusion is the dominant transport mechanism [ Desaulniers et al , 1981; Johnson et al , 1989; Shackelford and Daniel , 1991; Liu and Ball , 1998; Navarro et al , 2000; Jang and Kim , 2003; Landais , 2004; Huysmans and Dassargues , 2007].…”

Section: Governing Mathematical Equationsmentioning

confidence: 99%

A class of analytical solutions for multidimensional multispecies diffusive transport coupled with precipitation‐dissolution reactions and porosity changes

Hayek¹,

Kosakowski²,

Jakob³

et al. 2012

Water Resources Research

View full text Add to dashboard Cite

[1] One of the challenging problems in mathematical geosciences is the determination of analytical solutions of nonlinear partial differential equations describing transport processes in porous media. We are interested in diffusive transport coupled with precipitation-dissolution reactions. Several numerical computer codes that simulate such systems have been developed. Analytical solutions, if they exist, represent an important tool for verification of numerical solutions. We present a methodology for deriving such analytical solutions that are exact and explicit in space and time variables. They describe transport of several aqueous species coupled to precipitation and dissolution of a single mineral in one, two, and three dimensions. As an application, we consider explicit analytical solutions for systems containing one or two solute species that describe the evolution of solutes and solid concentrations as well as porosity. We use one of the proposed analytical solutions to test numerical solutions obtained from two conceptually different reactive transport codes. Both numerical implementations could be verified with the help of the analytical solutions and show good agreement in terms of spatial and temporal evolution of concentrations and porosities.Citation: Hayek, M., G. Kosakowski, A. Jakob, and S. V. Churakov (2012), A class of analytical solutions for multidimensional multispecies diffusive transport coupled with precipitation-dissolution reactions and porosity changes, Water Resour. Res., 48, W03525,

show abstract

Equivalent diffusion coefficient and equivalent diffusion accessible porosity of a stratified porous medium

Cited by 14 publications

References 44 publications

New homogenization approaches for stochastic transport through heterogeneous media

New homogenization approaches for stochastic transport through heterogeneous media

Equivalent Transport Parameters for Volatile Organic Compounds in Coextruded Geomembrane–Containing Ethylene-Vinyl Alcohol

A class of analytical solutions for multidimensional multispecies diffusive transport coupled with precipitation‐dissolution reactions and porosity changes

Contact Info

Product

Resources

About